Threshold models for river flow extremes

We model extreme river flow data from five UK rivers with distinct hydrological properties. The data exhibit significant and complex nonstationarity, which we model using a nonlinear function of hydrological covariates corresponding to soil saturation, latent flow of the river and rainfall. We additionally consider season as a covariate, although the hydrological covariates explain most of the seasonal effect directly. The standard approach to modelling data of this kind is to fix a threshold and to model exceedances of this threshold using the generalised Pareto distribution. We identify a number of problems with this approach in nonstationary cases. To overcome these issues, we propose the use of a censored generalised extreme value distribution for threshold exceedances. The data analysis illustrates a number of features of model fit and in particular the stability of the model parameters and return levels to threshold choice. Copyright © 2012 John Wiley & Sons, Ltd.