Demonstrating the value of beaches for adaptation to future coastal flood risk

Cost-effective coastal flood adaptation requires a realistic valuation of losses, costs and benefits considering the uncertainty of future flood projections and limited resources for adaptation. Here we present an approach to quantify the flood protection benefits of beaches accounting for the dynamic interaction of storm erosion, long-term shoreline evolution and flooding. We apply the method in Narrabeen-Collaroy (Australia) considering uncertainty in different shared socioeconomic pathways, sea-level rise projections, and beach conditions. By 2100, results show that failing to consider erosion can underestimate flood damage by a factor of 2 and maintaining present-day beach width can avoid 785 million AUD worth assets from flood damage. By 2050, the flood protection and recreational benefits of holding the current mean shoreline could be more than 150 times the cost of nourishment. Our results give insight on the benefits of beaches for adaptation and can help accelerate financial instruments for restoration.

Flood maps. Land parcels value, area and type Building value, area and type.

Beach recreational value assessment
Obtention of the avoided loss of recreation by subtracting the recreational value of the scenarios with erosion from the recreational value of the scenarios without erosion. We measured beach recreation using contingent valuation (travel cost method) following [9].
Available beach area. Value of beach recreation per unit area.

Benefit-cost proxy
Comparison of the avoided flood damage and loss of recreation associated with SLR with the cost of holding the mean shoreline (excluding seasonal and inter-annual variations) with nourishment.
Avoided flood damage. Avoided loss of beach recreation.
Cost of nourishment.
Table S1 Summary of modelling approaches and data required for their application associated with the different steps of the methodology.

Steps Assumptions Uncertainty Limitations
Nearshore downscaling SLR is the most uncertain climate driver of coastal flooding and erosion. Wave conditions and storm surges will not change in the future.
Range of SLR scenarios (from 0.100 m to 2.321 m) that results from considering 2 emissions scenarios, SLR driving processes associated with 2 confidence levels, and Inherent to the skill of the wave generation model to simulate physical processes (e.g., wave diffraction poorly represented).
The bathymetry does not change beyond the depth of closure.
3 trajectories associated with 3 percentiles ( [10]). Discarding the use of wave and storm surge projections because of the sign of the change and its uncertainty in the area ( [11; 12]). Propagation of the full frequency-direction spectra rather than the aggregated parameters to have a highfidelity description of wave climate ( [13]).
Long-term topobathymetry update SLR is the main driver of long-term morphological changes, as we did not identify any significant long-term trend from the subaerial beach volume time-series analysis. The present-day topobathymetry is in equilibrium.
Associated with SLR, as we developed one long-term topo-bathymetry for each SLR scenario.
Inherent to the profile translation model, as the profile kinematics considered are a simplification of reality.

Storm definition and
surf-zone storm modelling The peak of the storm depends on wave and sealevel conditions and the duration of the storm depends on wave conditions exceeding a threshold. A set of calibration parameters ( [14]) is representative for all the profiles.
30-year storm determined empirically, as we had 30 years of wave data and so we avoided extrapolation. Associated with SLR, as we combined the present-day 30 years storm with each SLR scenario.
Inherent to the storm definition method and the skill of the hydromorphodynamic model to simulate physical processes (e.g., beach flattening). As we run XBeach in its 1D version, we missed 2DH hydrodynamics that can occur locally (e.g., rips).

Short-term topobathymetry update
The present-day topobathymetry is in equilibrium.
Associated with SLR and the two magnitudes of storm erosion (at the peak of the storm and after passing the storm), as we developed two short-term topo-bathymetries over each long-term topobathymetry.
Inherent to the skill of the storm morphodynamic model and the topobathymetry interpolation procedure.

Coastal flood modelling
The short-term topobathymetry that incorporates erosion at the peak of the storm represents the baseline for the storm condition (flooding over an uneroded beach). The short-term topobathymetry that incorporates erosion at the passing of the storm represents the baseline for the poststorm condition (flooding over a beach previously eroded by a recent storm). Land uses will not change in the future.
Associated with SLR and the two beach conditions (storm and poststorm), as we obtained two flood maps for each SLR scenario combined with the present-day 30storm considering two shortterm topo-bathymetries per each SLR scenario.
The hydraulic model is forced with hydrodynamic conditions computed externally and runs over an emerged topo-bathymetry updated externally (decoupled processes). Inherent to the skill of the hydraulic model to simulate physical processes (e.g., it solves a simplification of the shallow water equations in large cells).

Flood protection
The value of land and buildings will not change in the future.
Associated with SLR and the two beach conditions, as we obtained the avoided flood Inherent to the vulnerability functions. value assessment The The vulnerability functions will not change in the future. Land uses will not change in the future. Future damage (damage subject to repair or replacement) occur due to the present-day 30-year storm over SLR, as we found that SLR inundation does not reach any buildings or infrastructures. There is no loss of economic activity (loss of profit) associated with the flooding of commercial buildings.
damages for each scenario (storm and poststorm conditions combined with SLR scenarios).

Beach recreational value assessment
Each unit area provides the same recreation and is worth the same. Users will have the same preferences in the future. The discount rate is fixed and does not vary based on the risk of loss of beach area.
Associated with SLR and the two beach conditions (storm and poststorm), as we obtained the avoided loss of beach recreation for each scenario (storm and poststorm conditions combined with SLR scenarios).
Inherent to the approach used to compute the accounting value of beach recreation.
Benefit-cost proxy Sediment availability. One nourishment intervention per scenario.
A single price for regeneration campaigns. The cost of nourishment will not change in the future.
Associated with SLR, as we obtained the benefit-cost proxy for each SLR scenario. Storms are part of the TWL but no storm erosion is considered.
First-pass benefit-cost ratio that simply results from the quotient of the value of the beach and the value of its conservation.

Mean sea-level rise scenarios considered
One of the main sources of uncertainty in future climate is mean sea-level rise (SLR). We have chosen a set of SLR scenarios that cover a wide range of values and combined them with the same storm. This wide range is given by considering: 2 emissions scenarios formulated in terms of shared socioeconomic pathways and their associated level of radiative forcing (SSPx-y) to understand the sensitivity of our decisions to different futures; 2 confidence levels to consider SLR-driving processes of medium and low confidence; and, for each combination of emissions-confidence scenarios, 3 potential SLR trajectories associated with 3 percentiles of the distribution of the results of the climate models included in the AR6 ( [10]). For a given scenario, each SLR trajectory therefore shows an evolution of the SLR over time with a different acceleration rate.
As for time horizons, we consider 2050 and 2100. They are two milestones given by the IPCC and adopted by users for adaptation needs. There is ongoing research to assess the suitability of these milestones from surveys conducted to stakeholders. [15] showed that 2100 is the time horizon most widely used for SLR planning in many countries, and that it is followed by 2050.
For both 2050 and 2100, we consider 12 different SLR values that cover a range of futures that expands from 0.100 m (SSP2-4.5 medium-confidence 5th percentile) to 2.321 m (SSP2-4.5 low-confidence 95th percentile). We show all these values in Table S3 (medium confidence AR6 SLR regional projections near the study beach) and in Table S4 (the same as in Table S3 but for low confidence).
The emissions scenarios considered are the AR6 SSP2-4.5 and SSP5-8.5, which correspond to temperature increases in 2100 of 2.7°C and 4.4°C, respectively. The choice of these scenarios is due to the fact that it has been recognised in the literature that their predecessors in the AR5 (RCP4.5 and RCP8.5) are the most widely used in many countries for SLR adaptation planning ( [15]).
• The SSP2-4.5 is an intermediate scenario. CO2 emissions are near current levels before starting to decline by 2050, but do not reach zero by 2100. Socio-economic factors follow their historical trends, with no significant change. Progress toward sustainability is slow, with disparate development and income growth. In 2100, the global mean temperature is 2.7°C warmer than pre-industrial levels. • The SSP5-8.5 is a very high emissions scenario. Current levels of CO2 emissions roughly double by 2050. The economy grows rapidly at the cost of the exploitation of fossil fuels and energy-intensive lifestyles. In 2100, the global mean temperature is 4.4ºC warmer than pre-industrial levels.
The range of SLR values resulting from the combination of emissions scenarios and percentiles covers the mean values of the SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5.8.5. For instance, the 5th percentile of the SSP2-4.5 is slightly higher than the 5th percentile of the SSP1-2.6 (0.100 m vs 0.081 in 2050; and 0.305 m vs 0.179 m in 2100 considering medium confidence processes) and lower than the 50th percentile of the SSP1-2.6 (0.176 m in 2050; and 0.391 m in 2100 considering medium confidence processes). The same applies for low confidence processes and for the SSP3-7.0 vs the SSP5-8.5.  The IPCC has acknowledged in its last 3 assessments reports that the main uncertainty in SLR projections is due to the limited confidence in the modelling of future melt dynamics of the Antarctic and Greenland Ice Sheet. However, it was not until the AR6 that the IPCC has presented for the first time a lowlikelihood-high impact scenario (LLHI scenario; also referred to in the literature as "high-end" scenario, [16], and "H++" scenario, [17]) showing a SLR of 1.7 m by 2100 and more than 15 m by 2300 that could not be excluded under high emissions ( [10]). Additionally, research suggests that LLHI scenarios can be useful for decision makers considering time scales up to centennial and having high risk aversion or low uncertainty tolerance ( [18]). In these cases, the emerging practice is to consider likely scenarios together with low-likelihood-high impacts (LLHI) scenarios ( [15]; [19]). Further, there is evidence that LLHI scenarios are used for virtual stress tests on critical infrastructure (e.g., Thames river barrier, or the Netherlands; [17]). In summary, the reasons for using these LLHI scenarios in this study are that: (1) they cannot be excluded yet; and (2) they can be used for some coastal adaptation problems.

Glossary
Term Definition adopted in this article Beach flood protected area Increase in flooded area resulting from flood modelling due to consideration of erosion compared to no consideration of erosion.

Beach flood protected value
The flood damage that occurs in the flood protection area. The flood protection value of the beach is therefore the benefit in terms of avoided flood damage if the present-day shoreline (or mean shoreline) were to remain fixed.

Beach nourishment
The adding of sediment onto or directly adjacent to an eroding beach ( [25]).

Shoreline
Coastline including storm, seasonal and inter-annual variations (observed coastline).
Mean shoreline Coastline excluding storm, seasonal and inter-annual variations (long-term coastline).

Resilience
The ability to bounce back and return to a previous state after a disturbance and the capacity for transformation ( [26]).

Tipping points
Critical thresholds in a system that, when exceeded, can lead to a significant change in the state of the system, often with an understanding that the change is irreversible ( [26]). Table S7 Glossary with key terms and the definitions adopted in this article.