1. COSMO General Meeting, Moscow, Russia. 6-10 September 2010. Further Single-Column Testing and Implementation into the COSMO Model of the TKE-Scalar Variance Second-Order Turbulence-Convection Scheme 7 September 2010 Ekaterina Machulskaya and Dmitrii Mironov German Weather Service, Offenbach am Main, Germany (ekaterina.machulskaya@dwd.de, dmitrii.mironov@dwd.de)

2. COSMO General Meeting, Moscow, Russia. 6-10 September 2010.  Single-column tests: dry convective PBL, nocturnal stratocumuli, shallow cumuli, stably-stratified PBL  Modified statistical SGS cloud scheme: parallel experiments  TKE-scalar variance scheme within a full-fledged COSMO model: implementation, parallel experiment, problems  Conclusions and outlook Outline

3. Single-Column Tests: Dry Convective PBL Mean potential temperature in shear-free convective PBL. Red – TKE scheme, blue – TKE-scalar variance scheme, black dashed – LES data.

4. Single-Column Tests: Nocturnal Stratocumuli Fractional cloud cover (left) and cloud water content (middle) in DYCOMS-II. Red – TKE scheme, blue – TKE-scalar variance scheme. Black solid curve in the right figure shows LES data.

5. Single-Column Tests: Shallow Cumuli Fractional cloud cover (upper row) and cloud water content (lower row) in BOMEX. Red – TKE scheme, blue – TKE-scalar variance scheme. Black solid curves in the middle figures show LES data. Gaussian skewed

6. Single-column tests: shallow cumuli (cont’d) Potential temperature variance (two left panels) and total water variance (two right panels) in BOMEX. Red – TKE scheme, blue – TKE-scalar variance scheme. Black solid curves in the middle figures show LES data.

7. 1 0.5 0 Linear approximation of the error function (Gaussian distribution) Exponential tail Cloud fraction Normalised saturation deficit Strong mean undersaturation = shallow cumuli case Single-column tests: shallow cumuli (cont’d) Important! Non-Gaussian correction is introduced into the expression for the buoyancy flux in the TKE equation

8. Modified Statistical SGS Cloud Scheme: Parallel Experiments Exp 7680 – COSMO-EU model with modified SGS cloud scheme, January 2010 Exp 7692 – COSMO-EU model with modified SGS cloud scheme, June 2010 Pressure over COSMO-EU domain in June 2010 (00UTC forecasts). Red – Exp7692, blue – COSMO-EU.

9. Modified Statistical SGS Cloud Scheme: Parallel Experiments (cont’d) T2m TD2m deficit Exp 7680, COMO-EU, January 2010 (00UTC forecasts) Verification over COSMO-DE domain

10. Modified Statistical SGS Cloud Scheme: Parallel Experiments (cont’d) red – Exp7692, blue – COSMO-EU routine total cloud cover low-level cloud cover COSMO-EU domain, June 2010

11. TKE-scalar variance scheme within a full-fledged COSMO model TKE-scalar variance scheme is implemented into full-fledged three-dimensional COSMO model Parallel experiments are being performed Exp 7771 – with Gaussian SGS cloud scheme Exp 7778 – with modified (skewed) SGS cloud scheme Problems numerical stability (hope to improve the situation using non- local formulation for turbulence length scale) more physically sound parameterisation of non-Gaussian effects within the SGS cloud scheme is needed

12. LES and Modelling of SBL over Heterogeneous and Homogeneous Surfaces by D. Mironov, P. Sullivan (NCAR) and E. Machulskaya Blue – homogeneous SBL, red – heterogeneous SBL.

13. Tiled TKE-Temperature Variance Closure Model Transport (prognostic) equations for TKE and for the temperature variances including third-order transport Algebraic (diagnostic) formulations for temperature flux, for the Reynolds-stress components, and for turbulence length scale Tile approach where different tiles have different surface temperature Surface fluxes are computed as weighted means of fluxes over individual tiles is non-zero at the surface in heterogeneous SBL Input parameters of numerical experiments are similar to LES (except for piece-wise vs. sinusoidally varying surface temperature)

14. Tiled TKE-Temperature Variance Model: Results Blue – homogeneous SBL, red – heterogeneous SBL.

15. COSMO General Meeting, Moscow, Russia. 6-10 September 2010.  Single-column tests show that the use of TKE-scalar variance scheme brings about some improvements as to fractional cloud cover, second-moment profiles, and evolution of turbulence moments in time, although problems remain  Modified SGS statistical cloud scheme (effect of shallow cumuli à la Bechtold et al. 1995) is favourably tested through parallel experiments; scores are neutral to slightly positive  TKE-scalar variance scheme is implemented into full-fledged three-dimensional COSMO model, parallel experiment is being performed, performance is monitored, results of verification will be reported later  Comprehensive testing through parallel experiments (key issues: numerical stability, computational efficiency), preparation of documentation  Improve a parameterisation of the turbulence length/time scale (e.g. non-local vs. Blackadar)  Improve description of non-Gaussian effects within the SGS statistical cloud scheme (Bechtold et al. 1995, modifications do not seem to be sufficient) Conclusions and Outlook

16. COSMO General Meeting, Moscow, Russia. 6-10 September 2010. Thank you for your attention! Acknowledgements: Vittorio Canuto, Peter Bechtold, Sergey Danilov, Evgeni Fedorovich, Jochen Förstner, Vladimir Gryanik, Thomas Hanisch, Donald Lenschow, Chin-Hoh Moeng, Ned Patton, Pier Siebesma, Peter Sulluvan, Jeffrey Weil, and Yun-Ichi Yano.