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Multivariate drought characteristics using trivariate Gaussian and Student t copulas


Correspondence to: Songbai Song, College of Water Resources and Architectural Engineering, Northwest A&F University, No.23 Weihui Road, Yangling, Shaanxi, 712100, China.



This study aims to investigate the changing properties of drought events in Weihe River basin, China, by modeling the multivariate joint distribution of drought duration, severity and peak using trivariate Gaussian and Student t copulas. Monthly precipitations of Xi'an gauge are used to illustrate the meta-elliptical copula-based methodology for a single-station application. Gaussian and Student t copulas are found to produce a better fit comparing with other six symmetrical and asymmetrical Archimedean copulas, and, checked by the goodness-of-fit tests based on a modified bootstrap version of Rosenblatt's transformation, both of them are acceptable to model the multivariate joint distribution of drought variables. Gaussian copula, the best fitting, is employed to construct the dependence structures of positively associated drought variables so as to obtain the multivariate joint and conditional probabilities of droughts. A Kendall's return period (KRP) introduced by Salvadori and De Michele (2010) is then adopted to assess the multivariate recurrent properties of drought events, and its spatial distributions indicate that prolonged droughts are likely to break out with rather short recurrence intervals in the whole region, while drought status in the southeast seems to be severer than the northwest. The study is of some merits in terms of multivariate drought modeling using a preferable copula-based method, the results of which could serve as a reference for regional drought defense and water resources management. Copyright © 2011 John Wiley & Sons, Ltd.