The Impact of Submerged Breakwaters on Sediment Distribution along Marsh Boundaries

Human encroachment and development on coastlines have led to greater amounts of armoring of shorelines. Breakwaters are a common feature along coastlines, which are used to dampen wave energy and protect shorelines from flash floods or overwash events. Although common, their effects on sediment transport and marsh geomorphology are poorly understood. To address this gap, our study quantifies the effects of breakwaters on sediment transport and marsh evolution under different wave regimes using Delft3D-SWAN, a dynamic geomorphodynamic numerical model. Model configurations used the same numerical domain, but scenarios had different sediments, waves, tides, basin slopes and breakwater distances from the shoreline to explore how waves and tidal currents shape coastal margins. Model results suggested breakwaters were responsible for an average wave damping between 10–50%, proportional to the significant wave height across all modeled scenarios. Shear stress at the beginning of the marsh and the volume of sediment deposited at the end of the simulation (into the marsh behind the breakwater) increased on average between 20–40%, proportional to the slope and distance of the breakwater from the shoreline. Sediment trapping, defined as the ratio between the volume of sediment housed into the salt marsh behind and away from the breakwater, was found to be less than 1 from most model runs. Study results indicated that breakwaters are advantageous for wave breaking to protect shorelines from the wave’s energy, however, they might also be an obstacle for sediment transport, negatively affecting nourishment processes, and, consequently, impeded long-term salt marsh survival. Identifying a balance between waves dampening and shoreline nourishment should be considered in the design and implementation of these structures.


Introduction
Coastal environments are the most economically important and intensely used among all areas inhabited by humans [1,2]. In fact, it has been estimated that around half of the world's population presently lives within 200 km of the coast, and this value is likely to double by 2025 [1,3]. Coastal regions are both widely regarded and protected, due to their immense ecological, social and economic benefits, e.g., essential fish habitat, food production, transportation hub, etc. [2,3] Concern over the decline or loss of valuable coastal ecosystem services has been mounting over the past several decades due to growing threats to their long-term viability (e.g., human encroachment, habitat degradation, sea-level rise). To protect and maintain the boundaries of coastal regions, a common practice is to transform, alter, and armor shorelines with a variety of structures, such as seawalls, breakwaters or bulkheads, that reduce waves energy and shoreline erosion [4][5][6]. However, a full accounting of the ecological damage associated with these structures is rarely performed, considered, or even well understood prior to infrastructure construction, but may be substantial once completed [4,6,7]. For example,

Model Description
We present modeling results on how breakwaters affect the resilience of salt marshes under different wave conditions in a rectangular basin with rectangular cells, whose long cell dimension is parallel to the coast. The different run configurations use the same domain, but with different sediments, waves, tides, basin slopes and distances of the breakwater to the shoreline.
Delft3D [33,34] is an open-source computational fluid dynamics package that simulates fluid flow, waves, sediment transport, and morphological changes at different timescales. An advantage of Delft3D is the full coupling of the hydrodynamic and morphodynamic modules, so that the flow field adjusts in real-time as the bed topography changes. The equations of fluid motion, sediment transport, and deposition are discretized on a 3D curvilinear, finite-difference grid and solved by an alternating direction implicit scheme. For our model, we used the bi-dimensional formulation of the hydrodynamic and morphodynamic models implemented in Delft3D.
The generation and propagation of waves in shallow water is computed by SWAN, which is able to mimic random, short-crested waves in the open ocean and in shallow water regions. The key processes incorporated in SWAN are wave-wave interactions, wave refraction, and wave dissipation, that includes bottom friction [35] and wave breaking [36].
Here, we present the essential model equations, but further details can be found in Lesser et al. (2004) [34].
The mass-balance equation in Cartesian coordinates for an incompressible fluid with shallow water approximation, which is solved by Delft3D is: where → V is the velocity vector with component u, v, w along the x, y and z direction. The momentum equations for unsteady, incompressible and turbulent flow is: where D → V Dt is the material derivate, ρ is the fluid density, → V is the flow velocity, p is the pressure and τ is the fluid shear stress tensor which has order two.
Due to the shallow water approximation, the vertical momentum equation is reduced to the hydrostatic pressure equation; the vertical and horizontal eddy viscosity instead are computed by the k-ε model [37] and a large eddy simulation method [38], respectively.
The suspended sediment transport is calculated by solving the three-dimensional advection-diffusion equation: where C is the mass concentration, D the diffusion coefficient, → V the velocity field and R describes sources or sinks of the quantity C.
For cohesive sediments, the exchange between the water column and the bed in term of erosion and deposition are calculated with Partheniades-Krone formulations [39], while for non-cohesive sediments, the exchange is computed by the Van Rijn method [40], in which the formulation depends on the diameter of the suspended sediment (see Supplementary Materials).
Changes in bed bathymetry are computed from the gradients in sediment transport vectors as follow: where ε por is the bed porosity, z b is the bed level (positive up) (m), S x , S y are the total sediment transport components per unit width in the x and y directions (m 2 /s), and T d is the deposition or erosion rate of the suspended sediment (m/s). The evolution of the wave motion is instead described by SWAN, solving the spectral action balance equation: where the left-hand side is the kinematic part of the equation. The first term represents the local change rate of action density in time, while the second and the third one describes propagation of action in geographical space (along the x-y direction with velocity c x and c y respectively). The fourth term represents shifting of the relative frequency due to variations in depths and currents, the fifth is the depth-induced and current-induced refraction, and lastly, the quantities c σ and c θ are the propagation velocities in the spectral space. The right-hand side of the equation contains the source/sink term that represents all physical processes, including generation, dissipation, or wave energy redistribution. The model simulates the hydrodynamic and sediment transport processes involved in the morphological evolution of a salt marsh, in the presence of subtidal breakwater. The numerical domain The breakwater was imported into the model as an integral part of the bed level, but with a noneroding bottom, which made the structure waterproof. The height of the structure varied with xd ( Figure 1b), while length and width were fixed at 100 m and 10 m, respectively.
In the vertical direction, five-meter-deep layer of mixed cohesive and non-cohesive sediments was originally accessible for erosion at the bottom of the domain. Neumann conditions were imposed on the North and South boundary, while on the East boundary different conditions were fixed: incoming waves, incoming sediment concentration and water level variation.
We wanted to simulate the most realistic and natural conditions possible found among coastal wetland environments in Chesapeake Bay. For this reason, we referred to and adopted values from Wiberg et al. (2019), who, in her experiment in Virginia Coastal Reserve, measured waves between 0.03 and 0.52 m and bathymetric slopes between 0.28% and 1.05%. For sediments instead, we referred to Russ and Palinkas (2018) [41], which, in their study, confirmed high mud content in sediment deposits in Chesapeake Bay, also registering median diameters between 50 and 300 µm.
We set up our runs varying the basin slope (0.4% and 0.8%), the breakwater distance to the shoreline (xd) (50 m, 100 m, 150 m), wave's height (0.2 m, 0.3 m, 0.5 m, 0.7 m), tide (±0.2 m ±0.4 m), sediment concentration (0.2 kg/m 3 0.4 kg/m 3 ) and the sand fraction diameter D50 (100 µm 150 µm). Non-cohesive sediments were characterized by a specific density of 2650 kg/m 3 and dry bed density of 1600 kg/m 3 , while characteristics of the cohesive sediment were chosen in agreement with values provided by Berlamont et al. (1993) [42]. Specific density was 2650 kg/m 3 , dry bed density was 500 kg/m 3 and setting velocity was 0.5 mm/s. Wave parameters (Hs and Tp) were selected to simulate waves generated into the bay, so we analyzed the previously mentioned Hs values with a period Tp of 5s and a direction orthogonal to the shoreline. We imposed these values at the East boundary. Wave reflection was not accounted for in the wave model, so that wave energy was dissipated at the coastline.
The bottom stress was modelled with Chézy's formulation. We used two different values of this parameter, one for the bed level of the domain (CD = 60) and one for the breakwater roughness (CD = 20). The initial condition of the models consisted of an initial water level fixed at 0.4 m. The suspended sediment eddy diffusivities were a function of the fluid eddy diffusivities and were calculated using horizontal large eddy simulation and grain settling velocity. The horizontal eddy diffusivity coefficient was defined as the combination of the subgrid-scale horizontal eddy viscosity, computed The breakwater was imported into the model as an integral part of the bed level, but with a non-eroding bottom, which made the structure waterproof. The height of the structure varied with x d (Figure 1b), while length and width were fixed at 100 m and 10 m, respectively.
In the vertical direction, five-meter-deep layer of mixed cohesive and non-cohesive sediments was originally accessible for erosion at the bottom of the domain. Neumann conditions were imposed on the North and South boundary, while on the East boundary different conditions were fixed: incoming waves, incoming sediment concentration and water level variation.
We wanted to simulate the most realistic and natural conditions possible found among coastal wetland environments in Chesapeake Bay. For this reason, we referred to and adopted values from Wiberg et al. (2019), who, in her experiment in Virginia Coastal Reserve, measured waves between 0.03 and 0.52 m and bathymetric slopes between 0.28% and 1.05%. For sediments instead, we referred to Russ and Palinkas (2018) [41], which, in their study, confirmed high mud content in sediment deposits in Chesapeake Bay, also registering median diameters between 50 and 300 µm.
We set up our runs varying the basin slope (0.4% and 0.8%), the breakwater distance to the shoreline ( Non-cohesive sediments were characterized by a specific density of 2650 kg/m 3 and dry bed density of 1600 kg/m 3 , while characteristics of the cohesive sediment were chosen in agreement with values provided by Berlamont et al. (1993) [42]. Specific density was 2650 kg/m 3 , dry bed density was 500 kg/m 3 and setting velocity was 0.5 mm/s. Wave parameters (H s and T p ) were selected to simulate waves generated into the bay, so we analyzed the previously mentioned H s values with a period T p of 5s and a direction orthogonal to the shoreline. We imposed these values at the East boundary. Wave reflection was not accounted for in the wave model, so that wave energy was dissipated at the coastline. The bottom stress was modelled with Chézy's formulation. We used two different values of this parameter, one for the bed level of the domain (C D = 60) and one for the breakwater roughness (C D = 20). The initial condition of the models consisted of an initial water level fixed at 0.4 m. The suspended sediment eddy diffusivities were a function of the fluid eddy diffusivities and were calculated using horizontal large eddy simulation and grain settling velocity. The horizontal eddy diffusivity coefficient was defined as the combination of the subgrid-scale horizontal eddy viscosity, computed from a horizontal large eddy simulation, and the bac kground horizontal viscosity, here set equal to 0.001 m 2 /s 2 [43,44]. To satisfy the numerical stability criteria of Courant Frederichs-Levy, we used a time step ∆t = 3 s [34]. To decrease the simulation time, a morphological scale factor of 50 was used in our models (a user device to multiply the deposition and erosion rate in each ∆t). A sensitivity analysis showed that a morphological factor of 50 was acceptable.
Combining all the variables for run combinations (Table 1), we obtained 192 different simulations to run, from which the results were extracted. For symbols notation of Table 1 and Equations (1)-(5), refer to Table 2.

Results
Our focus was on the Delft3D models for simulating the hydrodynamics of flow and sediment transport, coupled with the SWAN wave analysis model. To understand how breakwaters impact salt marshes' resilience, we first analyzed the wave damping and the hydrodynamic, followed by morphodynamics.
This modeling analysis revealed some key findings: breakwaters are efficient at breaking waves and reducing wave energy delivered the shoreline; the shear stress decreases with increasing breakwater distance to the shoreline and it also increases proportionally to wave heights. The slope also affects the shear stress. Slope was positively correlated with a greater magnitude of shear stress, which directly impacted marsh scarp erosion, since a steeper sloped basin eroded to a greater extent. However, the higher basin slope allowed more sediment deposition into the marsh. Similarly, model scenarios with the closest distance of the breakwater from the shoreline and those with higher incoming waves also promoted deposition into the marsh. Last, comparing deposition into the marsh behind the breakwater with an area not covered by the structure, we found that breakwater is likely to block sediments, since deposition far from the breakwater was higher.
In the following, a detailed analysis of model results and coastal geomorphological implications is reported.

Hydrodynamic Results
The breakwater was found to efficiently dampen between 10-50% of the incoming wave heights under all configurations ( Figure 2). The wave damping was inversely proportional to x d and proportional to H s following a power law (R 2 = 0.51), while the slope did not affect this specific process. Our results (Figure 2b) were markedly consistent with the wave damping results of Wiberg et al. (2019) [15], who also observed a reduction of between 10-50% of incoming waves in a similar coastal environment at the Virginia Coastal Reserve (VCR).   The magnitude of the u velocity component was inversely proportional to Hs and slope, and proportional to xd following a power law (Figure 4 0.95 < R 2 < 0.98), which described how increasing the waves and distance of the breakwater to the shoreline allowed these vortices to direct water behind the breakwater and raise the wave crests vertically (Figure 4).   The magnitude of the u velocity component was inversely proportional to Hs and slope, and proportional to xd following a power law (Figure 4 0.95 < R 2 < 0.98), which described how increasing the waves and distance of the breakwater to the shoreline allowed these vortices to direct water behind the breakwater and raise the wave crests vertically (Figure 4).  The magnitude of the u velocity component was inversely proportional to H s and slope, and proportional to x d following a power law (Figure 4 0.95 < R 2 < 0.98), which described how increasing the waves and distance of the breakwater to the shoreline allowed these vortices to direct water behind the breakwater and raise the wave crests vertically (Figure 4). The shear stress peak due to the presence of the breakwater was clearly identified (Figure 5a), while the shear stress value into the marsh increased with wave height, slope and tide (Figure 5b). The shear stress value at the marsh scarp (x = 200 m) for all runs, as a function of xd, tide and waves, revealed how the magnitude of the shear stress was proportional to Hs and inversely proportional to xd and the tide, while the slope increasing effect augmented the erosion at the marsh edge (Figure 5c). Shear stress was correlated with the dimensionless variable for all distinct runs with slope 0.4% (R 2 = 0.70) and 0.8% (R 2 = 0.67). The shear stress peak due to the presence of the breakwater was clearly identified (Figure 5a), while the shear stress value into the marsh increased with wave height, slope and tide (Figure 5b). The shear stress value at the marsh scarp (x = 200 m) for all runs, as a function of x d , tide and waves, revealed how the magnitude of the shear stress was proportional to H s and inversely proportional to x d and the tide, while the slope increasing effect augmented the erosion at the marsh edge (Figure 5c). Shear stress was correlated with the dimensionless variable for all distinct runs with slope 0.4% (R 2 = 0.70) and 0.8% (R 2 = 0.67). The shear stress peak due to the presence of the breakwater was clearly identified (Figure 5a), while the shear stress value into the marsh increased with wave height, slope and tide (Figure 5b). The shear stress value at the marsh scarp (x = 200 m) for all runs, as a function of xd, tide and waves, revealed how the magnitude of the shear stress was proportional to Hs and inversely proportional to xd and the tide, while the slope increasing effect augmented the erosion at the marsh edge (Figure 5c). Shear stress was correlated with the dimensionless variable for all distinct runs with slope 0.4% (R 2 = 0.70) and 0.8% (R 2 = 0.67).

Morphodynamic Results
Breakwaters impacted the shoreline damping waves and created a low energy zone behind the structure, allowing sedimentation. Our results demonstrated how sediment accumulation into the marsh at the end of the simulations was inversely proportional to the distance of the breakwater to the shoreline and proportional to H s . The distance of the breakwater from the shoreline plays an important role on sediment transport. Breakwater distance to shoreline was negatively correlated with the amount of sediment deposited into the marsh (Figure 6a). The volume deposited was proportional to H s and inversely proportional to x d and the tide, following a power law correlation (0.50 < R 2 < 0.52), while the slope increasing increase the sediment accumulation into the marsh (Figure 6b). Figure 6a also shows how a greater distance of the breakwater from the shore leads to greater erosion of the marsh scarp, an aspect that will be taken up later in the manuscript.

Morphodynamic Results
Breakwaters impacted the shoreline damping waves and created a low energy zone behind the structure, allowing sedimentation. Our results demonstrated how sediment accumulation into the marsh at the end of the simulations was inversely proportional to the distance of the breakwater to the shoreline and proportional to Hs. The distance of the breakwater from the shoreline plays an important role on sediment transport. Breakwater distance to shoreline was negatively correlated with the amount of sediment deposited into the marsh (Figure 6a). The volume deposited was proportional to Hs and inversely proportional to xd and the tide, following a power law correlation (0.50 < R 2 < 0.52), while the slope increasing increase the sediment accumulation into the marsh (Figure 6b). Figure 6a also shows how a greater distance of the breakwater from the shore leads to greater erosion of the marsh scarp, an aspect that will be taken up later in the manuscript. We identified and quantified several important structural (e.g., breakwater position) and environmental characteristics (wave height bathymetric slope) on sediment deposition within marshes; we calculated the deposited volume as the difference between the initial bed level and the bed level at the end of the simulation into the saltmarsh behind the breakwater, and then multiplied by the area of the cells in order to obtain the total deposited volume. The estimation was therefore We identified and quantified several important structural (e.g., breakwater position) and environmental characteristics (wave height bathymetric slope) on sediment deposition within marshes; we calculated the deposited volume as the difference between the initial bed level and the bed level at the end of the simulation into the saltmarsh behind the breakwater, and then multiplied by the area of the cells in order to obtain the total deposited volume. The estimation was therefore punctual made cell by cell. With regards to the wave height abatement, on the other hand, an average wave damping was calculated during a tide cycle. However, the tide was found to play a dominant role in marsh erosion (Figure 7). This role was illustrated using the erosion ratio, defined as the final x d over the initial value of x d as function of the tide for all the x d , wave heights and for the two different values of concentration. We observed the tide to be strongly and positively correlated with the erosion at the marsh boundary. The erosion ratio for the 0.8 m tide condition, which reached the marsh platform at low tide, was greater than the 0.4 m tide condition, as increasing both the breakwater distance to the coastline and the wave height was observed to increase shoreline erosion. Additionally, the lower suspended sediment concentrations lead to higher erosion. It is also possible to observe how wave heights equal to 0.7 do not follow the same behavior as the other wave heights, but only cause deposition in the marsh (Figure 7). This mismatch is due to the great energy that the model develops in the presence of such waves, in environments governed by a very low energy regime.
The eroded volume of the marsh scarp from model configurations found to cause erosion (see Figure 7), as function of the dimensionless variable x d * Tide/H s 2 , for the two different slopes and tides, is summarized in Figure 8.  (Figure 9). The simulation demonstrated that the higher sediment concentration (Plot a) allows more sedimentation in the area protected by the breakwater and into the marsh.
Sandy sediments, on the other hand, were not considerably distributed within the calculation domain, due to the low energy developed by the hydrodynamics of our model.
An important aspect related to the sediment deposition into the salt marsh appeared, after comparing the volume accumulated behind the breakwater (into the marsh) and far away from it, revealing how breakwaters block sediment transport and prevent nourishment of the marsh ( Figure 10).
Water 2020, 12, x FOR PEER REVIEW 9 of 18 model develops in the presence of such waves, in environments governed by a very low energy regime. Figure 7. Ratio between the breakwater distance to the shoreline as function of the tide. The increasing of tide and breakwater distance to the coast increase the erosion at the marsh boundary, except for wave heights equal to 0.7 m, which mainly results in deposition into the marsh.
The eroded volume of the marsh scarp from model configurations found to cause erosion (see Figure 7), as function of the dimensionless variable xd* Tide/Hs 2 , for the two different slopes and tides, is summarized in Figure 8. A linear correlation between the dimensionless variable and the eroded volume for the slope = 0.4% and tide = ±0.2 m (Figure 8a), slope = 0.4% and tide = ±0.4 m (Figure 8c). Another linear correlation between the dimensionless variable and the eroded volume for the slope Figure 7. Ratio between the breakwater distance to the shoreline as function of the tide. The increasing of tide and breakwater distance to the coast increase the erosion at the marsh boundary, except for wave heights equal to 0.7 m, which mainly results in deposition into the marsh. = 0.8% and tide = ±0.2 m (Figure 8b), slope = 0.8% and tide = ±0.4 m (Figure 8d). Collectively, these relationships demonstrate how the erosion was proportional to the slope, tide, wave height and the breakwater distance to the shoreline.  (Figure 9). The simulation demonstrated that the higher sediment concentration (Plot a) allows more sedimentation in the area protected by the breakwater and into the marsh.
Sandy sediments, on the other hand, were not considerably distributed within the calculation domain, due to the low energy developed by the hydrodynamics of our model. An important aspect related to the sediment deposition into the salt marsh appeared, after comparing the volume accumulated behind the breakwater (into the marsh) and far away from it, revealing how breakwaters block sediment transport and prevent nourishment of the marsh ( Figure  10). We compared two 100 × 200 m check volumes, centered on transect 1 and 2 into the salt marsh (Figure 10a,b). In particular, we highlighted the ratio between the sediment accumulation behind and far away from the breakwater, into the marsh, as function of the final breakwater distance to the shoreline (Figure 10c). Volume ratio was defined as the ratio between the deposited volume on transect 1 over the deposited volume on transect 2, into the salt marsh. For most of runs the volume ratio was lower than 1 (Figure 10c), meaning that sediments were blocked by the breakwater, while without breakwater more sediments are allowed to reach the marsh.
A typical morphodynamic response due to the presence of breakwater is the scouring effect happening at the tip of the structure, as is shown on our results on Figure 10b. This behavior happens naturally with submerged structures and has commonly been observed in previous studies, such as Sumer et al. (2000) [45]. We compared two 100 × 200 m check volumes, centered on transect 1 and 2 into the salt marsh (Figure 10a,b). In particular, we highlighted the ratio between the sediment accumulation behind and far away from the breakwater, into the marsh, as function of the final breakwater distance to the shoreline (Figure 10c). Volume ratio was defined as the ratio between the deposited volume on transect 1 over the deposited volume on transect 2, into the salt marsh. For most of runs the volume ratio was lower than 1 (Figure 10c), meaning that sediments were blocked by the breakwater, while without breakwater more sediments are allowed to reach the marsh.
A typical morphodynamic response due to the presence of breakwater is the scouring effect happening at the tip of the structure, as is shown on our results on Figure 10b. This behavior happens naturally with submerged structures and has commonly been observed in previous studies, such as Sumer et al. (2000) [45].
Runs with wave heights 0.7 m do not follow the trend of the others because of the great amount of energy that this configuration generated into the model and were excluded from the chart (but see discussion for more commentary on this scenario).

Discussion
Our numerical experiment that couples Delft3D-SWAN models generates plausible results about sediment transport around breakwaters and the influence of waves and tides in shallow coastal bays.
Simulation results demonstrate how breakwaters were responsible for an average wave dampening of 10-50% (Figure 2), similar to empirical studies by Wiberg et al. (2019) [15], who measured the same range of wave dampening under similar coastal environment conditions at VCR. Additionally, Wiberg et al. (2019) [15] underline the importance of the incoming waves direction and the position of the structure itself regarding the breaking process. Our runs kept the same incoming waves direction perpendicular to the breakwater, and the same structure position parallel to the shoreline. The inference of our study is limited to our specific study conditions; nevertheless, they provide insight on the fundamental physical forces and principals underlying sediment load transport and fate.
The distance of the breakwater to the shoreline also affected the hydrodynamics, reducing the shear stress value as the distance increased. Sediment deposition into the salt marsh was primarily driven by wave height and the distance of the breakwater to the shoreline. Greater wave heights were associated with greater sediment suspension and transport, while increasing breakwater distance to shore decreased the amount of deposition, due to the lower transport energy of waves that were broken further offshore. This is in agreement with the study of Birben et al. (2005) [46], which investigated the effect of breakwaters' parameters on sediment accumulation. They found that the deposition in the area protected by the breakwater was inversely proportional to the breakwater distance to the shoreline and that the deposition and transport of sediments decreases with decreasing wave height. Our modeling approach and results can be used to help guide future breakwater design to promote salt marshes stability and longevity. Future breakwaters' deployment should consider placing these structures in locations that allow marsh nourishment (closer to the coastline), avoiding sediments' accumulation offshore and reducing coastal erosion.
The erosion at the marsh boundary was mostly governed by the tide. When the water level reached the marsh platform, waves had more erosion power, as they dissipated their energy directly on the marsh edge, while higher water levels allowed the dissipation to happen through the marsh platform, with less impacts on marsh boundary erosion. These results are also similar to Tonelli et al (2010) [47], who observed that water level plays an essential role on marsh boundary erosion. Such erosional behavior was confirmed in our results (Figure 7), where the ±0.4 m tidal condition, which reached the marsh platform at low tide, eroded more than the ±0.2 m condition and was always higher than the platform level. Moreover, Figure 8 illustrates the effect of tide and slope on the erosion, demonstrating how increasing tide and slope increased the erosion of the marsh scarp.
Results regarding the influence of the tide on the functioning of breakwaters highlights how higher water levels inhibit the protective performance of breakwaters, suggesting they could be drowned by sea level rise (SLR) and quickly become ineffective. Future modeling efforts may want to consider examining this scenario to better understand legacy infrastructure performance in the face of climate change. We have already begun to observe the failure of some breakwaters in the Chesapeake Bay (Figure 11), as well as clear signs of erosion, in part due to accelerating SLR in this system. The presence of the breakwater is also likely to trap sediments and create less deposition in the area protected by it, compared to an area without obstacles ( Figure 10).
This fact shows an important aspect about breakwaters and their behavior. They are efficient at breaking waves and reducing their energy, but on the other hand they can be an obstacle for sediments and consequently for salt marsh survival.
Moreover, the breakwater distance to the shoreline was significantly inversely related to the amount of sediment transported and deposited into the marsh; therefore, the best structure configuration, with respect to marsh nourishment (amount of sediments that can reach the vegetation), would be one with the closest distance to the shoreline ( Figure 10). In addition, wave heights help the solid transport as the higher is the wave, the greater the amount of deposition into the salt marsh, while a flatter slope will lead to less deposition.
Our model shows how greater waves cause more erosion; however, this trend is not followed by the 0.7 m wave height, as it mainly causes deposition enriching in the marsh (Figure 7). Treating wave heights equal to 0.7 m as a storm-level [15], our results are in agreement with Castagno et al. (2018) [48] who demonstrated, using Delft3D, that extreme events are likely to enrich coastal wetlands with more sediments.
As our model points out, the water level and therefore the increase in sea level are crucial to consider for the long-term functioning of breakwaters, since they are likely to become less efficient with accelerating SLR. A recently advanced engineering concept to cope with the growing threat SLR is the use of hybrid infrastructures, which combines built and natural solution for coastal defense and is thought to exploit the benefits that accompany each approach. Hybrid infrastructure that can adapt to changing environmental conditions, such as coral or oyster reefs working in conjunction with grey structure to dampen incoming waves, is an attractive alternative that can sustainably stabilize the shoreline, while also contributing immense ecological value [49,50]. The advantage of integrating breakwaters and other in-water infrastructure with oysters is that the reefs these organisms form may grow with SLR [51,52], providing greater guarantees that these structures could provide protection to coastal environments long after the grey structure has been drowned (see supplemental material Figure S1). Principals established in this study are highly applicable for the design of fully-integrated hybrid infrastructures wishing to use oysters and other reef-forming species, while also ensuring marsh habitat is also considered and protected.
A long-term analysis of coastal dynamics has also been simulated to look at the effect that breakwaters can have on long-shore sediment transport ( Figure 12). Our results show how, over time, breakwaters tend to close their rear deposits, blocking solid transport and creating morphodynamic The presence of the breakwater is also likely to trap sediments and create less deposition in the area protected by it, compared to an area without obstacles ( Figure 10).
This fact shows an important aspect about breakwaters and their behavior. They are efficient at breaking waves and reducing their energy, but on the other hand they can be an obstacle for sediments and consequently for salt marsh survival.
Moreover, the breakwater distance to the shoreline was significantly inversely related to the amount of sediment transported and deposited into the marsh; therefore, the best structure configuration, with respect to marsh nourishment (amount of sediments that can reach the vegetation), would be one with the closest distance to the shoreline ( Figure 10). In addition, wave heights help the solid transport as the higher is the wave, the greater the amount of deposition into the salt marsh, while a flatter slope will lead to less deposition.
Our model shows how greater waves cause more erosion; however, this trend is not followed by the 0.7 m wave height, as it mainly causes deposition enriching in the marsh (Figure 7). Treating wave heights equal to 0.7 m as a storm-level [15], our results are in agreement with Castagno et al. (2018) [48] who demonstrated, using Delft3D, that extreme events are likely to enrich coastal wetlands with more sediments.
As our model points out, the water level and therefore the increase in sea level are crucial to consider for the long-term functioning of breakwaters, since they are likely to become less efficient with accelerating SLR. A recently advanced engineering concept to cope with the growing threat SLR is the use of hybrid infrastructures, which combines built and natural solution for coastal defense and is thought to exploit the benefits that accompany each approach. Hybrid infrastructure that can adapt to changing environmental conditions, such as coral or oyster reefs working in conjunction with grey structure to dampen incoming waves, is an attractive alternative that can sustainably stabilize the shoreline, while also contributing immense ecological value [49,50]. The advantage of integrating breakwaters and other in-water infrastructure with oysters is that the reefs these organisms form may grow with SLR [51,52], providing greater guarantees that these structures could provide protection to coastal environments long after the grey structure has been drowned (see Supplementary Materials Figure S1). Principals established in this study are highly applicable for the design of fully-integrated hybrid infrastructures wishing to use oysters and other reef-forming species, while also ensuring marsh habitat is also considered and protected.
A long-term analysis of coastal dynamics has also been simulated to look at the effect that breakwaters can have on long-shore sediment transport ( Figure 12). Our results show how, over time, breakwaters tend to close their rear deposits, blocking solid transport and creating morphodynamic structures known as salients and tombolos, as is shown in many papers in the literature, such as Hanson et al. (1991) [53]. The Figure shows how these morphodynamic structures tend to be less accentuate with increasing breakwater distance to the shoreline.    [54] offers an important analysis on how material accumulated in reservoirs might be reused in nourishment works. They reported a study case of the Guardialfiera reservoir in Italy, but this application suggests how such an approach can be tested, for instance, also in the restoration of coastal wetlands along the eastern shore of the United States.

Conclusions
Understanding sediment transport dynamic is a key aspect for the protection and the survival of salt marshes. In this study we investigated breakwater effects on sediment supply and morphological changes for a vegetated shoreline. The presence of the breakwater certainly reduces the incoming waves by dissipating the energy and protecting the coast, as clearly shown in Figure 11. However, the breakwater distance to the coast affects sediment transport and may inhibit marsh nourishment if not properly considered during planning and deployment activities. Greater distances are associated with less sediment deposition and more erosion of the marsh scarp.
The slope, tide and wave heights play different roles in the sediment supply for the vegetation: (a) slope was positively correlated with greater amounts of deposition into the salt marsh; (b) tide or water level at similar elevations to the marsh platform was more likely to erode; (c) higher waves were observed to bring more sediments towards the marsh, but they also have more erosion power. Our study, which highlights the conflicting effects of breakwater (coastal protection vs. marsh malnourishment), is relevant and applicable for field studies and future coastal management in areas such as Chesapeake Bay. Study results also suggest that more research is needed to help find a balance between waves dampening and sediments supply during the design and implementation of breakwater infrastructures.