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