Reliability of Weibull and Ulbrich Distributions for Estimating the Energetic Characteristics of Rainfall

Abstract

The knowledge of the rainfall drop size distribution (DSD) at the land surface is fundamental for understanding precipitation mechanisms affecting soil erosion processes. The most used analytical form of raindrop size parameteri-zation is that proposed by Ulbrich [1]. While, rarely, the distribution proposed by Weibull [2] has been used. In this paper, the reliability of these theoretical raindrop size distributions to reproduce about 5000 DSDs detected by an optical disdrometer at El Teularet (Spain) is presented. The parameters of both Weibull and Ulbrich distributions were estimated using the Momentum Method, in which the measured values of the median diameter and the median volume diameter were set equal to the ones calculated by each theoretical distribution. The disdrometric measurements allowed to positively test the applicability of the theoretical distri-butions and to evaluate their reliability in reproducing the main DSD statistics. Both Weibull and Ulbrich distributions, using a specific terminal velocity equation, allowed to theoretically determine the kinetic power of rainfall. These equations demonstrated that the rainfall kinetic power per unit volume of rainfall depends on two parameters of the distribution and, as a consequence, on the disdrometric characteristics of precipitation. Finally, the accuracy of the relationships for esti-mating the kinetic power of rainfall, theoretically deduced by both Weibull and Ulbrich distributions, was positively tested.