On the Uncertainty and Changeability of the Estimates of Seasonal Maximum Flows

Abstract

A classical approach to flood frequency modeling is based on the choice of the probability distribution to best describe the analyzed series of annual or seasonal maximum flows. In the paper, we discuss the two main problems, the uncertainty and instability of the upper quantile estimates, which serve as the design values. Ways to mitigate the above-mentioned problems are proposed and illustrated by seasonal maximum flows at the Proszówki gauging station on the Raba River. The inverse Gaussian and generalized exponential distributions, which are not commonly used for flood frequency modeling, were found to be suitable for Polish data of seasonal peak flows. At the same time, the heavy tailed distributions, which are currently recommended for extreme hydrological phenomena modeling, were found to be inappropriate. Applying the classical approach of selecting the best fitted model to the peak flows data, significant shifts in the upper quantile estimates were often observed when a new observation was added to the data series. The method of aggregation, proposed by the authors, mitigates this problem. Elimination of distributions that are poorly fitted to the data series increases the stability of the upper quantile estimates over time.