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

1. 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: lykossov@inm.ras.ru

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) statisticalapproach (“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) 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 timehttp://www.cpc.ncep.noaa.gov/products/globalprecip • 4) Archive NDP048, containing multiyear data of routine observations on 225 meteorological stations of the former USSRhttp://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.

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) 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 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.

24. Response to the increasing of CO2 CMIP models (averaged) INM model

26. 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.

27. 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

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: lykossov@inm.ras.ru, glazunov@inm.ras.ru

32. 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 atmosphere-Earth interface intoenergy 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. Synoptical variations Boundary-Layer flows Energy range Inertial range Dissipation range

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

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

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 ofMPI 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 ofFORTRAN-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 (m3)

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 Particle concentration Wind Particles are ejecting near the surface (along the dotted line). The maximal number of particles is about 10 000 000.

48. Ea 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 S U Es H,LE Snow “Upper” ice Water “Lower” ice Ground 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

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

50. Kolpashevo