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

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

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

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 -0.75 0.0 0.0 0.75 0.0 0.15 0.0 0.05 hd_corr_p hd_corr_q 0.5

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^4 [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, 2853-2864

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

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

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

Cases COSMO-7 and COSMO-2: 2 Oct. 2008 12UTC: CFL (crash in assimilation) 10 Feb. 2008 00UTC: Stratus 24 May 2009 06UTC: Convection 21 Feb. 2009 00UTC: Spurious grid point precipitation 29 June 2009 06UTC: Spurious convection 5 May 2009 06UTC: Cold air pool in COSMO-2 Test suite: 2 weeks in winter: 2008 03 10 – 2008 03 26 3 weeks in summer: 2008 07 24 – 2008 08 16 both periods with 0 & 12 UTC forecasts and data assimilation

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.

Results (ii) Grid point precipitation Max: 96mm Reference: COSMO-2 24h 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

Results (iii) Cold air pool Reference: COSMO-2 12h 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

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!

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 18 2008 Reference HDIFF experiment

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

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)

Summary and Recommendations Experiments and kinetic energy spectra suggest a choice for the diffusion coefficients of the wind inside the domain as: 0.15 for COSMO-2 and 0.25 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).