Non-stationarity in peaks-over-threshold river flows:a regional random effects model

Under the influence of local- and large-scale climatological processes, extreme river flow events often show long-term trends, seasonality, inter-year variability and other characteristics of temporal non-stationarity. Properly accounting for this non-stationarity is vital for making accurate predictions of future floods. In this paper, a regional model based on the generalised Pareto distribution is developed for peaks-over-threshold river flow data sets when the event sizes are non-stationary. If observations are non-stationary and covariates are available then extreme value (semi-)parametric regression models may be used. Unfortunately the necessary covariates are rarely observed and, if they are, it is often not clear which process, or combination of processes, to include in the model. Within the statistical literature, latent process (or random effects) models are often used in such scenarios. We develop a regional time-varying random effects model which allows identification of temporal non-stationarity in event sizes by pooling information across all sites in a spatially homogeneous region. The proposed model, which is an instance of a Bayesian hierarchical model, can be used to predict both unconditional extreme events such as the m-year maximum, as well as extreme events that condition on being in a given year. The estimated random effects may also tell us about likely candidates for the climatological processes which cause non-stationarity in the flood process. The model is applied to UK flood data from 817 stations spread across 81 hydrometric regions