Automated tail-informed threshold selection for extreme coastal sea levels

Abstract. Peaks over threshold (POT) techniques are commonly used in practice to model tail behaviour of univariate variables. The resulting models can be used to aid in risk assessments, providing estimates of relevant quantities such as return levels and periods. An important consideration during such modelling procedures involves the choice of threshold; this selection represents a bias-variance trade-off and is fundamental for ensuring reliable model fits. Despite the crucial nature of this problem, most applications of the POT framework select the threshold in an arbitrary manner and do not consider the sensitivity of the model to this choice. Recent works have called for a more robust approach for selecting thresholds, and a small number of automated methods have been proposed. However, these methods come with limitations, and currently, there does not appear to be a 'one size fits all' technique for threshold selection. In this work, we introduce a novel threshold selection approach that addresses some of the limitations of existing techniques. In particular, our approach ensures that the fitted model captures the tail behaviour at the most extreme observations, at the cost of some additional uncertainty. We apply our method to a global data set of coastal observations, where we illustrate the robustness of our approach and compare it to an existing threshold selection technique and an arbitrary threshold choice. Our novel approach is shown to select thresholds that are greater than the existing technique. We assess the resulting model fits using a right-sided Anderson-Darling test, and find that our method outperforms the existing and arbitrary methods on average. We present and discuss, in the context of uncertainty, the results from two tide gauge records; Apalachicola, US, and Fishguard, UK. In conclusion, the novel method proposed in this study improves the estimation of the tail behaviour of observed coastal water levels, and we encourage researchers from other disciplines to experiment using this method with their own data sets.