Design discharge as a random variable: A risk study

Abstract

We consider two partial duration series models for flood analysis. In one, flood exceedances are treated as mutually independent and identically distributed, while in the other they are taken as identically distributed only on a seasonal basis (but mutually independent both within and between seasons). The maximum likelihood estimates of the parameters appearing in each of the two models are obtained, and the probability density functions of these estimates are determined. The distribution functions of (1) the design exceedance XT,n, corresponding to a given return period T and to n years of record, and (2) the return period T, corresponding to a given discharge X and n years of record, are then deduced. Finally, the risk encountered in the construction of a hydraulic project based on a certain design discharge is studied. Our results are applied to the partial duration series of the St. Paul station, in Minnesota on the Mississippi River. Some of these results are compared with those obtained by a previous study in which a Bayesian approach was followed.