Development of an Atmospheric Climate Model with Self-Adapting Grid and Physics

1. Development of an Atmospheric Climate Model with Self-Adapting Grid and Physics Michael Herzog, C. Jablonowski, R. Oehmke, J. E. Penner, Q. Stout, B. van Leer University of Michigan, Ann Arbor, MI in collaboration with GSFC and NCAR SciDAC Mar 2004

2. Motivation • Convection parameterization very different among current AGCMs and CTMS • Convection crucial for: - hydrological cycle - cloud radiative forcing - aerosol indirect effects • Solution: resolve convection

3. Motivation (cont.) • Convective regions: high spatial resolution, non-hydrostatic framework required • Large scale flow: low spatial resolution, hydrostatic assumption sufficient • Adaptive mesh refinement with adaptive physics: accurate treatment of dynamics, computationally efficient

4. AGCM with AMR as a versatile tool • Static refinement:area of interest • alternative to nested grid approach • advantages: • consistent formulation of high and low resolution areas • large scale and small scale features fully coupled • arbitrary spatial distribution of areas of interest • Dynamic refinement: feature of interest • storm tracks, hurricanes • frontal precipitation, Asian monsoon • tornadoes, convection • Combination of static and dynamic refinement

5. Basic Concept • subdivide grid in blocks of constant size • refinement step: 1 block replaced by 4 new blocks • reduced grid: coarsening steps in longitude

6. Refinement Block-wise Adaptive Grid Reduced Grid • resolution of adjacent blocks can differ by factor 2 • parallel computing easy due to block structure • overlap regions require communication

7. Coupling of Blocks • dynamical core on uniform lat-lon grid inner cell ghost cell • ghost cell information from adjacent blocks with coarser, same or finer resolution • interpolation connects blocks of different spatial resolution • ensure flux consistency between blocks

8. Program Library for Block-wise Adaptive Grid(Robert Oehmke, Quentin Stout) • creates initial grid (regular or reduced) • keeps track of position of each block and relation between adjacent block • does communication between blocks • does refinement/coarsening • controls load balancing and nearest neighbor optimization • library handles block indices, does parallelization

9. Interface Routines • for communication: • provide buffer size • pack & unpack buffer if blocks on different processor • copy data for blocks on same processor • consider all neighbor correlations: same, refined, coarsened (including interpolation) • for adaptation: • calculate adaptation flag (refinement criteria) • get & put data for adaptation • do interpolation to finer or coarser grid • interface routines handle data for adaptive grid library

10. Hydrostatic Dynamical Core • based on Lin/Rood dynamical core as used in NASA/NCAR FVCCM • finite volume Flux-Form Semi-Lagrangian (FFSL) scheme • terrain-following floating Lagrangian vertical coordinate • hydrostatic

11. Non-Hydrostatic Dynamical Core • based on extension of hydrostatic core • hydrostatic core: • pressure based Lagrangian vertical coordinate  3d problem reduced to 2d • non-hydrostatic core: • mass based coordinate system • predicting Dp in each layer  Lagrangian vertical coordinate • specific volume is additional prognostic variable • pressure gradient force: • based on pressure forcing acting on a volume • pressure anomaly & local hydrostatic reference profile • vertical remapping

12. Dynamical Core: Issues • latitudinal grid shift: no polar cap for scalar quantities • reduced grid capability non-hydrostatic core: • modified advection scheme • prediction of polar flow • (almost) no polar filtering: Shapiro instead of FFT filter • local, time dependent hydrostatic reference profile for density and pressure (r*, P*) hydrostatic non-hydrostatic

13. Coupling Non-hydrostatic / Hydrostatic Propagation of a non-hydrostatic pressure perturbation in one-layer atmosphere hydrostatic east of 205o longitude, contour lines represent refinement level divergence based refinement criterion, non-hydrostatic hydrostatic Specific volume anomaly

14. Propagation of a Non-Hydrostatic Pressure Perturbation after 200 min simulation signal propagates with speed of sound refinement follows divergence in hydrostatic region non-hydrostatic hydrostatic Specific volume anomaly

15. Difference Non-hydrostatic / Hydrostatic • no reflection or noise at interface • signal weakening due to hydrostatic ghost cell update Propagation of a non-hydrostatic perturbation after 200 min simulation Difference in specific volume anomaly

16. Tests in Shallow Water Approximation(Christiane Jablonowski and Michael Herzog) • hydrostatic: behavior of an one-layer incompressible fluidprognostic quantities: height of the fluid, horizontal wind • uniform versus reduced grid • static and dynamic adaptation • coarse/fine grid interfaces

17. Advection of a Cosine BellShallow water test case 1 (Williamson et al., 1992) refinement level n => dlref=2-n dlinit

18. Advection of a Gaussian Hillsigma = 2 degree(max.) resolution: 0.625 degree no refinement three levels of refinement • almost identical results, but computationally different

19. Performance of Advection Tests 5o  0.625o, uniform grid, #blocks constant #cells increased by factor 64 time step reduced by factor 8 ---------------------------------------------- total difference 512 5o  0.625o, including adaptation #blocks increased by factor 2-4 time step reduced by factor 1-2 work for extra blocks & adaptation ---------------------------------------------- total difference 18 (30 times faster than uniform grid)

20. Global Steady State Geostrophic Flow: Reduced Grid and Static Adaptation Shallow water test case 2 (Williamson et al., 1992)

21. Global Steady State Geostrophic Flow: L2 Error Norm

22. Zonal flow over an Isolated Mountain: Dynamic Adaptation Shallow water test case 5 (Williamson et al., 1992) vorticity based refinement criterion tracks regions of strong curvature

23. 3D Tests in Hydrostatic Approximation(Christiane Jablonowski) • hydrostatic: behavior of a layered incompressible dry atmosphereprognostic quantities: layer thickness, potential temperature, horizontal wind • uniform versus reduced grid • static and dynamic adaptation • coarse/fine grid interfaces

24. 3D Baroclinic wave test case: Initial data(Jablonowski and Williamson, 2004) • Baroclinically and barotropically unstable • Statically, inertially and symmetrically stable • v = 0 m/s, ps = 1000 hPa • orography field balances the zonal wind at the ground • realistic temperature distribution at upper levels

25. 3D Baroclinic wave test case • small perturbation in zonal wind triggers baroclinic instability • 5 degree uniform grid does not resolve the wave train

26. 3D Baroclinic wave test case:Static Refinement • 2 refinements along the storm track capture the wave accurately

27. 3D Polvani et al. (2004) Baroclinic Wave Test Case: Dynamic Adaptations • with refinement baroclinic wave is more accurately predicted • sensitive relative vorticity threshold: 0.75*10-5 1/s

28. Summary • developed and tested first dynamically adaptive hydrostatic dynamical core, based on: • NASA/NCAR’s finite volume dynamical core • block data structure • adaptive grid library for the sphere • developed and coupled non-hydrostatic, fully compressible dynamical core • extension of the hydrostatic model • numerically consistent with hydrostatic formulation • adaptation works: fast and accurate

29. Outlook This project phase (spring/summer 2004) • continue testing non-hydrostatic code • add vertical remapping • 3D idealized global tests:uniform/reduced grid, static/dynamic adaptation, hydrostatic/non-hydrostatic coupling, refinement criteria • publish results of first project phase

30. Outlook Next project phase (starting fall 2004) • high resolution tests with non-hydrostatic code • performance improvements: AMR library and dycore • adaptation of orography • vertical adaptation • couple moist physics (collaboration with NCAR) • evaluate current parameterizations of convection