RAINFALL DEFICITS - DISTRIBUTION OF MONTHLY RUNS

A probabilistic model is derived to describe temporal series of monthly rainfall deficits in terms of the number of runs, run length and rainfall depth per run. A rainfall deficit is defined as a submedial value in a set of rainfalls which have equal durations. With allowance for symmetry, the joint distribution is also applicable to surfeits or supramedial values. Classic run theory supplies exact, parameter-free, probability density functions for a number of runs and run lengths. Some simple assumptions on the generation of deficit rainfalls lead to a two-parameter gamma density for rainfall depth per run. The model is tested with 130 years of data from a rainfall station, and examples are given of its use in estimating an extreme value distribution of minima and in determining properties of the longest expected deficit run length in a stated period. The theoretically based model should provide a useful description of temporal rainfall patterns of varying durations particularly for the application of statistical decision theory to problems concerning hydrological drought. © 1990.