Copula based drought frequency analysis considering the spatio-temporal variability in Southwest China

Summary Drought frequency analysis is a prerequisite for drought resistance planning and drought risk management. Drought is a spatio-temporal dynamic process, usually characterized by its duration, spatial extent, and severity. Copula based multivariate frequency analysis has been widely used to calculate drought frequency. However, the spatial extent is scarcely considered in previous studies, due to the fact that drought event is usually identified either for a fixed spatial scale or for a fixed temporal scale. This study develops a regional drought frequency analysis model based on trivariate copulas by considering the spatio-temporal variations of drought events. Drought duration, drought affect area, and drought severity are identified first, and their trivariate joint distribution is constructed later. The model is applied for drought frequency analysis in Southwest China during 1961–2012. A variety of probability distribution functions and copula functions (including elliptical, symmetric and asymmetric Archimedean) are used as candidate choices, and the most appropriate ones are selected based on goodness of fit using different methods. The robustness of drought frequency analysis is then evaluated and discussed. The results show that drought frequency analysis needs to fully consider the three characteristic parameters (duration, affect area, and severity) reflecting drought spatio-temporal variability. And the drought return period estimated by the copula-based trivariate frequency analysis appropriately integrates the effects of drought duration, affect area and severity, which is a reliable drought statistical measurement. The 2009–2010 drought, which has a return period of about 94 years, is the most severe one in Southwest China during the period of 1961–2012. The Joe and Gumbel copulas are found to be more suitable to estimate the joint distribution of drought duration, affect area and severity, and the Asymmetric (nested) function forms perform better than the symmetric functions.

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