Development and testing of the moist second-order turbulence-convection model including transport equations for the scalar variances Ekaterina Machulskaya 1 and Dmitrii Mironov 2 1 Hydrometeorological Centre of Russian Federation, Moscow, Russia 2 German Weather Service, Offenbach am Main, Germany COSMO General Meeting, Offenbach am Main, Germany 7-11 September 2009

Outline Moist TKE-Scalar Variance closure model Outline of test cases DYCOMS-II: Nocturnal stratocumuli BOMEX: Shallow cumuli Conclusions and outlook

Moist TKE-Scalar Variance Closure Model Prognostic equations for TKE and for variances of scalars (liquid water potential temperature, total water specific humidity) Diagnostic equations for the scalar fluxes and for the Reynolds- stress components Algebraic expression for turbulence length (time) scale Statistical SGS cloud scheme, either Gaussian (Sommeria and Deardorff 1977), or with exponential tail to account for the effect of cumulus clouds (Bechtold et al. 1995) Optionally, prognostic equations for temperature and humidity triple correlation (to determine temperature and humidity skewness)

Outline of Test Cases DYCOMS-II Nocturnal marine stratocumuli (LES and some observational data) Prescribed surface fluxes of heat and moisture, prescribed large-scale subsidence, prescribed radiation heating Fractional cloud cover of order 80%, profiles of some second-order moments available (LES), no well-documented second-moment budgets BOMEX Trade-wind shallow cumuli (LES and some observational data) Prescribed surface fluxes of heat and moisture, prescribed large-scale subsidence, prescribed radiation heating, prescribed large-scale drying rate of the sub-cloud layer, prescribed z-dependent geostrophic wind (baroclinicity) Fractional cloud cover of order 10%, profiles of some second-order moments available, some LES-based second-moment budgets available for similar cases

Sc Case Liquid water specific humidity. Left: TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue). Right: LES data (Stevens et al. 2005)

Sc Case Vertical virtual potential temperature (buoyancy) flux. Left: TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue).

Sc Case (cont’d) Fractional cloud cover simulated by the TKE model (red) and by the TKE-Scalar Variance (TKE-TPE) model (blue). Data suggest cloud fraction of order 0.8

Sc Case (summary) TKE-Scalar Variance model performs well and slightly better than TKE model However, vertical resolution is more critical Fractional cloud cover simulated by the TKE model (red) and by the TKE-Scalar Variance (TKE-TPE) model (blue) at high vertical resolution (left) and low vertical resolution (right). LES: cloud fraction = 0.8

Cu Case Variance of the total water specific humidity. Left: TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue). Right: LES data (Cuijpers et al. 1996)

Cu Case (cont’d) Fractional cloud cover with Gaussian SGS statistical cloud scheme. TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue). Data suggest cloud fraction of order 0.1

Cu Case (cont’d) Fractional cloud cover with the  l and q t profiles taken from LES. Curves shows cloud cover with non-Gaussian SGS statistical cloud scheme (includes exponential tail to account for the effect of cumuli). Gaussian SGS cloud scheme gives no clouds! Data suggest cloud fraction of order 0.1

Cu Case (cont’d) Linear approximation of the error function (Gaussian distribution) Exponential tail Cloud fraction Normalised saturation deficit Strong mean undersaturation = shallow cumuli case

Cu Case (cont’d) Fractional cloud cover simulated by the TKE-Scalar Variance model using Gaussian (blue) and non-Gaussian (green) SGS statistical cloud scheme.

Cu Case (summary) SGS cloud-cover parameterisation is crucial for successful simulation of Cu Not only fractional cloud cover should be parameterised realistically, but also the effect of cumuli on the buoyancy production of TKE must be accounted for (fractional coverage of Cu is small, but the effect on fluxes is large – no way to describe this effect with Gaussian schemes!) Models (both TKE and TKE-Scalar Variance) have insufficient mixing in the upper part of the Cu cloud layer

Conclusions and Outlook Moist TKE-Scalar Variance model shows reasonable performance (better than TKE model, but there is room for improvement) The use of prognostic equations for the scalar triple correlations causes numerical problems (small time step is required); expert assistance is requested A comprehensive data set on second-moment budgets (from LES) is very desirable (otherwise component model testing is very difficult) Consolidation of the TKE-Scalar Variance model Formulation of the best-compromise version in terms physics, numerical stability, and computational efficiency Implementation into the COSMO model (effort should be co-ordinated with WG2 and WG6)

Thank you for your attention! Thanks are due to Pier Siebesma (KNMI) for discussions and helpful suggestions.

Stuff Unused

Sc Case (cont’d) Vertical virtual potential temperature (buoyancy) flux. Left: TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue). Right: LES data (Steven et al. 2005)

Cu Case (cont’d) Fractional cloud cover with Gaussian SGS statistical cloud scheme. TKE model (red) vs. TKE-Scalar Variance (TKE-TPE) model (blue). Data suggest cloud fraction of order 0.1

Cu Case (cont’d) Liquid water potential temperature (left) and total water specific humidity (right) simulated by the TKE-Scalar Variance model using Gaussian (blue) and non- Gaussian (green) SGS statistical cloud scheme.