Federal Department of Home Affairs FDHAFederal Office of Meteorology and Climatology MeteoSwiss
Atmosphere at rest experiments with the latest COSMO version and
comparison with EULAG
Oliver Fuhrer, MeteoSwiss
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
Why does not everything cancel?
1
1 and BC determine p’ completely.
3
2
2 and 3 only cancel out to precision of discretization.
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 atmosphereN = 0.01 s-1
• Initial stateT0 = 288.15 K, p0 = 105 Pa, dT/dlogp = 42
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 mh = 4000 m
Crash!!!
Sensitivity: Mountain Height
Sensitivity: Mountain Width
Sensitivity: Timestep
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
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 atmosphereN = 0.01 s-1
• Initial stateT0 = 288.15 K, p0 = 105 Pa, dT/dlogp = 42
• Rayleight sponge (> 13 km)
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 mh = 4000 m
Crash!!!
Crash!!!
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)
(crash)
7.1 10-13
2.3 10-2
8.5 10-2
1.4 10-1
(crash)
(crash)
–
7.1 10-13
4.9 10-2
9.1 10-2
1.6 10-1
(crash)
(crash)
–
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)
(crash)
7.1 10-13
2.3 10-2
8.5 10-2
1.4 10-1
(crash)
(crash)
–
7.1 10-13
4.9 10-2
9.1 10-2
1.6 10-1
(crash)
(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
–
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