On the Use of Johnson SB in Modelling Drop Size Distribution

Numerous fields of atmospheric and hydrological sciences require the parametric form of the drop size distribution (DSD), to measure the multi-wavelength rain attenuation for satellite systems, evaluate the below cloud scavenging coefficient of the aerosol by precipitation, as well as estimate rainfall rate from radar measurements and in cloud resolving and weather forecasting models. In Literature, many distributions, such as Gamma, Lognormal and Weibull, have been used to this aim, even if none of these have shown undisputed superior performances in representing DSDs. This is probably due to the complexity of rainfall, which is a discrete phenomenon, made by drops, able to take a great variety of forms. Here, the Johnson SB (JSB), a four parameters distribution with bounded domain, is presented as a valid DSD model, alternatively to the ones presently used. The ability in describing DSD is demonstrated by an extensive statistical investigation based on the use of Skewness-Kurtosis plane, AIC and BIC indices and Kolmogorov-Smirnov goodness-of-fit test. The practical capabilities of JSB in estimating the rain variables, namely rainfall rate (R), reflectivity (Z) and mean mass diameter (Dmass), compared to the ones obtained by the standard untruncated Gamma distribution, are also examined. The accuracy of fit is evaluated in terms of correlation coefficient, bias, root mean square error (RMSE) and fractional standard error (FSE) between the measured and the estimated rain variables. The data used for these analyses were collected in 14 field campaigns at different climate regimes, using three types of disdrometers, JWD, Thies and 2DVD (the latter from Global Precipitation Measurement, GPM, mission). The outcomes of this study demonstrate the accuracy of Johnson SB in approximating the natural DSD, suggesting its use in hydrometeorology, to make applications in cloud and microphysical models.