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

Abstract

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%.

Fig. 1. Max. non-linear effects on extreme sea levels.

The figure indicates how non-linear changes extreme sea levels (defined here as the 99th percentile threshold exceedances) for (a) the entire World, (b) Europe, (c) Japan, and (d) the USA. Water level decreases from non-linear effects are shown in red (i.e., water levels are lower than from a linear superposition of tide and non-tidal residual alone) and increases in blue. Tidal range has been derived from OTIS tidal constituents.

Fig. 2. Characteristics of tide and the dependence τ.

The subpanels highlight dependencies between (a) tide at extreme sea level and non-linear effects, (b) dependence τ and non-linear effects, and (c) dependence τ and tide at extreme sea level. Non-linear effects <0 causes extreme sea level decreases and non-linear effects >0 increases. Sites dominated by the tide are defined as having a tidal contribution >50%; at sites dominated by non-tidal residual, the non-tidal contribution is >50%.

Fig. 3. Global map of temporal changes in the dependence τ.

Shown are site specific changes in dependence measure τ through time (at least 60 years) with increasing (blue) and decreasing (red) dependencies. Significant trends are shown as bold circles. If the changes are correlated significantly with the observed sea level rise as provided by the permanent service for mean sea level (PSMSL) database, sites are highlighted as triangles.

Fig. 4. Global map of sea level rise vs. non-linear effects.

For all sites, the years when sea level rise (assuming a warming of +1.5 °C by 2100 in global temperatures at the median probability) exceeds non-linear effects (based on the 99th percentile) are shown. The marker size indicates the range (max.-min.) of possible outcomes if other than the median probability sea level rise (i.e., the 5 to 95% probability) projections are used.

Fig. 5. Global map of interpolated non-linear effects (TSIe) influences on extreme sea levels.

The figure indicates how changes in non-linear effects (TSIe) extreme sea levels at interpolated (small dots) and observational (bold dots) stations which have been derived using the regression model of Eq. (1). Sites with negative (i.e., reduced extreme sea levels shown red) and positive (i.e., increased extreme sea levels shown blue) non-linear effects are separated according to the colour gradient.