Using Copulas in Hydrology: Benefits, Cautions, and Issues

This paper discusses the bivariate modeling of extreme tails of correlated hydrological random variables. We take a copula approach and model the dependence structure independently of the marginal distributions. We apply results from the classical extreme value theory to choose marginal distributions for excesses of high thresholds and consider six copula families to capture the dependence structure of these excesses. While copulas can differ somewhat in the degree of association that they provide, differences in which part of the distribution this association is more pronounced can be substantial. We discuss certain pertinent properties of copulas and give some insight to assist the practitioner in their selection. We examine the effects of model misspecification and the impact of the chosen method of estimation, targeting the estimated quantities frequently used by hydrologists. A simulation study shows not only the dangers of improper copula selection, but also the possible benefits of using a bivariate approach to estimate univariate quantities. We apply the methodology to the study of low-flow events and analyze two Canadian hydrometric data sets.