Multivariate Modeling of Annual Instantaneous Maximum Flows Using Copulas

Abstract

Although copula functions have been successively applied to flood frequency analysis, their application has usually been restricted to modeling bivariate dependence. This is because higher-dimensional expressions are only available for a few copula families, which may not have enough flexibility in modeling complex dependence structures. However, vine copulas, which have been recently introduced as an innovative method, can overcome such limitations. In this study, vine copulas are used for multivariate modeling of annual instantaneous maximum flows of three main tributaries located in the Euphrates River Basin, which is one of the most important sources of water for Turkey. The performance of vine copulas was compared with commonly used Archimedean (Clayton, Frank, and Gumbel-Hougaard) and elliptical (Gaussian and Student’s t) copulas. Statistical tests and tail-dependence assessments found the vine copulas to be most suitable for describing the dependence structure between variables. The developed vine copulas were used to obtain joint and conditional return periods of maximum flows, which can be useful for hydrologic design and management of water resources structures in the basin.