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Episodic mixing and buoyancy-sorting (EMBS) models have been proposed as a physically more realistic alternative to entraining plume models of cumulus convection. Applying these models to shallow nonprecipitating clouds requires assumptions about the rate at which undilute subcloud air is eroded into the environment, an algorithm to calculate the eventual detrainment level of cloud-environment mixtures, and the probability dis- tribution of mixing fraction. A diagnostic approach is used to examine the sensitivity of an EMBS model to these three closure assumptions, given equilibrium convection with known large-scale forcings taken from phase III of the Barbados Oceanographic Meteorological Experiment (BOMEX). The undilute eroding rate (UER) is retrieved and found to decrease exponentially with height above cloud base, suggesting a strong modulation by the cloud size distribution. The EMBS model is also used to calculate convective transport by individual clouds of varying thickness. No single cloud from this ensemble can balance the large-scale BOMEX forcing; the observed equilibrium requires a population of clouds with a cloud size distribution that is maximum for small clouds and decreases monotonically with cloud size. The EMBS model depends sensitively on the assumptions governing the detrainment of positively buoyant mixtures. In particular, given the requirement that positively buoyant mixtures detrain at their neutral buoyancy level, there is no positive definite undilute eroding rate that is consistent with the BOMEX forcing. The model is less sensitive to the assumed distribution of cloud-environment mixtures, given a multiple mixing treatment of positively buoyant parcels and detrainment at the unsaturated neutral buoyancy level.

Episodic Mixing and Buoyancy-Sorting Representations of Shallow Convection: A Diagnostic Study