Johnson SB as general functional form for raindrop size distribution

Abstract

Drop size distribution represents the statistical synthesis of rainfall dynamics at particle size scale. Gamma and Lognormal distributions have been widely used in the literature to approximate the drop diameter variability, contrarily to the natural upper boundary of the variable, with almost always sitespecific studies and without the support of statistical goodness-of-fit tests. In this work, we present an extensive statistical investigation of raindrop size distribution based on eight data sets, well distributed on the Earth's surface, which have been analyzed by using skewness-kurtosis plane, AIC and BIC indices and Kolmogorov-Smirnov test. Here for the first time, the Johnson SB is proposed as general functional form to describe the drop diameter variability specifically at 1 min time scale. Additional analyses demonstrate that the model is well suitable even for larger time intervals (!1 min).

On the functional form of particle number size distributions: influence of particle source and meteorological variables

“…The great flexibility and versatility of this distribution, together with its boundedness (which matches the physical limitations of the analysed aerosol particles) make the Johnson SB a good candidate for this purpose. The use of this distribution has also been inspired by (Cugerone and De Michele, 2015;D'Adderio et al, 2016); and (Cugerone and De Michele, 2017), where the authors have recently demonstrated the accuracy of this probability function in modelling the number size distribution of drops at the ground, a particular case of PNSD. Furthermore, the outcomes of this study are in accordance with the works of (Yu and Standish, 1990) and (Liu and Liu, 1994), in which JSB was firstly proposed for this aim.…”

Investigating raindrop size distributions in the (L‐)skewness–(L‐)kurtosis plane

“…In particular in CMRD they exceed 50%, except for CFC. This fact means that Johnson SB is the distribution able to describe the DSD variability with the lowest uncertainty, according to both CMRD and LMRD, in line with Cugerone and De Michele (2015). On the contrary, the truncated gamma is the distribution characterized by the worst results, having the highest percentages of OO‐couples.…”

“…The absence of counts in the smaller bins during this time interval, when heavy rain events occur, leads to the ‘dead‐time’ errors. The use of a dead‐time correction matrix (Sheppard and Joe, 1994) is of questionable utility (Tokay and Short, 1996; Cugerone and De Michele, 2015), therefore we have decided to not adopt it.…”

“…Firstly, it is necessary to calculate the empirical couple (β * 3 , β * 4 ) ((τ * 3 , τ * 4 )) and to evaluate if the position of the calculated couple in CMRD (LMRD) is inside or outside the theoretical domain of Johnson SB. Secondly, the Johnson SB distribution should be fitted to the sample DSD (the maximum likelihood method has been applied here; Appendix B in Cugerone and De Michele, 2015, gives details) and the parameters θ * estimated. Consequently, 10 000 Johnson SB samples with sample size N * and parameters θ * are generated and their skewness and kurtosis (L-skewness and L-kurtosis) are calculated, obtaining a skewness (L-skewness) sample and a kurtosis (L-kurtosis) sample.…”

“…the left and right truncated gamma (Brawn and Upton, 2008). Alternatively, lower‐ and upper‐bounded distributions can be considered like the Johnson SB (Cugerone and De Michele, 2015). Note that this distribution has already been used to describe the early stage of the evolution of drops due to coagulation (Tang and Lin, 2013).…”