Phase space parametrization of rain: the inadequacy of the gamma distribution

TL;DR

This paper demonstrates the inadequacy of the gamma distribution for modeling rain drop sizes and introduces a new phase space parametrization based on standardized moments that captures rainfall variability across locations.

Contribution

It proposes a novel, functional form-independent parametrization of drop size distributions using standardized moments, revealing invariant properties of rainfall.

Findings

Gamma distribution is not suitable for drop size PDFs

A new parametrization based on standardized moments is effective

Rainfall properties are invariant across different locations

Abstract

We show that the Gamma distribution is not an adequate fit for the probability density function of drop diameters using the Kolmogorov-Smirnov goodness of fit test. We propose a different parametrization of drop size distributions, which not depending by any particular functional form, is based on the adoption of standardized central moments. The first three standardized central moments are sufficient to characterize the distribution of drop diamters at the ground. These parameters together with the drop count form a 4-tuple which fully describe the variability of the drop size distributions. The Cartesian product of this 4-tuple of parameters is the rainfall phase space. Using disdrometer data from 10 different locations we identify invariant, not depending on location, properties of the rainfall phenomenon.