Trivariate copulas for characterisation of droughts

Abstract

Australian agriculture is at serious risk from drought, and wa- ter resource infrastructure and management can mitigate the effects. The consequences of droughts depend on their intensity, duration and severity. These variables are correlated and the dependence structure is here described by copulas. Copulas are multivariate uniform dis- tributions which allow for the dependence structure to be modelled independently of the marginal distributions. Trivariate Gaussian and Gumbel copulas are fitted to the data from a rainfall district in NSW. We assess the goodness of fit of the data to the different forms using several criteria. The data are best described by a Gumbel copula and three parameter Weibull marginal distributions.