Wet and dry epoch durations of spatially averaged rain rate, their probability distributions and scaling properties

Abstract

This article is concerned with the notion of duration of wet and dry epochs in stochastic processes of spatially averaged (instantaneous) rain rate over a given region. Gamma, Lognormal, and Inverse Gaussian parametric families of probability distributions have been considered as candidate models for the distribution of such durations. Goodness of these model's fit to data of dry and wet epoch durations obtained from real time series of spatially averaged rain rate, has been tested with Pearson's $\chi ^2$-test. The parameters of each of these models have been estimated by maximum likelihood and method of moments, based on TOGA-COARE measurements of tropical rainfall. The hypotheses of independence and identical distribution (i.i.d.) among durations of dry or wet epochs have also been tested using a certain version of the Wald-Wolfowitz test. Finally, the effect of spatial scale on the moments of dry and wet epoch durations has also been investigated, pointing to self-similarity of the underlying random structures over space. The main result of this study is that among the three candidate models, Inverse Gaussian is the one conforming most adequately with all the classical testing criteria implemented here, and also with the newly established scaling behavior of both dry and wet epoch duration processes over space. This is a remarkable finding, considering that the Inverse Gaussian family has recently been also justified from a theoretical viewpoint as a reasonable model for the probability distributions of dry and wet epoch durations.