Some Statistical Properties of a Homogeneous and Stationary Shallow Cumulus Cloud Field

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Abstract
Some statistical properties of homogeneous and stationary shallow cumulus cloud fields are studied. The work is motivated by the observation that the number of cumulus clouds in a large-scale tropical weather system is usually very large. It seems necessary to introduce statistical methods in solving the problem of cumulus parameterization. The study is based upon the assumption that a shallow cumulus cloud field in a homogeneous and stationary state is composed of a large number of statistically independent clouds or cloud groups. The physical basis for this assumption is discussed. Two statistical properties of cloud fields are investigated. The spatial distribution of independent cloud groups is first derived and is given by the Poisson distribution. This distribution is found to agree very well with data of some cloud radar observations. Certain constraints imposed on cloud fields by large-scale circulations and surface conditions are then discussed. The cloud group distribution as a function of vertical moisture transport rates of cloud groups at the cloud-base level is also derived. It is shown that under certain conditions this distribution also gives the size distribution of cloud groups. A comparison of this derived size distribution with the size distribution obtained from cloud radar observations is made. The agreement between the derived and the observed distributions appears quite encouraging.

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