Combining the Massflux Approach with a Statistical Cloud Scheme

In statistical cloud schemes the cloud fraction is directly related to the normalized saturation deficit (Q1). This Q1 is determined by the distance of the (gridbox) mean state to the mean saturation normalized by the horizontal variance of the atmospheric state. Estimates of the horizontal variance of the conserved atmospheric state variables (e.g. liquid water potential temperature and total water) are therefore needed. Up to now, statistical cloud schemes have been used frequently in combination with diffusion schemes for turbulent transports. In this approach horizontal variances are determined by the turbulent flux and a typical convective velocity scale. At present mass flux schemes have proven to be more succesfull than diffusion schemes to represent turbulent fluxes in shallow cumulus layers. Therefore it is natural to combine the mass flux approach with a statistical cloud scheme. In order to do this estimates of the horizontal variance due to mass flux activity are needed. We obtained estimates of the variances from a simplified budget equations for the horizontal variance We show the result of the scheme for the intercomparison cases in GCSS working group 1 of Cumulus clouds (BOMEX and ARM) and Cumulus rising into Stratocumulus (ATEX). Results of the scheme show a good agreement with the LES results for these cases.