دانلود رایگان مقاله عملکرد اتصالات مدل های نظری متداول جهت توزیع اندازه قطرات باران

Abstract

Modelling raindrop size distribution (DSD) is a fundamental issue to connect remote sensing observations with reliable precipitation products for hydrological applications. To date, various standard probability distributions have been proposed to build DSD models. Relevant questions to ask indeed are how often and how good such models fit empirical data, given that the advances in both data availability and technology used to estimate DSDs have allowed many of the deficiencies of early analyses to be mitigated. Therefore, we present a comprehensive follow-up of a previous study on the comparison of statistical fitting of three common DSD models against 2D-Video Distrometer (2DVD) data, which are unique in that the size of individual drops is determined accurately. By maximum likelihood method, we fit models based on lognormal, gamma and Weibull distributions to more than 42.000 1-minute drop-by-drop data taken from the field campaigns of the NASA Ground Validation program of the Global Precipitation Measurement (GPM) mission. In order to check the adequacy between the models and the measured data, we investigate the goodness of fit of each distribution using the Kolmogorov–Smirnov test. Then, we apply a specific model selection technique to evaluate the relative quality of each model. Results show that the gamma distribution has the lowest KS rejection rate, while the Weibull distribution is the most frequently rejected. Ranking for each minute the statistical models that pass the KS test, it can be argued that the probability distributions whose tails are exponentially bounded, i.e. light-tailed distributions, seem to be adequate to model the natural variability of DSDs. However, in line with our previous study, we also found that frequency distributions of empirical DSDs could be heavy‐tailed in a number of cases, which may result in severe uncertainty in estimating statistical moments and bulk variables.

6. Conclusions

The raindrop size distribution can be expressed as the product of the concentration of the raindrops and the probability distribution of drop sizes in a volume of air. The former can be directly obtained from disdrometer data by calculating the zeroth moment of the DSD, while determining the latter is the focus of this paper. As follow-up of Adirosi et al. (2015), in this study three well known and widely adopted theoretical distributions (namely gamma, lognormal and Weibull) have been fitted to almost 42.000 1-minute drop spectra measured by two-dimensional video disdrometers. The main purpose of this work is to assess how often and how good the most commonly used models fit the empirical data, searching for the conditions under which each model performs best. In order to achieve such an objective, we follow an up-todate statistical approach based on the maximum likelihood fitting method and the Kolmogorov–Smirnov goodness-of-fit test. Furthermore, we carry out two different fitting procedures by using (i) the probability distribution of drop diameters at ground, and (ii) the more commonly used probability distribution of drop diameters per unit volume. The availability of large drop-by-drop datasets from four different regions in USA and Italy has allowed us to perform a robust statistical analysis whose findings are not sitespecific. The main conclusions drawn in this work are summarized in the following