A New Class of Probability Distributions for Describing the Spatial Statistics of Area-averaged Rainfall

TL;DR

This paper introduces a new probability distribution model based on log-infinitely divisible distributions to accurately describe the extreme variability and multiscaling properties of area-averaged rainfall over tropical oceans.

Contribution

It presents a novel class of probability laws that relate spatial scales and explain the multiscaling behavior of rainfall intensity.

Findings

Accurately models the frequency of intense rain events.

Explains the power law scaling of rainfall moments.

Predicts the spectrum of multiscaling exponents.

Abstract

Rainfall exhibits extreme variability at many space and time scales and calls for a statistical description. Based on an analysis of radar measurements of precipitation over the tropical oceans, we introduce a new probability law for the area-averaged rain rate constructed from the class of log-infinitely divisible distributions that accurately describes the frequency of the most intense rain events. The dependence of its parameters on the spatial averaging length L allows one to relate spatial statistics at different scales. In particular, it enables us to explain the observed power law scaling of the moments of the data and successfully predicts the continuous spectrum of scaling exponents expressing multiscaling characteristics of the rain intensity field.