Accounting for Seasonality in Extreme Sea Level Estimation

Storm surges pose an increasing risk to coastline communities. These events, combined with high tide, can result in coastal flooding. To reduce the impact of storm surges, an accurate estimate of coastal flood risk is necessary. Specifically, estimates are required for the return level of sea levels (still water), which is the level with annual exceedance probability p. This estimate is used as an input to determine the height for a coastal defence, such as a sea wall. The return level estimation requires statistical analysis based on extreme value theory, as we need to know about the frequency of events that are more extreme than those previously observed.

Large storm surges exhibit seasonality, they are typically at their worst in the winter and least extreme in the summer. This seasonal pattern differs from that of the tide, whose seasonality is driven astronomically, resulting in tidal peaks at the spring and autumn equinoxes. Hence, the worst levels of these two components of still water level are likely to peak at different times in the year, and so statistical methods that treat them as independent variables are likely to over-estimate return levels.

We focus on the skew surge: the difference between the observed and predicted high water within a tidal cycle. Williams et al. (2016) show that tide and skew surge are independent conditional on the time of year. Batstone et al. (2013) used this property to derive estimates used for UK coastal flood defences. They used generalised Pareto distributions for the skew surge tail but did not account for the separate seasonality of tide and skew surge.

This work aims to model how the distribution of skew surges changes over a year and we combine our results with the known seasonality of tides to derive estimates of still water level return levels. We compare our results with the Batstone et al. (2013) approach at a few locations on the UK coastline.

References:

Batstone, C., Lawless, M., Tawn, J., Horsburgh, K., Blackman, D., McMillan, A., Worth, D., Laeger, S. and Hunt, T., 2013. A UK best-practice approach for extreme sea-level analysis along complex topographic coastlines. Ocean Engineering, 71, pp.28-39.

Williams, J., Horsburgh, K.J., Williams, J.A. and Proctor, R.N., 2016. Tide and skew surge independence: New insights for flood risk. Geophysical Research Letters, 43(12), pp.6410-6417.