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M. Satoh H. Tomita K. Goto The Integrated Modeling Research Program

Next generation climate model: Development of the nonhydrostatic icosahedral atmospheric model at Frontier Research System for Global Change. M. Satoh H. Tomita K. Goto The Integrated Modeling Research Program Frontier Research System for Global Change.

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M. Satoh H. Tomita K. Goto The Integrated Modeling Research Program

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  1. Next generation climate model: Development of the nonhydrostatic icosahedral atmospheric model at Frontier Research System for Global Change M. Satoh H. Tomita K. Goto The Integrated Modeling Research Program Frontier Research System for Global Change EU-Japan Symposium on Climate Research 4-5 March 2003, Brussels, Belgium

  2. Contents • Nonhydrostatic ICosahedral Atmospheric Model (NICAM) Introduction Nonhydrostatic modeling Icosahedral grid modeling Runs on ES

  3. Motivation • Mission • Development of a high resolution atmospheric global model on the Earth Simulator • 10 km or less in horizontal, 100 levels in vertical • Cloud resolving global model • Climate study • Strategy of development • Quasi-uniform grid: the icosahedral grid • Spectral method is inefficient in high resolution simulations. • Legendre transformation • Massive data transfer between computer nodes • The latitude-longitude grid point method has the pole problem. • Severe limitation of time interval by the CFL condition. • Inhomogeneous near the poles. • Non-hydrostatic equations system: a new conservative scheme

  4. Development procedure Coupling with Ocean, Land, Ice, Bio models Computational tuning on ES 2003- 2002 Non-hydrostatic Global Climate Model Dynamical Core + Physics Dynamical Core of Global Nonーhydrostatic Model Icosahedral grid + Nonhydrostatic equations 2000-01 Global Shallow Water Model Icosahedral or Conformal cubic grids Regional Cartesian Nonhydrostatic model New dynamical scheme StrechedRegionalClimateModel Study of physical processes using regional nonhydrostatic model Physical tuning

  5. Outline of a nonhydrostatic modeling • Characteristics of the non-hydrostatic model • Dry formulation and results • Moist formulation • Squall line experiments Non-hydrostatic modeling

  6. Characteristicｓ of the nonhydrostatic model (1) • Fully compressible non-hydrostatic equations: • Horizontally explicit and vertically implicit time integration with time splitting • The Helmholtz equation is formulated for vertical velocity not for pressure: • a switch for a hydrostatic/non-hydrostatic option can be introduced. • Conservation of the domain integrals. • The finite volume method using flux form equations of density, momentum and total energy. • Tracer advecion: • Third order upwind, or UTOPIA • Consistency with Continuity • Exact treatment of moist thermodynamics (Ooyama 1990, 2001). • Dependency of latent heat on temperature and specific heats of water substance • Transports of water, momentum, and energy due to rain. • An accurate transport scheme for rain. • Conservative Semi-Lagrangian scheme with 3rd order

  7. Characteristicｓ of the nonhydrostatic model (2) • Physics • Warm rain (bulk method), no ice yet • Turbulence: Mellor and Yamada Level 2, 2.5; Deardorff; Smagorinsky • Surface flux: Louis(1982) • Radiation: MSTRN8 (Nakajima et al, 2000) • A subset of the three-dimensional global non-hydrostatic model • A test bed of new dynamical schemes. Development of the conservative scheme. • Physics: cloud schemes (warm/ice), radiation, turbulence • Study of cloud-radiation interaction and cumulus parameterization: Radiative-convective equilibrium experiments • Model hierarchy: can be used as 1D-vertical, 2D-horizontal-vertical, and 3D-regional models.

  8. Dry formulation • Conservative flux form equations for density R, momentum V, and internal energy E: where and

  9. Time integration scheme: time splitting • Large time step: t, small time step τ Leap-frog or RK2

  10. The flux division method (Klemp et al.2000)

  11. Small time integration(1) • Explicit for U and V • Implicit for R, W, E: using • 1D-Helmholtz eq. for W α=0：Hydrostatic option

  12. Small time integration(2) • Integrate for R in the flux form • Energy correction: integrate for total energy in the flux form where E: internal energy, K: kinetic energy, and G: potential energy:

  13. Density current experiment (Straka et al, 1993) Initial cold bubble: θ’ = ｰ15K Δx = Δz = 50m Δt = 0.1s

  14. Moist formulation with warm rain • Prognostic variables: • water vapor qv • cloud water qc • rain water ql • total density ρ • momentum V= (U, V, W)= (ρu, ρv, ρw) • Sensible part of internal energy Ea: Effects of specific heats of water substance are considered:

  15. Governing equations (Ooyama, 1990,2000）

  16. Squall line exp.: 2D, Δx=1.25km Cloud water and rain Precipitation Water & Energy budgets

  17. Squall line exp.: ３D: 100km x 125km x 21km t=150min qcz=7.3km θz=0.1km qcz=1.4km t=200min

  18. Outline of an icosahedral grid modeling Icosahedral grid modeling • Grid generation • Advection terms and Coriolis term • Life cycle of extratropical cyclones experiment • Held and Suarez experiments

  19. Grid generation Each side of icosahedron whose vertices are on a sphere is projected onto the sphere. (glevel-0) By connecting the mid-points of the geodesic arcs, four sub-triangles are generated. (glevel-1) By iterating this process, a finer grid structure is obtained. (glevel-n) # of gridpoints 11 interations are requried to obtain the 5km grid interval. Grid Generation Method (0) grid division level 0 (1) grid division level 1 (2) grid division level 2 (3) grid division level 3

  20. level 8 (~28km) level 7 (~56km) level 10 (~7km) level 9 (~14km)

  21. Advection of momentum and Coriolis term Only the advection term is evaluated with the Cartesian components.

  22. Grid Optimization by Spring Dynamics (2) • Another application of spring grid • We can construct the clustered grid by tuning the spring. Example of the clustered grid (a) High resolution hemisphere (b) Low resolution hemisphere  For the regional prediction or climate model

  23. Modelconfiguration

  24. Life Cycle of Extratropical Cyclone Exp.(1) Polvani and Scott(2002) glevel 10 Δx=7km glevel 6 Δx=112km glevel 8 Δx=28km

  25. Life Cycle of Extratropical Cyclone Exp.(2) glevel 6 glevel 8 glevel 10

  26. Held & Suarez Dynamical Core Exp.（１） • Test configuration • Radiation • We use a simple radiation as Newtonian Cooling of temperature field： where • Equilibrium temperature is zonally symmetric as: where • Surface fricrion • Surface friction is imposed in the lower atmosphere as a Rayleigh damping ： • where

  27. Held & Suarez Dynamical Core Exp.（４） • Zonal mean of zonal wind • glevel-5 (b) glevel-6 (c) glevel-7 • Δx～240km ～120km ～60km GME(DWD) IFS(ECMWF) ni=64(g-level 6) T106

  28. Energy spectrum Comparison with spectral model(２) glevel-6 vs T159 ： 2Δx=2π/N=240km N/2 4Δx N 2Δx

  29. Computational Performance (1) • Performance on the Earth Simulator • Earth Simulator • Massively parallel super-computer based on NEC SX-5 architecture. • 640 computational nodes. • 8 vector-processors in each of nodes. • Peak performance of 1CPU : 8GFLOPS • Total peak performance：　8x8x640 = 40TFLOPS

  30. Computational Performance (2) • Scalability of our model • Configuration • Horizontal resolution : glevel-8 • Vertical layers : 100 • Fixed • The used computer nodes increases from 10 to 80. • Results • Green　：　ideal speed-up line • Red 　：　actual speed-up line  Our model has a good scalability!

  31. Comparison with spectral model (1) AFES: AGCM for the Earth Simulator: A very fast spectral model in the world • Computational time for 1step • AFES：L = 2πR / N ~Ｏ(Ｎ3) • NICAM： L = 2Δx • NICAM： L = 4Δx ~Ｏ(Ｎ2) NICAM is more efficient than AFES at least for T1279 or glevel10

  32. Comparison with spectral model(２) • Maximum time step and one-day simulation time If L = 2 πR / N = 4 Δx • Time step of NICAM can be larger than AFES At T1279 & glevel-10, NICAM is faster than AFES.

  33. Summary • A new regional non-hydrostatic model using a new conservative scheme. • Conservation of mass and total energy. • A newly tuned icosahedral grid. • Quasi uniform grid using the spring dynamics. • A stretched grid => a regional climate model • A new dynamical core of the nonhydrostatic icosahedral grid model: Validation of the dynamical core • The Life cycle of extratropical cyclones experiment. • the Held & Suarez experiment. • Measurement of computational performance on the Earth Simulator. • A very good scalability and a good sustained performance ( 40% of peak performance ). • Superior to a spectral model.

  34. References • Icosahedral grid • Tomita et al., (2001) : “Shallow Water Model on a Modified Icosahedral Geodesic Grid by Using Spring Dynamics”, J. Comput. Phys., 174, 579-613 • Tomita et al., (2002) : “An Optimization of the Icosahedral Grid Modified by the Spring Dynamics”, J. Comput. Phys., 183, 307-331 • Nonhydrostatic scheme • Satoh (2002) : “Conservative scheme for the compressible non-hydrsostatic model with horizontally explicit and vertically implicit time integration scheme”, Mon.Wea.Rev., 130, 1227-1245 • Satoh (2003) : “Conservative scheme for a compressible non-hydrsostatic models with moist processes”, Mon.Wea.Rev., in press. • Global nonhydrostatic icosahedral model • Tomita et al., (2002a) : “Development of a nonhydrostatic general circulation model using an icosahedral grid”, Parallel CFD 2002, in press • Goto et al., (2002) : “Computational performance of dynamical part of next generation climate model using an icosahedral grid on the Earth Simulator”, Parallel CFD 2002, in press • Tomita et al., (2002b) : “The Non-hydrostatic Icosahedral Global Model for the Earh Simulator”, Max-Planck Institute for Meteorology technical Report 2002 • Tomita et al., (2002c) : “Global nohydrostatic dynamical core on the icosahedral grid Part I : Model description and fundamental tests”, in preparation • Physical processes • Nasuno et al., (2002) : “Resolution Dependence of a Tropical Squall Line”, submitted to Mon.Wea.Rev

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