The Costs of Sea-Level Rise: Coastal Adaptation Investments vs. Inaction in Iberian Coastal Cities

Iberian coastal cities are subject to significant risks in the next decades due to climate change-induced sea-level rise. These risks are quite uncertain depending on several factors. In this article, we estimate potential economic damage in 62 Iberian coastal cities from 2020 to 2100 using regional relative sea-level rise data under three representative concentration pathways (RCP 8.5, RCP 4.5 and RCP 2.6). We analyze the expected accumulated damage costs if no adaptation actions take place and compare this scenario to the investment cost of some adaptation strategies being implemented. The results show that some adaptation strategies are less costly than the potential damage under inaction. In other words, it is economically rational to invest in adaptation even in a context of high uncertainty. These calculations are very relevant to inform climate change adaptation decisions and to better manage the risk posed by sea-level rise. Moreover, our findings show the importance of a good understanding of the shape of the sea-level rise and damage cost distributions to calculate the expected damage. We show that using the 50th percentile for these calculations is not adequate as it leads to a serious underestimation of expected damage and coastal risk.


Introduction
Sea-level rise is one of the main consequences of anthropogenic climate change [1]. Sea level worldwide was stable from approximately 7000 years before present until the end of the 19th century, but since then the geological and tide gauge record presents signs of acceleration [2]. During the 20th century, a significant acceleration of sea-level rise has occurred, quantified at about 1.2 mm per year from 1901 to 1990 [3,4]. The same analysis applied to the period 1993-2010 revealed a much larger acceleration, of about three millimetres per year [4]. Other calculations [5] show an increasing sea-level rise since 2010 of up to 4.4 ± 0.5 mm yr −1 , so since the 1880s, the global sea level has increased more than 20 cm and continues rising at more than 4 mm yr −1 [6]. Nonetheless, sea-level rise can vary significantly in magnitude and rate of change regionally and these differences can be of up to four times larger in some areas [7].
The global sea-level rise projections by the Intergovernmental Panel for Climate Change (IPCC) [1], as well as the regionalized assessments for each emission scenario (representative concentration pathways, RCP), foresee an acceleration in sea-level rise over the course of the present century [8][9][10][11]. Sea-level rise will accelerate in the future and over the next centuries even if emissions stabilize [12]. The magnitude of change, however, remains uncertain because it depends on the ambition of mitigation The rest of the paper is organised as follows: Section 2 presents a summary of the foreseen impacts of sea-level rise in the Iberian coastal areas. Section 3 describes the methods used; the results are presented in Section 4, and the overall discussion is included in Section 5.

The Impacts of and Adaptation to Sea-Level Rise in the Iberian Peninsula
Coastal risks have increased in the Iberian Peninsula during the last decades. The urban development model and the overexploitation of some resources have put enormous pressure on these coastal areas, causing biodiversity loss and environmental degradation, while increasing their exposure and vulnerability to climatic events [26]. In some areas of the Basque Coast, habitat and ecosystem destruction induced by sea-level rise could generate losses of up to 2.3 million euros per hectare [27]. The increase in flood exposure in certain areas of the Spanish Mediterranean coast (Murcia and Alicante) has been directly linked to two urban development peaks, between 1978-1982 and 1997-2007 [28]. In fact, the Spanish Mediterranean coast has high or very high vulnerability and exposure values, compared to other areas of the Mediterranean subject to larger hazards. This situation repeats, however, in other densely populated areas such as the French southwest coast and the north Adriatic coast [29].
Assuming that the trend of rising sea levels continues during the first half of the century, flood-risk could increase by 2040 by 8% in the Atlantic and Cantabrian coasts of Spain and the Alboran Sea, 6% in the Canary Islands and between 2% and 3% in the rest of the Mediterranean coast and the Gulf of Cádiz [30]. In some locations, the frequency and intensity of extreme events are expected to increase in the future. For example, in the city of Bilbao, located on the Cantabrian coast, the intensity, measured as the change in the flood level, could increase from 3.85 m in 2010 to 4 m in 2040, and its frequency will increase from once every 50 years (2010) to once every 15 years in 2040 [30]. In Barcelona, however, changes in intensity are not expected and the increase in frequency is expected to be smaller: the return period could vary from once every 50 to once in 40 years [30,31]. In Portugal, sea-level rise and changes in storminess are expected to cause higher coastal flooding and erosion, among other impacts such as coastal wetland inundation and retreat, and have been identified as one of the most important consequences of climate change [32,33]. The coast north of Lisbon and the Algarve were identified as the areas most at risk [32]. Recent studies have addressed these areas of the Portuguese coast in further detail, identifying the areas of Aveiro [34], south of Porto, and the Algarve as hotspots for coastal inundation and erosion [35,36]. Moreover, it has been estimated that 900 km 2 of the Portuguese coast could be subject to flood risk in 2050, considering 50 year return period extreme events and empirical sea-level rise projections. At the end of the century, the areas at risk of coastal flooding could increase by 27%, where Lisbon, Faro and Aveiro are the districts most at risk [37,38].
With regards to coastal protection and adaptation to climate change, Spain was already among those countries in Europe with a larger expenditure in the period between 1998 and 2015 [39]. Projections to 2040 estimate that the population exposed to permanent flooding on the Cantabrian coast could reach 2-3%. If extreme events are also incorporated, the exposed population could range between 4% and 9%. As for the economic impact, at the end of the century, permanent flood damage in the Bay of Biscay could reach between 1 billion euros (0.1% of regional GDP(2008)) under RCP 4.5 and 8 billion euros (0.6% of regional GDP(2008)) under a high-end sea-level rise scenario. Direct average damage could double if extreme weather events are considered [30].

Estimating the Costs of Adaptation Inaction
The methodological approach followed in this study to assess the costs due to sea-level rise if adaptation is not implemented is summarised in Figure 1. The first step is to identify the cities for our assessment. A recent study estimated the economic damage due to coastal flood height for 600 European cities, as well as the adaptation costs, obtained as a function of defence height [19]. This is done in a deterministic way. Of all these cities, we focus on those located in the Iberian Peninsula, our target study zone. Our sample includes 62 main coastal cities in Portugal and Spain, as shown in Figure 2. The second step is estimating future sea-level rise in each city using a stochastic method and considering three scenarios (RCP 2.6, 4.5 and 8.5) as described next in Section 3.1.1. The third step is calculating, also with a stochastic approach, the annual and accumulated expected damage due to sea-level rise in each of our 62 cities. This is explained in Section 3.1.2.

Modelling Projected Sea-Level Rise in Each City
First, local sea-level rise data for each city is taken from a database that includes the probabilistic distribution of sea-level rise under three emission scenarios (RCP 2.6, 4.5 and 8.5) in 2030, 2050 and 2100, for more than a thousand tide gauges worldwide [9]. With regard to sea-level rise projections, RCP 8.5 represents the highest emission or the business-as-usual scenario where no climate mitigation policies are adopted; RCP 4.5 describes a middle of the road scenario, and RCP 2.6 is the deep-emission reduction scenario, compatible with a 2 • C warming. The database presents a number of sea-level rise percentiles to a large tide gauge dataset worldwide. For every city in our sample, the closest tide gauge is selected using the Haversine distance between the coastal city and the tide gauges [40]. From the dataset, a total of 27 sea-level rise percentiles with values of xx.0th and xx.5th were selected for each city, scenario and selected year, where xx is an integer between zero and 100. Note, however, that the percentiles are irregularly spaced, while regularly spaced percentiles are needed to apply the methodology proposed. For this reason we calculated an additional 174 percentiles using shape-preserving piecewise cubic interpolation. Thus, 201 percentiles of sea-level rise evenly distributed between 0 and 100 were estimated, spaced by 0.5 (see Figure 1).
As the objective is to estimate the expected (average) damage, the average sea-level rise is calculated using these 201 percentiles. The expected sea-level rise for city i at time j is denoted by E(SLRi,j). This average value is greater than the corresponding 50th percentile, which indicates that the tail of the distribution is long, and thus, it is possible that risks are underestimated if median values are used. This again confirms that knowing the full distribution, additionally to estimating average values, may be of great importance for adequate risk management. This process is followed for each city, each year (2030, 2050 and 2100) and the three aforementioned RCPs.
Note that these percentiles are chosen in order to find the best manner to represent the shape of all distributions. An alternative to this approximation is the so-called parametric approach that consists of calibrating a distribution with two or three parameters [40]. However, this method is not recommended in this case as it may cause important calibration errors that lead to differences between the value of the original percentiles and those obtained from the modelled distribution. Consequently, it will negatively impact the calculation of expected values. We thus argue, in this case, in favour of using the percentiles for calibration as explained above.
As an illustration, Figure 3 shows a standard cumulative distribution function for sea-level rise for nine representative Iberian coastal cities in the year 2100 considering the highest emission scenario, RCP 8.5. The ten cities were selected for being those with the largest population based on data from Eurostat (European Commission, Brussels, Belgium). Figure 4 shows how cumulative distribution functions may evolve in time, illustrated by the case of Barcelona. One can see that the probabilities of sea-level rise being less than or equal to 50 cm in 2100 are 25% under RCP 8.5, 48.25% under RCP 4.5 and 61% in RCP 2.6.

Estimation of Economic Damage
A recent study presented the economic damage and adaptation costs as a deterministic function of coastal flood height and height of the defences, respectively, for 600 European coastal cities [19]. The deterministic damage functions used in this work for each of the 62 coastal cities in our sample are taken from the aforementioned study [19]. These functions provide an estimation of damage as a function of sea-level height. The inundation model used to obtain the damage functions used a digital terrain model of 25 m resolution, and hydraulically connected areas were calculated for different coastal flood levels between 0 and 12 m at intervals of half a metre. The damage cost functions [19] were built based on the economic value of the assets exposed to coastal flooding. This exposure was measured considering the economic value of land use, which in turn is based on country level data from a previous study [41], and then adjusting the monetary estimates to 2016 prices by using inflation rates and consumer price index (see [19](p. 5) for further details).
The cost curves [19] are not linear, that is, at higher levels of sea-level rise (SLR), we might obtain, in some cases, higher than proportional costs ( Figure 5). Accordingly, the damage distribution is not a linear transformation of the sea-level rise distribution. We denote using E(Di,j) the expected annual damage value for the city i at the time j. Using the sea-level rise percentiles, we calculate 201 damage values for each city at year j. As these values are equally likely, the expected value is calculated as their average value. Figure 5 illustrates the annual damage depending on local sea-level rise in nine cities of our sample as taken from the damage function database [19]. Note that these deterministic functions are non-linear and not time-dependent, as damage depend only on flood depth. The time component will be incorporated when combined with the sea-level rise scenarios, which vary with time. We define the annual costs of adaptation inaction as the expected damage under three sea-level rise scenarios, which we estimate for the years 2030, 2050 and 2100. Next, we estimate the expected costs for the rest of the years between 2020 and 2100 using shape-preserving piecewise cubic interpolation. Last, we accumulate the calculated damage from 2020 onwards to obtain the accumulated cost of inaction in 2030, 2050 and 2100 [42].

Measuring the Investment Costs of Adaptation
Adaptation costs for each city were obtained from the study that developed the damage function database [19], which includes the protection needs to be calculated for each city. Adaptation costs are defined based on a theoretical urban protection strategy which consists of a hypothetical defence (adaptation infrastructures, such as dikes or seawalls) that responds to the protection needs in each city. A country-specific dike-construction cost range is used as a proxy for the investment needed for such defences [19]. We acknowledge that this is a rather limited analysis of adaptation options as cities may identify a wide portfolio of both soft and hard adaptation options. However, this is a limitation of the available data but can well illustrate the use of the method proposed in this paper.
A range of adaptation investment costs needed (minimum and maximum cost estimates) are provided in [19]. The average value of this range is also calculated. Based on the available data and for illustrative purposes, two different strategies are assumed to assess adaptation investment needs: • The first strategy aims at reducing climate change risk, for example by building a defence that can only be overcome in a certain percentage of the cases by a given year under one of the RCP scenarios. In this case we have defined 5% and 0.5% of the cases by the year 2100 under RCP 8.5. In other words, this option requires building an infrastructure to protect from sea-level rise percentiles 95th and 99.5th. We have named this strategy as "risk tailoring".

•
The second strategy consists of building defences of standard height (e.g., 2 m or 3 m) and comparing the protection level and costs with the "risk tailoring" strategy.
The costs of adaptation investment for each city and scenario are then compared to the accumulated costs of inaction estimated previously in Section 3.1.2, to determine in which cases the benefits of adaptation (in terms of avoided damage or costs) exceed its costs. Note that for simplicity it is assumed defences protect the city of coastal flood heights smaller or equal to their height, but we acknowledge that waves could act on adjacent areas or circumvent the defences in some cases.
A summary of the methodological steps followed in this section is described in Figure 6 below. Figure 6. Summary of the methodological approach followed to estimate adaptation investment needs in each city under three sea-level rise scenarios. Investment costs are then compared to the accumulated costs of inaction to assess adaptation benefits.
Discount rates can also be incorporated into the modelling. On this occasion, however, we have decided not to include them for two main reasons. First, setting the appropriate discount factor may become a rather difficult task, especially when such long terms are considered, as fat tails may exist and potential damage (even with very low probability) can be so high [43,44]. There is plenty of literature discussing this issue [45][46][47] and no clear consensus exists on how to address this (see [48] for a more detailed discussion). Small variations in how the discount rates are applied may have substantial effects on the economic damage and the investment results. Second, in this study we are interested in analysing the decision of inaction and investing in adaptation without the interference of other factors, so we chose to avoid their effect on the calculations. The higher the discount rate the lower the value of the benefit (or costs) will be in the future, but there are other factors that may also substantially affect the results that have not been considered, such as the growth rate in the value of the properties at risk. In fact, one could expect that damage will increase as the value of the properties increase, and therefore, it is the difference between the growth rate and the discount rate that really matters. The impact of discount rates on actual values of investments (or benefits) occurring over long periods of time is always very significant. In any case, with net discunt rates of 1% and 2%, investing in adaptation would still be a good decision in our study (see Table S10 in the Supplementary Materials).

Local Sea-Level Rise and the Costs of Inaction
We calculate three sea-level rise percentiles for each city and the accumulated damage in 2030, 2050 and 2100. Table 1 shows the results in 2100 for the 10 coastal cities with the largest population, under RCP 8.5. The results for all cities and scenarios are provided in the supplementary information. We present the RCP 8.5 in Table 1 because of the greater influence of this RCP on the sea-level rise risk [49]. Note that Bilbao, Valencia and Barcelona are the coastal cities with the largest expected accumulated damage in the case of inaction. Both the sea-level rise percentiles and the damage grow rapidly over time, particularly in the second part of the century, in line with studies for other cities worldwide [49]. An illustration of accumulated expected damage for four cities in the top ranking of damage is shown in Figure 7. To show that averages and median values may differ substantially we present the differences in damage for some cities and years in Table 2. Average damage have been calculated using the full distribution of sea-level rise probabilities, and the damage curves are shown in Figure 5. Damage in Table 2 correspond to the selected years, and they are not accumulated data. As expected, by 2100, differences in mean and average values are very important. This is mainly driven by two effects: (1) the shape of the sea-level rise distribution and (2) the shape of the damage curves. The main and very important conclusion here is that, in the long term, the use and estimation of median values (50th percentile) provide insufficient information and can lead to underestimating coastal risks and consequently to under protection. The methodology proposed in this paper should help overcome this limitation by offering complete information on the risk faced.
In more detail, it can be noted that the shape distribution effect is caused by skewness. Positive skewness is obtained when the distribution has an asymmetric tail extending toward more positive values. In these right-skewed distributions, the mean is greater than the median, and the former is affected by extreme sea-level rise values. The skewness found for Barcelona, Lisbon, Valencia, Porto and Bilbao has also been included in Table 2. Note that skewness increases with time, causing a growing impact of extreme values in the mean values of sea-level rise. Table 2. Differences in the six largest cities between expected annual damage and damage using the 50th percentile under RCP 8.5. The skewness of the sea-level rise distribution is also presented for each city.  Table 3 shows the accumulated damage for a total of 62 Iberian cities and per country for the three scenarios. Damage for RCP 8.5 are very significant, but even in the most favourable scenario (RCP 2.6) important accumulated damage are expected due to sea-level rise. In this case, we focus on the "risk tailoring" strategy of building protective defences of a height that would only be surpassed in 5% and 0.5% of the cases (under the scenario RCP 8.5 in 2100). These are the heights for the 95th and 99.5th percentiles. Results are shown in Table 4. One can see that inaction is costlier than implementing adaptation in all cases, as expected damage are much greater than the adaptation costs. If defences are to be exceeded only in 5% of the cases, this means that protection height in the top cities with the largest damage would need to be higher than 1 m, and between 1.61 m and 1.80 m to avoid damage in 99.5% of the cases. Table 4 shows an interval (minimum and maximum values) of infrastructure construction costs taken from [19] for each city, depending on its characteristics and defence height. The average is the mean of these two values.  Barcelona  2060  113  171  318  595  459  859  388  727  Lisbon  946  119  181  223  425  323  614  273  520  Valencia  2504  102  161  326  645  472  932  399  788  Porto  602  112  174  87  164  126  236  106  200  Bilbao  4592  120  180  424  702  613 1,015 518  858  Málaga  832  111  168  127  221  184  319  155  270  Palma de Mallorca  1288  119  176  240  531  347  767  293  649  Alicante  991  102  161  164  289  237  417  200  353  Vigo  551  123  184  154  283  223  409  189  346  Gijón  945  122  182  211  348  305  503  258  425

The Economic Damage of Sea-Level Rise
In this paper, we propose a model for the calculation of accumulated expected damage under uncertainty. The model uses an expanded version of the projected sea-level rise percentiles [9] and a deterministic function that depends on flood height (in our case, sea-level height) [19]. The combination of both provides a group of stochastic damage distributions that allow us to calculate annual expected damage and, consequently, also the expected accumulated damage. Accumulated average damage in all 62 cities of our sample exceed 1700 million euros in 2030, and the difference between the results under RCP 4.5 and RCP 8.5 is 45 million euros. However, by the end of the century, accumulated damage reach 41,200 million euros under RCP 4.5 and more than 50,400 million euros in the highest emission scenarios (RCP 8.5). Accumulated damage increase by more than 20 times by 2100 and the difference between RCP 4.5 and RCP 8.5 could reach 10 billion euros (Table S8 and Table S9).
Furthermore, our results show that limiting the assessments to median values (50th percentile) significantly underestimates the potential damage. While differences between median and average values might be small by 2030, they increase considerably by one order of magnitude by the end of the century. For example, in Barcelona the difference between median and average damage is 0.5 million euros in 2030, but increases to almost 4 million euros in 2100 (Table 2). This difference occurs because the shape of the sea-level rise distribution is positively skewed, i.e., the distribution is not symmetrical but has a heavier upper tail The shape of the distribution of the damage is also another cause of important underestimations in the medium term when calculating expected damage. These findings are consistent with previous studies that warned about the larger potential risk of climate-induced impacts.
Damage costs do not account for coastal erosion or ecosystem loss, impacts that are both expected to be relevant in the Iberian Peninsula. Additionally to their intrinsic value, ecosystems provide a number of services to people that can be monetised [50]. The value of services such as storm protection or erosion control provided by salt marshes and mangroves worldwide is estimated to be 194,000 $/ha/year [51], which has not been accounted for in this study. Of course, one should acknowledge that other important factors such as shoreline evolution have to be integrated into a cost-benefit analysis to account for the complexities of coastal defence solutions, as argued earlier by other authors [52]. In this case, we have simplified this part of the analysis to focus on the impact of uncertainty on the economic estimates but by no means do we neglect the need to integrate those factors.

Comparing the Costs of Inaction to Protection Investment Costs
Two different adaptation options have been explored in this study: the first is based on tailoring the level of risk cities might decide to protect themselves from. This is illustrated through the assumption that coastal or city managers decide to protect each city for 95% or 99.5% of the cases under RCP 8.5 by 2100. In the first case, with protection strategies to face 95% of the cases, investment needs in the largest coastal cities by population would range between 87 (Porto) and 1015 (Bilbao) million euros. Investment costs almost double if a higher protection threshold (99.5%) is considered, and these would vary between 164 (Porto) and 1015 (Bilbao) million euros. The second adaptation option explored the investment costs needed for certain protection heights (2 and 3 m). In the case of 3 m protection infrastructures, construction costs range between 404 and 2368 million euros.
An important finding of this analysis is that adaptation costs in the long term are much smaller than the increasingly expensive costs of inaction, and thus, investing in adaptation is a good decision when comparing costs and benefits of the actions, a finding in line with previous research carried out in this area of study [53].
Of course, one should acknowledge that many other adaptation options that have not been considered in this paper may exist, and that many other criteria other than economic costs and benefits may be worth being taken into account when making such decisions. Another clear finding is that adaptation investment needs will be smaller under more favourable scenarios (RCP 2.6 and RCP 4.5). However, even under the most optimistic scenario (RCP 2.6), expected damage will be very important in the second half of the century. In other words, despite strong emission reduction efforts being really effective, adaptation will be inevitable. This is to highlight the importance of the need to implement both mitigation and adaptation policies.
Our findings show that not adapting to climate change is not, by any means, a good strategy in the medium and long term. Note that, even if many types of adaptation options should be considered when protecting coasts from climate risks, the building of defence infrastructures that require strong investments would be justified based on the accumulated damage by 2100, which are much greater than the investment costs of protection. Moreover, the adaptation strategies considered in this paper are shown to be very cost-effective in every city studied and reduce considerably the probability of experiencing high economic damage by the end of the century.

Policy Implications
In this paper we propose a method to avoid the underestimation of climate risk and estimate what the size of it may be for the case of 62 cities in the Iberian peninsula. We have used two infrastructure-based adaptation options for illustrative purposes. This has been done because the data needed for the analysis is available in these cases, and not because we argue that these solutions should be the ones implemented. Results show that the underestimation of damage can be very important if we consider median values instead of the average (expected) damage. Therefore, we argue that strong efforts should be made to understand the full probability distributions of sea-level rise and the consequent economic damage, for each city, emission scenario and year. Not accounting for all these may lead to investment decisions (and even maladaptation) that underestimate future risks and cannot respond to them.
The method can also be applied to adequately assess the cost effectiveness of other adaptation options when data becomes available. The purpose of the paper has been to propose a methodology and illustrate the case for sea-level rise and hard adaptation measures for which good data was available. Other pieces of research should help us to better consider alternative adaptation options or even other impacts related to the adaptation options considered. Nonetheless, the main message of this paper remains, not accounting for the full distribution of sea level rise as well as damage costs is a clear and very significant underestimation of climate risks that may lead to inadequate policy decisions.