Comparison of different approaches to fit log-normal mixtures on radar-derived precipitation data

Abstract

Mixture models of precipitation frequency distributions describe the precipitation spectrum more adequately than simple probability distributions. The estimation of mixture distribution parameters by the maximum likelihood approach is commonly known. The reliability of these models and their parameters derived by the maximum likelihood method and by temporal classifications over Saxony was investigated using a radar-based precipitation product on a daily basis. Therefore, two different 'unsupervised' classification approaches were applied, a cluster analysis and a neural network, to derive subpopulation estimates. The temporal classification summarized high-resolution spatial grids of daily precipitation fields into 10 precipitation classes. The mixture model evaluation consists of two parts. First, an information criterion was calculated to describe the model complexity and the significance of the number of parameters. Second, the qualities of the fitted models were compared with the database through ordinary Kolmogorov-Smirnov tests and Kolmogorov-Smirnov tests in the context of field significance. Under the assumption of log-normal distributed precipitation, the neural network delivered the best mixture models for a spatial resolution of 2 and 3 km while the cluster analysis delivered the better initial parameters for an expectation-maximization algorithm on mixture distributions over the considered domain. © 2014 Royal Meteorological Society.