COSMO General Meeting, Moscow, Russia September 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

COSMO General Meeting, Moscow, Russia September  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

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.

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.

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

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.

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

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.

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

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

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

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.

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)

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

COSMO General Meeting, Moscow, Russia September  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

COSMO General Meeting, Moscow, Russia September 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.