Investigating changes in rainfall characteristics using the copula approach
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Multivariate characterization of rainfall processes has been an important aspect of many hydro-meteorological applications in the past. Frequency analysis of average storm intensity, duration, volume and inter-arrival time is useful for simulation studies, rainfall simulators and for deriving flood frequency distributions, among others. The correlation structure among these features has a significant effect on surface runoff and may also reflect regional climatic characteristics. A perceptible shift in these inter-relationships, in a longer time frame, may indicate correspondence to possible climatic changes in the region. Bivariate frequency modeling of these rainfall processes has been proposed and done in the past by employing bivariate exponential, bivariate normal, Box-Cox-transformed bivariate normal and bivariate Gumble distributions. Such conventional distributions are restrictive in having to use marginals from the same family of distributions and sometimes in having restrictions on the range of admissible dependence. Some of these conventional multivariate formulations involve Pearson's linear correlation coefficient that is not invariant to the non-linear monotone transformations and thus are not appropriate for deriving inter-variate dependence characteristics. The concept of copula, which is relatively new, overcomes such limitations by allowing the combination of different and arbitrary types of marginals as well as by offering a wider choice of dependence functions. Copulas are becoming increasingly popular in various fields, including finance, biomedical, and reliability engineering. A number of copula applications have been made in hydrologic engineering in which multivariate interdependence of variables is important. A few copula formulations have been recently proposed for bivariate and trivariate rainfall frequency analysis, involving storm rainfall intensity, duration, and/or depth. This paper presents an application of the copula-based approach for determining long-term changes in rainfall characteristics in terms of multivariate features. 2009 Taylor & Francis Group.
