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A Probabilistic View on Raindrop Size Distribution Modeling: A Physical Interpretation of Rain Microphysics

AbstractThe raindrop size distribution (RDSD) is defined as the relative frequency of raindrops per given diameter in a volume. This paper describes a mathematically consistent modeling of the RDSD drawing on probability theory. It is shown that this approach is simpler than the use of empirical fits and that it provides a more consistent procedure to estimate the rainfall rate (R) from reflectivity (Z) measurements without resorting to statistical regressions between both parameters. If the gamma distribution form is selected, the modeling expresses the integral parameters Z and R in terms of only the total number of drops per volume (NT), the sample mean [m = E(D)], and the sample variance [σ2 = E(m − D)2] of the drop diameters (D) or, alternatively, in terms of NT, E(D), and E[log(D)]. Statistical analyses indicate that (NT, m) are independent, as are (NT, σ2). The Z–R relationship that arises from this model is a linear R = T × Z expression (or Z = T−1R), with T a factor depending on m and σ2 only and...