On the method of probability weighted moments in regional frequency analysis

Abstract

In regional flood frequency analysis it is of interest to estimate high quantiles of a local river flow distribution by gathering information from similar stations in the neighborhood. E. g., the popular Index Flood (IF) approach is based on an assumption termed regional homogeneity, which states that the quantile curves of those stations only differ by a site-specific factor, the so-called index flood, and it is assumed that the station's distribution is known up to some finite-dimensional parameter. In this context the method of probability weighted moments (or equivalently L-moments) is most popular for parameter estimation. While the observations often can be regarded as independent in time, a challenge arises from the fact that river flows from nearby stations are strongly dependent in space. To the best of our knowledge, none of the approaches from the literature based on the IF-model and on L-moments is able to take spatial dependence adequately into account. Our goal is to fill this gap. We present asymptotic theory that does not ignore inter-site dependence, which, for instance, allows to evaluate estimation uncertainty. As an application of this theory, a test procedure to check for regional homogeneity under index-flood assumptions is given and reviewed in a simulation study.