Scale dependence of spatiotemporal intermittence of rain

Abstract

It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area‐ and/or time‐averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential formula fits the observed scale dependence of the zero‐rain probability. The proposed formula makes it apparent that the space‐time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an explanation of the observed behavior in terms of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory.