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

Abstract

Skewness–kurtosis (β3−β4) and L‐skewness–L‐kurtosis (τ3−τ4) planes are proposed here as diagnostic tools to guide the identification of drop size distributions (DSDs) of rainfall at the ground. Firstly, we have determined β3−β4 and τ3−τ4 domains of 13 distribution families, namely normal, exponential, gamma, truncated gamma, log‐normal, truncated log‐normal, Weibull, hyperbolic, generalized hyperbolic, log‐logistic, skewed Laplace, Johnson SB and Johnson SU. These include those most used to represent DSDs and, in general, particle size distributions (PSDs). Secondly, we have considered 1 min and 2 min disdrometric data, collected at six sites in the United States, and reported the empirical couples (β3,β4) and (τ3,τ4) in the moment diagrams. The location uncertainty of the empirical couples in the diagrams, mostly due to the occurrence of sampling errors, has been thoroughly investigated. The variability of the empirical DSD couples (β3,β4) and (τ3,τ4) is well described by truncated gamma, truncated log‐normal and Johnson SB over the other considered distributions. However, a Monte Carlo analysis has shown that the Johnson SB is the most adequate distribution in describing the drop size variability, being characterized by the lowest level of uncertainty.

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

“…This plane was introduced by (Craig, 1936) and then updated by various authors, e.g. (Balakrishnan et al, 1994) and (Cugerone and De Michele, 2017). The skewness-kurtosis (β 3 − β 4 ) plane presents the skewness (Eq.…”

“…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.…”