Generalized least squares and empirical bayes estimation in regional partial duration series index‐flood modeling

Abstract

A regional estimation procedure that combines the index‐flood concept with an empirical Bayes method for inferring regional information is introduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior information of the model parameters is inferred from regional data using generalized least squares (GLS) regression. Two different Bayesian T‐year event estimators are introduced: a linear estimator that requires only some moments of the prior distributions to be specified and a parametric estimator that is based on specified families of prior distributions. The regional method is applied to flood records from 48 New Zealand catchments. In the case of a strongly heterogeneous intersite correlation structure, the GLS procedure provides a more efficient estimate of the regional GP shape parameter as compared to the usually applied weighted regional average. If intersite dependence is ignored, the uncertainty of the regional estimator may be seriously underestimated and erroneous conclusions with respect to regional homogeneity may be drawn. The GLS procedure is shown to provide a general framework for a reliable evaluation of parameter uncertainty as well as for an objective appraisal of regional homogeneity. A comparison of the two different Bayesian T‐year event estimators reveals that generally the simple linear estimator is adequate.