Is the Weibull distribution reliable to describe the rainfall kinetic power and momentum in Mediterranean environments?

Understanding the characteristics of the rainfall drop size distribution (DSD) at the land surface is crucial for elucidating the mechanisms of precipitation that affect soil erosion processes. This study aims to both apply the Weibull distribution to more than 47,000 DSDs detected at Palermo (Italy) and El Teularet (Spain) experimental sites and deduce theoretically relationships for estimating the rainfall kinetic power and momentum of a DSD distributed as Weibull law having known parameters. The study confirms that the theoretical Weibull distribution can accurately reproduce measured DSDs, with highly consistent fitting results using the moment method (MM) for estimating its parameters. The results indicate that rainfall kinetic power and momentum are closely related to the characteristics of the DSD. No statistically significant correlation between the parameters of the Weibull distribution and rainfall intensity is detected. Moreover, the analysis highlights that the η parameter turns out to be related to the coefficient of variation of the DSD, and the parameter N0 represents the total number of drops, making the Weibull distribution physically based. Furthermore, a comparison between the Weibull and Ulbrich distributions allows for the conclusion that, although both models exhibit similar performance in terms of fitting and reliability when describing rainfall kinetic power and momentum, the Weibull distribution offers advantages related to parameter estimation. Specifically, its parameters, unlike those of Ulbrich, possess a physical, and not merely statistical, significance. The study concludes that the Weibull distribution is highly reliable for characterizing rainfall kinetic power and momentum in two experimental sites located in the Mediterranean region, and rainfall intensity cannot serve as a variable to comprehensively represent the characteristics of precipitation.