Probabilistic characterization of drought properties through copulas

This paper shows an application of copulas to the probabilistic analysis of drought characteristics. Drought occurrences are analyzed by the Standardized Precipitation Index (SPI) computed on the mean areal precipitation, aggregated at 6 months, observed in Sicily between 1921 and 2003. Assuming a drought period as a consecutive number of intervals where SPI values are less than 1, several characteristics are determined, namely: drought length, mean and minimum SPI values, and drought mean areal extent. Results of a preliminary analysis based on Kendall’s correlation and upper tail dependence coefficient, computed on observed and resampled data, show significant dependence properties between almost all the considered pairs. The four-dimensional joint distribution required to correctly model the stochastic structure of variables is determined by resorting to copula approach. This allows flexibility in choosing suitable marginals and dependence structure, and in simplifying the inference procedure as well. Drought return periods are then computed as mean interarrival time, taking into account two drought characteristics at a time by means of the corresponding bivariate marginals of the fitted four-dimensional distribution. Application of the proposed methodology to Sicilian precipitation series shows a good correspondence between empirical and theoretical joint return periods, thus indicating that copulas are adequate to jointly model drought characteristics and to compute exceedance probabilities of drought events.