A comparison between the Gumbel–Hougaard and distorted Frank copulas for drought frequency analysis
Drought is a global phenomenon and is a common characteristic of extreme climate. It is widely considered as the world's costliest natural disaster since their effects are especially devastating to the agricultural and social economy. Effective water resource infrastructure and management is required for the mitigation of drought, and this requires drought risk assessment. Essential characteristics of drought are severity, average intensity and duration, which are highly correlated. Copulas are multivariate uniform distribution functions with uniform marginals, which provide a flexible approach to model their relationship. For an extreme drought event to be modelled, the upper–tail dependence must be investigated. The construction of an alternative copula form is introduced through a transformation called a distortion, to allow for more versatile modelling of tail dependence. Data from a rainfall district in New South Wales is considered and the Gumbel–Hougaard copula and distorted Frank copulas are fitted to the drought characteristics. Goodness–of–fit and upper tail correlations of these copulas are analysed and discussed. Finally, conditional annual drought recurrence intervals are calculated and compared for these fitted copulas.
Keywords: drought frequency analysis, distortions, modelling, tail dependence, rainfall, Australia, Gumbel–Hougaard copula, distorted Frank copulas, drought recurrence intervals, annual drought recurrence, water resource management, drought risk assessment