Assessment of Tidal Range Changes in the North Sea From 1958 to 2014.

We document an exceptional large-spatial scale case of changes in tidal range in the North Sea, featuring pronounced trends between -2.3 mm/yr at tide gauges in the United Kingdom and up to 7 mm/yr in the German Bight between 1958 and 2014. These changes are spatially heterogeneous and driven by a superposition of local and large-scale processes within the basin. We use principal component analysis to separate large-scale signals appearing coherently over multiple stations from rather localized changes. We identify two leading principal components (PCs) that explain about 69% of tidal range changes in the entire North Sea including the divergent trend pattern along United Kingdom and German coastlines that reflects movement of the region's semidiurnal amphidromic areas. By applying numerical and statistical analyses, we can assign a baroclinic (PC1) and a barotropic large-scale signal (PC2), explaining a large part of the overall variance. A comparison between PC2 and tide gauge records along the European Atlantic coast, Iceland, and Canada shows significant correlations on time scales of less than 2 years, which points to an external and basin-wide forcing mechanism. By contrast, PC1 dominates in the southern North Sea and originates, at least in part, from stratification changes in nearby shallow waters. In particular, from an analysis of observed density profiles, we suggest that an increased strength and duration of the summer pycnocline has stabilized the water column against turbulent dissipation and allowed for higher tidal elevations at the coast.

Non-linear interaction modulates global extreme sea levels, coastal flood exposure, and impacts.

We introduce a novel approach to statistically assess the non-linear interaction of tide and non-tidal residual in order to quantify its contribution to extreme sea levels and hence its role in modulating coastal protection levels, globally. We demonstrate that extreme sea levels are up to 30% (or 70 cm) higher if non-linear interactions are not accounted for (e.g., by independently adding astronomical and non-astronomical components, as is often done in impact case studies). These overestimates are similar to recent sea-level rise projections to 2100 at some locations. Furthermore, we further find evidence for changes in this non-linear interaction over time, which has the potential for counteracting the increasing flood risk associated with sea-level rise and tidal and/or meteorological changes alone. Finally, we show how accounting for non-linearity in coastal impact assessment modulates coastal exposure, reducing recent estimates of global coastal flood costs by ~16%, and population affected by ~8%.

Sea-level rise induced amplification of coastal protection design heights.

Coastal protection design heights typically consider the superimposed effects of tides, surges, waves, and relative sea-level rise (SLR), neglecting non-linear feedbacks between these forcing factors. Here, we use hydrodynamic modelling and multivariate statistics to show that shallow coastal areas are extremely sensitive to changing non-linear interactions between individual components caused by SLR. As sea-level increases, the depth-limitation of waves relaxes, resulting in waves with larger periods, greater amplitudes, and higher run-up; moreover, depth and frictional changes affect tide, surge, and wave characteristics, altering the relative importance of other risk factors. Consequently, sea-level driven changes in wave characteristics, and to a lesser extent, tides, amplify the resulting design heights by an average of 48-56%, relative to design changes caused by SLR alone. Since many of the world's most vulnerable coastlines are impacted by depth-limited waves, our results suggest that the overall influence of SLR may be greatly underestimated in many regions.