atmosphere at rest experiments with the latest cosmo version and comparison with eulag

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