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Emad Habib, Witold F. Krajewski, and Grzegorz J. Ciach


This study discusses questions of estimating correlation coefficient of point rainfall as observed at two measuring stations. The focus is on issues such as sensitivity to sample size, extreme rain events, and distribution of rainfall. The authors perform extensive analysis based on a two-point data-driven rainfall model that simulates the intermittence and extreme variability of rainfall using a bivariate mixed-lognormal distribution. The study examines the commonly used product–moment estimator along with an alternative transformation-based estimator. The results show a high level of bias and variance of the traditional correlation estimator, which are caused mostly by significant skewness levels that characterize rainfall observations. Application using data from a high-density cluster indicated the advantages of using the alternative estimator. The overall aim of the study is to draw the attention of researchers working with rainfall to some commonly disregarded issues when they seek accurate and reliable correlation information.

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Grzegorz J. Ciach, Witold F. Krajewski, and Gabriele Villarini


Although it is broadly acknowledged that the radar-rainfall (RR) estimates based on the U.S. national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) stations contain a high degree of uncertainty, no methods currently exist to inform users about its quantitative characteristics. The most comprehensive characterization of this uncertainty can be achieved by delivering the products in a probabilistic rather than the traditional deterministic form. The authors are developing a methodology for probabilistic quantitative precipitation estimation (PQPE) based on weather radar data. In this study, they present the central element of this methodology: an empirically based error structure model for the RR products.

The authors apply a product-error-driven (PED) approach to obtain a realistic uncertainty model. It is based on the analyses of six years of data from the Oklahoma City, Oklahoma, WSR-88D radar (KTLX) processed with the Precipitation Processing System algorithm of the NEXRAD system. The modeled functional-statistical relationship between RR estimates and corresponding true rainfall consists of two components: a systematic distortion function and a stochastic factor quantifying remaining random errors. The two components are identified using a nonparametric functional estimation apparatus. The true rainfall is approximated with rain gauge data from the Oklahoma Mesonet and the U.S. Department of Agriculture (USDA) Agricultural Research Service Micronet networks. The RR uncertainty model presented here accounts for different time scales, synoptic regimes, and distances from the radar. In addition, this study marks the first time in which results on RR error correlation in space and time are presented.

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