Comparison of different fittings of drop spectra for rainfall retrievals

It is widely acknowledged that a thorough characterization of the raindrop size distribution (DSD) may address many needs regarding the remote sensing of precipitation, which is central to new research challenges related to the estimation and management of water resources. In particular, the third and higher moments (up to the sixth) of DSD are proportional to relevant hydrological and meteorological parameters (i.e., rain rate, liquid water content, radar reflectivity, and kinetic energy). Therefore, the retrieval process of these quantities is usually based upon higher-order statistics that are mainly influenced by the upper part of the DSD (i.e., its tail behavior). In this study, we first investigate the effects on rainfall integral parameters of truncating the DSD at upper drop diameters when assuming heavy- and light-tailed distributions. Then, we compare both the tails (i.e., large drops only) and the entire empirical distributions of thousands of disdrometer-measured raindrop spectra with four common theoretical distributions characterized by different tail behaviors (i.e., heavy- and light-tailed distributions): the Pareto, lognormal, gamma, and Weibull distributions. In particular, we analyze the relative quality of each distribution (relative ranking) by means of a straightforward method. Observational data consist of 1-min spectra collected by two-dimensional video disdrometers (2DVD) during three pre-launch field campaigns of the NASA Global Precipitation Measurement (GPM) mission located in (i) Rome (HyMeX SOP 1, (ii) Central Oklahoma (MC3E,), and (iii) Eastern Iowa (IFloodS). The results obtained from the analysis of the three datasets were consistent with each other, and they show that the lighter-tailed distributions are in better agreement with the observed size spectra than the heavier-tailed distributions. However, we also found significant departures of empirical drop spectra from light-tailed distributions, especially when fitting only the tail of the distributions. These departures may imply a dramatic increase of uncertainty in the statistical estimation of high-order DSD moments, thus making the retrieval process unreliable.