3. T q sat(T) qtqt. (T,q t ) Statistical cloud scheme Determine cloud cover and liquid water using the sub-grid variability :

4. Go over to one variable: For a certain PDF, cloud cover and liquid water can be written as a function of just one variable: Main Problem: How to determine  s ? (for simplicity: ) s  q t -q sat (p,T)

5. How to parameterize variance? Link it to convection/turbulence schemes using a variance budget: Production Dissipation Lenderink& Siebesma 2000 Variance due to convectionVariance due to turbulence

6. Variance due to/coupled with turbulence: Very simple: = (0.02q s ) 2 (Lenderink) Simple: l turb =40 (Siebesma) l turb =0.2z for z 900m (Chaboureau & Bechtold) Less simple (stability dependent): l turb from moist CBR (implementation Colin Jones) Even without convective or turbulent activity (free atmosphere) some variance is needed!

7. Project: Statistical cloud scheme (from simple to complex) First 1D tests cases (start with BOMEX): 1.Use cloud cover (a c ) diagnostically 2.Use a c and q l prognostically Subsequently 3D 1.Test cases 2.Long time verification

8. Problems with Hirlam KF convection: Intermittent behavior Negative buoyant cloud (T V_UPDRAFT < T V_ENVIRONMENT ) Artificially looking closure for shallow convection Mass flux does not decrease (enough) with height Results for Bomex are disappointing Fundamental problems? (Sander Jonker) Code is complex, hard to understand (and slow)

9. q profile BOMEX with standard Hirlam KF

10. Some of the adaptations to KF: Fractional entrainment/detrainment according to Siebesma (2003) Vertical velocity equation (Gregory, 2001) More simple and physically appealing closure (Grant, 2001)  Good results with convection and statistical cloud scheme for Bomex

11. q profile BOMEX with adaptations

12. Variance BOMEX LES Hirlam (40 lvls) with modified KF

13. Cloud cover Bomex LESHirlam with modified KF

14. Our conclusion: It is not appealing to build further developments on the current Hirlam KF code. Two alternatives: 1.KF from Meso-NH 2.Latest ECMWF IFS convection code Peter Bechtold coded 1 and currently works on 2. His advice: Use 2 (performance, speed, use of AROME is compatible with 2, synergy, etc.) => Implement 2 in Hirlam(1D)

15. Provisional results: Hirlam 1d with new ECMWF convection, old Sundqvist condensation and moist CBR (Colin Jones)