On the Application of Copula Theory for Determination of Probabilistic Characteristics of Springflood

L. S. Kuchment and V. N. Demidov

Considered is the possibility of using copula theory for creating joint probability distributions of spring flood peak discharges and flow volumes taking account of the relations between discharges and flow volumes. For approximation of marginal distributions, Gumbel distribution was used for peak discharges, and two-parameter gamma distribution, for flow volumes. Joint two-dimensional distribution was built as a marginal distribution function which was set as one of the three one-parameter Archimedean copulas using different ways of determining their parameters. The best results were obtained for Gumbel–Hougaard copula using the method of maximum likelihood to determine its parameters. Major flood risk estimates determined from one- and two-dimensional probability distributions of their characteristics were compared with each other. Demonstrated are the benefits of using two-dimensional probability distributions of flood characteristics as compared with one-dimensional distributions for probabilistic estimation of floods. The data on spring flood peak discharges and flow volumes in the Belaya and Vyatka rivers were used for this study.