An analytical formulation of return period of drought severity

Planning and management of water resources systems under drought conditions often require the estimation of return periods of drought events characterized by high severities. Among the several methods proposed for describing droughts, the run method is the most suitable to provide an objective identification and characterization of drought events. According to such a method, droughts are identified as consecutive intervals where the investigated hydrological variable is continuously below a fixed. threshold, and may be described by means of two characteristics, namely,drought duration and drought severity. Since both characteristics are necessary to estimate water deficit risks, frequency analysis of drought events cannot be based on the same approach generally used for flood analysis, such as maximum annual series or partial duration series of a single characteristic. In particular, the evaluation of return period for drought events needs to consider both duration and severity in order to take into account the pluriannual duration of several droughts. Very often a reliable analysis of the probabilistic structure of droughts based on the observed samples, using an inferential approach, cannot be properly carried out due to the limited number of drought events which can be identified even on quite long historical series. This problem has been faced by Shiau and Shen (2001), who have determined the conditional distribution of drought severity given a drought duration on the basis of generated hydrological series. In this paper their approach is extended by deriving analytically the parameters of the probability distribution of drought severity based on the stochastic process describing the underlying hydrological variable. More specifically, a gamma distribution is adopted to model drought severity and its parameter are theoretically determined as a function of the threshold level and the coefficient of variation of annual precipitation series assumed independent and lognormal distributed. Then, the return period of drought events with severity greater than or equal to a fixed value is computed as the mean interarrival time of drought events with a certain severity or greater. Such procedure has been applied on 88 annual series of data recorded in Sicilian rainfall stations, by computing for each series the return period corresponding to drought of fixed severity and by plotting the spatial distribution in order to provide a description of drought spatial variability at a regional level.