Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data

Multivariate flood frequency analysis, involving flood peak flow, volume and duration, has been traditionally accomplished by employing available functional bivariate and multivariate frequency distributions that have a restriction on the marginals to be from the same family of distributions. The copula concept overcomes this restriction by allowing a combination of arbitrarily chosen marginal types. It also provides a wider choice of admissible dependence structure as compared to the conventional approach. The availability of a vast variety of copula types makes the selection of an appropriate copula family for different hydrological applications a non-trivial task. Graphical and analytic goodness-of-fit tests for testing the suitability of copulas are beginning to evolve and are being developed; there is limited experience of their usage at present, especially in the hydrological field. This paper provides a step-wise procedure for copula selection and illustrates its application to bivariate flood frequency analysis, involving flood peak flow and volume data. Several graphical procedures, tail dependence characteristics, and formal goodness-of-fit tests involving a parametric bootstrap-based technique are considered while investigating the relative applicability of six copula families. The Clayton copula has been identified as a valid model for the particular flood peak flow and volume data set considered in the study.