mathematical modeling of natural and anthropogenic change of regional climate and environment

International Conference on Environmental Observations, Modeling and Information Systems ENVIROMIS-200417-25 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: [email protected]

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)

3

-1.2

-1.17

-1.12

-1.2

-1.09

-0.78

-0.87

-0.98

-1.17

-1.13

-1.13

-1.08

-1.2

-1.2

-1.38

-1.39

-1.08

-1.2

-1.42

-1.46

-1.68

-1.48

-1.68

-2.02

-2.07

-2.02

-2.46

-2.38

-2.29

-2.23

-2.25

-2.32

-2.16

-1.94

-1.83

-1.61

-1.37

-1.22

-1.2

-1.28

-1.29

-1.28

-1.04

-0.87

-0.85

-0.91

-1.01

-1.1

-1

-0.63

-0.57

-0.6

-0.87

-0.99

Decades

C degrees

Annually mean air temperature in Khanty-Mansiisk for the time period from 1937 to 1999 (Khanty-Mansiisk Hydrometeocenter).

1

193719381939194019411942194319441945194619471948194919501951195219531954195519561957195819591960196119621963196419651966196719681969197019711972197319741975197619771978197919801981198219831984198519861987198819891990199119921993199419951996199719981999200020012002

3.7-1.5-0.3-8.2-3.8-2.5-3.35.8-0.72.40.52.49-8.80.34.42-0.26.70.3-0.43.83.1-3.36.9-1.5-3.7-1.20.2-0.6-2.1-10.2-4.91.8-11-5.9-5.133.6-4.83.9-4.1-2.66.2-2.45.46.6-0.51.2-33.9-3.3-4.93-0.76.747.1-1.4-6.92.1-1.2-1.2-4.33.9

19371936193719381939194019411942194319441945194619471948194919501951195219531954195519561957195819591960196119621963196419651966196719681969197019711972197319741975197619771978197919801981198219831984198519861987198819891990199119921993199419951996199719981999200020012002

-1.5-3.42.12.70.7-2-41.43.9-1.9-0.51.6-0.20.83.93.2-2.9-0.61.3-2.72.1-5.5-52.42.5-5.5-5.64.6-1.55.75.6-2.53.6-1.4-31.92.14.2-0.21.31.92.1-0.5-0.9-4.73.15.33.64.32.15.97.83.5-4.71.32.83.45.83.25.73.4-5.562.14.4

1937-461938-471939-481940-491941-501942-511943-521944-531945-541946-551947-561948-571949-581950-591951-601952-611953-621954-631955-641956-651957-661958-661959-681960-691961-701962-711963-721964-731965-741966-751967-761968-771969-781970-791971-801972-811973-821974-831975-841976-851977-861978-871979-881980-891981-901982-911983-921984-931985-941986-951987-961988-971989-981990-99

189191192192193195193192191191190188188188186186189188187186189188186185187183184183184183183182182182184183188189188188192193191191190190188186187190189190190190

1937-461938-471939-481940-491941-501942-511943-521944-531945-541946-551947-561948-571949-581950-591951-601952-611953-621954-631955-641956-651957-661958-661959-681960-691961-701962-711963-721964-731965-741966-751967-761968-771969-781970-791971-801972-811973-821974-831975-841976-851977-861978-871979-881980-891981-901982-911983-921984-931985-941986-951987-961988-971989-981990-99

-1.2-1.17-1.12-1.2-1.09-0.78-0.87-0.98-1.17-1.13-1.13-1.08-1.2-1.2-1.38-1.39-1.08-1.2-1.42-1.46-1.68-1.48-1.68-2.02-2.07-2.02-2.46-2.38-2.29-2.23-2.25-2.32-2.16-1.94-1.83-1.61-1.37-1.22-1.2-1.28-1.29-1.28-1.04-0.87-0.85-0.91-1.01-1.1-1-0.63-0.57-0.6-0.87-0.99

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1936-2002 ( -10,8)

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1

3.912.810.46.4

7.812.310.46.4

6.711.310.46.4

7.211.910.46.4

3.711.710.46.4

3.77.510.46.4

7.811.810.46.4

14.521.710.46.4

16.323.210.46.4

17.221.810.46.4

6.712.810.46.4

10.719.110.46.4

14.620.510.46.4

9.817.710.46.4

5.4910.46.4

8.714.910.46.4

13.620.210.46.4

4.123.810.46.4

9.622.110.46.4

8.613.110.46.4

10.615.810.46.4

13.220.710.46.4

18.724.310.46.4

16.320.210.46.4

11.815.610.46.4

7.814.610.46.4

5.110.710.46.4

13.921.910.46.4

15.620.710.46.4

9.414.310.46.4

5.911.310.46.4

C degrees

Air temperature. May 2003 (Khanty-Mansiisk Hydrometeocenter)

2

0.4

3.9

6.3

5.4

2.2

0

0

7.3

0

0

4.3

1.2

4.9

27.9

64 . 47

(). 2003.

1

2003.

-

13.912.810.40-6.36.400

27.812.310.401.86.4000.4

36.711.310.4036.4003.9

47.211.910.4046.4006.3

53.711.710.402.36.4005.4

63.77.510.401.46.4002.2

77.811.810.402.56.400

814.521.710.406.96.400

916.323.210.4011.76.400

1017.221.810.4012.86.4000

116.712.810.4036.4000

1210.719.110.401.56.400

1314.620.510.407.46.400

149.817.710.406.56.4007.3

155.4910.402.16.400

168.714.910.402.26.4000

1713.620.210.405.86.400

184.123.810.408.96.400

199.622.110.4014.56.400

208.613.110.4036.4000

2110.615.810.403.36.400

2213.220.710.403.66.400

2318.724.310.4013.86.400

2416.320.210.4013.96.4004.3

2511.815.610.407.16.4001.2

267.814.610.404.66.4004.9

275.110.710.4016.400

2813.921.910.406.96.400

2915.620.710.4010.16.400

309.414.310.4066.400

315.911.310.4036.40027.9

509.3168.363.8

Features of the climate system as physical object-IBasic 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 shirtterm 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 modelingTo 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 5) 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 models1) ECMWF reanalysis ERA-15 (1979-1993 ..), 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.

Large-scale hydrothermodynamics of the atmosphere Subgrid-scaleprocessesparameterization

,

,

,

,

,

where

.

_1119850510.unknown

_1119850544.unknown

_1120137379.unknown

_1120137402.unknown

_1119850556.unknown

_1119850536.unknown

_1119850482.unknown

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

No. of layers in soil temp. calculations

No. of layers in soil moist. calculations

Model

Country

Soil model complexity

Canopy representation

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

T42L18

T63L45

4x5 L21

T159L50

T63L30

T42L18

T62L18

T42L18

3.75x2.5 L58

3.75x2.5 L19

T47L32

4x5 L20

T42L30

T42L18

4x5 L24

4x5 L15

bucket

force-restore

multi-layer diffusion












bucket

bucket

const. canopy resistance

intercept. + transpiration




intercept.+transpiration+CO2









no

no

3

2

24

4

4

6

3

2

4

4

3

2

3

6

1

1

1

2

24

4

3

6

2

3

4

4

3

3

3

6

1

1

CCSR, Japan

CNRM, France

INM, Russia

ECMWF, UK

JMA, Japan

NCAR, USA

NCEP, USA

PNNL, USA

UGAMP, UK

UKMO, UK

CCCMA, Can

GLA, USA

MRI, Japan

SUNYA, USA

UIUC, USA

YONU, Korea

PAGE

35

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. LykosovInstitute of Numerical Mathematics RAS, Moscow

INM coupled atmosphere - ocean general circulation model

AGCM

- Finite difference model with spatial resolution 5x4 and 21 levels in sigma-coordinates from the surface up to 10 hPa.

- In radiation absorption of water vapour, clouds, CO2, 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 2.5x2, 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 Projecthttp://www-pcmdi.llnl.gov/cmipCMIP 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 CO2CMIP 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.

Model

T

LC

NCAR-WM

3.77

?

GFDL

2.06

-

LMD

1.97

-

CCC

1.93

-

UKM03

1.86

-

CERF

1.83

-

CCSR

1.75

-

CSIRO

1.73

+

GISS

1.70

-

UKMO

1.59

-

BMRC

1.54

+

ECHAM3

1.54

-

MRI

1.50

-

IAP

1.48

+

NCAR-CSM

1.26

+

PCM

1.14

+

INM

0.99

+

NRL

0.75

+

Mesoscale non-hydrostatic modelingMM5 - Penn State/NCAR Mesoscale Modeling System http://www.mmm.ucar.edu/mm5Program code: Fortran77, Fortran90, C. Hybrid parallelization (shared and distributed memory) + vectorizationDocumentationImplemented 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: [email protected], [email protected]

Geophysical Boundary Layers (GBLs) as elements of the Earth climate systemAtmospheric Boundary Layer HABL ~ 102 - 103 mOceanic Upper Layer HUOL ~ 101 - 102 mOceanic Bottom Layer HOBL ~ 100 - 101 m

GBL processes control:

1) transformation of the solar radiation energy at the atmosphere-Earth 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 flowcoherent semi-organized structures (large eddies and waves)chaotic three-dimensional turbulence

Turbulence in PBLs

Rough surface Large scales Stratification

Inertial range Dissipation range Energy range Synoptical variationsBoundary-Layer flows

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 ClosureEquation for turbulent kinetic energy (of subgrid-scale motions): Equation for turbulent kinetic energy dissipation:Constraint on maximal value of sub-grid turbulence length scale:

Finite-difference approximation on C grid

Explicit time scheme of predictor-corrector type (Matsuno scheme)

Numerical scheme

Calculation of tendenciesdiffusionCoriolis forcegravityadvection

pressure gradientdiffusionadvectiondiffusionadvectionBoundary conditionsVelocity components

Calculation of eddy viscosity and diffusioncoefficientsSumming up of tendencies, dissipationTemperature, moisture, salinitySolver for the Poisson equationCalculation of the Poisson equation R.H.S., dissipationproduction, dissipation, non-linear terms velocity componentstemperature, moisture, salinity

, dissipation

Parallel version of models is developed to be mainly used on supercomputers with distributed memoryProcesor-to-processor data exchange is realized with the use of MPI standard non-blocked functions of the data transfer-receive 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 MVS1000- of Joint Supercomputer Center (768 processors, peak productivity - 1Tflops)

PARALLEL IMPLEMENTATION

Extreme case:

Domain 768 x 768 x 256 (= 150 994994) 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.

EMBED MSGraph.Chart.8 \s

_1113840107.xls

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 . (1986). , bottom - model results

Turbulent flow between buildingsWind 2.24 /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:

where xi (i=1,2,3) particle coordinates, m mass of particle, f drag force.

To calculate f , the Stokes formula is used:

r , , V , .

EMBED Equation.3

EMBED Equation.3

_1143542808.unknown

_1148897591.unknown

An example of the particle transport by the turbulent flow between buildings Wind Particle concentrationParticles are ejecting near the surface (along the dotted line). The maximal number of particles is about 10 000 000.

SnowUpper iceWaterGroundLower iceUH,LEEsEaSThermodynamics of shallow Reservoir (Stepanenko & Lykosov, 2003, 2004)

1) One-dimensional approximation.

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 velocityH sensible heat fluxLE latent heat fluxS shirt-wave radiationEa incoming long-wave radiation Es outgoing long-wave radiation

Mathematical formulation

- for water and ice:

, - heat conductivity - for snow:

- temperature

- liquid water

- for ground:

- temperature

- liquid water

- ice

Kolpashevo

Simulated snow surface temperature versus measured one on meteorologicalstation Kolpashevo (1961)Quality of snow surface temperature reproduction is an indicator of quality of heat transfer parameterization in the atmospheric surface layer snow system.

Accuracy of temperature measurementson meteorological station is about 0.5 .

Syrdakh Lake

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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mathematical modeling of natural and anthropogenic change of regional climate and environment

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