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Multivariate modeling of droughts using copulas and meta-heuristic methods

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Abstract

This study investigated the utility of two meta-heuristic algorithms to estimate parameters of copula models and for derivation of drought severity–duration–frequency (S–D–F) curves. Drought is a natural event, which has huge impact on both the society and the natural environment. Drought events are mainly characterized by their severity, duration and intensity. The study adopts standardized precipitation index for drought characterization, and copula method for multivariate risk analysis of droughts. For accurate estimation of copula model parameters, two meta-heuristic methods namely genetic algorithm and particle swarm optimization are applied. The proposed methodology is applied to a case study in Trans Pecos, an arid region in Texas, USA. First, drought severity and duration are separately modeled by various probability distribution functions and then the best fitted models are selected for copula modeling. For modeling the joint dependence of drought variables, different classes of copulas, namely, extreme value copulas, Plackett and Student’s t copulas are employed and their performance is evaluated using standard performance measures. It is found that for the study region, the Gumbel–Hougaard copula is the best fitted copula model as compared to the others and is used for the development of drought S–D–F curves. Results of the study suggest that the meta-heuristic methods have greater utility in copula-based multivariate risk assessment of droughts.

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Acknowledgments

This research was supported by the Department of Science and Technology (DST), Govt. of India to the first author to carry research work at Texas A&M University through the Better Opportunities for Young Scientists in Chosen Areas of Science and Technology (BOYSCAST) fellowship. The first author thanks the DST for providing financial support for the BOYSCAST research programme.

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    M. Janga Reddy

  2. Department of Biological and Agricultural Engineering & Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, 77843, USA

    Vijay P. Singh

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  1. M. Janga Reddy
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Correspondence to M. Janga Reddy.

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Reddy, M.J., Singh, V.P. Multivariate modeling of droughts using copulas and meta-heuristic methods. Stoch Environ Res Risk Assess 28, 475–489 (2014). https://doi.org/10.1007/s00477-013-0766-2

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