Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions

Karmakar and Simonovic (2008) describe the methodology of assigning appropriate marginal distributions for three flood characteristics. It is found that the gamma distribution is best fitted for peak flow (P), and a nonparametric distribution from the orthonormal series method best fits to volume (V) and duration (D), based on the root mean square error, Akaike information criterion and Bayesian information criteria. In addition, the chi-square test is performed to check the significance of fitness. In this paper, a methodology is developed to derive bivariate joint distributions of the flood characteristics using the concept of copulas, considering a set of parametric and nonparametric marginal distributions for P, V and D to mathematically model the correlated structure among them. In the conventional method of flood frequency analysis, the marginal distribution functions of peak flow, volume and duration are assumed to follow some specific parametric distribution function. The concept of copulas relaxes the restriction of traditional flood frequency analysis by selecting marginals from different families of probability distribution functions for flood characteristics. The present study performs a better selection of marginal distribution functions for flood characteristics by parametric and nonparametric estimation procedures, and demonstrates how the concept of copulas may be used for establishing a joint distribution function with mixed marginal distributions. The results obtained are useful for hydrologic design and planning purposes. The methodology is demonstrated with 70 years of stream flow data of Red River at Grand Forks of North Dakota, USA.