Capabilities of the Johnson SB distribution in estimating rain variables

Numerous fields of atmospheric and hydrological sciences require the parametric form of the raindrop size distribution (DSD) to estimate the rainfall rate from radar observables as well as in cloud resolving and weather forecasting models. This study aims to investigate the capability of the Johnson SB distribution (JSB) in estimating rain integral parameters. Specifically, rainfall rate (R), reflectivity factor (Z) and mean mass diameter (Dmass) estimated by JSB are compared with those estimated by a three- parameter Gamma distribution, widely used by radar meteorologists and atmospheric physicists to model natural DSD. A large dataset consisting of more than 155,000 one-minute DSD, from six field campaigns of Ground Validation (GV) program of NASA/JAXA Global Precipitation Measurement mission (GPM), is used to test the performance of both JSB and Gamma distribution. The available datasets cover a wide range of rain regimes because of the field campaigns were carried out in different seasons and locations. Correlation coefficient, bias, root mean square error (RMSE) and fractional standard error (FSE) between estimated and measured integral parameters are calculated to compare the performances of the two distributions. The capability of JSB in estimating the integral parameters, especially R and Z , resulted very close to that of Gamma distribution. In particular, for light precipitation, JSB is superior to Gamma distribution in estimating R with FSE of 11% with respect to values ranging between 25% and 37% about for Gamma. Comparison of the estimated and measured DSDs shows that the JSB distribution reproduces the natural DSD quite accurately