Drought Analysis Using Trivariate Copulas Conditional on Climatic States

Droughts are an inevitable consequence of meteorological variability, and the design of water resource infrastructure and management strategies to mitigate their effects requires assessment of the risk. Crucial characteristics of droughts are related to their peak intensities, durations, and severities. These variables are typically correlated and copulas provide a versatile means to model their dependence structure. In Australia, for example, drought severity is associated with the El-Nin approximate to o Southern Oscillation. Data from two rainfall districts in New South Wales, one on the east and the other on the west of the Great Dividing Range, are considered. These rainfall data are categorized into three states, El-Nin approximate to o, Neutral, and La-Nin approximate to a, according to the prevailing Southern Oscillation Index. Gumbel-Hougaard copulas and t-copulas are fitted to the droughts in the three states. The copula parameters are estimated separately for each state, and the differences are analyzed. The goodness-of-fit of the Gumbel-Hougaard and t-copulas are compared, and the limitations of the two copula models are discussed. The times between drought events are also analyzed according to the El-Nin approximate to o Southern Oscillation state they occur in. The fitted copulas are used to estimate annual recurrence intervals of at least one of the three variables, and of all three variables, exceeding critical values taking into account of the mixture of states.