Flood Frequency Analysis Using Copula with Mixed Marginal Distributions

In flood frequency analysis, a flood event is mainly characterized by peak flow, volume and duration. These three variables or characteristics of flood are random in nature and mutually correlated. In this article, a methodology is developed to derive bivariate joint distributions of the flood characteristics using the concept of copula considering a set of parametric and nonparametric marginal distributions for peak flow, volume and duration to mathematically model the correlated nature among them. A set of parametric distribution functions, and nonparametric methods based on kernel density estimation and orthonormal series are used to determine the marginal distribution functions for peak flow, volume and duration. In 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 copula relaxes the restriction of traditional flood frequency analysis by selecting marginals from different families of probability distribution functions for flood characteristics. The present work performs a better selection of marginal distribution functions for flood characteristics by parametric and nonparametric estimation procedures, and demonstrates how the concept of copula may be used for establishing joint distribution function with mixed marginal distributions. The methodology is demonstrated with seventy years streamflow data of Red River at Grand Forks of North Dakota, US. The research work reported here is already submitted by the authors as a manuscript for review to Water Resources Research, AGU.