Phase Space Parameterization of Rain: The Inadequacy of Gamma Distribution

Abstract

AbstractThe authors test the adequacy of gamma distribution to describe the statistical variability of raindrop diameters in 1-min disdrometer data using the Kolmogorov–Smirnov goodness-of-fit test. The results do not support the use of this distribution, with a percentage of rejected cases that increases with the sample size. A different parameterization of the drop size distribution is proposed that does not require any particular functional form and is based on the adoption of statistical moments. The first three moments, namely the mean, standard deviation, and skewness, are sufficient to characterize the distribution of the drop diameter at the ground. These parameters, together with the drop count, form a 4-tuple, which fully describes the variability of the drop size distribution. The Cartesian product of this 4-tuple of parameters is the rainfall phase space. Using disdrometer data from 10 different locations, invariant, location-independent properties of rainfall are identified.