We use hydrodynamic simulations of tide and surge, and scenarios of regional sea-level rise, as input to a coastal inundation model in order to generate hazard maps for several return periods (2, 5, 10, 25, 50, 100, 250, 500, and 1000 years). These are combined with exposure maps and vulnerability curves (depth–damage functions) in the impact assessment model, using a set-up similar to the GLOFRIS impacts module developed by Ward et al. (2013) and extended for future simulations by Winsemius et al. (2016). The global coastal flood impacts are assessed at a horizontal resolution of 30′′×30′′ and simulated for the different return periods. After calculating the impacts for the different return periods, EAD is calculated by taking the integral of the exceedance probability–impact curve (Meyer et al., 2009). Figure 2 shows the different input layers for the flood risk assessment and benefit–cost analyses (note that different sea-level rise and socioeconomic scenarios are used, and just one is shown in Fig. 2 as example). The following section describes the flood risk simulations in detail.

To estimate the costs associated with the different adaptation objectives, we use the same methodology as Ward et al. (2017), which calculates the costs of flood protection by summing the maintenance and investment costs over time for raising dikes to prevent flooding. The following section describes the calculation of costs of adaptation and the adaptation objectives in more detail.

In order to calculate the costs of adaptation, first dike heights need to be calculated. The current dike height calculations are taken from a recent study by van Zelst et al. (2020). Their methodology is to first derive coastal segments and perpendicular coast-normal transects (766 034 transects in total). For each transect, bed levels are constructed, and subsequently, hydrodynamic conditions and wave attenuation are derived. Lastly, the resulting sea water levels are translated into dike heights. The coastlines are derived from OpenStreetMap (OSM) and moved 100 m inwards to smoothen the coastlines and to position the lines at a likely place to establish a dike system. Transects are derived perpendicular to the coastlines for each 1′×1′ cell that has a coastline segment. Each transect is described by its slope, ocean bathymetry, foreshore, elevation, and surge levels, among other things. To capture most foreshores, the transects are stretched 4 km inward and seaward. The main source of bed-level data is the Earth Observation-based (USGS Landsat and Copernicus Sentinel 2) high-resolution intertidal elevation map (20 m horizontal and 30–50 cm vertical accuracy) of Calero et al. (2017). As this dataset does not contain data for all bed levels along the transects, the gaps are filled by ocean bathymetry data from GEBCO (30′′, 10 m vertically) and topography data from MERIT (3′′, 2 m vertically). The water levels are derived from the GTSR dataset (Muis et al., 2016) and corresponding wave conditions at different return periods from the ERA-Interim reanalysis (Dee et al., 2011). With a lookup table, consisting of numerical modelling results, the wave attenuation over the foreshore is determined. Due to the unknown direction, incoming waves are assumed to run perpendicular to the coast. Finally, current dike heights with respect to the surge level are calculated with the empirical EuroTop formulations (Pullen et al., 2007) and are based on a standard 1 : 3 dike profile without berms and with a maximum allowed overtopping discharge of 1 L m-2 s-1. This is representative of a low-cost dike. We exclude coastlines where there is no built-up area or no inundation is simulated.

In order to calculate future dike heights, sea-level rise from the RISES-AM project (Jackson and Jevrejeva, 2016) is used in the calculation of the crest heights for different return periods. This is done by adding sea-level rise directly to the crest height. Next to sea-level rise, future dike heights are calculated with subsidence levels (see Sect. 2.1.1.). Subsidence is assumed to take place directly on the dike and therefore computed on the crest height, which is similar for sea-level rise calculations.

The costs of raising dikes are estimated by calculating the total length of dike heightening per grid cell and multiplying by a unit cost set to USD 7 million km m-1 based on reported costs in New Orleans (Bos, 2008). This value of USD 7 million km m-1 is within a reasonable range when compared to various studies (Aerts et al., 2013; Jonkman et al., 2013; Lenk et al., 2017). This includes the costs of investment, groundwork, construction and engineering, property or land acquisition, environmental compensation, and project management. Subsequently, the costs are converted to USD 2005 power purchasing parity (PPP) using GDP deflators from the World Bank and average annual market exchange rates from the European Central Bank for each country. Construction index multipliers, based on civil-engineering construction costs, adjust the construction costs to account for differences between countries (Ward et al., 2010). The lengths of the dikes are estimated using the 766 034 coastline transects. Maintenance costs are represented as percentages of investment costs and are set to 1 % yr-1.

Finally, a benefit–cost analysis is performed by calculating the benefits and costs for adaptation until 2100 for sub-national regions. These regions are defined as the next administrative unit below the national scale in the Global Administrative Areas Database (GADM). The benefits and costs are discounted with a discount rate of 5 % until 2100 (lifespan of investment) and with operation and maintenance (O&M) costs of 1 %. It is assumed that investments are made in 2020 and construction is finished in 2050. During this time period, benefits and costs for investment are assumed to increase linearly. We use the net present value (NPV) shown in Eq. (2) and benefit–cost ratios (BCRs) shown in Eq. (3) as indicators of economic efficiency: 2NPV=∑t=1nBt-Ct1+rt-C0,3BCR=∑t=1nBt1+rt/∑t=1nCt1+rt+C0, where t denotes the time in years, n the lifespan of the investment, r the discount rate, Bt the benefits per year, Ct costs per year expressed as maintenance costs, and C0 the initial investment costs.

The benefit–cost analysis is carried out for two different sea-level rise scenarios (RCPs) and five different socioeconomic scenarios (SSPs). All the results are shown for two scenario combinations (van Vuuren et al., 2014), namely RCP4.5–SSP2 and RCP8.5–SSP5. The former is used for a “middle-of-the-road” scenario with medium challenges for mitigation and adaptation (Riahi et al., 2017) that can broadly be aligned with the Paris Agreement targets (Tribett et al., 2017), while the latter is used as a “fossil-fuel development” world (Kriegler et al., 2017). Results of the other combinations can be found in the Supplement.

Globally, the estimated EAD increases by a factor of 150 between 2010 and 2080 if we assume that no adaptation takes place in the middle-of-the-road scenario RCP4.5–SSP2. Figure 3 shows the top 15 countries that contribute to this coastal flood risk, in 2010 (Fig. 3a) and 2080 (Fig. 3b) – note the different scales on the x axis. China, Bangladesh, and India have the highest flood risk in absolute terms in 2010. In 2080, these three countries remain in the top four if no adaptation takes place and are joined by the Netherlands. The 15 countries shown account for 89 % of coastal flood risk worldwide in 2010 (USD 19.6 billion per year globally). Although the countries in the top 15 change between current and future assuming no adaptation, the total share of EAD residing in the top 15 countries remains approximately the same: 87 % of global flood risk in 2080 if no adaptation takes place (USD 3 trillion per year globally for RCP4.5–SSP2 and USD 6.8 trillion for RCP8.5–SSP5).

For all four adaptation objectives, a globally aggregated overview of the benefits, costs, BCR, and NPV is provided in Table 1. All objectives have a positive NPV and BCR higher than 1, indicating that globally the benefits in terms of reduced risk would exceed the investment and maintenance costs. Note that only regions with positive NPV are included for the optimize adaptation objective. The absolute-risk-constant adaptation objective has the lowest BCR, while the optimize adaptation objective has, by definition, the highest BCR. Higher costs and benefits are found for the RCP8.5–SSP5 scenario compared to the RCP4.5–SSP2 scenario, as a result of the larger EAD (and therefore avoided EAD) under this scenario. On average, the costs are ca. 25 % larger in the former, and the benefits roughly double.

The top 15 countries that contribute the most to coastal flood risk for the four adaptation objectives for RCP4.5–SSP2 in 2080 are shown in Fig. 4. The total share of EAD residing in the top 15 countries remains approximately the same: 94 % of global flood risk in the protection constant adaptation objective (USD 767 billion per year globally), 93 % in the absolute-risk-constant adaptation objective (USD 238 billion per year), 90 % in the relative-risk-constant adaptation objective (USD 421 billion per year), and 91 % in the optimize adaptation objective (USD 242 billion per year globally). Note that EAD can increase in the future for the absolute-risk-constant adaptation objective in certain regions, as we cap protection standards at 1000. The simulated optimal protection standards of the Netherlands are lower than in the protection constant adaptation objective, resulting in a high future EAD of USD 60.9 billion per year. This is because the simulated marginal costs of dike heightening up to a protection standard of 1000 years outweigh the marginal benefits. However, it should be noted that the benefits do exceed the costs up to a 1000-year protection standard and that if this were implemented, the future EAD for the Netherlands in the optimize adaptation objective would therefore be much lower than shown in Fig. 4. Figure S2 in the Supplement shows the top 15 countries for RCP8.5–SSP5.

In order to show spatial patterns of the four adaptation objectives, the following results are shown at the sub-national scale in Figs. 5–8. Here, results are shown for RCP4.5–SSP2 only. The same results for RCP8.5–SSP5 can be found in Figs. S2–S5, and the data for all scenario combinations can be found in the Supplement. Although there are some differences between the results for RCP4.5–SSP2 and RCP8.5–SSP5, the overall patterns are very similar.

In the protection constant adaptation objective, the benefits outweigh the costs for the majority of the regions (82 %; 643 of the 784 sub-national regions assessed). Nevertheless, this would still lead to an increase in relative risk (i.e. EAD as a percentage of GDP) in the future for 82 % (641) of the regions assessed. Therefore, only raising dikes to keep up with the current protection standard would lead to a substantial increase in future risk in the majority of the world's regions for scenario RCP4.5–SSP2. Sub-national regions in southern Asia, southeastern Asia, eastern Australia, the eastern and western coast of North America, and parts of Europe have the highest BCR and NPV (Fig. 5). Note that the protection standards (Fig. 5a) are the same as the current protection standards (Fig. 2d).

In the absolute-risk-constant adaptation objective (Fig. 6), it is clear that dikes would need to be upgraded to have high protection standards (usually between 100 and 1000 years) in order to keep risk constant at current levels. The costs to achieve this are high (globally, more than twice as high as under the protection constant adaptation objective), and therefore a lower number of sub-national regions (79 %; 623) have a positive BCR, although this is still very high. In most sub-national regions, the risk relative to GDP decreases in the future if this adaptation objective is implemented, although 5 % (38) of the sub-national regions show an increase in risk relative to GDP.

In the relative-risk-constant adaptation objective (Fig. 7), the protection standards required are generally lower than in the absolute-risk-constant adaptation objective. The highest protection standards required are found in eastern Asia and parts of North America. A similar number of sub-national regions have a BCR higher than 1, as is the case for the absolute-risk constant, namely 79 % of the sub-national regions assessed. To keep relative risk constant or absolute risk constant some sub-national regions need to have a future protection standard that is higher than 1000 years (the highest return period assessed in this study). Because of this, the relative change in risk in the relative-risk-constant adaptation objective increases for 5 % (36) of the regions assessed.

In the optimize adaptation objective (Fig. 8), the highest optimal protection standards are generally found in eastern Asia, southeastern Asia, southern Asia, and the Gulf Coast of the USA. High protection standards are also found in parts of Europe and other parts of the USA, parts of western and eastern Africa, some parts of South America, and southeastern Australia. The highest change in protection standards compared to current is found in southern Asia and southeastern Asia. In most sub-national regions, the benefits exceed the costs when upgrading protection standards (89 %). However, in some sub-national regions the BCR is less than 1 (indicated with hatched lines). The highest values of NPV (Fig. 8c) are found in parts of southern Asia and southeastern Asia, North America, and northwestern Europe. While most sub-national regions show a positive return on investment, there is still an increase in relative risk in 32 % of the sub-national regions assessed, under the optimize adaptation objective. In these cases, it is economically efficient to implement protection measures up to a certain level, yet the economic costs of keeping EAD as a percentage of GDP constant would exceed the avoided damages. Regions where this is especially the case include Europe, North America, South America, Japan, and Australia, as shown in Fig. 8d. Many sub-national regions with decreases in relative risk can be found in southern Asia, southeastern Asia, parts of the Gulf Coast of the USA, New South Wales in Australia, several sub-national regions in Africa, and some parts of South America, among others. In these regions, the increase in risk is generally very high, which means that the costs of investment in protection are lower than the avoided damages relative to GDP. Generally, in these regions, protection standards and/or absolute dike heights increase the most.

In the middle-of-the-road scenario of RCP4.5–SSP2, where the world will face intermediate adaptation and mitigation challenges, we see that most of the sub-national regions assessed would economically benefit from adaptation. We further see that the adaptation objectives differ in changes in relative risk and the level of adaptation that would take place. For instance, in the protection constant adaptation objective we see that although the protection standards stay the same, the relative risk increases for most sub-national regions. This can be explained by the increase in the severity and frequency of the flood hazard due to sea-level rise and subsidence and the increase in exposure of assets due to socioeconomic change. Compared to the optimize adaptation objective, the protection constant adaptation objective under-protects in most sub-national regions. In the absolute-risk-constant adaptation objective we see that relative risk decreases in most sub-national regions while protection standards increase greatly. Due to climate change, socioeconomic change, and subsidence, we see an increase in GDP exposed to flooding. Therefore, protection standards must increase vastly in order to meet the same level of absolute risk. In this adaptation objective, most sub-national regions are over-protected compared to the optimize adaptation objective. In the relative-risk-constant adaptation objective, we see that some sub-national regions are over-protected, while other sub-national regions, for instance in southeastern Asia, are under-protected. The optimize adaptation objective shows the most economically feasible results in terms of maximizing NPV and has the highest BCR in most regions. In the fossil-fuel development scenario of RCP8.5–SSP5, where mitigation will face large and adaptation small challenges (van Vuuren et al., 2014), we see that higher protection standards are required in order to keep risk constant and to maximize NPV (see Figs. S3–S6). The results of the adaptation objectives can be used as a first proxy to indicate the sub-national regions in which adaptation through structural measures may be economically feasible. Moreover, the results indicate regions where adaptation is needed in order to maximize NPV and which objectives under- or over-protect sub-national regions compared to the optimize adaptation objectives. Due to the scope of this study, local-scale models and assessments should be used for the design and implementation of individual adaptation measures.

In Fig. 9, we show the percentage of the total costs of the optimize adaptation objective (Fig. 9a) that can be attributed to each of the following risk drivers: climate change (in this case sea-level rise; Fig. 9b), optimizing current protection standards (Fig. 9c), socioeconomic change (Fig. 9d), and subsidence (Fig. 9e). The results are shown for the RCP4.5–SSP2 scenario and only for sub-national regions that have a BCR higher than 1 in the optimize adaptation objective.

The total costs exceed USD 1 billion for 4 % of the sub-national regions assessed and exceed USD 1 million for 87 %. For most parts of the globe, climate change (in this case sea-level rise) contributes the most to the costs of adaptation, exceeding 50 % of the total costs in 98 % of the sub-national regions (Fig. 9a) and exceeding 90 % of the total costs in 58 % of the sub-national regions. However, the other drivers can also play an important role but are dwarfed in absolute terms by the costs related to sea-level rise. For example, in southern Asia, southeastern Asia, and eastern Africa, optimizing to current conditions and socioeconomic change are important drivers and, in some cases, the most important driver. There are some other regional exceptions where climate change is not the most dominant driver of adaptation costs. Moreover, locally land subsidence due to groundwater extraction can cause huge flood problems and bring large costs in some areas (Dixon et al., 2006; Yin et al., 2013) but are not seen when aggregated to the sub-national regions of this study. However, there are a few regions where subsidence is a more dominant driver (i.e. parts of India, China, Japan, and Taiwan). The results show that climate change is not the most dominant driver in four of the five countries that have the highest share of future EAD if no adaptation takes place (i.e. China, Bangladesh, India, and Indonesia). Generally, the same patterns are found in the attribution results for the RCP8.5–SSP5 scenario, which can be found in the Fig. S7.

Figure 10 shows the attribution of the costs for the same scenario and adaptation objective, aggregated to the World Bank regions. In all the regions (except southern Asia), sea-level rise is the most dominant driver, accounting for between 27 % (southern Asia) and 79 % (Europe and central Asia) of the costs of adaptation. The costs of increasing dike height to achieve optimal protection under current conditions are highest in the Global South. This is especially the case for the eastern Asia and the Pacific and southern Asia regions, with values of 22 % and 38 % respectively. The relative contribution of socioeconomic change is largest in eastern Asia and the Pacific, southern Asia, and sub-Saharan Africa, with values of 20 %, 26 %, and 27 % respectively. Of all drivers, subsidence is the least dominant, with values up to 9 % (eastern Asia and Pacific) and 10 % (Middle East and northern Africa). Figure S8 shows the attribution aggregated to the World Bank regions for RCP8.5–SSP5.

In this section, we show the sensitivity of the results to the use of different SSPs, sea-level rise projections, discount rates, and O&M costs. In Table 2, we show results (of BCR) standardized to a baseline scenario with the following assumptions: RCP4.5, SSP2 (middle of the road), discount rate of 5 %, and O&M of 1 %. We employed a one-at-a-time sensitivity analysis, so for each row in the table only one parameter has changed, and the values shown are standardized by calculating the relative change. All associated BCRs for the standardized values shown in Table 2 are still higher than 1. Globally, BCRs range between 45 and 119 for the different model runs (73 for the reference). At the global scale the BCRs are most sensitive to the use of the different SSPs and discount rates. They cause the largest changes in BCR, with standardized values of 0.44 and 2.17 found in southern Asia and sub-Saharan Africa. Differences in SLR input affect the BCR by a factor of up to 0.38. Europe and central Asia and North America are the least sensitive to the changes in input parameters. The O&M costs show BCRs that are more in line with the reference model run, with higher or lower values up to 0.18.

Hallegatte et al. (2013) performed a study on future flood risk for 136 major coastal cities. They estimated an EAD of USD 6 billion for current conditions, while in our study we find an EAD of USD 19.6 billion. Our estimates of EAD are higher, which is to be expected given the difference in extent of the studies where we estimate risk for all global coastlines as opposed to 136 major coastal cities in their study. Hallegatte et al. (2013) projected future risk increasing up to USD 60–63 billion if protection standards are kept constant by 2050. In our study we find an EAD of USD 84 billion by 2050 when keeping protection standards constant (RCP4.5–SSP2 scenario). If no adaptation is implemented in 2050, Hallegatte et al. (2013) estimate EAD to be over USD 1 trillion, whereas we find USD 1.1 trillion.

Hinkel et al. (2010) attributed adaptation costs to sea-level rise using dikes for the European Union. They estimated this to be between USD 2.6 billion and 3.5 billion. In our results we find values between USD 12.9 billion and 22.7 billion for the European Union for the scenarios RCP4.5 and RCP8.5 respectively. In a follow-up study, Hinkel et al. (2014) estimate global costs of protecting the coast with dikes. They estimate a range of USD 12–71 billion, while our study estimates the global costs of adaptation for the optimize adaptation objective between USD 152 billion and 208 billion for the RCP4.5–SSP2 and RCP8.5–SSP5 respectively. It should be noted that Hinkel et al. (2010, 2014) use a demand function for safety where dikes are raised following relative sea-level rise and socioeconomic development, while we do not use that function and optimize protection standards by maximizing NPV. This adaptation objective allows dynamic optimization per sub-national region and can result in higher adaptation costs as long as the net benefits increase. Additionally, we use different scenarios than those used in Hinkel et al. (2010, 2014).

Lastly, we compare our results of economic feasibility for sub-national regions and coastlines to the findings of Lincke and Hinkel (2018), in which they found that it is economically feasible to invest in protection for 13 % of the coast globally. Using their method they found a lower share of protected coastline compared to previous studies (Nicholls et al., 2008b; Tol, 2002). In our study, we found that for the optimize adaptation objective, 89 % of the sub-national regions have a BCR higher than 1, indicating that it is economically feasible to implement adaptation in many regions through raising dikes. In our study, the benefit–cost analysis is carried out at the sub-national scale, whereby dikes are only raised on coastal reaches where our transects show there to be potential hazard (inundation) and urban exposure. If we calculate the percentage of the entire global coastline for which this leads to dike heightening in our model with a BCR higher than 1, it amounts to 3.4 % of the global coastline. This is lower than the value in Lincke and Hinkel (2018), but we reason that this difference is a result of the difference in spatial aggregation, where the distance between our transects is 1 km horizontal resolution at the Equator, whilst Lincke and Hinkel (2018) raise dikes along the coast of entire coastal segments, which have lengths ranging from 0.009 to 5213 km, with a mean of 85 km. This can explain why we have a lower percentage of coast that is feasible to protect than Lincke and Hinkel (2018).

While our model scheme does not include dynamic inundation modelling, it does include resistance factors similar to those used by Vafeidis et al. (2019) in order to account for water-level attenuation. It therefore represents an advance to previous studies that have used planar inundation modelling methods (i.e. bathtub models). An improvement could be made by using a dynamic inundation modelling scheme (Vousdoukas et al., 2016) but at the cost of increased computing time. Another improvement can be made by including waves in our inundation modelling, which is found to be an important component in inundation modelling (Vousdoukas et al., 2017). The inundation modelling scheme can be further improved by increasing the resolution from 30′′ to a higher resolution in order to better understand local-scale signals and patterns, since the scale of assessment and resolution of input data have a significant implication on flood risk model results (Wolff et al., 2016). However, we stress that this study aims to understand global flood risk and general patterns at the sub-national scale, and this study can be used as a first proxy, indicating feasibility of adaptation through structural measures, such as dikes.

For this study, results are shown for the scenario RCP4.5–SSP2 and RCP8.5–SSP5 in the Supplement. The range of sea-level rise input values (between the 5th percentile of RCP4.5 and the 95th percentile of RCP8.5) cover a wide range of sea-level rise uncertainty (approximately 0.3–0.7 m at the Equator in the Atlantic Ocean). While in reality the effects of climate change will continue to rise beyond 2100 even if the Paris Agreement is met (Clark et al., 2016), our study examines adaptation objectives until 2100. Results for all combinations of these two RCPs together with all five SSPs can be found in the Supplement.

Several uncertainties exist on the cost calculation side. The first is the monetary value we assumed for the costs of dike heightening. Although we account for differences in costs between countries by using different construction factors and market exchange rates, in reality the costs might differ between regions and may be higher due to local conditions (both physical and socioeconomic). We also use a linear cost function for dike heightening. Using this linear cost function for large-scale studies has been found to be a reasonable assumption according to Lenk et al. (2017).

Another important uncertainty in this study is the current protection standards estimated with the FLOPROS modelling approach, as data on flood protection along the global coastlines are not available. These only provide a first-order estimate of current protection standards per sub-national region. In Fig. S1, a validation of the coastal protection standards estimated with the FLOPROS modelling approach is provided. Values are shown for several locations for which reliable reported estimates of protection standards are available. These reported values are either shown as a range (minimum and maximum reported values) or a single value. Overall, the model performs well. The only location for which the reported values provide a range, and the FLOPROS model lies outside this range, is Durban. However, note that reported values are for the city of Durban, whilst the FLOPROS model value is for the state in which it is located. An improvement to this study could be made by, for instance, mapping flood protections globally by using Earth Observation-based methods.

In this study, several uncertainties exist with assumptions on expected damages per occupancy type. First, we assumed the percentage of occupancy type per grid cell to be the same for all locations, whilst in reality it is spatially heterogeneous, and secondly, we assumed the building density per occupancy type. An improvement could be made by using machine learning to improve accuracy of urban land cover and building types (Hecht et al., 2015; Huang et al., 2018). We also used depth–damage curves per occupancy type, but in reality, these curves also differ between buildings in these occupancy types. To further improve the exposure data of our framework, the Global Human Settlement Layer (Pesaresi et al., 2016) can be used for high-resolution population mapping.

The sub-national regions where no adaptation objective shows a positive BCR should not mean that no adaptation to coastal flood risk should take place. In fact, other adaptation measures (or a combination of multiple measures) besides raising dikes might be more economically feasible in any regions studied, including those with BCRs higher than 1. In this study we only assumed grey infrastructure as adaptation measures, but there are also other measures to reduce flood risk. For instance, the vulnerability can be improved by wet- or dry-proofing buildings (Aerts et al., 2014), or people and assets can be moved to less flood-prone areas in order to reduce the exposure to floods (McLeman and Smit, 2006). Lastly, several local studies show the benefits of nature-based or hybrid adaptation measures (Cheong et al., 2013; Jongman, 2018; Temmerman et al., 2013). Vegetation on the foreshore has a significant role in the breaking of waves (Shepard et al., 2011) and attenuates storm water levels (Zhang et al., 2012). An improvement could be made by including other adaptation measures besides grey infrastructure as adaptation measures.