Communities have turned to nature-based solutions to bolster coastal resilience and protection in the face of rising sea levels and increasing storminess. Marshes have significant wave attenuation properties and can play an important role in coastal protection for many communities (Gedan et al., 2011; Temmerman et al., 2013). Previous field, lab, and modeling research has documented the ability of marsh vegetation to reduce the energy and height of storm waves. Despite both making landfall in southern Louisiana in 2005 as category 3 hurricanes, Hurricane Rita was less deadly than Hurricane Katrina, largely because Rita traveled over at least 30 km of wetland before reaching a major populated center (Day et al., 2007). A flume experiment by Möller et al. (2014) using natural marsh found that up to 60% of observed wave height reduction was due to the presence of vegetation. This builds on the meta-analysis of Shepard et al. (2011), which found that marsh vegetation attenuates smaller, more frequent waves and plays a significant role in shoreline stabilization. Wamsley et al. (2009) modeled Hurricanes Katrina and Rita on southern Louisiana marshes and found that restoration decreased storm wave heights, though the amount of attenuation was variable among different marshes.

Many restoration projects seek to maximize the ecosystem service of wave attenuation, but how much marsh restoration is enough to deliver benefits remains unclear. Salt marsh restoration projects often employ a combination of techniques, including increasing tidal flow through removal of existing restrictions (Burdick and Roman, 2012), increasing marsh elevation (through natural sedimentation associated with increased flow or augmented sedimentation such as thin-layer deposition; U.S. Army Corps of Engineers, 2022), and increasing vegetation cover through physical planting of appropriate native species (Sparks et al., 2013). While wave attenuation is often cited as an important benefit to marsh restoration, and studies have quantified wave attenuation in the field (Möller and Spencer, 2002; Lightbody and Nepf, 2006; Jadhav et al., 2013), lab (Möller et al., 2014; Rupprecht et al., 2017), and in model settings (Loder et al., 2009; Wu et al., 2016; Marsooli et al., 2017), wave energy reduction as a function of marsh restoration is less studied.

Reduction in wave height and subsequent wave energy has cost-effective implications for coastal resilience; reduction of wave energy, in turn, reduces wave-driven flooding. Salt marshes and mangrove systems have been found to be two to five times less expensive than submerged breakwaters for wave heights up to 0.5 m (Narayan et al., 2016). Narayan et al. (2017) found that during Hurricane Sandy in 2012, wetlands in the northeastern United States avoided more than $600 million in direct flood damage. Management decisions, however, consider effort and cost trade-offs in marsh restoration scenarios. Sparks et al. (2013) found that small-scale experimental Juncus roemerianus plots planted at half density were largely more or equally cost-effective for both planting cost and effort when compared to plots planted at full density. Smith et al. (2018) analyzed the resistance of various types of shorelines in North Carolina, United States, to Hurricane Matthew (2016), and found that constructed/planted salt marshes with an offshore rock sill were more resistant to the hurricane’s impacts than both traditional hardened shorelines and natural marshes. Given this context, research into wave attenuation as a function of marsh vegetation and, indirectly, marsh restoration, provides valuable insight critical to guiding efforts to optimize funding, effort, and overall cost effectiveness of restoration projects.

This study uses a series of model simulations to determine empirical relationships among wave attenuation, percent vegetated, and marsh unvegetated-vegetated ratio (UVVR). The empirical relationships presented in this study span a variety of characteristics (including vegetated/unvegetated ratio, vegetation distribution, storm intensity, and general marsh morphology) and can be applied by restoration practitioners to determine appropriate restoration planting targets to maximize wave attenuation.

Studies have quantified wave attenuation by marsh vegetation in field (Möller and Spencer, 2002; Lightbody and Nepf, 2006; Jadhav et al., 2013) and lab (Möller et al., 2014; Rupprecht et al., 2017) settings. Highly sophisticated and often computationally expensive models have been used to examine wave attenuation across specific locations (Loder et al., 2009; Marsooli et al., 2017) or within relatively small spatial constraints (Wu et al., 2016). Framing wave energy reduction as a function of marsh restoration, however, has been less studied. This study was specifically designed with a management perspective in mind, using generalized and representative model input to broadly look at relationships between marsh vegetation distribution and wave attenuation in a functional restoration context. Practitioners may be more familiar with and better able to implement percent cover measurements as part of an intensive monitoring program. UVVR measurements, particularly the datasets available for entire United States coastline through the U.S. Geological Survey (Couvillion et al., 2021), may be more appropriate for identification of vulnerable areas suitable for restoration. As such, this study has been framed in terms of both UVVR and percent vegetative cover to maximize its utility in multiple applications.

The amount of vegetation cover in a marsh, in tandem with its elevation capital, influences its ability to reduce wave energy. Regardless of marsh morphology, a marsh with 50% vegetated (UVVR 1) is likely able to reduce storm wave energy by 95% within the first 100 m; which represents a strong benchmark value for hazard mitigation. Marshes with ponding morphology are better able to reduce wave energy compared to marshes with channel morphology, especially at lower wave intensity and reduced vegetation scenarios. This is likely due to a focusing effect of the channels, which can funnel larger waves further than if they were traveling over a smoother, more vegetated topography. Marshes with a leading mudflat performed better than channeled and ponded marshes and nearly as well as the fully vegetated scenarios. This is likely due to a combination of consistent vegetation, uninterrupted by major topographic features, and the general ability of the system to reduce wave heights and subsequent wave energy through increasing platform elevation and decreasing water depth. Though model runs with no vegetation indicate that wave energy is reduced substantially by the reduction in water depth and its associated wave breaking, a 95% reduction in wave energy when including vegetation is of critical importance. In 50% vegetated (UVVR 1) scenarios, for example, wave heights fall from almost 2 m to approximately 40 cm in the high-intensity wave scenario and from 0.9 m to less than 20 cm in the low-intensity wave scenario. While this study is limited by specific vegetation configurations and storm conditions by design, the 50% vegetated (UVVR 1) benchmark is consistent across a wide range of wave intensities and marsh morphologies.

Given this benchmark, a marsh restoration project designed with at least 50% vegetated cover (UVVR ≤ 1) could maximize the ecosystem service of wave attenuation. This success metric can be incorporated by practitioners when determining overall planting density and distribution. While planting distribution and density requirements may vary from project to project, maintaining at least 50% vegetation (UVVR ≤ 1) in a marsh at least 100 m in width could provide substantial coastal protection from storm waves. The 50% vegetation benchmark is supported in the literature; small-scale experimental plots of Juncus roemerianus planted at half density (roughly equivalent to UVVR∼1) in the Grand Bay National Estuarine Research Reserve in Mississippi, United States, were similarly or more cost effective in regards to both planting cost and effort than planting the plots at full density (roughly equivalent to UVVR ≤ 0.1), particularly because total vegetated coverage was similar between both the full and half density plots approximately 2 years after planting (Sparks et al., 2013). While our study randomly placed vegetation throughout the model domain, specific planting patterns (for instance, grouping plants in clusters or clumps instead of planting the plugs in a systematic grid) may also substantially increase future plant yield and survival (Silliman et al., 2015). These decisions will become even more important as the knowledge and practice of nature-based solutions continues to expand (Castagno et al., 2021).

Considering trade-offs is important for maximization of restoration success and cost-effectiveness. In situations where only a smaller leading edge can be planted, maintaining at least 75% vegetated cover (UVVR ≤ 0.33) in a 50-m-wide area will provide an 80–90% reduction in wave energy. In the case of homeowners, who may only be able to restore a smaller stretch of marsh in front of their properties, a 10 m vegetated edge under low-energy conditions will provide >50% reduction in wave energy and >80% reduction under high-intensity conditions. Practitioners, planners, and managers can use the relationships presented in Figure 4 to decide trade-offs, e.g., planting a 30-m leading edge at 50% vegetated cover (UVVR 1) may be sufficient if restoration emphasis is placed primarily on wave energy reduction of high-intensity storms.

It is important to consider, however, that a restored marsh’s lifespan is largely dependent on sediment supply (Ganju, 2019), so a sparsely vegetated, restored system that lacks sufficient sediment input will have a limited lifespan. Marsh lifespan calculations for the model domain indicate that 50% vegetated cover (UVVR∼1) corresponds to a lifespan of ∼200 years under background scenarios. With 1.0 m SLR by 2100, the maximum scenario considered in this study, marsh lifespan decreases to 75 years. Alternatively, 90% vegetated cover (UVVR ∼ 0.1) corresponds to a model marsh lifespan of ∼3,500 years under background SLR conditions and ∼200 years for 1.0 m SLR. It is important to consider that this is a conservative case; average elevation for the model marsh at 1.2 m is already relatively high, and marshes with lower elevation capital will have even shorter lifespans.

Desired lifespan of the restoration project should also be considered when determining vegetation density. For example, assuming moderate SLR projections (0.5 m SLR by 2100) and a baseline price of $1.25 per 5-cm plug of Spartina alterniflora (2021 bulk-purchase value from New England Wetland Plants, a common distributor for New England restoration projects) with 10 plugs per square meter, planting the model domain at 50% cover (UVVR 1) would cost ∼$614 thousand for a marsh with a lifespan of 120 years, whereas planting the model domain to 90% (UVVR 0.1) would cost less than twice as much (∼$1.1) million for a lifespan almost four times that of the reduced density scenario. Planting the model domain to 90% instead of 50% would also provide increased wave attenuation benefits, with percent reduction in wave energy increasing to ∼99% under medium- and high-intensity wave scenarios.

The relationships between UVVR and wave attenuation can also be applied to existing marshes to determine their utility for coastal protection in attenuation of storm waves. UVVR and percent cover are directly related, but UVVR is determined through aerial imagery and less labor intensive than boots-on-the-ground field studies (Ganju et al., 2016). As previously mentioned, UVVR values are available for entire contiguous United States coastline through the U.S. Geological Survey (Couvillion et al., 2021) and can be generated through analysis of existing infrared aerial photography (Ganju et al., 2016). A marsh area of ≥100 m with a UVVR value of ≤1 (≥50%) has the capacity to reduce wave energy by ∼95%. Spatial analysis of UVVR across multiple marshes or within individual marshes can identify areas that are particularly capable of reducing storm wave energy (highly vegetated) or that may benefit from restoration (UVVR ≥ 1). While more resource-intensive, surveys incorporating aerial imagery for UVVR analysis have great utility in assessing the resilience of larger areas of marsh as part of an initial baseline assessment of a site or a long-term monitoring program.

Focusing marsh protection and restoration efforts specifically on flood risk reduction has the potential to significantly bolster the resilience of vulnerable coastal communities. Analysis of coastal protection ecosystem services for hazard-mitigation valuation and insurance practices has already begun for coral reef (Reguero et al., 2020) and mangrove systems (Menéndez et al., 2020). Incorporating this understanding of how much restoration is necessary to provide significant wave energy benefits into Federal Emergency Management Agency Benefit-Cost Analyses for hazard mitigation or future flood risk models strengthens the argument for nature-based solutions to coastal protection and shoreline stabilization. This is of particular importance in areas where marshes are the primary form of natural coastal protection (e.g., the northeastern United States, where the climate is prohibitive for mangrove or coral reef protection, among other locations). Lifespan estimates are an important consideration when selecting vegetation density, since marshes with greater elevation capital and/or more vegetation have longer lifespans and tend to be more resilient to sea-level rise. Since the relationship between UVVR and wave attenuation is roughly linear within UVVR’s functional limits for wetlands, the straightforward equations presented in this study can be applied easily in a wide variety of contexts. Future research, including the application of more sophisticated or detailed models, analysis of model sensitivities to a spectrum of vegetation and wave characteristics, and field-based ground truthing could enhance the ability to refine these relationships and our understanding of how marsh restoration can be leveraged to maximize coastal protection benefits.

This study found a substantial reduction in storm wave energy when the first 100 m of a marsh is at least 50% vegetated, though lifespan estimates, including both marsh elevation and desired UVVR, for restored marshes are important factors when considering overall restoration investment and return decisions. As coastal communities continue to grow more vulnerable to sea-level rise and increased storminess, it becomes even more important to maximize coastal protection benefits through nature-based solutions, including marsh restoration. The benchmarks and empirical relationships presented in this study have significant implications for coastal practitioners and managers seeking timely performance goals and metrics for marsh restoration, enhancement, and creation.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

KC and NG conceived the manuscript. KC performed the model runs, analyzed the results, and wrote the first draft of the manuscript. NG, MB, AB, and SS offered critical insight and edits to the manuscript. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.