Parameterization of Drop Size Distribution with Rainfall Rate: Comparison of the N(D) and R(D) Functions; and Relationship between Gamma and Lognormal Laws

Abstract

enin (West Africa) are analyzed with ????(????) and ????(????) functions. The ????(????) function represents the number of raindrops per unit of volume and by interval of diameters, while the ????(????) function represents the rainfall rate per range of diameters. Meteorological variables that are formulated with the ????(????) function can also be formulated with the ????(????) function. In addition, the ????(????) function has the advantage of being independent of the falling drop speed which is not measured well enough by the disdrometers. In this paper, the averages of DSDs per rainfall class are modeled by the gamma and lognormal laws. The parameters of these models are adjusted according to the rain rate. We thus obtained DSD parameterized with the rate of rain. Evaluating the efficiency of this parameterization, we noticed that the ????(????) function estimates its useful moments better than the ????(????) function. Moreover, we have noted that DSD modeling by the gamma law is not significantly different from DSD modeling by the lognormal law. Furthermore, we have established a relation between the shape parameters of these two laws.