1. Federal Department of Home Affairs FDHA Federal Office of Meteorology and Climatology MeteoSwiss Stability of the COSMO turbulence scheme Oliver Fuhrer TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A AA

2. Vertical level distribution Test-chains in July 2007 using operational (L60.2) and a new (L60.1) vertical level distributions Three test cases 12.7.2006 (convection) 23.12.2006 (fog) 18.1.2007 (Kyrill) BL TP

3. Improvement? L60.1 verfies very badly (upper air, wind, T 2m ) unrealistic surface fluxes (e.g. SH)

4. TKE Instability L60.1L60.2 23.12.2006 (fog) gridpoint (60,180) Strong checkerboard instability in TKE-field Same effect also 12.7.2006 (convection) and 18.1.2007 (Kyrill)

5. Turbulence Scheme 1.5-order closure following Mellor-Yamada (1982) Prognostic equation for Horizontal transport of TKE is neglected Numerics is separate from other prognostic variables turbulent transport shear productionbuoyant production dissipation tendency

6. Diffusion of TKE Diffusion equation is solved in q and not TKE… Due to bug, COSMO solves “wrong” equation…

7. Stability of TKE-diffusion If equation is solved explicitly, stability constraints apply In COSMO, the diffusion constant is limited Default value for securi = 0.85 is wrong!!!

8. Change of limiter L60.1 ( securi=0.5 )L60.2 ( securi=0.85 ) Instability removed Forcing at boundaries still with unrealistic values Why does L60.2 work with securi=0.85 and L60.1 not?

9. Typical TKE values

10. So why the difference? Local numerical stability depends on level thickness

11. Semi-implicit diffusion has less stringent stability constraints Bug removed: solve “correct” diffusion equation Requirements in CPU and memory are larger Solution: Semi-implicit diffusion

12. Operational level distribution L60.2 ( implicit )L60.2 ( explicit ) Solution slightly modified

13. New level distribution L60.1 ( implicit )L60.1 ( securi=0.5 ) Solution slightly modified Stronger diffusion of peaks explicit

14. Conclusions & Outlook Default setting of namelist parameter should be securi=0.5 Bug in turbdiff.incf → COSMO solves “wrong” equation Explicit TKE-diffusion for ∆z ≤ 30m almost always limited by numerics and not physical Semi-implicit TKE-diffusion is more costly but solves the problem Convergent solutions can be achieved with SCLM Consider handling TKE-diffusion in slow_tendencies.f90 as for other variables Almost happy, but…

15. Problem I tkvm ∆z=10m TKE ∆z=10m tkvm ∆z=20m TKE ∆z=20m

16. Hypothesis I Mixing coefficients are defined as follows… q and are smooth functions of height Oscillations must come from stability function Feedback onto mean variables → oscillations IF (fh2.GE. 0.0) THEN ! stabile Schichtung … ELSE ! labile Schichtung … ENDIF

17. Problem II