On the Spatial Distribution of Cloud Particles

Abstract

Recent studies have led to the statistical characterization of the spatial (temporal) distributions of cloud (precipitation) particles as a doubly stochastic Poisson process. This paper arrives at a similar conclusion (larger-than-Poissonian variance) via the more fundamental route of statistical physics and significantly extends previous findings in several ways. The focus is on the stochastic structure in the spatial distribution of cloud particles. A new approach for exploring the stochastic structure of clouds is proposed using a direct relation between number density variance and the pair correlation function. In addition, novel counting diagrams, particularly useful for analyzing counts at low data rates, demonstrate droplet clustering and striking deviations from Poisson randomness on small (centimeter) scales. These findings are shown to agree with pair correlation functions calculated for droplet counts obtained from an aircraft-mounted cloud probe. Time series of the arrival of each droplet are used to bin the data evenly so as to avoid corruption of the statistics through the operations of multiplication and division. Furthermore, it is shown that statistically homogeneous series of particle counts exhibit super-Poissonian variance. Since it is not always practical or feasible to obtain such direct measurements, the possibility of studying cloud texture using a revival of the idea of coherent microwave scatter from cloud droplets is discussed, including a more complete interpretation of Bragg scatter that seems to explain some recent observations in clouds. Finally, the appearance of clustering and the subsequent geometric distribution of droplet counts are interpreted using basic considerations of turbulence.