Evaluation of Extreme Sea-Levels and Flood Return Period using Tidal Day Maxima at Coastal Locations in the United Kingdom

Abstract. Tidal storm surges can result in significant damage and inundation if sea defences are insufficiently robust. Coastal planners need to know the risk of flooding so that sea defences and coastal developments can be specified and sited appropriately. Since Gumbel's original work on extreme value statistics, several modifications and new methods have been proposed for evaluating the risk of tidal inundation, with the Skew Surge Joint Probability Method (SSJPM) recently gaining popularity. However, SSJPM is complex, often requiring manual intervention, and is difficult to automate. Guided by the search for a method specifically applicable to tides that is amenable to automation, this paper proposes several modifications to Gumbel's original approach. The novel technique is termed TMAX since its initial time unit is one tidal day, rather than the usual annual maxima (AMAX). Compared to AMAX, the TMAX method offers more efficient use of extreme data events, provides reduced variance in design height, and more efficiently handles missing data. The results of TMAX are compared with those of a recent study using the SSJPM method at 35 United Kingdom identical coastal locations, showing broad agreement. This new approach provides a robust mechanism for extreme tide analysis and better informs strategies for coastal management and resilience.