1. Performance of a Semi-Implicit, Semi-Lagrangian Dynamical Core for High Resolution NWP over Complex Terrain L.Bonaventura D.Cesari

2. Outline of discretization approach Semi-implicit, semi-lagrangian two time level discretization (2d tests: Bonaventura JCP 2000) Finite volume approach for the divergence Weakly nonlinear system Ax+f(x)=b, symmetric and well-conditioned for any orography 2nd order in time, 4th order in space SL advection scheme Improved interpolation at the boundary for SL advection (joint work with G.Rosatti, University of Trento)

3. Computational grid

4. Application to open channel flow

5. 2D Gallus-Klemp lee wave test case Vorticity=O(10e-4)

6. 3D linear lee waves

7. Setup of tests for comparison of numerical efficiency 180*180*40 =O(1.3e+6) gridpoints dx=2 km, dz=300 m, dt=40 s Some 1000 m high mountains A -8 K temperature anomaly (cold bubble) on top of each mountain IBM SP4 of CINECA (48 nodes with 16 CPUs each, 1.5 Ghz for each CPU) native xlf90 compiler and all standard optimizations switched on Comparison against LokalModell of DWD

8. Parallel run with 16 processors Total CPU time for 1 hour CPU time solver COMM time solver CPU time advection COMM time advection Fastest /slowest ratio SE328 s91 s13.4 s156 s40.8 s1.07 SI Z 207 s119 s13.4 s65.4 s7.4 s1.02

9. Parallel run with 36 processors (3D lee wave test) Total CPU time for 1 hour CPU time solver COMM time solver Fastest /slowest ratio SE 88.95 s 45.03 s 11.95 s1.4 s SI Z 56.40 s 26.16 s 5.12 s 1.03 s

10. Comparison of speed up

11. Comparison with terrain following semi-implicit LM Difficulty of a fair comparison (different stopping criteria and implementation details) Slower convergence of iterative solver for terrain following semi-implicit Residual 1% of initial value Residual 0.1% of initial value Residual 0.01% of initial value SI iterations62150 SIZ iterations81721

12. Conclusions Semi-implicit, semi-lagrangian method using finite volume discretization of the divergence and improved lower boundary condition Gain in efficiency over terrain following coordinates, good parallel performance

13. Development plans Further testing (Boulder storm, Scania test) ARPA-SMR: development of a full SI-SL NWP model in the framework of the COSMO consortium adapting the LokalModell physics MPI: test tube for numerical methods to be used in ICON, the new global nonhydrostatic dynamical core