Accounting for seasonality in extreme sea-level estimation

D’Arcy, Eleanor and Tawn, Jonathan A. and Joly, Amélie and Sifnioti, Dafni E. (2023) Accounting for seasonality in extreme sea-level estimation. Annals of Applied Statistics, 17 (4). pp. 3500-3525. ISSN 1932-6157

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Abstract

Reliable estimates of sea-level return-levels are crucial for coastal flooding risk assessments and for coastal flood defence design. We describe a novel method for estimating extreme sea-levels that is the first to capture seasonality, interannual variations and longer term changes. We use a joint probabilities method, with skew-surge and peak-tide as two sea-level components. The tidal regime is predictable, but skew-surges are stochastic. We present a statistical model for skew-surges, where the main body of the distribution is modelled empirically while a nonstationary generalised Pareto distribution (GPD) is used for the upper tail. We capture within-year seasonality by introducing a daily covariate to the GPD model and allowing the distribution of peak-tide to change over months and years. Skew-surge-peak-tide dependence is accounted for, via a tidal covariate, in the GPD model, and we adjust for skew-surge temporal dependence through the subasymptotic extremal index. We incorporate spatial prior information in our GPD model to reduce the uncertainty associated with the highest return-level estimates. Our results are an improvement on current return-level estimates, with previous methods typically underestimating. We illustrate our method at four U.K. tide gauges.