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International Conference on Environmental Observations, Modeling and Information Systems ENVIROMIS-2004 17-25 July 2004, Tomsk, Russia Mathematical modeling.

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Presentation on theme: "International Conference on Environmental Observations, Modeling and Information Systems ENVIROMIS-2004 17-25 July 2004, Tomsk, Russia Mathematical modeling."— Presentation transcript:

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:

2 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.

3 The Climate System(T. Slingo, 2002)





8 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.

9 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.

10 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?

11 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

12 Observational data to verify models 1) ECMWF reanalysis ERA-15 (1979-1993 г.г.), ERA-40 (1957-2001) 2) NCEP/NCAR (National Center of Environment Protection/National Center of Atmospheric Research, USA), 1958-1997, 3) Precipitation from 1979 to present time 4) Archive NDP048, containing multiyear data of routine observations on 225 meteorological stations of the former USSR 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.

13 Large-scale hydrothermodynamics of the atmosphere Subgrid-scale processes parameterization

14 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.

15 T.J. Philips et al. (2002). Large-Scale Validation of AMIP II Land-Surface Simulations


17 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).


19 Sensitivity of the climate system to small perturbations of external forcing (invited lecture at the World Climate Conference, Moscow, 29 September – 3 October, 2003) 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

20 INM coupled atmosphere - ocean general circulation model


22 The climate model sensitivity to the increasing of CO 2 CMIP - Coupled Model Intercomparison Project 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.


24 Response to the increasing of CO 2 CMIP models (averaged) INM model


26 Global warming in CMIP models in CO 2 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.

27 Mesoscale non-hydrostatic modeling MM5 - Penn State/NCAR Mesoscale Modeling System Program code: Fortran77, Fortran90, C. Hybrid parallelization (shared and distributed memory) + vectorization Documentation Implemented by V. Gloukhov (SRCC/MSU) on MVS-1000M




31 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:,

32 Geophysical Boundary Layers (GBLs) as elements of the Earth climate system Atmospheric Boundary Layer H ABL ~ 10 2 - 10 3 m Oceanic Upper Layer H UOL ~ 10 1 - 10 2 m Oceanic Bottom Layer H OBL ~ 10 0 - 10 1 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).

33 Dynamic structure of GBLs Three types of motion: totally organized mean flow coherent semi-organized structures (large eddies and waves) chaotic three-dimensional turbulence

34 Turbulence in PBLs ● Rough surface ● Large scales ● Stratification

35 Inertial range Dissipation range Energy range Synoptical variations Boundary-Layer flows

36 Differential formulation of models

37 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:

38 Finite-difference approximation on “C” grid Explicit time scheme of predictor-corrector type (Matsuno scheme) Numerical scheme

39 Calculation of tendencies diffusion Coriolis force gravity advection pressure gradient diffusion advection diffusion advection Boundary conditions Velocity components Calculation of eddy viscosity and diffusion coefficients Summing up of tendencies ТКЕ, ТКЕ dissipation Temperature, moisture, salinity Solver for the Poisson equation Calculation of the Poisson equation R.H.S. Input-output, post-processing ТКЕ, ТКЕ dissipation production, dissipation, non-linear terms velocity components temperature, moisture, salinity ТКЕ, ТКЕ dissipation

40 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 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- М of Joint Supercomputer Center (768 processors, peak productivity - 1Tflops)


42 Spectra of kinetic energy calculated using results of large-eddy simulation of the convective upper oceanic layer under different spatial resolution (m 3 )

43 von Karman votrex street behind a round cylinder, Re =200: top - from М. ван Дайк (1986). Альбом течений жидкости и газа, bottom - model results


45 Turbulent flow between buildings Wind 2.24 м/s


47 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.

48 Snow “Upper” ice Water Ground “Lower” ice U H,LE EsEs EaEa S Thermodynamics 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 velocity H – sensible heat flux LE – latent heat flux S – shirt-wave radiation E a – incoming long-wave radiation E s – outgoing long-wave radiation

49 Mathematical formulation - for water and ice:, - heat conductivity - for snow : - temperature - liquid water - for ground : - temperature - liquid water - ice

50 Kolpashevo

51 Simulated snow surface temperature versus measured one on meteorological station 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 measurements on meteorological station is about 0.5 ℃.

52 Syrdakh Lake



55 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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