The texture of rain: Exploring stochastic micro-structure at small scales

Abstract

Summary The main theme of this review is the importance of a discrete approach to describing rain at spatial scales comparable to inter-drop separation. We propose that the pair correlation function should be used to define and measure the texture of rain. To that end, we discuss the pivotal role of the Poisson process for examining this micro-structure of rain. The importance of statistical stationarity and the essential distinction between a Poisson distribution and a Poisson process are emphasized. It is argued that the correlation-fluctuation theorem (which relates drop count variance to the pair-correlation function) is ideally suited for scale-dependent exploration of rain micro-structure in the discrete “shot noise” limit. The likelihood of spurious negative correlations at fine spatial scales is pointed out as instruments are pushed to their resolution limits. One of the consequences is that possibly spurious Poisson statistics at a given spatial scale may result from a cancellation on sub-scales. We then proceed to examine implications of stochastic microstructure and show that the notion of spatially variable and random concentration (or size distribution) does not always provide an adequate description of rain texture.