Nonstationarity in peaks‐over‐threshold river flows: A regional random effects model

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Abstract
Under the influence of local‐ and large‐scale climatological processes, extreme river flow events often show long‐term trends, seasonality, interyear variability, and other characteristics of temporal nonstationarity. Properly accounting for this nonstationarity 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 nonstationary. If observations are nonstationary 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 that allows identification of temporal nonstationarity 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 them‐year maximum and 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 that cause nonstationarity in the flood process. The model is applied to UK flood data from 817 stations spread across 81 hydrometric regions.

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