We first consider the GEV parameters for extreme water levels (Fig. 3), then the frequency increases (Fig. 4), followed by the SLR threshold that doubles exceedance of the 50-yr water level (Fig. 5).

The spatial variability in the GEV location parameter (μ) is shown in Fig. 3A. Globally, 99% of the values of μ fall between 0.50 and 2.13 m. The location parameter strongly resembles the M 2 tidal amplitude45 yet is also influenced by global wave climate. The parameter is largest in the North Pacific and North Atlantic due to large tides and the occurrence of extratropical storms that track mainly west to east, producing large, latitudinally-isolated waves. The scale parameter (σ) ranges from 0.024 to 0.118 m (Fig. 3B) and is correlated to the location parameter with r = 0.47. In other words, the regions that experience the largest water levels also experience the largest variance in those levels. The spatial variability of the shape parameter (k) is uncorrelated with that of the other GEV parameters.

The shape parameter ranges from −0.18 to 0.20 (Fig. 3C) with a global mean of −0.024. Notably, the geographic regions in Fig. 3C with large (positive) values of the shape parameter are regions with high densities of tropical storm tracks, i.e., the Tropics and lower mid-latitudes of the western Pacific and Atlantic Oceans. The range and geographic variability of the shape parameter in Fig. 3C is remarkably similar to previously reported results for the shape parameter of extreme wave heights46, underscoring the importance of wave-driven water-level components (See Extended Data Figs 3 and 8 for details) and the role of tropical cyclones on the magnitude and spatial distribution of the shape parameter.

In theory, negative values of the shape parameter, i.e., bounded water-level distributions, are expected based on the notion that upper bounds on tide, storm surge, and maximum wave heights exist due to limiting processes (e.g., wave breaking and physical limits in wind speed, fetch, and duration prevent unbounded wave heights). On the other hand, positive values of the shape parameter, i.e., unbounded water-level distributions, indicate the probability of exceedingly large yet inconsistent water-level events relative to an annual event. In practice, both positive and negative values of the shape parameter are possible because of the limited amount of data available for parameter estimation and the possibility of outliers. Thus, it is difficult to assess, a priori, whether the large values of the shape parameter result from a proper characterization of the variability of tropical cyclones or from the presence of outliers among a temporally-limited data set. We expect that more than 21 years of data (used here) would likely improve the characterization of extreme events due to tropical cyclones and the estimation of the shape parameter.

The dashed and solid lines in panel C (Fig. 3) represent contours of k that are significantly different from zero at the 75% and 95% confidence levels, respectively. The near-zero mean and the limited extent of the statistically significant non-zero values of the shape parameter in Fig. 3C suggests that the Gumbel distribution [the GEV family when k = 0, as in Hunter41 and IPCC3] might suffice for global-scale assessments of SLR impacts. However, for smaller-scale regions of interest, particularly the Caribbean Sea, the Central North Pacific, and North Atlantic, the variability of the shape parameter should be accounted for when predicting the effects of SLR.

Next, we discuss how the global GEV parameters characterize the increased frequency of flooding due to SLR (Figs 4 and 5). Although the behavior of the scale parameter is well known [as introduced by Hoozemans et al.33, and further explored in Hunter41 and IPCC3], these figures provide the first continuous, global demonstration of that behavior, as well as the first incorporation of wave-driven water levels.

The factor of increase in frequency of the 50-yr extreme water-level event, f inc , and the future return period of the former 50-yr extreme water level due to SLR, \(50\,{f}_{{inc}}^{-1}\), are shown in Fig. 4. For fixed SLR, decreasing values of the scale and shape parameters increase f inc and thus reduce the return period of the present 50-yr water level. The increase in f inc is larger in the Tropics (white lines on Fig. 4) compared to the Extratropics. The results presented in Fig. 4 and Table 1 indicate that the average factor of increase in flooding, f inc , in the Tropics with only 10 cm of SLR is approximately 25 times present levels, and the former 50-yr event occurs every 4.9 years. Outside the Tropics, the average factor of increase is 5.5, and the former 50-yr event occurs every 10.9 years. Note that the results given in Table 1 do not exactly follow the reciprocal relationship between the increase in frequency (f inc ) and the reduction in return period (\(50\,{f}_{{\rm{inc}}}^{-1}\)) because of the spatial averaging operation. Finally, we note that the estimated increase in flooding potential is purely due to SLR and not due to possible future changes in wave climate or storm patterns.

The upper bound of the doubling SLR, μ 2x , (Fig. 5) is estimated as the upper limit of the 95% confidence intervals of the GEV parameter estimates using Eq. (4) in Methods. As shown in Fig. 5, only 5–10 cm of SLR, expected under most projections to occur between 2030 and 2050 5, doubles the flooding frequency in many regions, particularly in the Tropics, and would occur even more rapidly in areas where regional SLR exceeds the eustatic rate12. Less than 5 cm of SLR doubles the frequency of the 50-yr water level in the tropical Atlantic and northwestern Indian Ocean. The maps of increased flooding potential (Figs 4 and 5) suggest a dire future for the top 20 cities (by GDP) vulnerable to coastal flooding due to SLR47, and for many wave-exposed cities such as Mumbai, Kochi, Grande Vitoria, and Abidjan which may be significantly affected by only 5 cm of SLR. Less than 10 cm of SLR doubles the flooding potential over much of the Indian Ocean, the south Atlantic, and the tropical Pacific. Only 10 cm of SLR doubles the flooding potential in high-latitude regions with small shape parameters, notably the North American west coast (including the major population centers Vancouver, Seattle, San Francisco, and Los Angeles), and the European Atlantic coast. The only regions where 15 cm of SLR does not double the flooding potential are regions with large shape parameters (likely influenced by tropical storm tracks): the mid-latitudes of the northwestern Pacific below Japan, the mid-latitudes of the northwestern Atlantic (the U.S. east coast, Gulf of Mexico, and Caribbean Sea), and the southwest tropical Pacific encompassing Fiji and New Caledonia (discussed below).

The Tropics experience limited water-level variance due to consistently smaller wave heights (due to latitudinal gradients in storm activity) and smaller tide ranges (due to the presence of tidal amphidromes) throughout the region. Consequently, SLR represents a larger percentage of the water-level variance as explained in Fig. 2 and Methods. The mid-latitudes of the northwestern Pacific and the northwestern Atlantic experience smaller increases in extreme water-level frequency due to large values of the scale and shape parameter, respectively. Notably, the mid-latitudes of the northwestern Pacific below Japan experience large values of the scale parameter without correspondingly large values of the location parameter as in most of the north Pacific and north Atlantic, possibly due to the consistency of tropical storms in the region. The mid-latitudes of the northwestern Atlantic (e.g., the U.S. east coast, Gulf of Mexico, and Caribbean Sea), on the other hand, have elevated values of the shape parameter due to the intermittent occurrence of tropical cyclones, which correspond to elevated probabilities of large extremes rather than bounded extremes. This suggests that although the continued and accelerating impacts of SLR-driven nuisance flooding is a major concern in many of these areas16, the rare occurrence of extreme events (e.g., hurricanes) – and not SLR – will remain the dominant hazard on wave-exposed coastlines in the lower mid-latitudes of the western Pacific and Atlantic for several decades.