## Introduction

The impacts of coastal flooding are substantial and growing given population growth, coastal development and climate change1,2,3,4. Unfortunately, these risks are often discounted in development choices5,6. Coastal development also causes losses in coastal habitats, which will further heighten risks7,8,9,10. There is a pressing need to advance risk reduction and adaptation strategies to reduce flooding impacts4,6,11.

Coral reefs serve as natural, low-crested, submerged breakwaters, which provide flood reduction benefits through wave breaking and wave energy attenuation. These processes are functions of reef depth and secondarily rugosity12,13,14,15,16. The flood reduction benefits of coral reefs and other coastal habitats are predicted to be high and even cost effective in comparison to traditional approaches13,17,18,19.

Reefs have experienced significant losses globally in living corals and reef structures from coastal development; sand and coral mining; overfishing and destructive (e.g., dynamite) fishing; storms; and climate-related bleaching events8,20,21,22,23. There is clear evidence of reef flattening globally from the loss of corals and from the bioerosion and dissolution of the underlying reef carbonate structures14,24,25,26,27. Not all reefs are declining, and reefs can recover from bleaching, overfishing and storm impacts, but the overall pattern of significant losses across geographies is clear20,21. Scientists and international agencies, including the Intergovernmental Panel on Climate Change and the World Bank, have expressed grave concern about the current and future condition of coral reefs, and the loss of the benefits they provide28,29,30.

Although reefs and other coastal habitats can provide flood protection benefits, they are rarely accounted for directly in coastal management, because these services are not quantified in terms familiar to decision-makers, such as (loss of) annual expected benefits12. Provisioning services such as fish or timber production, which represent products that are harvested from ecosystems, have been valued globally and considered in resource management decisions31,32. Regulating services, which represent benefits provided when ecosystems are left intact such as flood and erosion reduction, have rarely been rigorously valued globally using process-based models, although there is work towards this end33,34.

Better valuations of the protection services from coastal habitats could inform decisions to meet multiple objectives in risk reduction and environmental management35,36,37,38. One important pathway through which these services may be considered is in national economic accounts35. The United Nations has identified a general approach for assessing ecosystem services in these accounts39. The World Bank has developed guidelines for how these approaches could be applied to assess risk reduction benefits of coral reefs to inform decisions on coastal zone management, development loans, and adaptation grants12.

Natural flood protection benefits are amenable to spatially explicit quantification, because of the broader work on assessments of flood risks and artificial coastal defenses. Robust, process-based flooding models are widely used in the engineering and insurance sectors to inform risk management and development decisions. These process-based models value benefits by comparing the flood damages avoided in scenarios with and without structures (e.g., seawalls or reefs)12,40. These models have recently been used to quantify ecosystem benefits in local studies (e.g., within bays) and in a couple of national studies41,42,43,44. However these flooding studies do not provide a probabilistic assessment of economic risk at any scale.

Using process-based flooding models, we estimate the annual expected benefit of coral reefs for protecting people and property globally. Building on earlier methods and recommended approaches3,12,45, we compare flooding for scenarios with and without reefs for four storm return periods. The without reefs scenarios assume only a decrease of 1 m in the height and roughness of coral reefs. We estimate the land, population and built capital flooded across all coastlines with coral reefs to a 90 m resolution (Fig. 1). We then derive the annual expected benefit of coral reefs for flood damage reduction from local to global levels.

## Results

### Assessing damages and estimating annual benefits

We followed existing approaches for assessing the damages to built capital as a function of the flooding level4. We calculated the percentage of built capital that has been damaged (D) for a given flooding level h and a certain coefficient k that must be calibrated as D(h) = h/(h + k). This curve indicates that as flooding level increases, the percent of damages to built capital also increases. While there is debate about the right k to choose, we have followed others in using k = 0.54, which means that the built capital flooded at 1 m of depth loses 50% of its value. We follow standard terminology where the total built capital flooded is the exposure of assets and the value lost is the damages. The economic benefits of flood protection are the avoided damages.

In addition to assessing risk and damages for particular events (e.g., 100-year storm event), we also examined average annual expected loss90. To estimate annual risk, we integrated the values under the curve that compares built capital damaged by storm return period, i.e., the integration of the expected damage by the probability of the storm events4.

### Sea level rise

We assessed the potential added impacts of sea level rise and reef loss by considering the additional land area flooded in 2100 by storm return period under a business-as-usual (high) emissions scenario, representative concentration pathway (RCP) 8.5. To estimate the added effects of sea level rise and reef loss, we recalculated the flood heights at every cross-section worldwide considering all the prior factors and adding the local relative sea level rise projected in Slangen et al.61 for RCP 8.5 by 2100 (see Supplementary Information for more details). Once the projected flood heights were calculated, the assessment of flooding level and total area of land affected followed the same approach as above.

### Sensitivity analyses

We conducted extensive sensitivity analyses for parameters across the models and find that the results are robust to changes in the key parameters across their natural ranges of variability. These tests are summarized here and described more fully in the Supplementary Information. The flooding model is the most critical model for estimating flood heights. After testing all parameters in the model, we identified that the estimates for reef friction, water depth, and the wave breaking parameters were the main ones affecting the run-up contribution to flood heights. We examined the effects of changes in these parameters by incrementally changing them across their range of variability and running tens of thousands of profiles across different reef types (Supplementary Table 4). In sum, changes in the estimates of the friction (Cf = 0.08–0.20) and wave breaking (γcoral = 0.2–0.6) parameters have only small effects with only approximately 10% changes in run-up from the minimum to maximum of these parameter estimates. Changes in water depth from 0.1–1 m had the largest effects on the results. Each 10 cm change in depth changed the run-up contribution by ~2%. Additional uncertainties of input data such as digital elevation models or population data on global flooding models have been discussed by Hinkel et al.4

We also did sensitivity analyses on the damage function model with other parametrizations of k (k = 0.2, 0.3, 0.4). Lowering k lowers the total value of the built capital damaged, but has little effect on the relative effectiveness (% difference) of reefs for risk reduction. Lower k values slightly increase the relative effectiveness of reefs making our use of k = 0.5 the most conservative for comparisons.

### Data availability

All results are mappable and downloadable at http://maps.oceanwealth.org/. The underlying data sets including Global Waves and the Python source codes for key analyses are available on request from IHCantabria at ihdata@ihcantabria.com.