Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds

We present a statistical cloud scheme based on the subgrid-scale distribution of the saturation deficit. When analyzed in large-eddy simulations (LES) of a typical cloudy convective boundary layer, this distribution is shown to be bimodal and reasonably well-fitted by a bi-Gaussian distribution. Thanks to a tracer-based conditional sampling of coherent structures of the convective boundary layer in LES, we demonstrate that one mode corresponds to plumes of buoyant air arising from the surface, and the second to their environment, both within the cloud and sub-cloud layers. According to this analysis, we propose a cloud scheme based on a bi-Gaussian distribution of the saturation deficit, which can be easily coupled with any mass-flux scheme that discriminates buoyant plumes from their environment. For that, the standard deviations of the two Gaussian modes are parametrized starting from the top-hat distribution of the subgrid-scale thermodynamic variables given by the mass-flux scheme. Single-column model simulations of continental and maritime case studies show that this approach allows us to capture the vertical and temporal variations of the cloud cover and liquid water.