The Lognormal Distribution and Cumulus Cloud Populations

Abstract

It is shown that the lognormal distribution describes the frequency distributions of height, horizontal size, and duration of cloud and radar echo populations in many different regions and convective situations. Two hypotheses are suggested to explain this phenomenon. The first postulates a growth process of cloud parcels, in which growth by entrainment of environmental air occurs by a random process that obeys the law of proportionate effects. The second postulates a formation process for clouds, in which the clouds are formed by the merger of random boundary-layer convective elements. The information presented in this paper should be useful for the parameterization of cumulus convection in larger scale models, and for the understanding and modeling of cloud formation and development.