Shallow cumulus clouds play a key role in the vertical distribution of heat and water vapor in the atmosphere, and accurate representation of this transport is a priority for boundary layer cloud parameterizations in climate models. Episodic mixing and buoyancy-sorting models (EMBS) have been proposed as physically realistic alternatives to the entraining plume model that underlies many parameterizations of cumulus convection. Many uncertainties exist however in the specification of physical parameters in these models. The uncertainties include 1) the mixing rate between the ascending undilute subcloud air and its surrounding environmental air; 2) the detrainment criterion and 3) the mass distribution of cloudy air mixtures.

We use a diagnostic approach based on BOMEX data to investigate the adequacy and sensitivity of the EMBS representations of shallow convective clouds. The convective mass flux and cloud detrained water tendency are retrieved for BOMEX. Further, a particularly important free parameter, the undilute mixing rate, is diagnosed. We find that the diagnosed undilute mixing rate decreases exponentially with height in these models, in contrast to the near-constant vertical mixing profile commonly assumed in literature. We propose that this exponential dependence is an indication of the significant influence of the cloud size distribution within the large-scale cloud field.

We further use EMBS models to investigate single cloud and cloud ensemble effects and show that while single clouds exhibit symmetric cooling and moistening near their tops, and warming and drying near their bases, an exponentially-distributed ensemble of such clouds cools significantly near the inversion layer, but warms only slightly near cloud base, as required for consistency with the BOMEX equilibrium sounding. Examination of the water vapor tendency for this ensemble shows moistening throughout the cloud layer with a peak near the inversion. Again this is closely tied to the cloud size distribution, which emerges as an an important parameter that needs to be included in buoyancy-sorting parameterizations of shallow cumulus convection.