Tide-surge interaction and its role in the distribution of surge residuals in the North Sea

Storm surges are the sea level response to meteorological conditions. Scientists and engineers need to understand the interaction of surges with the tide in order to provide better estimates of extreme sea level for use in coastal defense. Using data from five tide gauges, spaced equally along the North Sea coastline around the UK, we show that the mode of peak residual occurrence is everywhere 3 to 5 hours before the nearest high water. We reveal a previously unobserved mode that falls 1 to 2 hours prior to high water, although this cluster is not associated with the highest residuals. A simple mathematical explanation for surge clustering on the rising tide is presented. The phase shift of the tidal signal is combined with the modulation of surge production due to water depth in a model that provides a good description of the residual data set. The results contain several features of interest for flood risk management. We show that large, locally generated surges are precluded close to high water. For physically realistic arrival times of any travelling surge component, the residual peak will avoid high water for any finite tidal phase shift. Furthermore, increasing the tidal range reduces the risk of residual peaks near high water. We draw attention to the existence of critical time and space scales for surge development and decay. For reliable operational forecasts of sea level, coastal numerical models need to reproduce both tides and surges with improved accuracy.