George J. Huffman

A Stochastic Model of Cumulus Clumping

Abstract Observations show that cumulus clouds often occur in long-lived mesoscale groups, or clumps. Five possible explanations of clumping are surveyed. The “mutual protection hypothesis,” that clumps occur because cumulus clouds create and maintain, in their near environments, relatively favorable conditions for the development of succeeding clouds, is examined at length. This idea is tested through the use of a simple time-dependent model in which clouds, triggered at randomly selected locations, tend to stabilize their environment in the face of a prescribed constant forcing. Results show that clumping occurs when the cloud-induced stabilization rate is strongest at an intermediate distance from a cloud, and that it does not occur when the stabilization rate decreases monotonically away from a cloud.

Entrainment and detrainment in a simple cumulus cloud model

Abstract A cumulus clouds size, shape and internal properties can be predicted, provided that the rate of entrainment is determined by a suitable entrainment parameterization theory. A cumulus cloud model based on such a theory is analogous to the mixed-layer models of the planetary boundary layer (PBL) and the upper ocean. The entrainment rate is closely related to turbulent transport near the cloud boundary. The mixing-length theory suggested by Asai and Kasahara (1967) is examined in this light. An alternative theory is suggested, which completely removes the strong scale-dependence of the Asai-Kasahara model. Scale-dependence is reintroduced by including the perturbation pressure term of the equation of vertical motion. For a given sounding, the new model predicts deeper clouds than the Asai-Kasahara model. This results both from the entrainment assumption used, and from the effects of the perturbation pressure. The expected cloud-top entrainment rate is zero for the simple model considered, although...