Transcript Invited lecture "Mathematical modeling of natural and antropogenic
Slide 1
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
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-96
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89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 2
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 3
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 4
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 5
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 6
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 7
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 8
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 9
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 10
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 11
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 12
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 13
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 14
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 15
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 16
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 17
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 18
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 19
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 20
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 21
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 22
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 23
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 24
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 25
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 26
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 27
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 28
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 29
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 30
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 31
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 32
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 33
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 34
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 35
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 36
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 37
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 38
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 39
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 40
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 41
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 42
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 43
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 44
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 45
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 46
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 47
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 48
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 49
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 50
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 51
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 52
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 53
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 54
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 55
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 56
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 2
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 3
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 4
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 5
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 6
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 7
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 8
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 9
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 10
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 11
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 12
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 13
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 14
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 15
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 16
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 17
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 18
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 19
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 20
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 21
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 22
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 23
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 24
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 25
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 26
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 27
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 28
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 29
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 30
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 31
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 32
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 33
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 34
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 35
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 36
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 37
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 38
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 39
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 40
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 41
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 42
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 43
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 44
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 45
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 46
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 47
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 48
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 49
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 50
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 51
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 52
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 53
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 54
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 55
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
THANK YOU
for YOUR ATTENTION
Slide 56
International Conference on Environmental Observations,
Modeling and Information Systems ENVIROMIS-2004
17-25 July 2004, Tomsk, Russia
Mathematical modeling of natural and
anthropogenic change of regional climate
and environment
V.N. Lykosov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru
Climate System
• 1. ATMOSPHERE – the gas envelope of the Earth (oxygen, nitrogen,
carbon dioxide, water vapor, ozone, etc.), which controls the solar radiation
transport from space towards the Earth surface.
• 2. OCEAN – the major water reservoir in the system, containing salted
waters of the World ocean and its seas and absorbing the basic part of the
incoming solar radiation (a powerful accumulator of energy).
• 3. LAND – surface of continents with hydrological system (inland waters,
wetlands and rivers), soil (e.g. with groundwater) and cryolithozone
(permafrost).
• 4. CRYOSPHERE – continental and see ice, snow cover and mountain
glaciers.
• 5. BIOTA – vegetation on the land and ocean, alive organisms in the air,
water and soil, mankind.
The Climate System(T. Slingo, 2002)
19
37
-46
19
39
-48
19
41
-50
19
43
-52
19
45
-54
19
47
-56
19
49
-58
19
51
-60
19
53
-62
19
55
-64
19
57
-66
19
59
-68
19
61
-70
19
63
-72
19
65
-74
19
67
-76
19
69
-78
19
71
-80
19
73
-82
19
75
-84
19
77
-86
19
79
-88
19
81
-90
19
83
-92
19
85
-94
19
87
-96
19
89
-98
C degrees
Annually mean air temperature in Khanty-Mansiisk for the time
period from 1937 to 1999 (Khanty-Mansiisk
Hydrometeocenter).
0
-0,5
-1
-1,5
-2
-2,5
-3
Decades
Air temperature. May 2003 (Khanty-Mansiisk
Hydrometeocenter)
30
25
C degrees
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Среднесуточная температура
Средняя температура
Максимальная температура
Норма
Features of the climate system as physical object-I
• Basic components of the climate system – atmosphere and
ocean – are thin films with the ratio of vertical scale to
horizontal scale about 0.01-0.001.
• On global and also regional spatial scales, the system can be
considered as quasi-twodimensional one. However, its density
vertical stratification is very important for correct description
of energy cycle.
• Characteristic time scales of energetically important physical
processes cover the interval from 1 second (turbulence) to
tens and hundreds years (climate and environment variability).
• Laboratory modelling of such system is very difficult.
Features of the climate system as physical object-II
• It is practically impossible to carry out specialized physical
experiments with the climate system.
• For example, we have no possibility to “pump” the atmosphere by the
carbon dioxide and, keeping other conditions, to measure the system
response.
• We have shirt–term series of observational data for some of
components of the climate system.
• Conclusion: the basic (but not single) tool to study the climate system
dynamics is mathematical (numerical) modeling.
• Hydrodynamical climate models are based on global models of the
atmosphere and ocean circulation.
Objectives of climate modeling
To reproduce both “climatology” (seasonal and monthly means) and
statistics
of
variability:
intra-seasonal
(monsoon
cycle,
characteristics of storm-tracks, etc.) and climatic (dominated modes
of inter-annual variability such as El-Nino phenomenon or Arctic
Oscillation)
To estimate climate change due to anthropogenic activity
To reproduce with high degree of details regional climate: features of
hydrological cycle, extreme events, impact of global climate change
on regional climate, environment and socio-economic relationships
Fundamental question (V.P. Dymnikov): what climatic parameters
and in what accuracy must by reproduced by a mathematical model
of the climate system to make its sensitivity to small perturbations of
external forcing close to the sensitivity of the actual climate
system?
Computational technologies
• Global climate model (e.g. model with improved spatial resolution
in the region under consideration) implemented on computational
system of parallel architecture (CSPA)
•
Methods of “regionalization”:
1) statistical approach (“downscaling”);
2) hydrodynamical mesoscale simulation ( e.g., mesoscale model
ММ5) requires CSPA;
3) large-eddy simulation of geophysical boundary layers (requires
CSPA)
• Assessment of global climate change and technological impact on
regional environment
Observational data to verify models
• 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001)
http://www.ecmwf.int/research/era
• 2) NCEP/NCAR (National Center of Environment Protection/National
Center of Atmospheric Research, USA), 1958-1997,
http://wesley.wwb.noaa.gov/reanalysis.htm
• 3) Precipitation from 1979 to present time
http://www.cpc.ncep.noaa.gov/products/globalprecip
• 4) Archive NDP048, containing multiyear data of routine observations on
225
meteorological
stations
of
the
former
USSR
http://cdiac.esd.oml.gov/ftp/ndp048
• Numerical experiments with modern global climate models produce a
large amount of data (up to 1Gb for 1 month). This requires special
efforts for its visualization, postprocessing and analysis.
where
Large-scale hydrothermodynamics of the atmosphere
u
1
RT
f
tg v
Fu
dt
a
a cos
du
u
f
tg
dt
a
dv
1
RT
Fv
u
a
t
dT
dt
u
v
FT
c p
t
a
cos
a
RT
t
Subgrid-scale
processes
parameterization
,
u
v cos
0,
a cos
dt
dt
RT
,
1
dq
d
,
u
F q ( C E ),
a cos
v
a
.
,
Parameterization of subgrid-scale processes
• Turbulence in the atmospheric boundary layer, upper ocean layer
and bottom boundary layer
• Convection and orographic waves
• Diabatic heat sources (radiative and phase changes, cloudiness,
precipitation, etc.)
• Carbon dioxide cycle and photochemical transformations
• Heat, moisture and solute transport in the vegetation and snow cover
• Production and transport of the soil methane
• Etc.
T.J. Philips et al. (2002). Large-Scale Validation of
AMIP II Land-Surface Simulations
Table 2. Model codes and features of the sixteen AMIP2 models analysed in Zhang et al. (2002)
Code
Resolution
Land-surface components
Soil model
No. of layers
No. of layers
Model
in soil temp.
in soil moist.
Country
calculations
calculations
Canopy representation
complexity
A
T42L18
bucket
const. canopy resistance
3
1
CCSR, Japan
B
T63L45
force-restore
intercept. + transpiration
2
2
CNRM, France
C
4x5 L21
multi-layer diffusion
intercept. + transpiration
24
24
INM, Russia
D
T159L50
multi-layer diffusion
intercept. + transpiration
4
4
ECMWF, UK
E
T63L30
multi-layer diffusion
intercept. + transpiration
4
3
JMA, Japan
F
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
NCAR, USA
G
T62L18
multi-layer diffusion
intercept. + transpiration
3
2
NCEP, USA
H
T42L18
multi-layer diffusion
intercept. + transpiration
2
3
PNNL, USA
I
3.75x2.5 L58
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UGAMP, UK
J
3.75x2.5 L19
multi-layer diffusion
intercept.+transpiration+CO2
4
4
UKMO, UK
K
T47L32
multi-layer diffusion
intercept. + transpiration
3
3
CCCMA, Can
L
4x5 L20
multi-layer diffusion
intercept. + transpiration
2
3
GLA, USA
M
T42L30
multi-layer diffusion
intercept. + transpiration
3
3
MRI, Japan
T42L18
multi-layer diffusion
intercept.+transpiration+CO2
6
6
SUNYA, USA
4x5 L24
bucket
no
1
1
UIUC, USA
4x5 L15
bucket
no
1
1
YONU, Korea
N
O
P
The Taylor diagram for the variability of the latent heat flux at the
land surface as follows from results of AMIP-II experiments
(Irannejad et al., 2002).
Sensitivity of the climate system to
small perturbations of
external forcing
(invited lecture at the World Climate Conference,
Moscow, 29 September – 3 October, 2003)
V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S.
Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov
Institute of Numerical Mathematics RAS, Moscow
INM coupled atmosphere - ocean general
circulation model
AGCM
- Finite difference model with spatial resolution 5°x4° and 21 levels in sigmacoordinates from the surface up to 10 hPa.
- In radiation absorption of water vapour, clouds, CO 2, O3, CH4, N2O, O2 and
aerosol are taken into account. Solar spectrum is divided by 18 intervals, while
infrared spectrum is divided by 10 intervals.
- Deep convection, orographic and non-orographic gravity wave drag are considered
in the model. Soil and vegetation processes are taken into account.
||
Non-flux-adjusted coupling
||
OGCM
-The model is based on the primitive equations of the ocean dynamics in spherical
sigma-coordinate system. It uses the splitting-up method in physical processes and
spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in
the vertical with an exponential distribution.
The climate model sensitivity to
the increasing of CO2
CMIP - Coupled Model Intercomparison Project
http://www-pcmdi.llnl.gov/cmip
CMIP collects output from global coupled ocean-atmosphere general
circulation models (about 30 coupled GCMs). Among other usage, such models
are employed both to detect anthropogenic effects in the climate record of the
past century and to project future climatic changes due to human production of
greenhouse gases and aerosols.
Response to the increasing of CO2
CMIP models (averaged)
INM model
Global warming in CMIP
models in CO2 run and
parameterization of lower
inversion clouds
T - global warming (K), LC - parameterization
of lower inversion clouds (+ parameterization
was included, - no parameterization, ? - model
description is not available). Models are ordered
by reduction of global warming.
M odel
T
LC
N C A R -W M
GFDL
3.77
2.06
?
-
LM D
1.97
-
CCC
1.93
-
UKM03
1.86
-
CERF
1.83
-
C C SR
1.75
-
C S IR O
1.73
+
G IS S
1.70
-
UKM O
1.59
-
BM RC
1.54
+
ECHAM 3
1.54
-
MRI
1.50
-
IA P
1.48
+
N C A R -C S M
1.26
+
PCM
1.14
+
IN M
0.99
+
NRL
0.75
+
Mesoscale non-hydrostatic modeling
• MM5 - Penn State/NCAR Mesoscale
Modeling System
http://www.mmm.ucar.edu/mm5
• Program code: Fortran77, Fortran90, C.
Hybrid parallelization (shared and
distributed memory) + vectorization
• Documentation
• Implemented by V. Gloukhov
(SRCC/MSU) on MVS-1000M
International Conference on
Computational Mathematics ICCM-2004,
21-25 June, 2004, Novosibirsk, Russia
Large-Eddy Simulation of
Geophysical Boundary Layers on
Parallel Computational Systems
V.N. Lykosov, A.V. Glazunov
Russian Academy of Sciences
Institute for Numerical Mathematics, Moscow
E-mail: lykossov@inm.ras.ru, glazunov@inm.ras.ru
Geophysical Boundary Layers (GBLs) as
elements of the Earth climate system
• Atmospheric Boundary Layer HABL ~ 102 - 103 m
• Oceanic Upper Layer
HUOL ~ 101 - 102 m
• Oceanic Bottom Layer
HOBL ~ 100 - 101 m
GBL processes control:
• 1) transformation of the solar radiation energy at the atmosphereEarth interface into energy of atmospheric and oceanic motions
• 2) dissipation of the whole Earth climate system kinetic energy
• 3) heat- and moisture transport between atmosphere and soil (e.g.
permafrost), sea and underlying ground (e.g. frozen one).
Dynamic structure of GBLs
Three types of motion:
• totally organized mean flow
• coherent semi-organized structures (large
eddies and waves)
• chaotic three-dimensional turbulence
Turbulence in PBLs
Rough surface
● Large scales
● Stratification
●
Synoptical variations
Boundary-Layer flows
Energy range
Inertial range
Dissipation range
Differential formulation of models
Models are based on Reynolds’ type equations obtained after spatial averaging of Navier-Stokes equations and added by equations of heat and moisture (or salt):
Turbulent Closure
Equation for turbulent kinetic energy (of subgrid-scale motions):
Equation for turbulent kinetic energy dissipation:
Constraint on maximal value of sub-grid turbulence length scale:
l
c E
3/2
,
Numerical scheme
• Finite-difference approximation on “C” grid
• Explicit time scheme of predictor-corrector type (Matsuno scheme)
Calculation of tendencies
Velocity components
diffusion
Coriolis force
gravity
Calculation of
eddy viscosity and diffusion
coefficients
advection
pressure gradient
Temperature, moisture, salinity
Calculation of the Poisson
equation R.H.S.
Solver for the Poisson equation
diffusion
advection
ТКЕ,
ТКЕ
dissipation
ТКЕ, ТКЕ dissipation
diffusion
advection
production, dissipation,
non-linear terms
Summing up
of tendencies
Input-output,
post-processing
Boundary conditions
velocity components
temperature,
moisture, salinity
ТКЕ, ТКЕ dissipation
PARALLEL IMPLEMENTATION
• Parallel version of models is developed to be
mainly used on supercomputers with distributed
memory
•Procesor-to-processor data exchange is realized
with the use of MPI standard
• non-blocked functions of the data transferreceive
•3-D decomposition of computational domain
• on each time step, processes are co-exchanged
only by data which belongs to boundary grid
cells of decomposition domains
• The Random Access Memory (operative
memory) is dynamically distributed between
processors (the features of FORTRAN-90 are
used)
• Debuging and testing of parallel versions of
models is executed on supercomputer MVS1000М of Joint Supercomputer Center (768
processors, peak productivity - 1Tflops)
“Extreme” case:
Domain 768 x 768 x 256 (= 150 994 994) grid points
574 processors
3D decomposition (12 x 12x 4)
MGD Poisson solver
15 Gbytes of memory
1 step of scheme ~ 20 s of computer time.
3%
6%
exchanges
7%
d iffu s io n
2%
10%
a d v e c tio n o f s c a la rs
a d v e c tio n o f m o m e n tu m
tu rb u le n t c lo s u re
58%
1%
b o u n d a ry c o n d itio n
a d d itio n a l p ro c e d u re s
13%
P o is s o n e q u a tio n
in c lu d ig e x c h a n g e s
Spectra of kinetic energy calculated using results of large-eddy simulation of the
convective upper oceanic layer under different spatial resolution (m3)
von Karman votrex street behind a round cylinder, Re =200: top - from
М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results
Turbulent flow between buildings
Wind 2.24 м/s
Lagrangian transport of fine-dispersive particle tracer
Large number of particles in turbulent flow generated by the LES-model of the atmospheric boundary layer.
The calculation of trajectories is carried out simultaneously with numerical integration of the hydrodynamic
part of the model.
● It is assumed that each of particles has non-zero mass and size. It is possible to sort particles in few groups
accordingly to their size and density.
The code of tracer transport is parallelized with the use of MPI. The data exchange between processors is
realized with the help of non-blocking transfers and takes place on the background of basic calculations.
Using results of calculations, the spatial distribution of the particle tracer concentration is calculated for each
time step.
On parallel computational system this algorithm allows to simultaneously calculate trajectories of tens
millions particles. The time which is needed to calculate the particles transport is significantly less then the
time of the ABL model integration.
● Equation of the particle motion in the air flow:
m x i f i i 3 mg ,
where xi (i=1,2,3) – particle coordinates, m – mass of particle, f – drag force.
● To calculate f , the Stokes formula is used:
f i 6 r (V i x i )
An example of the particle transport by the turbulent flow between buildings
Wind
Particle concentration
Particles are ejecting near the surface (along the dotted line). The maximal number
of particles is about 10 000 000.
Thermodynamics of shallow
Reservoir (Stepanenko & Lykosov,
2003, 2004)
Ea
U
H,LE
1) One-dimensional approximation.
Snow
2) On the upper boundary: fluxes
of momentum, sensible and latent heat,
solar and long-wave radiation
are calculated
On the lower boundary: fluxes are
prescribed
3) Water and ice: heat transport
Snow and ground: heat- and moisture
transport
U – wind velocity
H – sensible heat flux
LE – latent heat flux
S – shirt-wave radiation
Ea – incoming long-wave radiation
Es – outgoing long-wave radiation
“Upper” ice
Water
“Lower” ice
Ground
Es
S
Mathematical formulation
- for water and ice:
ñ
T
T
2
t
h
2
c
2
dh T
dt h
c
1 dh T
h dt
I
z
,
z
h
- for snow:
T
с
t
W
t
z
z
T
z
LF fr ,
F fr .
- temperature
- liquid water
- for ground:
c
T
W
t
I
t
t
z
T
W
T
c T W
L i Fi ,
z
z
z
W
W
z
z
- temperature
Fi ,
- liquid water
Fi .
- ice
- heat
conductivity
Kolpashevo
Simulated snow surface temperature versus measured one on meteorological
station Kolpashevo (1961)
Температура поверхности снега, 01.61
EДанные натурных измерений
EРезультаты моделирования
0
Quality of snow surface temperature
reproduction is an indicator of quality of
heat transfer parameterization in the
“atmospheric surface layer – snow” system.
Температура, С
-10
-20
-30
-40
-50
Accuracy of temperature measurements
on meteorological station is about 0.5 ℃.
0
5
10
15
20
25
30
35
Время, дни
Т е м п е р а т у р а п о в е р х н о с т и с н е г а , К о л п а ш е в о , 0 2 .1 9 6 1
-5
Тем пература, С
-1 0
-1 5
-2 0
-2 5
-3 0
Д а н н ы е н а т ур н ы х э кс п е р и м е н т о в
-3 5
Р е з ул ь т а т ы м о д е л и р о в а н и я
-4 0
0
5
10
15
В рем я, дни
20
25
30
Syrdakh Lake
Температура, С
-4
-3
-2
-1
0
1
2
3
4
5
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 11.Вертикальный профиль температуры в оз. Сырдах,
апрель 1977 г.
Температура, С
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
1
Глубина, м
2
3
4
наблюдения
эмпир. параметр.
e-параметр.
5
Рис. 13.Вертикальный профиль температуры в оз. Сырдах,
июнь 1977 г.
Ground temperature under Syrdakh Lake
(modeling results)
As follows from results of numerical experiments, the talik is stably existing
during all of integration time (20 years, 1965-1984). Its depth varies from 1.2 to 2
meters under the lake bottom.
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