1. Tuning the horizontal diffusion in the COSMO model
Marie Müllner, Guy de Morsier
COSMO User Workshop Zurich, 22 October 2009

2. Motivation The problem: From the operational COSMO-7
assimilation cycle on October 2, 2008
CFL crash!
(Baldauf 2008, JCP)
COSMO-7: cflmax=1.42 the extra smoothing for winds
above 0.95% cflmax had no impact!
CFL & wind on level 33
CFL-plot depends very much on the observations used
crash is difficult to reproduce
winds exactly along grid point rows or columns are uncoupled

3. Overview Motivation Code Changes Analysis tools: Response function
Kinetic energy spectra
Cases
Results of case studies
Verification
Summary and Recommendations

4. Values tested inside (bold blue: boundary values)
Code Changes
Changed the mask for the application of the horizontal diffusion: lhdiff_mask → hd_corr_in_x / hd_corr_bd_x
x: u (u,v,w), t, q, p (new)
Smooth transition at lateral and upper boundaries by using rmy coefficients from Davies relaxation and linear change below Rayleigh damping zone
Namelist parameter
Values tested inside (bold blue: boundary values)
Default
hd_corr_u
0.75
0.65
0.55
0.45
0.35
0.25
0.15
0.1
0.05
1.0
hd_corr_t
0.0
hd_corr_p
hd_corr_q
0.5

5. Analysis tools – Response function (i)
Wavelengths affected by the 4th order filter in linear, 1-dimentional stability analysis:
|λ²| = 1 - αΔt[6 - 8 cos(kΔx) + 2 cos(2kΔx)]/Δx^ [1]
where: λ : wave length
k : wave number α = hd_corr_*/(2π^4)
hd_corr_* : diffusion coefficient
Δt : integration time step
COSMO-7: Δt=60s; COSMO-2: Δt=20s
Δx : horizontal grid space
COSMO-7: Δx=6.6km; COSMO-2: Δx=2.2km
[1] Xue, M., 2000: High-order monotonic numerical diffusion and smoothing. Mon. Wea. Rev., 128,

6. Analysis tools – Response function (ii)
Amplification factors |λ²| after 180 times of filter application
i.e. 3h for COSMO-7
and
1h for COSMO-2
|λ²|
wave number kΔx p: 2Δx

7. Analysis tools (iii) Kinetic Energy Spectra:
One-dimensional spectral decomposition of the velocities (u, v, w) along east-west horizontal grid lines (EW) and along north-south grid lines (NS)
The energy densities are time averaged, from +6h to +24h of the forecast
The spectra are also averaged over the model levels between 3.5 and 10 km height
Same domain for COSMO-2 and COSMO-7

8. Analysis tools (iv) February 10th, 2008
“Effective” wave length ~15km ~7Dx
February 10th, 2008
Stratus with no precipitation and slow winds
Power spectra of the kinetic energy of COSMO-2
wave number
All directions have the same spectra yellow: East-West grey: North-South
At larger scales than the effective resolution, models differ!
wave number
Power spectra of the kinetic energy of COSMO-7
“Effective” wave length ~45km ~7Dx

9. Cases
COSMO-7 and COSMO-2: 2 Oct UTC: CFL (crash in assimilation) 10 Feb UTC: Stratus 24 May UTC: Convection 21 Feb UTC: Spurious grid point precipitation 29 June UTC: Spurious convection 5 May UTC: Cold air pool in COSMO-2
Test suite:
2 weeks in winter: – weeks in summer: –
both periods with 0 & 12 UTC forecasts and data assimilation

10. Results (i) CFL case Reference: COSMO-7 72h forecast
RK irunge_kutta=1 SL advection
Only HDIFF at lateral and upper boundaries with:
hd_corr_bd_u/t/p=0.75
HDIFF with: hd_corr_in_u=0.65
hd_corr_in_t/p/q=0
Similar peak with ..._u=0.55
All other choices of …_u:
.75, .45, .35, .25, .15, .05
have no peaks.

11. Results (ii) Grid point precipitation
Max: 96mm
Reference: COSMO h forecast
RK irunge_kutta=1
SL advection
Only HDIFF at lateral and upper boundaries
with hd_corr_bd_u/t/p=0.75
HDIFF with: hd_corr_in_u=0.15
hd_corr_in_t/p/q=0
Same result with ..._u=0.25
15mm

12. Results (iii) Cold air pool
Reference: COSMO h forecast
RK irunge_kutta=1
SL advection
Only HDIFF at lateral and upper boundaries
with hd_corr_bd_u/t/p=0.75
HDIFF with: hd_corr_in_u=0.25
hd_corr_in_t/p/q=0
Same result with ..._u=0.15
and …_t=0.15 or …_t=0

13. Results (iv) Cold air pool
COSMO-2
May 5, 2009 Convective precipitation
COSMO-2 All directions have different spectra, except for hd_corr_in_u=0.15 with or without diffusion of temperature
COSMO-7
COSMO-7 All the directions have the same spectra but hd_corr_in_u=0.25 has the weakest impact!

14. Verification of the test suite (i)
Operational verification with SYNOP and Upper-Air obs.
Main impact in summer
Upper-air: smaller biases for temperature, humidity. Also wind speed for COSMO-2
SYNOP (table right) green is the most present colour
Big impact on precip. and wind
Parameter
Score
Summer 7 2 eu ch
alps PS ME + - ~
STD
PMSL
T_2M
TD_2M
DD_10M ++
FF_10M
- -
+++
- - -
CLCT
- +
FBI 30%
FBI 80%
TOT_PREC
FBI 0.1 mm/12 h
FBI 1 mm/12 h
FBI 10 mm/12 h
VMAX_10M
Winter 7 2 eu ch
alps ~ +
- - - ++
- - -
COSMO-7 Europe
mean error
total precipitation
July 27-Aug Reference
HDIFF experiment

15. Verification of the summer period (ii)
Mean error in mm
HDIFF experiment COSMO-2 Reference
reduced peaks with lower negative bias for HDIFF
but reduced mean absolute error and standard deviation

16. Verification of the summer period (iii)
COSMO-2 Whole domain 10m wind diurnal cycle
Reference
HDIFF experiment
Observation
COSMO-2 Whole domain
10m wind gusts diurnal cycle
Also good results for other parameters (i.e. 2m temperature, dew point and cloud cover)

17. Summary and Recommendations
Experiments and kinetic energy spectra suggest a choice for the diffusion coefficients of the wind inside the domain as: for COSMO-2 and for COSMO-7
The other variables (temperature, pressure, moisture) should not be diffused in the inner domain
At the boundary the wind, temperature and the pressure should be diffused to get the same forcing
Outlook: More detailed verification results of the test suite (specially precipitation with fuzzy verification).