Gains from Copula-Based Multivariate Distribution Functions for Rainfall Processes

Study of multivariate character of rainfall processes is an important aspect for many hydrological applications. Modeling average storm intensity, duration and inter-arrival time is useful for simulation studies and rainfall simulators. The correlation structure between rainfall intensity and duration has been found to have a significant effect on surface runoff. Bivariate exponential, bivariate normal, Box-Cox-transformed bivariate normal and bivariate Gumble distributions have typically been proposed and applied for fitting these processes. Such conventional distributions are restrictive in many ways such as having to use marginals from the same family of distributions and in having restrictions on the range of admissible dependence. Many conventional multivariate formulations involve Pearson's linear correlation coefficient, either directly or indirectly through its relationship with the association parameter. As it is not invariant to non-linear monotone transformations, this correlation measure is not appropriate for deriving inter-variate dependence characteristics. The concept of copula, which is relatively new in statistics, overcomes such limitations by allowing combination of different and arbitrary types of marginals and by offering a wider choice of dependence functions as well. Rank-based copula approach also renders the copula method a desirable invariant property. Generation of multivariate random numbers employing the copula approach is a relatively easy procedure. This will help simulate many multivariate hydrological processes which hitherto were not able to be modeled on the basis of actual marginal distributions. Copulas are becoming increasingly popular in various fields, including finance, biomedical, reliability and engineering. A number of applications have been made in hydrologic engineering in which multivariate interdependence of variables is very important. A few copula formulations have been recently proposed for bivariate and trivariate rainfall frequency analysis, involving storm intensity and/or depth and duration. This paper presents a comparison of results from conventional and copula-based bivariate frequency distribution analyses for storm intensity and duration. The gains from copula-based approach are highlighted and comparison of results with those from a conventional method is presented.