Application of Copulas to Modeling Temporal Sampling Errors in Satellite-Derived Rainfall Estimates

Abstract

The dependence between temporal sampling error in satellite-derived rainfall estimates and rainfall rate is of scientific and practical interest. We explore the use of copulas to construct the needed joint distribution between the sampling error and the corresponding rainfall rate. Our approach is to first estimate the marginal distribution functions in a parametric way, and then use these with a number of copula functions in search of the one most appropriate. We use maximum likelihood to estimate the parameters of the copulas. We select the best-fitted parametric copula function as the one that gives the largest likelihood. Our findings have important implications for the interpretation and propagation studies of remote sensing precipitation uncertainties.