Overdispersion in peak over threshold (POT) flow data and its effect on flood frequency practice

Presentation at the 2014 British Hydrological Meeting The frequency of extreme flood events is generally assessed either via the analysis of block maxima (typically annual maxima) or via the analysis of the data points which exceed a fixed threshold (POT analysis). The analysis of annual maxima, combined with the assumption of a GLO distribution, is the most frequently used method in the UK. Flood frequency estimates can nevertheless vary considerably according to which probability distribution is assumed for the data at hand. This study discusses tools to better understand the properties of flow data and improve the choice of the probability distribution. Under some general conditions, it can be shown that the analysis of block maxima and POT data are asymptotically related. In particular, if the threshold exceedance process can be assumed to be a Poisson process and the exceedance magnitude assumed to follow a GPD distribution, the annual maxima distribution is shown to follow asymptotically a GEV distribution. Under the assumption of a Poisson process, the number of threshold exceedances should have equal mean and variance. Nevertheless, overdispersion (a larger variance than expected) is often observed for a large proportion of the POT counts. Annual maxima for which threshold exceedances follow some overdispersed Poisson process can be shown to be asymptotically distributed as a GLO distribution. This study investigates the observed overdispersion in the POT counts and the implications of such overdispersion on the distribution of annual maxima. The relationship between catchment descriptors and overdispersion is also investigated.