Estimating joint tail probabilities of river discharges through the logistic copula

Abstract

AbstractIn flood analysis, apart from extreme precipitation or sudden snow melt, also the duration or persistence of high water levels needs proper description. The purpose of this paper is to estimate tail probabilities from the joint distribution of variables such as one‐day annual maximum river discharges and its aggregate seven‐day annual maximum discharges. An application will be shown to the river Rhine in The Netherlands. The marginal distributions of the annual maxima (AM) exceeding certain thresholds are assumed to be bounded Strict Pareto and the logistic copula is used for the joint distribution. The main methodological issue discussed is the fitting of the logistic copula within a Bayesian framework. The estimation of parameters are obtained through a Markov Chain Monte Carlo simulation. In this respect, the paper provides a method for selecting the univariate and bivariate thresholds. Copyright © 2007 John Wiley & Sons, Ltd.