On Size Distributions of Cloud Droplets Growing by Condensation: A New Conceptual Model

Abstract

Observed turbulence and fluctuating microphysical properties of clouds lead the authors to assume that a cloud droplet size distribution results from a large number of random events associated with turbulence and to consider a droplet system with fluctuating cloud droplet size distributions constrained by conservation laws. This assumption in turn suggests multiplicity rather than uniqueness of cloud droplet size distributions, that is, different cloud droplet size distributions occurring with different probability. The authors argue from a system point of view that two characteristic cloud droplet size distributions can be identified without knowing the specific probability of occurrence. The maximum likelihood cloud droplet size distribution is obtained by applying Shannon?s maximum entropy principle; the minimum likelihood cloud droplet size distribution is obtained by studying the functional relationship between a cloud droplet size distribution and the corresponding energy change to form such a droplet population. The maximum and minimum likelihood cloud droplet size distribution for an ideal droplet system with conserved mass are derived to be, respectively, a Weibull distribution and a delta distribution. The unique properties of the two characteristic cloud droplet size distributions are associated with observed cloud droplet size distributions and ones predicted by the uniform condensation model. These associations suggest that the lack of agreement between cloud droplet size distributions predicted by the condensation model and those observed in real clouds may be a result of trying to compare two totally different characteristic cloud droplet size distributions of the same droplet system. The present study discusses the maximum and minimum likelihood cloud droplet size distributions and their relationship to observed and model-predicted cloud droplet size distributions. The proposed theory sets in a new context the discrepancy between observed and model-predicted cloud droplet size distributions and also provides an explanation for the scale dependence of observed microphysical properties.