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).

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Abstract. Particle number size distributions (PNSDs) have been collected periodically in the urban area of Milan, Italy, during 2011 and 2012 in winter and summer months. Moreover, comparable PNSD measurements were carried out in the rural mountain site of Oga-San Colombano (2250 m a.s.l.), Italy, during February 2005 and August 2011. The aerosol data have been measured through the use of optical particle counters in the size range 0.3-25 µm, with a time resolution of 1 min. The comparison of the PNSDs collected in the two sites has been done in terms of total number concentration, showing higher numbers in Milan (often exceeding 10 3 cm −3 in winter season) compared to Oga-San Colombano (not greater than 2×10 2 cm −3 ), as expected. The skewness-kurtosis plane has been used in order to provide a synoptic view, and select the best distribution family describing the empirical PNSD pattern. The four-parameter Johnson system-bounded distribution (called Johnson SB or JSB) has been tested for this aim, due to its great flexibility and ability to assume different shapes. The PNSD pattern has been found to be generally invariant under site and season changes. Nevertheless, several PNSDs belonging to the Milan winter season (generally more than 30 %) clearly deviate from the standard empirical pattern. The seasonal increase in the concentration of primary aerosols due to combustion processes in winter and the influence of weather variables throughout the year, such as precipitation and wind speed, could be considered plausible explanations of PNSD dynamics.

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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.