## Discussion

Global model outputs of tide, surge and wave setup have been used to develop historical time series of total sea level around the world’s coasts. These model results were extensively validated against global tide gauge data, showing good agreement. To estimate the extreme sea levels which occur during storm events, an extreme value analysis was applied to both model and tide gauge data. In order to estimate extreme sea levels over the twenty-first century, projected relative sea level rise for IPCC RCP4.5 and 8.5 was added to present day extreme sea levels. These projected extreme sea levels were then used to quantify global episodic coastal flooding in 2050 and 2100.

Results show that for RCP8.5, 0.5–0.7% of the world’s land area will be at risk of episodic coastal flooding by 2100 from a 1 in 100-year return period event (an increase of 48% compared to the present day), impacting 2.5–4.1% of the world’s population (increase of 52%) and threatening assets worth up to 12–20% of global GDP (increase of 46%). Note that these values assume no coastal defences or adaptation measures (see SM5). In many locations, coastal defences are commonly deployed and by 2100, it is expected that adaptation and specifically hard protection will be widespread, hence these estimates need to be seen as illustrations of the scale of adaptation needed to offset risk. Future studies that consider the impact of coastal adaptation and defences could logically build on the present results. As such, we regard the present analysis as a “first-pass” estimate of global impacts of sea level rise.

The analysis shows that tide and storm surge will account for 63% of the global area inundated by 2100, with relative sea level rise accounting for 32% and wave setup accounting for only approximately 5%. Furthermore, projected sea level rise will significantly increase the frequency of coastal flooding by 2100, with results herein showing that for most of the world, flooding associated with a present day 1 in 100-year event could occur as frequently as once in 10 years, primarily as a result of sea level rise. As the episodic events of storm surge and wave setup will, between them, contribute approximately 68% of projected coastal flooding, any climate change driven variations in the frequency and/or severity of storm events could have significant impacts on future episodic coastal flooding.

As noted previously, the present study has a global-scale focus. As such, a number of simplifying assumptions are necessary to render the problem computationally feasible. These simplifications and the resulting implications are discussed in detail in the Supplementary Material (SM5). A summary of these assumptions appears below.

The analysis undertaken is linear in nature. It is assumed that the total sea level (TSL) can be represented by the summation of T + S + WS. This explicitly ignores interactions between these processes. Extreme value analysis is undertaken to determine historic extreme sea levels (ESLH100). The linear assumption is again applied to determine future extreme sea levels (ESLF100) by the linear addition of projected relative sea level rise (RSLR) by the end of 2100. This assumes that changes in wind speed and wave height over the coming century will be small, which is consistent with a number of recent studies38,39,40. SM5 outlines the precedence for such linear superposition approaches for global-scale studies4,7,8,9,10,11 and concludes that the potential errors are relatively small compared to the uncertainties in the extreme value analysis and RSLR projections.

In order to calculate the magnitude of the wave setup (WS) at global scale, it is necessary to use relatively simple models16,18 and to assume a global average bed slope. These assumptions will most likely result in errors at specific locations. However, the analysis ultimately shows that WS is a relatively small component of the ESL, and hence the adopted “first-order” representation of WS appears justified.

To validate the model adopted above, extensive tide gauge data is used (see Fig. S1), as this is the only global water surface elevation data source available. An extensive comparison is undertaken for both ambient and extreme conditions. It should be noted, however, that it is likely that many tide gauges, due to their locations, will not respond to WS. Hence, this validation dataset has its limitations for this application. Although model and tide gauge data agree well at the global scale, there are clear differences at specific locations. For example, in more than 30% of examined locations, the RMSE related to the mean tidal amplitude is greater than 20%. This is largely associated with semi-enclosed basins or regions with wide shelves (e.g. Mediterranean Sea, Baltic Sea, Sea of Japan) and with regions of small tidal range (see Fig. S3, SM1).

The MERIT22 topographic model is used with a “bathtub” flooding model. This assumption is expected to generally overestimate flood extent41,42. Importantly, the analysis also assumes no flood protection is in place, such as dykes or other structures. As a result, the absolute values of flood extent will be over-estimated in many locations. For this reason, we emphasis relative changes in flood extent rather than absolute values.

The above assumptions mean that the present analysis may not model projected flooding at specific sites well. However, results show that, when aggregated to the global scale, the approach adopted here is able to produce first-order estimates of global flooding and its implications. In addition to these simplifying assumptions, both the ESL and RSLR estimates have associated statistical uncertainties. The present study considered these uncertainties in assessing statistical variability associated with estimated flooding extent. The full analysis, given in SM5 and Table S4, indicates the uncertainty associated with projected flooding in 2100 (RCP8.5) is approximately $$\pm 16.5\%$$.

## Methods

The analysis uses a significant number of global datasets which are combined to determine global projections of total sea level, extreme sea level, coastal flooding, populations affected and assets impacted for 2050 and 2100. The datasets are briefly described below and the process to combine and analysis them is shown diagrammatically in Fig. 4.

### Datasets

The various datasets used in this analysis are briefly described below:

### GTSR: Global tide and surge reanalysis (S)

The time series of coastal storm surge values were obtained from the GTSR dataset8 over the period (1979–2014). This dataset was generated with the Global Tide and Surge Model (GTSM), which uses the Delft3D Flexible Mesh software43 and was forced with wind fields from ERA-Interim14 downscaled to a temporal resolution of 10 min. GTSM has a spatially varying grid resolution which varies between 50 km in the deep ocean and 5 km in coastal areas.

### FES2014: Finite element solution (T)

FES is a finite element hydrodynamic model which solves the tidal barotropic equations and assimilates in-situ tide gauge and altimeter data13 (https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes/description-fes2014.html). The global model has a total of 2.9 M nodes and a spatial resolution of 1/16°.

### ERA-interim, GOW2 (WS)

ERA-Interim and GOW2 are global surface wave model reanalyses. These have been used to provide deep water wave conditions to estimate wave setup (WS). ERA-Interim (ERA-I) is a global atmospheric reanalysis from 197914. ERA-I uses the ECMWF Cy31r2 atmospheric model coupled with the WAM spectral wave model44. Both the atmospheric model and the wave model used in ERA-I incorporate satellite data assimilation. Output from the model is available at 0.7° global resolution. GOW215 is a global wave model hindcast. It uses the Wavewatch III45 model Version 4.18, forced with CFSR winds46. The hindcast is designed to provide higher resolution coastal wave data and hence uses a system of nested grids of resolution 0.5° in deep water, with finer scale ~ 25 km resolution in areas with water depths less than 200 m. In contrast to ERA-I which has satellite assimilation in both the wind and wave models, GOW2 has only assimilation in the forcing wind field. GOW2 hindcast data are available over the period 1979–2015.

In order to determine the wave setup, (WS), the nearshore (deep-water) wave conditions (significant wave height, $$H_{s0}$$ and wavelength, $$L_{0}$$) are required. As there is no widely validated and accepted global nearshore wave model dataset, both ERA-Interim14 and GOW215 were tested for this purpose. Wave setup was determined as a function of deep-water wave steepness ($$H_{s0} /L_{0}$$) and bed slope using both the SPM graphical approach16,17 and Stockdon et al.18. Bed slope was calculated from an offshore depth equal to $$2H_{s0}$$ to the shoreline17. The spatial resolution of the wave models is such that bed slope cannot be determined accurately for the present application (i.e. ERA-Interim approx. 80 km resolution and GOW2 ~ 25 km resolution). However, as the dependence on bed slope is expected to be relatively weak17, a range of representative values (1/15, 1/30, 1/100) which spans reported global shoreline bed slopes47,48 were tested instead (see SM1 and SM2). Based on the outcomes of this sensitivity analysis (see SM2), a representative bed slope of 1/30 was adopted at all locations. Also, as GOW2 has better spatial and temporal resolution than ERA-Interim, and as wave setup estimates derived from the two wave models are similar (see SM1, SM2, Table S3), GOW2 was used for subsequent analysis.

### GESLA-2: Global extreme sea level analysis version 2 (tide gauge data)

GESLA-221 is a dataset of global tide gauge observations. Although some of the tide gauges go back more than 100 years, the vast majority of the data are from 1950 onwards. Data are generally archived at a temporal resolution of 1 h or less and are available at a total of 1,355 stations. In the present analysis a total of 681 unique locations with data over the required period (see Fig. S1) were used to validate the various model results.

### DIVA: Dynamic interactive vulnerability assessment (output locations)

DIVA12 is a database for assessing coastal vulnerability from sub-national to global levels. The database, as such, is not used in this analysis. Rather, 9,866 DIVA locations have been used as the reference output locations for model results.

### MERIT DEM: Multi‐error‐removed improved‐terrain DEM (Topography)

MERIT DEM22 is a high accuracy global digital topographic dataset at 3 arc sec resolution (~ 90 m at equator) developed from existing spaceborne DEMs [SRTM3 v2.1 and AW3D-30 m v125,49] by eliminating major error components from the existing DEMs. The DEM data covers lands between 90°N–60°S, vertically referenced to the EGM96 geoid.

### MDOT: Mean dynamic ocean topography (MERIT DEM datum)

The MDOT36 is the difference between the time-averaged sea surface and the geoid. As the datum for the estimates of $$ESL^{H100}$$ is mean sea level and datum for the MERIT DEM topography is the geoid, the MDOT was used to bring these datasets to the same datum.

### GSHHG: Global self-consistent hierarchical high-resolution geography (Coastline)

GSHHG37 is a coastline dataset at multiple resolutions. Here, the “high resolution” (~ 0.2 km) coastline dataset was used to define the global coastline for calculations of flooding extent.

### GPWv4 Rev.11: Global population (population and asset exposure)

The NASA Socioeconomic Data and Applications Center (SEDAC) produce the GPWv4 Rev. 11 database of population count from 2015 census data on a 30 arc sec. (~ 1 km at equator) grid. This dataset was used to determine population and assets potentially exposed to flooding.

### GDP: Gross domestic product (asset exposure)

The gridded 2015 GDP data of Kummu et al.27 consists of GDP per capita (PPP) data on a 5 arc min grid (downscaled to 30 arc-sec to be consistent with the other datasets used). This dataset was used to estimate the value of assets potentially exposed to flooding.

### Analysis process

Consistent with the linear assumption (1), the time series of T (Fig. 4a), S (Fig. 4b) and WS (Fig. 4c) obtained from the respective datasets were interpolated to a consistent 10-min temporal resolution and assigned to the closest DIVA point. This generated an historical time series of TSL(t) at each point. The WS was estimated using both the SPM approach16 and Stockdon et al.18, both GOW2 and ERA-I wave models were tested with a range of different bed slopes. The Stockdon et al.18 approach is more sensitive to bed slope but for plausible bed slopes (i.e. < 1/30) consistent with SPM16 (e.g. see Fig. S11). Based on subsequent global comparisons with tide gauge data, a bed slope of 1/30 was adopted with the SPM approach. The RMSE was used to test the consistency of these model-derived time series at each location against tide gauge data (Fig. 4f) for ambient conditions (see SM1). The performance of the model results for extreme conditions was also tested by comparing upper percentile values with the tide gauges (Fig. 4f).

The 1 in 100-year return period extreme value sea levels (ESLH100) were determined from these model time series at each DIVA point (Fig. 4e). A wide range of different extreme value analyses (EVA) were tested. These include the peaks-over-threshold method with both Generalized Pareto Distribution (GPD) and the Exponential Distribution (EXP) and a variety of different threshold levels. The Annual Maximum approach was also tested using the Generalized Extreme Value Distribution (GEV) and Gumbel distribution (GUM) (Fig. 4e). These approaches were validated against corresponding EVA analysis of tide gauge data. These comparisons were undertaken for 1 in 20-year return periods, which require no extrapolation of the time series to this probability level and 1 in 100-year return periods (see SM 2). Based on this analysis it was found that a GPD distribution with a 98th percentile threshold gave the best agreement between model and tide gauges and inclusion of WS slightly reduced bias between model and tide gauge extreme value estimates (see SM2).

The projected future extreme sea level (ESLF100) (Fig. 4i) was determined by adding the relative sea level rise (RSLR) to ESLH100(Fig. 4h). Again, this was done at each DIVA point. Using a bathtub flooding assumption, the episodic coastal flooding was determined at each DIVA point with the ESL values assigned to areal regions using Thiessen polygons (see SM3). The coastal topography was determined using the MERIT digital elevation model with the coastlines defined using GSHHG dataset (Fig. 4j).

The population impacted by these flooded regions was determined from the gridded population data of the GPWv4 dataset (Fig. 4k) (see SM3). The value of assets impacted by the flooding was evaluated from the population impacted and the GDP using the relationships proposed by Hallegatte et al.5 and Hinkel et al.24 (Fig. 4l).

### Confidence limits

The estimates of extreme value sea levels are statistical quantities and to obtain estimates of the potential uncertainty in the projected $$ESL^{F100}$$, the 90th percentile confidence limits on each of the $$ESL^{H100}$$ values were determined using a bootstrap approach. Bootstrapping is a common approach to determine confidence limits for extreme value estimates40,50. Using this approach, we computed a sample of 1,000 bootstrapped $$ESL^{F100}$$ estimates taken randomly from the original data sample at each DIVA point. For each sample an estimate of $$ESL^{F100}$$ was determined and 5.0 percentile and 95.0 percentile values calculated from the 1,000 realizations to give the lower and upper 90th percentile confidence limits. The resulting 90th percentile confidence intervals are shown globally in Fig. 5. The results indicate that for 99% of the 9,866 locations, the span of the 90th percentile confidence interval (i.e. upper CL—lower CL, CL is the value of $$ESL^{H100}$$ at the confidence limit) is less than 1 m (i.e. $$\pm 0.5$$ m). As $$ESL^{F100}$$ values are commonly of order 4 m (see Fig. S12), the 90th percentile confidence limits are thus less than $$\pm 10\%$$ (see SM5). The confidence limits for $$ESL^{H100}$$ and $$ESL^{F100}$$ were used to determine the confidence limit span for area inundated, population exposed to flooding and assts exposed to damage. These values are shown in Table 1.