Raindrop size distribution: Fitting performance of common theoretical models |
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| Institution: | 1. Institute of Atmospheric Sciences and Climate (ISAC), National Research Council of Italy (CNR), Rome, Italy;2. Dipartimento di Ingegneria, Università degli Studi Roma Tre, Rome, Italy;1. Department of Physics and Earth Sciences, University of Ferrara, Ferrara, Italy;2. Institute for the Sciences of Atmosphere and Climate, CNR, Bologna, Italy;3. Nubila s.a.s., Bologna, Italy;1. Department of Physics, Yogi Vemana University, Kadapa, Andhra Pradesh, India;2. Taiwan International Graduate Program (TIGP), Earth System Science Program, Research Center for Environmental Changes (RCEC), Academia Sinica, Taipei, Taiwan;3. Institute of Atmospheric Science, College of Earth Science, National Central University, Zhongli City, Taiwan;4. Department of Coupled Ocean-Atmosphere-Land Processes Research, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan;5. Institute of Atmospheric Science, National Central University, Zhongli City, Taiwan;6. Institute of Space Science, National Central University, Zhongli City, Taiwan;1. Colorado State University, Fort Collins, CO, USA;2. CIRES, University of Colorado, Boulder, USA |
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| 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. |
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