A stochastic analysis of extreme droughts

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Abstract
A stochastic analysis is performed on the extreme drought duration defined to be the maximum dry interval for a point rainfall process. The assumptions underlying previous analyses are generalized to those of a nonhomogeneous Poisson process. Analytical results, which seem intractable in general, are derived for two particular forms of the intensity function of the Poisson process; for a general intensity function, simulation is recommended. Next, small time intervals such as the growing season of a crop are considered so that the assumption of a homogeneous Poisson rainfall process may be made and the effect of parameter estimation on the theoretical results may be studied qualitatively. To illustrate this point, four estimates of the intensity parameter are calculated by using precipitation data from Chicago and Austin. A good agreement is found between the theoretical and empirical distribution functions for the two parameter estimates calculated by use of the model developed in this investigation; on the other hand, a substantial bias is present for parameters calculated directly from the data. Finally, an approach is schematically indicated to extend the model to regional droughts by using stochastic superposition.

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