1. Federal Department of Home Affairs FDHA Federal Office of Meteorology and Climatology MeteoSwiss Atmosphere at rest experiments with the latest COSMO version and comparison with EULAG Oliver Fuhrer, MeteoSwiss

2. Introduction Why again? -experiments performed with EULAG, but different setup -latest COSMO model version (4.14) -more sensitivity studies What is tested? -terrain following coordinate transformation introduces additional truncation error term for flows which are nearly hydrostatic -how large is this error? Basic setup -topography -u = v = w = 0 -hydrostatic equilibrium

3. Why does not everything cancel? 1 1 and BC determine p’ completely. 3 2 2 and 3 only cancel out to precision of discretization.

4. Ideal test case I 2-dimensional Schaer et al. MWR 2002 topography Gal-Chen coordinates ∆x = 1 km, Lx = 320 km ∆z = 400 m, Lz = 20 km ∆t = 10 s Reference atmosphere N = 0.01 s -1 Initial state T 0 = 288.15 K, p 0 = 10 5 Pa, dT/dlogp = 42

5. Sensitivity: Topography height h = 0 m h = 300 m h = 1 m h = 500 m h = 10 m h = 1000 m h = 100 m h = 2000 m h = 4000 m Crash!!!

6. Sensitivity: Mountain Height

7. Sensitivity: Mountain Width

8. Sensitivity: Timestep

9. Sensitivity: Summary Mountain height / steepness play key role Explicit vertical advection (EVA) helps Timestep has small influence θ or θ’ dynamics worsens situation Independent of lower BC Explicit hyper-diffusion on model levels helps Time weighting (β) in fast-modes has no influence Order of horizontal advection has negligible influence

10. Ideal test case II 2-dimensional Schaer et al. MWR 2002 topography Gal-Chen coordinates ∆x = 1 km, Lx = 320 km ∆z = 400 m, Lz = 20 km ∆t = 10 s Reference atmosphere N = 0.01 s -1 Initial state T 0 = 288.15 K, p 0 = 10 5 Pa, dT/dlogp = 42 Rayleight sponge (> 13 km)

11. Sensitivity: Topography height h = 0 m h = 300 m h = 1 m h = 500 m h = 10 m h = 1000 m h = 100 m h = 2000 m h = 4000 m Crash!!!

12. Comparison COSMO vs. EULAG 2.0 10 -12 1.8 10 -5 1.0 10 -4 2.2 10 -4 4.5 10 -4 6.0 10 -3 (crash) 2.0 10 -12 6.4 10 -5 2.5 10 -4 6.4 10 -4 9.3 10 -3 (crash) 7.1 10 -13 2.3 10 -2 8.5 10 -2 1.4 10 -1 (crash) – 7.1 10 -13 4.9 10 -2 9.1 10 -2 1.6 10 -1 (crash) –

13. 2.0 10 -12 1.8 10 -5 1.0 10 -4 2.2 10 -4 4.5 10 -4 6.0 10 -3 (crash) 2.0 10 -12 6.4 10 -5 2.5 10 -4 6.4 10 -4 9.3 10 -3 (crash) 7.1 10 -13 2.3 10 -2 8.5 10 -2 1.4 10 -1 (crash) – 7.1 10 -13 4.9 10 -2 9.1 10 -2 1.6 10 -1 (crash) – Comparison EVA vs. IVA 1.8 10 -12 2.0 10 -5 1.1 10 -4 2.4 10 -4 4.7 10 -4 6.3 10 -3 2.9 10 -1 1.8 10 -12 7.1 10 -5 2.7 10 -4 6.6 10 -4 1.1 10 -2 3.1 10 +1 (crash) 6.8 10 -13 8.3 10 -3 1.4 10 -2 1.7 10 -1 4.9 10 -2 6.4 10 -2 5.8 10 -1 6.8 10 -13 1.3 10 -2 2.4 10 -2 3.6 10 -2 1.6 10 -1 2.3 10 +1 –

14. Conclusion Results with model version 4.14 are better than with model version 4.7 Results for stable experiments compare well to EULAG and are always within one order of magnitude Model still crashes for too steep and high topography Explicit vertical advection (EVA) and some explicit hyper- diffusion go some way in stabilizing model, but do not solve problem Other factors have little or not influence