A worldwide data science investigation of rainfall

Abstract

Abstract We perform a worldwide analysis of the rain drop size distribution using 166 dis-drometer datasets from 76 distinct sites for a total of 1,527,963 1-minute drop counts, 428,410 2-minute drop counts, and a total of 988,922,720 drops. Following data science tenets, we adopt a functional-agnostic description of the rain drop size distribution. In this way, we uncover the presence of an invariant structure of statistical relationship among the distribution parameters, not depending on location, synoptic origin, or type of disdrometer. The features of this structure are: 1) count-shape independence: there is no dependence between the drop count N and the shape of rain drop spectra. 2) mean-skewness prominence: the variability of the shape of rain drop spectra can be fully captured by its mean µ and skewness γ. 3) mean-skewness invariant parametrization: we derive empirical invariant functional forms expressing all other shape describing parameters in terms of the free parameters (µ, γ). The presented analysis reveals the global and local properties of the rain drops size distribution offering a coherent and universally applicable methodology to describe the rain drop size distribution.