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 whilst a non-stationary 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 tides 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 UK tide gauges.