On the Random Occurrence of Major Floods

Abstract

Plausible hydrologic arguments imply that floods can be represented as the successes or exceedances in a sequence of randomly spaced Bernoulli trials representing the occurrence of hydrograph peaks. This representation generalizes existing flood occurrence models by admitting an arbitrary probability distribution of the times between trials and an arbitrary criterion for distinguishing between floods and ordinary hydrograph peaks. Analysis of this model shows that at sufficiently small exceedance probabilities the probability distributions and moments of the interexceedance time, the waiting time to the next exceedance, and the number of exceedances approach those implied by the occurrence of trials in a Poisson process. This theory therefore constitutes a rational justification of Poisson models of flood occurrence as well as a rational explanation of empiric observations.