Proposal of the 'extreme rank plot' for extreme value analysis: With an emphasis on flood frequency studies

Abstract

To assess model 'fit' for flood frequency studies, the annual maximum flow sample is often plotted alongside the frequency curve in an extreme value plot. The comparison is ill advised because a value is speculatively assigned for each rank, in the form of a frequency (the plotting positions); in which case a model of the frequencies is being used to assess a frequency model. The modelled and observed, with attributed plotting positions, are incommensurable. The proposed method in this paper does not attempt to provide a frequency attributed to the ranks and instead attributes ranks to the model under investigation. If the model is used to simulate thousands of samples of the same size as the observed, a distribution of possible peak flow values for each rank can be obtained. For each simulated sample, descriptive statistics can be derived. In this way, statistical testing can be undertaken to compare the observed with the modelled. Using such methods, two or more models can also be compared. Examples are provided for Flood Estimation Handbook pooling and continuous simulation models along with a comparison of the two.