Coastal storms pose a significant threat, causing billions of dollars in damage annually, a cost projected to increase with climate change and sea-level rise. Traditional gray infrastructure solutions like seawalls, while effective in preventing overtopping, are expensive to maintain and can negatively impact neighboring coastlines. Natural shorelines, such as marshes, mangroves, and reefs, offer wave attenuation and other ecosystem services. This research focuses on the hybrid approach of combining marshes with seawalls, leveraging the wave-dampening properties of marshes to reduce wave load on seawalls and lessen the need for costly heightening. This hybrid approach promises economic efficiency and environmental benefits. The study addresses the lack of quantitative methods to incorporate marsh wave attenuation benefits into economic analyses, which hinders the widespread adoption of such nature-based solutions.

Previous research has established the protective role of salt marshes against wave action, storm surge, and erosion. However, existing wave attenuation models often rely on empirical drag coefficients, limiting their predictive capacity across different sites and vegetation types or seasons. These coefficients lack predictability for uncalibrated conditions, including changes in vegetation characteristics between sites or due to seasonal growth patterns. The economic benefits of using marshes for coastal protection have also been explored, but a comprehensive framework integrating wave attenuation modeling and economic analysis is lacking. This research aims to fill this gap.

The study develops a 1-D wave attenuation model based on first principles, accounting for species-specific plant morphology, structural stiffness, and reconfiguration (plant movement in response to wave velocity). The model incorporates wave dissipation mechanisms such as vegetation drag, shoaling, depth-induced wave breaking, and bed friction. Model validation was performed using field measurements from two sites in the Netherlands, demonstrating good agreement between predicted and measured wave heights. A benefit-cost analysis (BCA) was then conducted to assess the economic feasibility of marsh-fronted seawalls. The benefits included avoided seawall heightening costs and the value of environmental services provided by the marsh (habitat, aesthetics, improved water quality). Costs included marsh planting and marshland creation/stabilization. Low, medium, and high estimates for benefits and costs were obtained from the literature to perform a sensitivity analysis. The benefit-cost ratio (BCR) was calculated to determine the economic justification of the marsh-fronted seawall solution. The analysis considered sensitivity to vegetation type, seasonality, storm conditions (water depth and wave height), and discount rate. A real-world case study at Juniper Cove, Massachusetts was used to illustrate the application of the model and BCA in a practical setting. The hydrodynamic conditions for 10-, 50-, and 100-year storm events were obtained from the project's design report, and the 1-D wave model was applied along ten transects to account for the mildly curved coastline.

The 1-D wave attenuation model accurately predicted wave height reduction in marshes across diverse vegetation types, demonstrating its predictive capability for different sites and conditions. Wave attenuation varied significantly between plant species (up to a factor of two), with stiffer plants like *Phragmites australis* showing superior performance, although ecological considerations may limit their use. Healthy plants showed 8–17% greater wave attenuation than dormant plants. The benefit-cost analysis demonstrated that marsh-fronted seawalls generally have benefit-cost ratios (BCRs) greater than one, indicating economic justification. The BCR is sensitive to several parameters: increasing water depth reduces wave attenuation and the BCR; increasing wave height increases the BCR; the BCR decreases with increasing marsh width due to diminishing marginal benefits; and higher discount rates reduce the BCR. The Juniper Cove case study confirmed these findings and highlighted the significant impact of plant seasonality on the BCR, with dormant vegetation yielding lower BCRs, even falling below 1.0 at discount rates ≥ 6%. The study found that environmental services contribute over 50% of the total benefits in many scenarios, emphasizing their importance in the economic evaluation of nature-based solutions.

The study's findings provide strong support for the economic and ecological feasibility of marsh restoration in front of seawalls as a nature-based solution for coastal protection. The developed wave attenuation model offers a robust tool for predicting wave reduction in marshes, improving the accuracy of economic analyses. The sensitivity analysis reveals the importance of considering site-specific factors, such as vegetation type, storm conditions, and discount rates, in project planning. The high contribution of environmental services underscores the need for comprehensive valuation of ecosystem services to ensure the sustainable implementation of such nature-based solutions. The results also highlight the importance of considering plant seasonality and the potential need for supplementary flood-response measures during periods of reduced vegetation effectiveness.

This research demonstrates that integrating marshes with seawalls is an economically justified nature-based solution for coastal protection, offering significant cost savings and environmental benefits. The presented 1-D wave attenuation model and benefit-cost analysis framework offer valuable tools for coastal planners and engineers. Future research should focus on improving methods for mapping vegetation characteristics and refining ecosystem service valuation methodologies to reduce uncertainty in economic assessments. Investigating the long-term sustainability of marsh-fronted seawalls in the face of sea-level rise and considering the combined effects of reduced wave breaking on sediment resuspension and scouring are also important next steps.

The 1-D wave model assumes wave propagation perpendicular to the shoreline, limiting its applicability to coastlines with significant curvature. The BCA relies on literature-derived values for certain benefits and costs, introducing uncertainty. The model does not explicitly account for sediment dynamics or the potential for erosion reduction at the toe of the seawall, which could further enhance the economic benefits. Furthermore, the assessment of ecosystem services relies on existing valuation methods, which may still contain uncertainties.