Application of copulas for derivation of drought severity–duration–frequency curves

TLDR

The study develops a copula‑based probabilistic method to model drought severity–duration–frequency relationships in western Rajasthan, India. The authors analyze drought using a 6‑month standardized precipitation index, fit severity with a log‑normal distribution and duration with an exponential distribution, evaluate four copula families, and use the best (Gumbel–Hougaard) copula to compute conditional return periods and derive S‑D‑F curves. Severity follows a log‑normal distribution, duration an exponential distribution, and the Gumbel–Hougaard copula best captures their dependence, enabling accurate S‑D‑F curves that aid drought mitigation planning. © 2011 John Wiley & Sons, Ltd.

Abstract

Abstract This study presents copula‐based multivariate probabilistic approach to model severity–duration–frequency (S‐D‐F) relationship of drought events in western Rajasthan, India. Drought occurrences are analysed using standardized precipitation index computed on monthly mean areal precipitation, aggregated at a time scale of 6 months. After testing with a series of probability density functions, the drought variable severity is found to be better represented with log‐normal distribution, whereas duration is well fitted with exponential distribution. Four different classes of bivariate copulas – Archimedean, extreme value, Plackett, and elliptical families are evaluated for modelling joint distribution of drought characteristics. It is observed that the extreme value copula – Gumbel–Hougaard copula – performed better as compared with other classes of copulas, based on results of various statistical tests and upper tail dependence coefficient. The joint distribution obtained from best performing copula is then employed to determine conditional return period and to derive drought severity‐duration‐frequency (S‐D‐F) curves for the study region. The results of the study suggests that the copula method can be used effectively to derive the drought S‐D‐F curves, which can be helpful in planning and adopting suitable drought mitigation strategies in drought‐prone areas. Copyright © 2011 John Wiley & Sons, Ltd.