A diagnostic cumulus ensemble model is developed to study the effects of convective-scale downdrafts and mesoscale convective organization on the heat and moisture budgets of tropical cloud clusters. The model adopts the spectral representation of a cumulus ensemble and includes the vertical momentum budgets for both convective-scale updrafts and downdrafts. The downdrafts are initiated and maintained by the loading and evaporation cooling effects of rainwater which is generated in the updrafts tilting from the vertical. A theory for determining the updraft tilting angle based on the stability analysis of the rainwater budget equation is presented. Several simplified versions of the updraft model are also considered by assuming a constant tilting angle for each subensemble updraft. The diagnosed updraft tilting angle can be interpreted as the mean angle required for a statistically steady updraft subensemble to maintain its buoyancy against the loading effect of rainwater. These simplified versions of the updraft model are tested using the data taken during Phase III of the GARP Atlantic Tropical Experiment (GATE) for the diagnosis of the tilting angles for very deep cumulus clouds. We find a remarkable correlation between the diagnosed updraft tilting angle and the degree of mesoscale convective organization observed by radar. The horizontal distributions of the updraft tilting angle show local maxima in the regions of organized cumulus convection, while the distributions are more uniform when only scattered convection is present. We also find a negative spatial correlation between the diagnosed updraft tilting angle and the cloud work function, indicating the critical dependence of the tilting of cumulus clouds on the moist convective instability of the environment.
Ming–Dean Cheng (1989) studied this question.