Dmitrii Mironov-November 28

Turbulence Kinetic Energy - Scalar Variance Turbulence Parameterization Scheme for NWP Models


November 28, 2017 - 4:00 pm


November 28, 2017 - 5:00 pm


120 David L. Boren Blvd., Suite 5900, Norman, OK 73072   View map

Turbulence Kinetic Energy – Scalar Variance Turbulence Parameterization Scheme for NWP Models

A turbulence kinetic energy scalar variance (TKESV) turbulence parameterizaion scheme for moist atmosphere is presented. The scheme is formulated in terms of the total water specific humidity and the liquid water potential temperature, i.e. in terms of variables that are approximately conserved for phase changes in the absence of precipitation. The scheme carries prognostic equations for the turbulence kinetic energy and for the variances and co- variance of scalar quantities. The other second-moment equations, namely, the equations for the Reynolds stress and for the scalar fluxes, are reduced to the diagnostic algebraic expressions. The set of governing equations of the TKESV scheme and parameterizations (closure assumptions) for the pressure-scrambling terms, the third-order transport (diffu- sion) terms, and the molecular destruction (dissipation) terms are discussed. Particular attention is paid to the pressure-scrambling terms in the Reynolds-stress and scalar-flux equations. The other issues that receive careful consideration are the effect of clouds on mixing (treated with the aid of statistical cloud schemes) and the interaction of the boundary layer with the underlying surface.

Off-line single-column tests show a good performance of the TKESV scheme in various clear and cloudy boundary-layer regimes. The TKESV scheme was implemented into the limited-area NWP model COSMO (implementation into the global NWP model ICON is underway at the German Weather Service). The scheme was successfully tested through numerical experiments including the entire COSMO data assimilation cycle. Verification of results against observational data indicate perceptible improvements as to some scores,

e.g. bias and root-mean-square error of two-metre temperature and two-metre humidity, and marginal improvements with respect to fractional cloud cover. Some challenging issues that should be addressed in future work are outlined.



Machulskaya, E., and D. Mironov, 2013: Implementation of TKE–Scalar Variance mixing scheme into COSMO. COSMO Newsletter, No. 13, 25–33. (available from the web site of the Consor- tium for Small-Scale Modelling,


Mironov, D. V., and E. E. Machulskaya, 2017: A turbulence kinetic energy – scalar variance turbulence parameterization scheme. COSMO Technical Report, No. 30, Consortium for Small- Scale Modelling, 55 pp. (available from


Machulskaya, E., and D. V. Mironov, 2017: Surface boundary conditions for scalar variances and covariance consistent with the tile approach to compute surface fluxes. Submitted to Boundary- Layer Meteorol.