68-Copulas for Multivariate Flood Frequency Analysis.

Abstract

Flood frequency analysis is commonly accomplished by fitting univariate distributions to annual peak flows. Lognormal, gamma, log-Pearson, extreme value, logistic and Wakeby are the commonly employed flood frequency distributions. Hydrological processes, however, exhibit multivariate characteristics and simultaneous consideration two or more component processes may be required and advantageous in a variety of applications. Multivariate flood frequency analysis, involving flood peaks, volumes and durations has been done in the past on a limited basis and has been traditionally accomplished by employing readily available bivariate and multivariate frequency distributions that have marginals from the same family of distributions. Such an approach is highly restrictive in situations where underlying processes are characterized by marginals from different distribution families. This difficulty is usually overcome, in a limited way, by first normalizing or transforming the variables into similar marginals and then employing the available functional distribution forms. The concept of copula overcomes this limitation by allowing combination of arbitrarily chosen marginal types for obtaining joint and conditional multivariate distributions. It also provides a wider choice of admissible dependence structure and easier procedure for generating multivariate random samples, as compared to the conventional approach. A variety of copula families have been evolved and thus the selection of appropriate copula family for different applications is an important first step. The use of copula-based multivariate distributions in the field of hydrology has started only recently and optimal copula structures for hydrological applications are yet to be identified. This paper highlights the merits of copula concept and illustrates its application to multivariate flood frequency analysis by way of investigating relative applicability of six copulas families.