Assessing the Impact of an Artificial Reef to Mitigate Coastal Erosion Using the Phase Resolving Wave Model Funwave

A Fully Non-Linear Boussinesq wave phase resolving model (FUNWAVE) (Shi et al., 2012) is used to model extreme storm events and assess their impact on the shoreline. In addition, we explore the potential benefit of deploying an artificial reef to mitigate the erosion on the shoreline. Individual waves are modeled in the time domain including all of the physical processes associated with their propagation: breaking, refraction, diffraction, reflection and non-linear effects. The study site modeled in these simulations is located in South Kingstown, Rhode Island, including the Green Hill Beach area along the coast. A sensitivity study on the FUNWAVE Courant–Friedrichs– Lewy (CFL) input parameter is completed and a value of 0.15 is determined to best generate the intended wave spectrum for our simulated cases. Results compare identical simulations run in FUNWAVE for cases with and without a submerged reef, deployed for coastal protection. This comparison shows that the implementation of a submerged reef along the coastline can significantly reduce both shoreward current velocities and wave energy. Resulting wave energy transmission coefficients moderately correlate with expected simplified solutions presented in Grilli et al. (1994) although the more realistic case evaluated in this study shows a greater reduction in wave energy across the reef. FUNWAVE’s sediment transport module has proven to be difficult to use and has produced unreliable results for this study. The difference in coastal energy and current processes due to individual wave interaction with the seabed demonstrates the importance of utilizing a phase resolving model such as FUNWAVE to most accurately predict these conditions.


Introduction
Erosion-related damage to coastal structures and property costs around $500 million per year in the United States alone. Additionally, the federal government spends around $150 million in beach nourishment and erosion mitigation strategies per year (NOAA, 2013). Worldwide, natural offshore reefs work as submerged barriers, dissipating wave energy offshore and reducing coastal wave impacts such as shoreline erosion. These reefs have proven to be very effective in the reduction of wave energy through breaking and friction across the reef. To create the best coastal protection scenarios, artificial reefs are best designed for each specific case with factors such as local bathymetry and wave climate playing the largest role in design. One study by (Harborne et al., 2006) shows that coral reefs reduce shoreward wave energy transmission by 95 percent. Grilli et al. (1994) (Kennedy et al., 2008). Kennedy et al., (2008) show how variations in sandbar length and spacing affect these nearshore currents. This study found that "the width of the offshore directed rip current increases only slowly with an increase in the width of the available rip channel", caused by the minimal variation in the shoreward water volume available to return offshore. Findings show how reef location and surrounding depth affect currents.
Using numerical models to simulate storm events and their impact on the shoreline, provides a rigorous quantification of the coastal hazard to the local communities and lends the necessary information to plan these mitigation strategies. Current coastal erosion and sediment transport models estimate the impact of storm events on coastal areas based on local sedimentology and wave climate. The existing state of the art erosion model, XBeach (Roelvink et al., 2009), is a fully coupled model using four interconnected modules: wave, flow, sediment transport and geomorphology. While the flow module includes the long infragravity waves in the time domain, the wave module includes only short waves in the spectral domain. This approach has the advantage of being computationally efficient but simplifies the short-wave representation and 3 propagation. Short waves are assumed to be linear and while the refraction and breaking processes are included in their propagation, diffraction and reflection are not. While these simplifications are acceptable for general hazard assessment, they might not give realistic results when one desires to predict the flow in a built environment such as a coastal community with structures along the shoreline, or when one desires to study the effect of coastal or offshore structures to mitigate the storms, such as an artificial reef.
Individual waves can also cause localized damage to structures along the coast and are therefore worth considering in modeling efforts (Park et al., 2018 is free to the public on github.com. Access to any documentation for the program is also available online and was utilized for model setup, output assessment and troubleshooting purposes (Shi, 2020).
Southern Rhode Island is exposed to large storms and hurricanes which cause coastal erosion and damage to homes and businesses. Over the past five years the Rhode Island Shoreline Change Special Area Management Plan, known as Beach SAMP, produced a large amount of data and maps to assess the coastal risk in Rhode Island in terms of shoreline erosion and flooding (Beach SAMP, 2020;Spaulding et al., 2016;Spaulding et al., 2017). The methodology used to assess wave impacts and erosion along the shoreline has been constantly evolving to include increasingly complex processes.
For example, while modeling beach and dune erosion used semi-empirical formulation for long term erosion, simple empirical assumptions were initially used for event scale erosion (Grilli et al., 2017a). Subsequently complex 2-D numerical modeling using the coupled morpho-hydrodynamic model XBeach (Roelvink et al., 2009) was used to assess the change of the shoreline during extreme events (Schambach et al., 2018); further work validated the methodology for specific erosion stages as defined by (Stockdon et al., 2007), confirming the ability of the model to accurately simulate erosion for varying vegetation coverage (Naser et al., 2018). Recently, the modeling team significantly improved the hydrodynamic portion of the wave module, modeling the wave propagation in real time using FUNWAVE, which includes non-linear and dynamics effects, such as wave runup (Grilli et al., 2020).
In parallel to the refinement of the numerical approach, several mitigation approaches have been explored such as beach nourishment and nature-based dune reinforcement (Naser et al., 2018). A current master's student, Jennifer Brandes, is focusing on optimizing the design and location of a potential artificial submerged breakwater as an erosion mitigation solution deployed along the southern shore of RI.
The solution is inspired by current reef and living shoreline restoration projects (e.g., Reguero et al., 2018;Beck et al., 2018). Schambach et al., (2018), modeled the erosion along the southern coast of RI using the state-of the art geomorpho-dynamic model XBeach. The model was calibrated and validated with local measurements of beach volumes along Charlestown beach for Hurricane Irene (August, 2011) (Schambach et al., 2018). Hurricane Irene will similarly be used in this study to assess the validity of FUNWAVE's erosion module and the impact of an artificial reef on the local environment.

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The FUNWAVE Sediment Transport Module used in this study is part of the Boussinesq Model, incorporating sediment movement processes originating from the surf beat or infragravity waves, similar to other erosion models such as XBeach, as well as sediment transport initiated by the gravity wave propagation. Infragravity waves are low frequency surface gravity waves, who are normally defined in the frequency band between 0.04 Hz and 0.004 Hz (25 seconds to 4 minutes), as observed and described in many field studies such as (Elgar et al., 1993). These wavelengths correspond to the tail of the wave spectrum and are therefore much longer than most gravity waves produced by wind forcing; they have a significant importance shoreward of the surf zone, where short wave energy from swells and seas has dissipated due to wave breaking.
Infragravity waves are created through nonlinear interactions and radiation stress forcing under two focal circumstances. The first type of infragravity wave is developed offshore. These waves are created by radiation stress forcing which causes sea level variations in conjunction with wave groups. These waves are constrained by the motions of the wave group and are therefore called bound waves. The second type of infragravity wave is developed at the surf-zone through radiation stress forcing caused by breaking.
These waves are instantaneously free to propagate towards shore in the absence of the wave group due to short wave breaking (Longuet-Higgins, Michael S., and R. W.

Stewart, 1964).
To calculate the movement of larger diameter sediment and that moving along the bottom, this module uses the bedload formulas identified by Meyer-Peter and Müller, (1948), as shown in the formulation bellow (Eq. 1), with, , the transport rate of bed load in dry weight on unit channel width (kg s −1 m −1 ), τ , the flow shear stress acting 7 on the channel bed, τ , the critical shear stress, ρ , the seawater density, g, the acceleration of gravity, and, s, the unit time step. For sediment suspension, the empirically derived pick-up function proposed in van Rijn, (1984), is utilized to calculate the suspended load and its transport to other areas of the seabed in the model.
This function was determined through laboratory experiments and was compared to previously defined pick-up functions for both large (>1,000 µm), and small (<200 µm) particles.
The sediment module processes both cohesive (i.e. clay, silt and organic matter, frequently referred to as mud) and noncohesive sediment types (i.e. sand, gravel) in a similar fashion, utilizing the depth-averaged sediment concentration equation for advection and diffusion (Eq. 2).
In equation (2), P and D represent the erosion and deposition rate of sediment, respectively. The flow rate per unit width is represented by ( + ) (Shi et al., 2012), where H equals the total water depth, or the water depth, h + the free surface elevation, η. The ̅ variable is the depth-averaged sediment concentration and is nondimensional and normalized by the provided density of the sediment. K is a coefficient This thesis is structured as follows. Section 1 presents the introduction to concepts, objectives and the study site. In Section 2, the methodology used to produce the 8 objective's results is explained. In the next section, the results of the study are presented, Section 3, followed by the study's conclusions, in Section 4.

Objectives
This study uses the fully non-linear, fully dispersive numerical wave model FUNWAVE coupled with its sediment module to simulate extreme storms along the southern Rhode Island shoreline. A comparison with previous modeling efforts using the state-of-the art model XBeach is performed and differences are discussed. In addition, FUNWAVE is used to simulate selected mitigation strategies along the shoreline, in particular a submerged offshore artificial reef.
Results of this study will be presented in terms of: (1) transmission coefficients, (2) subaerial eroded volumes along the shoreline and (3) accretion volumes between the reef and shoreline. Additionally, maps will be produced of wave propagation and coastal erosion for the simulated wave climates for both current conditions and for a bathymetry modified with the addition of an artificial reef. This work strives to provide an initial framework for an impact assessment of selected RI coastal areas modified with an artificial reef.
The study evaluates the implementation of an offshore reef for beach nourishment and protection, bringing to light nearshore hydrodynamic processes. In particular it demonstrates the concentration of wave energy on specific areas of the shoreline suggesting the possibility of mitigating the hazard, rather than only increasing the shoreline resilience. The implementation of an artificial reef theoretically reflects and dissipates part of the propagating wave energy, inducing lower current velocities and 9 additional sediment deposition landward of the reef, consequently protecting the shoreline (Grilli et al., 1994). This reef effect has proven to be extremely efficient in natural reefs, resulting in an active field of research to restore damaged natural reefs (e.g., Reguero et al., 2018;Beck et al., 2018).
While the hydrodynamic module in FUNWAVE is fully calibrated and validated (Kirby et al., 2015) and therefore provides reliable wave elevation and velocity predictions, the erosion module is newly implemented and must be calibrated and validated at the study site. In this study, we aim to assess the accuracy of FUNWAVE when used with its sediment transport module, fully coupled with the hydrodynamic module, by comparing simulated erosion and measured erosion at the site for a selected historical storm (Irene, August 2011). Ultimately, we intend to assess the ability of a nature-based artificial reef deployed offshore of the study area to mitigate coastal erosion using FUNWAVE numerical simulations.

Study Site
The study area, Green Hill Beach (Figure 1), is situated on a stretch of coastline along southern Rhode Island consisting of a barrier beach system including dunes, beaches, lagoons and salt marshes, home to diverse vegetation and wildlife. The study area was chosen in a region where homes and fragile ecosystems border the coastline.
This area also contains coastal lagoons, which can significantly manipulate the impact of extreme storms on the coastline and is of particular interest across southern RI.
The region is also being used as part of a continuous effort performed in ocean engineering at URI since 2015 to improve coastal and risk hazard assessment associated to extreme storms and changing climate in Rhode Island (Grilli et al., 2017b;Grilli et al., 2017a;Spaulding et al., 2016;Spaulding et al., 2017;Schambach et al., 2018;Naser et al., 2018). The Coastal Resource Management Council (CRMC) and a local association, the Friends of Greenhill Pond, have also supported the ocean engineering coastal team to evaluate the feasibility of storm hazard mitigation strategies on the RI shoreline.
The study site grid was chosen within the southern RI region of interest to best utilize the FUNWAVE model in the region, given the focus and constraints of the thesis (Table 1). The long domain (~12km in the offshore direction) was chosen to allow for the creation of long-waves in the model. The thin, 1km width was chosen to be large enough for the implementation of a nearshore reef and to view nearshore processes but allow the model to be more computationally efficient. The Green Hill beach region is also a location along the coast of particular vulnerability to over-wash, as seen during historical storms, as well as damage to homes and property.  The study area is exposed to the Block Island Sound and the Atlantic to the south,

Methodology
The flow chart displayed in Figure 4 is representative of the FUNWAVE modeling process. Many inputs are available and compiled in an input file for the program. Once the simulation is begun, the inputs are read and the area to be modeled is divided into sub areas with each sub area placed on different processors for computational efficiency.

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A significant effort was devoted to pre-process the data necessary for the simulations: the built-up topography or Digital Elevation Model (DEM), the bathymetry and the land use data required to best represent the variable friction induced by the vegetation (Schambach et al., 2018). This allowed for the best representation of the hazard's impact, including erosion and wave changes with vegetation friction and impacts on structures. As each scenario produced a large quantity of output data, the outputs were received in binary format and processed using MATLAB. The outputs of the model include wave and water elevation, currents, suspended sediment and change in bed level. A sensitivity to the input parameters was addressed to assess their relative importance in the coastal processes. Relevant computational parameters were calibrated to optimize the accuracy of the FUNWAVE model prediction.

FUNWAVE model setup
The computational grid (2 by 2m) was set up to assess wave effects along the narrow study area, Green Hill Beach, and to capture the long infra-gravity waves impacting the shoreline. To do so, the grid was extended far enough offshore to allow wave grouping to occur (Lynett and Liu, 2005) resulting in a study grid of (1000m by 12640m) (Figure 1). The fine resolution is required to fully capture the wave spectrum  Simulated erosion was compared to coastal erosion survey data (Schambach et al., 2018) and to the numerical work in progress of the current Master's thesis candidate, Jennifer Brandes, modeling a similar reef using the XBeach model.
The Hurricane Irene storm event is simulated using storm surge and wave spectral parameters in offshore boundary conditions (BC) at the offshore boundary of the  Table 2.
The lateral BC, to the East and West of the study area, is set to periodic in the FUNWAVE model. This condition can be used for mostly straight coastlines, as in this study. With the periodic boundary condition turned on, anywhere wave breaking causes waves and currents to move laterally, towards the boundaries, water velocities moving at one lateral boundary are passed through to become an input on the opposite side. With the input waves normal to the domain in this study, this condition becomes most relevant in the nearshore region.

FUNWAVE calibration
The first portion of this thesis effort consists of the calibration of the hydrodynamic wave model, FUNWAVE at the study site using the historical storm Hurricane Irene.
First, we tested the convergence of the results to the grid size. The spectrum generated by the numerical wavemaker was compared to input spectrum.
A small and very long, 2x2 meter grid (500 x 6320) at the study area was used for this calibration and sensitivity study stage. However, such a small high grid discretization is not typically used in FUNWAVE, and standard input conditions resulted in abnormally large wave height results. The formation of large waves in the model occurred in both normal and simplified input conditions; in some instances, producing wave heights up to 5 times larger than the input wave height, causing the model to blow-up, initiating a simulation failure.
The source of the issue was identified as the combination of small grid sizing and large waves input into FUNWAVE, causing computational issues in the grid cell time steps. Consequently, a sensitivity study was conducted on the Courant-Friedrichs-Lewy (CFL) parameter, which describes how much information passes through grid cells in each time-step. A reduction in the CFL allows for more processing time of the partial differential equations in each time step for the 2x2 meter cells. Principally, the CFL parameter needs to be set low enough so that it allows the distance between grid points to be greater than the distance the solution travels is a timestep and carry all necessary information from the previous grid cell. Of the CFL values tested in the simulation, the lowest value of 0.15 produced a wave spectrum with a significant wave 20 height most representative of the input value. Lower CFL values may also produce accurate wave outputs but are likely not worth the computational time loss. Table 3 displays the outcome for each of the four simulations conducted in refinement of the CFL parameter. For each simulation, only the CFL input parameter was altered. The significant wave height input for each simulation was 4.42 meters. As the simulations with larger CFL values failed early, the resulting maximum significant wave height was taken after 1400s of simulation time and repeated for each simulation for comparison.   This simulation was completed for one hour of wave propagation. One hour was chosen for several reasons. First, with FUNWAVE being computationally consuming and supercomputer time limited, the shortest durations would best allow for multiple simulations to be run. Second, it has been shown (Grilli et al., 2020) that one hour of wavemaker input allows for the wave spectrum and currents to fully develop along the coastline, showing close to maximum wave heights that would normally be seen. While the FUNWAVE nonlinear wave representation would provide wave statistics slightly varying from linear wave theory, the linear wave theory can be useful to provide a rough estimate of the necessary number waves to represent a valid representative sea state.
Accordingly, Equation 3 (Grilli et al., 2020;Forristall, 1978), relating maximum wave height, Hmax ,significant wave height, Hs, and number of waves, J, shows that 23 approximately 3000 waves, or 10 hours of simulation are required to capture Hmax (assuming that a Rayleigh distribution with Hmax ~ 2 Hs). Using the same equation shows that 1 hour of simulation time in this study captures maximum waves height at least 84% of the 2Hs value, which is close to the 1% of the highest wave (~1.8 Hs).
Consequently, one hour of simulation was considered sufficient to represent a realistic sea state for this case study.

Simulation scenarios with reef implementation
The model is similarly forced with peak Hurricane Irene initial and boundary conditions for the study area altered with a submerged reef ( Figure 12). Two submerged reef scenarios are performed with widths extending from 10 (scenario 1) to 30 meters   Similar to the unaltered case, reef implemented simulations are completed for one hour of storm with grid and station output values recorded every 100 and 0.5 seconds, respectfully.

Green Hill Study Site Simulation -Energy Transmission
The efficiency of the submerged reef structure is first assessed by quantifying the wave energy reduction beyond the reef evaluating the wave transmission coefficient and the energy transmission coefficient based on transmitted energy calculations.
Significant wave height is calculated offshore of and shoreward of the reef, at each of the station locations surrounding the reef. The wave transmission coefficient (Ct) defined as the ratio of the offshore significant wave height, Hi to the transmitted wave height shoreward of the reef, Ht, is written as:

Ct = 4
Both Hi and Ht are derived using the zero-up crossing method over the water elevation time series provided at the virtual station locations.
The wave energy is similarly estimated on both sides of the reef using the zeroup crossing significant wave height in the formulation of the mean wave energy for each unit of wave crest, with E as the wave energy (J/m 2 ), ρ the water density (kg/m 3 ), g the acceleration of gravity (m/s 2 ) and Hs the significant wave height (m). Values of 9.81 m/s 2 and 1025 kg/m 3 are used for acceleration due to gravity and seawater density, respectively. The 29 energy transmission (ΔE) is estimated in absolute value as the difference of the energy offshore (Ei) and beyond the reef (Et) and as a relative coefficient (CE) being the ratio of Ei and Et.

Results and Discussion
FUNWAVE's modeling outputs were post-processed using custom MATLAB code to provide maps and graphics and more easily understand model outcomes.

Transmission Coefficient Comparison
The values of the transmission coefficients for simulations with and without submerged reefs are compared in Table 4. The virtual stations where these values were calculated are located as shown in Figure 15. The total energy transmission from offshore to the nearshore is also presented in Table 5. Comparisons show that the FUNWAVE model has a strong consistency producing offshore wave heights for the irregular wave case, with average offshore significant wave height values within 3 centimeters across simulations. It should also be noted that the energy reduction for the reef cases is significantly higher than that of the normal bathymetry case, with reef 2 providing the most energy reduction. This leads us to believe that wider reefs provide more energy reduction as width was the only variable that was changed between reefs.   to 22% less than the value of 0.85 estimated in the literature for solitary waves (Grilli et al., 1994), proving that the reef design provides a good energy reduction for the study area.

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The solitary case study addressed a similar issue, but solely for solitary waves and was performed using numerical and laboratory experiments for a large range of wave heights and reef depths (including immerged and emerged scenarios). Results are recalled in Figure 16,   (Grilli et al., 1994). Here, h'1 is the reef height/ water depth and H' is wave height/ water depth. Values less than 1 on the xaxis represent a submerged reef The comparison of the transmission coefficient value determined in this study with results from (Grilli et al., 1994) show a transmission reduction of 12%. While (Grilli et al., 1994) had simulated the reef effect for solitary waves, the current study simulates an irregular, dispersive and non-linear wave train. The error of the model in (Grilli et al., 1994)

Nearshore Velocity Comparison
It is evident from the comparison of the maps shown in Figure 17 that the deployment of a submerged reef along the coastline has a significant effect on currents.
The black lines in the figure represent current direction and strength with longer velocity vectors representative of stronger current. The reef reduces current velocities directly onshore of the reef, and greatly increases current velocities at the reef location.

Power Density Spectrum Comparison
To best resolve wave energy reduction by the reef, reflection was calculated by solving for the offshore energy difference with and without the reef. The power density spectrum shown in Figure 19  These low values, representative of no reflection at the submerged reef, seem to be slightly inconsistent with literature, such as in (Young and Testik, 2011)) where monochromatic waves were used to approximate reflection coefficients and had a good fit with measured data. The same approximation shows that reflection is mainly reliant on incident wave and reef height. When used on this studies scenario, reef reflection is predicted around 10% for reef 1 and reef 2, much larger than that modeled by FUNWAVE. One factor for this difference is likely the highly nonlinear waves used in these FUNWAVE simulations. This causes waves to act differently, such as having a majority of their energy and height translated into the wave crest, especially in the nearshore region, allowing for more of the wave to pass over the reef.

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Wave reflection is an important consideration in any coastal modeling around solid objects such as sea walls or steep beach faces and could play a larger role in the future modeling of different reef shapes and locations. Figure 19: Power Spectrum Density for Reef 1 (top) and Reef 2 (bottom) 200m offshore of the reef. The difference between the integral of the spectrum with and without a reef is representative of reflected energy.
To best understand the erosion and accretion calculated by the FUNWAVE sediment transport module, a comparison was made to the calibrated and verified XBeach model, using simulations run over the same study area with an identical wave climate and duration.
The resulting sediment erosion per meter of beach between MSL (NAVD88) and the dune crest at a transect in the center of the study area can be found in Table 6. Table   7 shows the resulting sediment change along the same transect, extending 2 meters below MSL to show sediment changes in the close nearshore region. These values are calculated from summing the erosion/ accretion volume along the transect line at the last time step in the simulation. Across the shoreline, sediment change is displayed in cubic meters, shown in Figure 20.     segments of the storm. The fundamental differences between the models adds an epistemic uncertainty that is difficult to isolate when using such a short time segment from an event. Results will still be briefly discussed in the following pages, keeping the above limitations in mind.
After Hurricane Irene, direct measurements on transects across the beach show a sub-aerial erosion on the order of 15 to 30 m 3 per meter of cross-shore beach length (Schambach et al., 2018). Over the 48 hours storm, XBeach simulations accurately reproduced these values on the order of 6 %. While the erosion observed during the current short simulation durations is not linearly representative of the erosion occurring during the full storm (no tides, or longer term sediment processes), a quick linear estimation would provide an erosion estimate of 2-3 orders of magnitude smaller than 42 observed during the full storm. Presuming that the short time is an acceptable tool to investigate the differences between the models, the relative acceptable agreement without a reef present leased us to believe we can also trust the differences when a reef is present. It's important to note FUNWAVE's expensive computational runtime, especially with the sediment transport module addition, combined with the need for a long grid to capture long-waves, excluded runtimes longer than the 1-hour simulation for the purpose of the current study.
Looking solely at the FUNWAVE sediment transport results ( Figure 22) some simple initial conclusions can be drawn. First, the addition of the reef induces strong erosion on the shoreward side of the reef toe. Second, although the reef creates slightly more erosion above MSL over the hour duration, it reduces erosion and promotes accretion just below MSL. This build up is backed by the values shown in Table 7 and could further protect the shoreline as the storm continues for more than an hour.

Conclusion
FUNWAVE is a powerful wave and coastal processes simulation tool. Long simulation runtimes lead us to believe that time-sensitive research might be more feasible utilizing other modeling tools. However, given a sufficient amount of time/ processing power this tool is able to produce extremely accurate and consistent nearshore wave modeling.
The value of the transmission coefficient, significantly departing from earlier studies (Grilli et al., 1994), provides an insight into the epistemic uncertainty associated with the choice of the model and the physics included in the model, during a hazard impact assessment. Despite FUNWAVE's perceived accuracy, this study needs to be compared to empirical measurements to assess the error associated with the numerical simulations.
From the resulting current velocities, it is evident that when a reef is deployed in this study area, highly focused wave induced currents are produced over the reef area with a much larger and calmer region shoreward of the reef. This is likely due to wave reflection, breaking and friction at the reef. Further current research in this area needs to be completed with a higher sampling frequency in the grid surrounding the reef. The case of a lone reef also reduces the chances of rip currents forming in reef gaps, typically seen between reef segments during a more realistic installation.
Looking at the frequency spectrums offshore of the reef locations, there seems to be no reflection induced by the deployment of the two reef examples in the model. This is likely due to the highly irregular waves transporting energy mostly above the MSL 45 and transmitting across the reef without reflecting. Reflection should be further studied for similar reef cases as theoretically it can play a small but significant role in energy reduction shoreward.
Although we have conclusively shown a reduction in wave energy and current velocities shoreward of the reef, when compared to the no reef case, sediment erosion along the shoreline does not completely reflect the other findings or identical simulations run in XBeach. The erosion above MSL is not reduced with the deployment of the reefs. While FUNWAVE is extremely capable and verified in wave and fluid mechanics, an initial look at FUNWAVE's sediment module, when compared to the validated XBeach model, shows it seeming to be working correctly coupled with the parameters used in this study. However, this initial work cannot be taken as a window into how the model would behave for the full storm. One reason for this is the short duration the waves spend interacting with the shoreline during this study's simulations (less than 1 hour). Further research, containing longer simulation times and more transect comparisons is needed to better evaluate FUNWAVE's sediment transport module. For the sake of this study, it is best to trust FUNWAVE's more widely validated irregular wave and current effects around the submerged reefs.