The ICON-Project: main goals

1. ICON The next generation global model at DWD and MPI-MCurrent development status and selected results of idealized testsGünther Zängland the ICON development team

2. The ICON-Project: main goals • Centralize Know-how in the field of global modelling at DWD and the Max-Planck-Institute (MPI-M) in Hamburg. • Develop a non-hydrostatic global model with static local zooming option(ICON: ICOsahedral Non-hydrostatic; http://www.icon.enes.org/). • At DWD: Replace global model GME and regional model COSMO-EU by ICON with a high-resolution window over Europe. Establish a library of scale-adaptive physical parameterization schemes (to be used in ICON and COSMO-DE). • At MPI-M: Use ICON as dynamical core of an Earth System Model (COSMOS); replace regional climate model REMO. Develop an ocean model based on ICON grid structures and operators. • DWD and MPI-M: Contribute to operational seasonal prediction in the framework of the Multi-Model Seasonal Prediction System EURO-SIP at ECMWF).

3. Requirements for next generation global models • Applicability on a wide range of scales in space and time→„seamless prediction“ • (Static) mesh refinement and limited area model (LAM) option • Scale adaptive physical parameterizations • Conservation of mass (chemistry, convection resolving), energy? • Scalability and efficiency on massively parallel computer systems with more than 10,000 cores • Operators of at least 2nd order accuracy

4. D. MajewskiProject leader DWD (till 05/2010) G. ZänglProject leader DWD(since 06/2010) static local mesh refinement, parallelization, optimization, numerics H. Asensio external parameters M. Baldauf NH-equation set K. Fröhlich physics parameterizations D. Liermann post processing, preprocessing IFS2ICON D. Reinert advection schemes P. Ripodas test cases, power spectra B. Ritter physics parameterizations M. Köhler physics parameterizations U. Schättler software design MetBw T. Reinhardtphysics parameterizations M. GiorgettaProject leader MPI-M M. Esch software maintenance A. Gassmann NH-equations, numerics P. Korn ocean model L. Kornblueh software design, hpc L. Linardakis parallelization, grid generators S. Lorenz ocean model C. Mosley regionalization T. Raddatz external parameters F. Rauser adjoint version of the SWM W. Sauf Automated testing (Buildbot) U. Schulzweida external post processing (CDO) H. Wan 3D hydrostatic model version Current project teams at DWD and MPI-M External: S. Reich, University of Potsdam: Time stepping schemes; R. Johanni: MPI-Parallelization

5. Present development status • Consolidated version of hydrostatic dynamical core with option to switch between triangles and hexagons as primal grid • Nonhydrostatic dynamical core for triangles and hexagons; basic testing and efficiency optimization finished • Two-way nesting for triangles as primal grid, capability for multiple nests per nesting level; one-way nesting mode and limited-area mode are also available • Positive-definite tracer advection scheme (Miura) with 2nd-order accuracy, 3rd-order PPM for vertical advection; 3rd-order horizontal in testing/optimization phase • OpenMP and MPI parallelization, blocking (selectable inner loop length) for optimal vectorization or cache use (depending on architecture) • Technical preparations for physics coupling available; so far, grid-scale cloud microphysics, saturation adjustment and convection are included • Dynamical core of ocean model currently under revision

6. Horizontal grid

7. Horizontal grid Primary (Delaunay, triangles) and dual grid (Voronoi, hexagons/pentagons)

8. Static mesh refinement (two-way nesting) latitude-longitude windows circular windows

9. Grid structure (schematic view) Triangles are used as primal cells Mass points are in the circumcenter Velocity is defined at the edge midpoints Red cells refer to refined domain Boundary interpolation is needed from parent to child mass points and velocity points

10. Nonhydrostatic equation system (triangular version) vn,w: normal/vertical velocity component K: horizontal kinetic energy : vertical vorticity component : density v: Virtual potential temperature : Exner function

11. Numerical implementation • Momentum equation: Rotational form for horizontal momentum advection (2D Lamb transformation), advective form for vertical advection, conservative advective form for vertical wind equation • Flux form for continuity equation and thermodynamic equation; Miura scheme (centered differences) for horizontal (vertical) flux reconstruction • implicit treatment of vertically propagating sound waves, but explicit time-integration in the horizontal (at sound wave time step; not split-explicit) • Two-time-level Adams-Bashforth-Moulton time stepping scheme • Mass conservation and tracer mass consistency

12. Implementation of two-way nesting • Flow sequence: 1 time step in parent domain, interpolation of lateral boundary fields/tendencies, 2 time steps in refined domain, feedback • Boundary interpolation of scalars (dynamical and tracers): RBF reconstruction of 2D gradient at cell center Linear extrapolation of full fields and tendencies to child cell points • Boundary interpolation of velocity tendencies RBF reconstruction of 2D vector at vertices Use to extrapolated to child edges lying on parent edge Direct RBF reconstruction of velocity tendencies at inner child edges • Weak second-order boundary diffusion for velocity

13. Implementation of two-way nesting • Feedback: Dynamical variables: bilinear interpolation of time increments from child cells / main child edges to parent cells / edges Additive mass-conservation correction for density Tracers: bilinear interpolation of full fields from child cells to parent cells, multiplicative mass-conservation correction Bilinear feedback is inverse operation of gradient-based interpolation For numerical stability, velocity feedback overlaps by one edge row with the interpolation zone Density and (virtual) potential temperature are used for boundary interpolation / feedback, rho*theta and Exner function are rediagnosed

14. One-way nesting and other options • One-way nesting option: Feedback is turned off, but Davies nudging is performed near the nest boundaries (width and relaxation coefficients can be chosen via namelist variables) • One-way and two-way nested grids can be arbitrarily combined • An arbitrary number of nested domains per nesting level is allowed • Multiple nested domains at the same nesting level can be combined into a logical domain to reduce parallelization overhead (exception: one-way and two-way nested grids have to be assigned to different logical domains) • An option to run computationally expensive physics parameterizations at reduced resolution is in preparation

15. Idealized tests Purpose: Validation of correctness of numerical implementation, assessment of convergence properties and numerical stability • Jablonowski-Williamson baroclinic wave test • Modified Jablonowski-Williamson baroclinic wave test with moisture and cloud microphysics parameterization • Mountain-induced Rossby wave test • Tracer advection test: Convergence study for advection of a tracer cloud in quasi-uniform flow

16. Development of baroclinic waves • Baroclinic wave case of Jablonowski-Williamson (2008) test suite • Nonhydrostatic dynamical core • Basic state: geostrophically and hydrostatically balanced flow with very strong baroclinicity; small initial perturbation in wind field • Disturbance evolves very slowly during the first 6 days, explosive cyclogenesis starts around day 8 • Grid resolutions 140 km and 70 km, 35 vertical levels • Results are shown after 10 days location of nest

17. Vertical velocity at ~1.8 km AGL on day 10 70 km 140 km 140 km, nested

18. Baroclinic wave test with moisture • Modified baroclinic wave case of Jablonowski-Williamson (2008) test suite with moisture and Seifert-Beheng (2001) cloud microphysics parameterization (one-moment version; QC, QI, QR, QS) • Initial moisture field: RH=70% below 700 hPa, 60% between 500 and 700 hPa, 25% above 500 hPa; QV max. 17.5 g/kg to limit convective instability in tropics • Transport schemes for moisture variables: Horizontal: Miura 2nd order with flux limiter Vertical: 3rd-order PPM with slope limiter • Grid resolutions 70 km and 35 km, 35 vertical levels • Results are shown after 14 days

19. Temperature at lowest model level on day 14 70 km 35 km 70 km, nested nest, 35 km

20. QV (g/kg) at 1.8 km AGL on day 14 70 km 35 km 70 km, nested nest, 35 km

21. Accumulated precipitation (mm WE) after 14 days 70 km 35 km 70 km, nested nest, 35 km

22. Rossby wave generation by a large-scale mountain • Mountain-induced Rossby-wave case of Jablonowski-Williamson test suite • Nonhydrostatic dynamical core • Basic state: isothermal atmosphere, zonal flow with max. 20 m/s • Standard setup with 2000-m high circular mountain at 30°N/90°E • “High-resolution” runs: 35 km mesh size; 35 levels • “Coarse-resolution” runs: 140 km • “Nested” runs: 140 km globally, double nesting to 35 km over mountain • Results are shown after 20 days

23. Vorticity (1/s) at surface level on day 20 high-resolution (35 km) coarse-resolution (140 km) nested (140-km domain)

24. Vorticity at surface level on day 20 (mountain region) high-resolution nested (35-km domain) coarse-resolution

25. Horizontal wind at surface level (barbs), vertical wind at 2.5 km AGL on day 20 (colours) high-resolution nested (35-km domain) coarse-resolution

26. Solid body rotation test case • Uniform flow along northeast direction • Initial scalar field is a cosine bell centered at the equator • After 12 days of model integration, cosine bell reaches its initial position • Analytic solution at every time step = initial condition Error norms (l1, l2, l∞) are calculated after one complete revolution for different resolutions

27. Linear vs. quadratic reconstruction quadratic L1 = 0.53764E-01 L2 = 0.45283E-01 • 140 km res. • c=0.2 • flux limiter linear L1 = 0.61346E-01 L2 = 0.51185E-01

28. Convergence rates Quadraticreconstruction Linearreconstruction

29. Summary • The nonhydrostatic dynamical core has been thoroughly tested and compares well with reference solutions from a spectral model; it appears to have good stability properties over steep topography • Two-way nesting also works numerically stable over long times (tested for integration times up to 100 days) and exhibits only very small disturbances along the nest boundaries • State-of-the-art transport schemes have been implemented for tracer advection; further investigations will be made to determine the optimal compromise between accuracy and computational cost • Now the focus will be directed towards completing physics coupling, incorporating real external parameter data, I/O parallelization, using real NWP analysis data as input, data assimilation, …

30. Thank you for your attention!