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Tuning the horizontal diffusion in the COSMO model

Tuning the horizontal diffusion in the COSMO model. Marie Müllner, Guy de Morsier COSMO General Meeting, 7 September 2009. CFL & wind on level 33. Motivation. The problem:. From the operational COSMO-7 assimilation cycle on October 2, 2008 CFL crash! (Baldauf 2008, JCP)

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Tuning the horizontal diffusion in the COSMO model

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  1. Tuning the horizontal diffusion in the COSMO model Marie Müllner, Guy de Morsier COSMO General Meeting, 7 September 2009

  2. CFL & wind on level 33 Motivation The problem: From the operational COSMO-7 assimilation cycle on October 2, 2008 CFL crash! (Baldauf 2008, JCP) COSMO-7: cflmax=1.42the extra smoothing for winds above 0.95% cflmax had no impact! • 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. 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 usingrmy coefficients from Davies relaxation and linear change below Rayleigh damping zone

  5. Analysis tools – Response function (i) • Wavelengths affected by the 4th order filter: |λ²| = 1-αΔt[6-8 cos(kΔx)+2 cos(2kΔx)]/Δx^4 [1] where: λ : wave length k : wave numberα = 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] Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra, Mon. Wea. Rev., 132. 3019-3032

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

  7. Analysis tools (iii) Kinetic Energy Spectra: • One-dimensional spectral decompositionof the velocities (u, v, w)along east-west horizontal grid lines (EW) andalong 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 levelsbetween 3.5 and 10 km height • Same domain for COSMO-2 and COSMO-7

  8. Effective wave length ~15km ~7Dx Power spectra of the kinetic energy of COSMO-2 wave number Power spectra of the kinetic energy of COSMO-7 Effective wave length ~45km ~7Dx wave number Analysis tools (iv) • February 10th, 2008 • Stratus withno precipitation andslow winds • All directions havethe same spectrayellow: East-Westgrey:North-South • Effective resolutionof each modelquite different!

  9. 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 chain: 2008 03 10 – 2008 03 26 both periods with 2008 07 24 – 2008 08 16 0 & 12 UTC forecasts With: • data assimilation • operational verification (SYNOP and Upper-Air)

  10. Results (i) CFL case Reference: COSMO-7 72h forecast RK irunge_kutta=1 SL advection Only HDIFF at lateral andupper 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. Max: 96mm 15mm Results (ii) Grid point precipitation Reference: COSMO-2 24h forecast RK irunge_kutta=1 SL advection Only HDIFF at lateraland 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

  12. Results (iii) Cold air pool Reference: COSMO-2 12h forecast RK irunge_kutta=1 SL advection Only HDIFF at lateraland 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. COSMO-2 COSMO-7 Results (iv) Cold air pool • May 5, 2009Convective precipitation • COSMO-2All directions havedifferent spectra, exceptfor hd_corr_in_u=0.15with or without diffusionof temperature • COSMO-7All the directions havethe same spectra buthd_corr_in_u=0.25 hasthe weakest impact!

  14. Verification of the summer period (i) • Green (better) is the most present colour, specially for wind and precipitation, although bad for C-2 COSMO-7Europe 10m wind July 27-Aug 18 2008 Reference HDIFF experiment COSMO-7 Europe total precipitation July 27-Aug 18 2008

  15. Verification of the summer period (ii) Mean error in mm HDIFF experiment COSMO-2 Reference

  16. Verification of the summer period (iii) COSMO-2Whole domain10m winddiurnal cycle Reference HDIFF experiment Observation COSMO-2 Whole domain 10m wind gustsdiurnal 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 windinside the domain as:0.15 for COSMO-2 and0.25 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) and second period (2 winter weeks).

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