Modeling Sediment Transport Around Artificial Reefs in Southern Rhode Island

This document contains two papers which address threats by tropical and extratropical systems in the northeastern United States. A suite of numerical models are used to assess waves, storm surge and coastal erosion during extreme storms. Modeling Waves and Sediment Transport Around Artificial Reefs: Simulation of the Impact of Multi-purpose Reefs on Dune Erosion in Southern Rhode Island Barrier Beaches The objective of this study is to set up a suite of numerical models capable of simulating the impacts of storms on coastal flooding and erosion, and use it to assess performance of mitigation measures. Three numerical models were used to analyze the possible erosion due to inundation and overwash for a small section of coast in southern Rhode Island. SWAN (Simulating Waves Nearshore), a third-generation wave model was used to compute the wave conditions. ADCIRC (ADvanced CIRCulation Model), a three-dimensional circulation model used atmospheric and tidal forcing to generate water levels, and currents. A regional coupled SWAN+ADCIRC model was used to calculate water levels and wave conditions over an unstructured mesh. XBeach, a sediment transport model, encompasses a barrier system on the southern coast of Rhode Island, and is nested within the regional domain. A non-uniform cartesian grid with a resolution across dunes of 5×10 meters is used to calculate the sediment transport during storms, the resolution decreases to 25×25 meters resolution at the boundaries. Hurricane Sandy (2012) was used to calibrate the models, where volume of erosion was compared along transects monitored by the University of Rhode Island. The model was then forced with winds from Hurricane Irene (2011) for validation. The regional model had a root mean squared error (RMSE) of 0.21 meters for storm surge, and a RMSE of 0.18 meters for offshore significant wave height. The nearshore model was able to estimate erosion with an error of 24.26%. Once validated, two synthetic storms from the North Atlantic Coast Comprehensive Study (NACCS) were modeled. These storms both produced storm surges of around the same magnitude in comparison to the 100-year event in Rhode Island. Development of a Realtime Wave and Storm Surge Forecasting Model For Rhode Island A set of MATLAB and bash programs were designed for preprocessing and automating the coupled wave and hydrodynamic model SWAN+ADCIRC for real time forecasting of waves and storm surge. The method allows the user to locally preprocess, package, and automate the system, while running the system externally using High Performance Computing (HPC). Each of the user input files are described, and the forecasting process is explained. The system is then applied to a SWAN+ADCIRC domain in Rhode Island, and tested during Stella, an extratropical event in March 2017, Nor’Easter Stella. The three day forecast system had a maximum offshore significant wave height Root Mean Squared Error (RMSE) of less than 1.2 m, and a storm surge RMSE of less than 0.2 meters during simulation of NorEaster Stella. The system was shown to be conveniently activated and monitored in the event of an emergency.

The objective of this study is to set up a suite of numerical models capable of simulating the impacts of storms on coastal flooding and erosion, and use it to assess performance of mitigation measures. Three numerical models were used to analyze the possible erosion due to inundation and overwash for a small section of coast in southern Rhode Island. SWAN (Simulating Waves Nearshore), a third-generation wave model was used to compute the wave conditions. ADCIRC (ADvanced CIRCulation Model), a three-dimensional circulation model used atmospheric and tidal forcing to generate water levels, and currents. A regional coupled SWAN+ADCIRC model was used to calculate water levels and wave conditions over an unstructured mesh. XBeach, a sediment transport model, encompasses a barrier system on the southern coast of Rhode Island, and is nested within the regional domain. A non-uniform cartesian grid with a resolution across dunes of 5×10 meters is used to calculate the sediment transport during storms, the resolution decreases to 25×25 meters resolution at the boundaries. Hurricane Sandy (2012) was used to calibrate the models, where volume of erosion was compared along transects monitored by the University of Rhode Island. The model was then forced with winds from Hurricane Irene (2011) for validation. The regional model had a root mean squared error (RMSE) of 0.21 meters for storm surge, and a RMSE of 0.18 meters for offshore significant wave height. The nearshore model was able to estimate erosion with an error of 24.26%. Once validated, two synthetic storms from the North Atlantic Coast Comprehensive Study (NACCS) were modeled. These storms both produced storm surges of around the same magnitude in comparison to the 100-year event in Rhode Island.

Development of a Realtime Wave and Storm Surge Forecasting Model For Rhode Island
A set of MATLAB and bash programs were designed for preprocessing and automating the coupled wave and hydrodynamic model SWAN+ADCIRC for real time forecasting of waves and storm surge. The method allows the user to locally preprocess, package, and automate the system, while running the system externally using High Performance Computing (HPC). Each of the user input files are described, and the forecasting process is explained. The system is then applied to a SWAN+ADCIRC domain in Rhode Island, and tested during Stella, an extrat-  Left: XBeach hourly input for NACCS 492 along the seaward boundary. Water elevation due to tide and surge (a) is applied in hourly increments, along with the 2-dimensional wave spectrum. The significant wave height (b), peak period (c), and peak direction (d) corresponding to the wave spectrum are shown for clarity. Right Overwash and dune profile changes before and after the storms were compared.
The validated model was used to analyze a hypothetical erosion mitigation effort, by altering the bathymetry within the model to simulate the presence of an artificial offshore reef. The impact on erosion was compared with and without the offshore reef, along both longshore and cross-shore transects and in two-dimensions across the entire domain. It was shown that in the collision and overwash regimes (i.e. Sandy, Irene) the artificial reef will protect dunes directly in its wake, however, foreshore erosion was accelerated. During a 100-year event, the reef will provide little to no protection to the dunes or beach. . Narragansett town beach is just one example of a location that has made efforts to maintain the coastline by restoring dunes and adding artificial sand to increase total beach area [44]. However, without protection from storms, restored beaches will likely continue eroding until they return to their natural equilibrium. While it is natural for the beach face to increase and decrease seasonally, beaches that are altered beyond the extent of these normal fluctuations will retreat due to sea level rise [10].
Historically, beach nourishment projects have focused on hardening the shoreline, recently, methods for erosion mitigation have taken a less invasive approach.
One approach is the construction of multi-purpose artificial reefs. Black

Objectives
The primary objective of this research is to develop and validate an accurate and efficient wave, storm surge, and sediment transport model for southern Rhode Island for assessing erosion and also mitigation measures. Two models will be developed to predict waves, water elevation, and nearshore sediment transport for the a region of coastline in southern Rhode Island. SWAN+ADCIRC, a hydrodynamic model developed by UNC (University of North Carolina) and Notre Dame will be used to calculate the wave heights and storm surge on a regional scale. XBeach, a sediment transport model developed by Deltares, TU Delft, and UNESCO-IHE, will be nested in the SWAN+ADCIRC model. Waves and water levels from the SWAN+ADCIRC model will be used as forcing for sediment transport. Bed level changes will be analyzed along dune transects, and throughout the nearshore model domain over the duration of the storm. This model will be used to analyze the potential impact of a 100-year storm, without assuming any changes of bathymetry due to sea level rise or receding shoreline. The focus will be on storm-scale analysis, with sediment transport simulations lasting a few days.
Hurricanes Irene (2011) and Sandy (2012) will be simulated to validate the model. The wave heights and storm surge within SWAN+ADCIRC will be compared to NOAA tidal and wave stations within the domain. Volume of beach erosion will be analyzed along three transects within the XBeach domain. Along each of the transects, which are measured bi-monthly, the measurements directly proceeding and following the event of interest are used. For the 100-year storm, the sediment transport will be analyzed along each of these transects.
Once the model was validated, the bathymetry in the XBeach model is altered to represent an artificial reef directly offshore from Charlestown beach. The accumulated erosion/accretion along the beach and dunes is compared to simulated results with and without the artificial reef present.

Numerical Models
This study uses ADCIRC, SWAN, and XBeach to estimate water levels, waves, and erosion, respectively, for a stretch of beach in southern Rhode Island.
The boundary conditions for the sediment transport model are produced using SWAN+ADCIRC.
SWAN is a third-generation wave model, developed by the Delft University of Technology [5]. It uses the spectral wave action balance equation to solve for the 2-Dimensional wave spectrum over the computational domain. It was coupled with ADCIRC, developed by the University of North Carolina, is an ocean model that uses the finite element method to solve for time dependent tidal and surge equations across an unstructured grid [7]. The numerical formulation of these models are summarized in Appendix A.
SWAN+ADCIRC was used to estimate the regional wave heights and water levels, and provide forcing for XBeach. XBeach, developed by Deltares, TU Delft, and UNESCO-IHE, is a sediment transport model developed for analysis of beach erosion in small domains [31]. It is a fully integrated sediment transport model, comprised of short wave, hydrodynamic or long wave, sediment transport, and morphologic modules. Appendix B contains further description and the mathematical formulation of XBeach. Lagoon. An XBeach model covering this domain is used for analysis of sediment transport during storms. In order to provide accurate input for this region, waves and tide need to be modeled on a much larger scale. Two computational domains were used for this research.  [9] produced a high resolution regional ADCIRC mesh based on the Northeast Coastal Ocean Forecast System (NECOFS) Gulf of Maine (GOM4) [7]. The mesh resolution along the southern coast of Rhode Island has been increased from 1000 to 200 meters (with 100 meter resolution near inlets). Figure 2 shows the regional domain, and the nesting of the nearshore domain over the mesh. flux within this region would be considerably less than an exposed strip of beach.

Area of Study
This reduces unrealistic sediment accretion near boundaries, as sediment should be preserved between Green Hill and the breachway.
The domain chosen extends beyond the area of interest, to prevent additional erosion or accretion due to the presence of the boundaries from affecting the results.
Obliquely incident wave directions tend to artificially accelerate erosion along the exposed boundary, and reduce erosion along the shadowed boundary in the XBeach model. To correct these issues, the domain size was increased using increasing grid spacing in these shadow zones. The resulting domain, shown in Figure 3 was 5000 by 3500 meters in the longshore and cross-shore directions, respectively.

Historic and Synthetic Storms
Four simulations of tropical storms were performed, which are shown in Figure   4. Hurricanes Irene (2011) and Sandy (2014) were used as validation for the SWAN+ADCIRC and XBeach models. Using save points from the NACCS study, two synthetic storms with peak water elevations close to the 100-year return period water elevation in Newport were chosen. The tropical storm parameters from these storms were applied to a symmetric Holland parametric wind field, and used to force the wave, surge, and sediment transport model.

Data Model Forcing and Bathymetric Data
The topographic data used for the XBeach domain is 1 meter resolution, on the state plane coordinate system, the z datum is in feet, and referenced to NAVD88.
Topographic data was taken using LIDAR, the data was made available online by the Rhode Island Geographic Information System [30]. This also allows for high resolution computation without the use of grid nesting.
The nodal spacing at the boundaries is approximately 100 km, while the nearshore resolution varies from 30-100 m. During a storm, tidal forcing is applied to each of the boundary nodes, and atmospheric forcing is applied across the entire domain.  [9] showed that if available, the WRF wind forcing provides the most accurate results for both waves and storm surge in the state of Rhode Island. Figure 6 shows a snapshot of the WRF forcing over the SWAN+ADCIRC domain. WRF was used as forcing for Sandy, and because it was unavailable, ECMWF was used for Irene.
The 10-meter U, V components, and surface pressure were applied to SWAN+ADCIRC by interpolating onto each node in the domain in hourly increments. ADCIRC interpolates these values internally for each computational time step (0.5 seconds), and the coupled SWAN model reads wind, water levels, and friction from ADCIRC and uses these to compute the wave conditions every 10 minutes.    Values of 0.3 and 0.25 were both used, in order to calibrate the XBeach model. Table 1 summarizes the parameters used for the sediment transport model.

Development of Beach Erosion Model
Validation of the regional model To validate the SWAN+ADCIRC model, wave data was compared offshore with measurements taken from the Scripps CDIP 154 buoy historical database [42]. Water elevations were compared to the Newport water elevation station in 6 minute increments, referenced to mean sea level, elevation in meters [5]. Addition-ally, three Acoustic Doppler Current Profilers that had been installed by Woods Hole Group from August 2010-October 2011 were used to validate nearshore wave heights during hurricane Irene (whgC, whgW in Figure 8). A hindcast of Hurricane Sandy was modeled to validate wave heights, and water levels within the domain.
First, the SWAN+ADCIRC model was run in order to compute the boundary inputs for XBeach. NECOFS WRF hindcast winds were obtained from UMASS Dartmouth 2 , and used to force the model. A comparison of the time series at the Newport water elevation station and CDIP 154 wave buoy can be seen in Figure   9.  Sandy was performed to further analyze the accuracy of the model. During the simulation, the 2-D wave spectrum was extracted from the node nearest to CDIP 154 buoy, and was compared with the measured 9-band spectra. Figure 11 compares the observed energy in 9 frequency bins with the corresponding wave spectrum in SWAN+ADCIRC. Table 2 shows the RMSE of the water levels from the NOAA Newport water level station, along with significant wave height, and 1-Dimensional spectrum from the CDIP 154 buoy. By breaking down the observed energy spectrum, the performance of the model can be further assessed. The greatest error was located in the bins between 12 and 16 seconds, these bins also contained the largest observed energy. The SWAN+ADCIRC model overestimates energy in the lower frequencies (16 s<Tp<22 s), and tends underes-timate the high frequency tail (Tp<5 s). However, the total energy of the model is close to the observations. dataset provided satisfactory results for both waves and surge. The error of peak significant wave heights offshore was -6.2%, and maximum water level error at the Newport tidal guage was 22%. Nearshore, the error for the peak significant wave heights observed in Charelstown, and Westerly, Rhode Island (whgW and whgC in Figure 8) were 10 and 13 percent, respectively. The nearshore model forcing for Irene was extracted from this model at the location of the XBeach domain origin.

Calibration of XBeach
Waves and water level were taken from the regional model during hurricane Sandy and used to force and calibrate the nearshore model. During hurricane Sandy, the Green Hill and Charlestown Breachway (GH and CBW in Figure 12) stakes were washed away. The Green hill stake was replaced, while the Charlestown Breachway transect was not. The reference change at Green Hill (approximately 10 m North of the previous measurement) was accounted for by shifting the reference points of the post-storm observations. Because the Charlestown Breachway stake was not replaced, there is no post-Sandy data along that transect, and data was not compared at this location during calibration.
Sandy resulted in minor dune over-topping throughout the domain. Figure   14 shows the simulated erosion throughout the XBeach domain during hurricane Sandy. A low-lying region between Green Hill and Charlestown experienced the     In Table 3  during the simulations of hurricanes Irene and Sandy. The simulated erosion for hurricane Irene is compared to the measured data in Figure 20, the percent error along each of these transects are in Table 5.   is only 24 hours. Figure 25 shows the bed level change for the two synthetic storm simulations, and Figure 26 shows the maximum inundation during the storm.
The track of synthetic storm 457 was similar to Hurricane Sandy, as the storm heading is towards the Northwest at landfall. However, the storm makes landfall in Rhode Island, and the RMW of the synthetic storm passes through Providence.

Effect of reef on erosion
Because the sediment transport was validated in the collision and overtopping regime, Sandy and Irene were simulated again, over an altered bathymetry in order to analyze the impact of an artificial reef on beach erosion during storm conditions.
The impact of the reef was compared by comparing the accumulated erosion with and without the artificial reef present. This was done in both 2-dimensions across the entire domain, and along a series of ten theoretical transects behind the reef, shown on the right in Figure 28. A cross-shore transect, 500 m in length, was created along the dune crest to analyze the effect of the artificial reef on overwash (plot a in Figure 29). Three 200 m long cross-shore transects span from the surf zone over the dune crest(plots b-d in in Fig. 29).
The presence of the artificial reef provided protection for the beach and dune face directly leeward of the reef. However, increased erosion occurred in the wake   During Hurricane Irene, the two Woods Hole Group data provided nearshore wave height measurements. The 'Center' ADCP was near the XBeach domain, and provided a good idea of the accuracy of the performance SWAN+ADCIRC model's wave predictions. The error between the peak modeled and observed significant wave height during Irene was less than 10% [9].

Synthetic Storms
A 100-year storm was modeled by generating a storm that matched the upper limit of the 95% confidence interval for the 1% annual recurrence water levels in Newport, Rhode Island (2.81 m NAD88) [5]. Two storms from the NACCS exceeded this value: 3.48 and 3.50 meters for storms 457 and 492, respectively.
The atmospheric forcing from these storms were used to force the regional model. [35] showed that the NACCS overestimated the water levels in Newport and Providence. Additionally, the low resolution in the southern coast of Rhode Island resulted in inaccuracies near coastal ponds. For storm number 457, the high resolution model showed good agreement for winds in relation to the NACCS study at the three save points shown in Figure 22. The peak water level in Newport in the regional model was 3.05 meters without tide. Additionally, the exclusion of the remainder of Ningret pond may adversely affect dune overwash in the study area.

Erosion Due to Synthetic 100-year Storms
Water elevation due to storm surge, wave set-up, and total storm duration are the greatest factors to consider when identifying threats of beach erosion due to storms. Although the waves and water levels during the NACCS 492 storm were greater than that of 497, the much slower traveling NACCS 457 had a much longer duration, leading to a more significant amount of erosion. The direction of swell does not have as great an impact on the eroded beach volume in comparison to the surge, wave height, and duration [32]. Once the storm enters the overwash regime, longshore transport is no longer the dominating factor on erosion.

Artificial Reef
Based on the results from hurricanes Irene and Sandy, the response sediment behind the artificial reef was affected by swell direction, magnitude of surge, and storm duration. For both Sandy, and Irene, the presence of the reef reduced the total impact of waves on the dunes. During Irene, waves came from a more southerly direction, reducing erosion on the eastern side of the Reef, and increasing erosion on the western side. During Sandy, more erosion was observed east of the reef, while less was observed to the west. The Dunes directly in the wake of the reef are almost completely protected (see transects a in Figure 28), but dunes towards the east are impacted slightly more.
To improve the impact of the artificial reef, building more reefs in series, as a segmented breakwater system would provide better protection from storms [41].
A larger region of coastline behind the reef would be protected, and reduce the impact of swell direction during storms. The structural integrity of a reef placed directly offshore should also be researched, as the assumption that the reef cannot be eroded is not realistic under extreme conditions. For hurricanes Irene, and Sandy, scour can be seen along the lee-side of the reef, and design changes may need to be made, in order to reduce erosion around the base.

Conclusion
In this work, SWAN+ADCIRC and XBeach models were calibrated using Hurricane Sandy, and validated using Irene for Sandy, and 24.26% for Irene.
The above methodology was used for a mitigation study along a section of the barrier beach within the domain. Hurricanes Irene and Sandy were simulated again using an altered bathymetry file containing a non-erodible artificial reef, as an effort to protect the beach and dunes behind it. The model results were compared to the control test to determine the magnitude of shoreline and dune mitigation in the area behind the reef. During Hurricane Sandy, erosion was mitigated along the dune crest leeward of the reef, mitigating dune erosion by as much as 2 meters.
Storms resulting in moderate overwash may be mitigated behind the reef, but events with severe surge and waves will not be mitigated. Neither of the NACCS storms were mitigated by the reef, as the magnitude of surge and tide during the peak reduced the frequency of wave breaking over the reef. Additionally, steep angled swells (i.e. large angle of incidence in relation to beach contours) will pass behind the reef, and erosion will not be mitigated.
Due to time restraints, variable friction was not considered in this study.      Table 7, and full codes are listed in Appendix D.

Methods
The presented Matlab and Bash scripts are designed to be distributed freely, and altered for the needs of the user. With the exception of Matlab, all software requirements for implementation are open source, and free. Upon activation, the system will download wind from the outside source specified by the user. In the case of this study, NECOFS (Northeast Coastal Ocean Forecasting System) [2] forcing was used 1 . The meteorological forcing will be used in the ADCIRC-SWAN model. Dates and tidal constituents in the SWAN and ADCIRC control files will be changed based on the dates corresponding to the meteorological forcing. The new input files will be moved into a folder, and sent to an external computer cluster for computation. Figure 30 summarizes these forecasting processes in a flow chart.
The functionality of these codes are explained in the following sections.

Bash and MATLAB Codes Requirements
A complete SWAN+ADCIRC model should be used in the required input explained below. Additionally, the user should have the software listed in Table 6 downloaded on the system.

Nodal Attributes in ADCIRC
The locations of each node from the ADCIRC grid and boundary information file (fort.14) are required. The nodal number, and corresponding longitude and latitude points should be saved in variable names node, x, and y, respectively within a file named FEM.mat. By saving the data into a .mat file, the fort.14 does not need to be executed every iteration, thus, saving computation time.

Meteorological Forcing
The meteorological forcing must be on a cartesian grid, as the global 10-meter wind velocities, and pressure are interpolated onto each of the nodes. It is advised that the meteorological forcing covers the entire grid, although it is not required.
The wind variables should be in units of meters per second (m/s), and pressure should be in meters of water (mH 2 O). As wind forcing sources vary significantly from one another, the user should edit the function metinput.m so the Lon, Lat, U, V, P, t, and dt are properly generated for each time step. The format of each of these variables are described in the provided metimput.m file, in Appendix D.3.1.
If the nodal attributes file domain is larger than the meteorological forcing, the boundary will be extended, a wind velocity of zero, and pressure of 10.332 mH20 (1013.25 mbar) will be applied to a new outermost boundary to prevent instabilities along this boundary. It should be noted that if the meteorological forcing does not cover the computational domain, results near the uncovered boundaries may have high uncertainties. An altered version of this code reads from a text file rather than prompting the user to manually enter the run date, duration and nodal factors. This information is provided in the tide fac.in file, and is automatically changed in preprocess1.m based on the date given in met inputs.m. The line numbers that correspond to each of the tidal constituents are included in tidelines.txt file, shown in Table 8. These specify the lines what will be changed by preprocess2.m, and which constituents will not be included.

Automation of SWAN control file
The SWAN control file (fort.26) does not need to be changed once an ADCIRC model has been configured. However, the reference dates within the file should be changed to prevent confusion when analyzing the output from multiple runs. The  Table 9. This should be followed by the strings that normally precede the input lines. Next, any custom lines can be added. The example model pulls output at the node on the grid near the NOAA 44097/CDIP 154 buoy, and uses the output for validation.

Automation
In order for the system to run properly, the location of the working folder, containing all the ADCIRC input, should be assigned to the HOMEdir variable. The lines at the beginning of the forecast script should also be changed to download the files used for meteorological forcing (refer to comments in Appendix D.2.1).
To remotely access the system where ADCIRC will be executed, a series of expect scripts are controlled by the bash script remote.sh. Enter the IP, and login credentials, along with strings the system returns while logging in. prep.sh will automatically login/run/logout the necessary ADCIRC prep functions. run.sh will execute the batch file on your system, which must be made separately based on user specifications.
After changing the user inputs, the functions within forecast can be added the environment by executing the following commands from the home directory of the forecasting system.
user@computer $ source f o r e c a s t This will add all the bash functions within the script named forecast into the local environment.
user@computer $ runONCE Should be used to run the entire process once user@computer $ runLOOP Should be used to begin an infinite loop. This terminal window will run and submit a run. Upon completion, it will wait until the specified time in forecast, and continue to execute daily until terminated by the user.
user@computer $ runLOCAL Can be used to run the system locally.

Application of Forecasting System in Rhode Island
The forecasting system was applied to a SWAN+ADCRIC model focused in Rhode Island during Nor'Easter Stella, which was the most significant extratropical event of the 2016−2017 winter season. The storm resulted in coastal flooding in New Jersey and as much as 5 feet of snow (1.5 m) to some areas [10] across the Northeast United States. This Storm provided an opportunity to test the accuracy of the described forecast system for both waves and surge. WRF wind model provided by NECOFS was applied to a mesh tested and validated by URI [9]. The atmospheric forcing and computational domain are shown in Figure 31.
The mesh has a resolution of 100 m nearshore, and was merged into GOM4 [2] to provide higher resolution in Rhode Island.
The forecast was executed two days before the arrival of Nor'Easter Stella.
As shown in Figures 32 and 33, the forecasting system more accurately predicts water levels and surge nearing days three and four of the model simulation. The Significant wave height is under-predicted by approximately 1m at the peak of the storm. Figure 33 shows the Root Mean Squared Error (RMSE) for both water level and waves during the duration of the forecast. The magnitude of error is greatest at the start of the simulation for water level, as the ramp function takes a number of days to bring tides up to phase. There was also a slight bump in error during the peak of the storm. The error of wave heights got larger as the forecasting period approached the peak of the storm.

Modeling Synthetic Storms Representing the 100-year Event
After hurricane Sandy, the USACE performed the North Atlantic Coastal Comprehensive Study [8], a coastal hazard study for resilience adaptation towards an increased risk to ports, coastal communities, and businesses. The study ad- If tides are added to the simulation, the peak water elevations during each of the NACCS storm 457 would be greater than NOAA's expected 100-year return period water elevation in Newport. The track of this storm can be seen in Figure 34.

Discussion and Conclusion
where: can be written as: where U and V are the depth averaged velocities. H is water column depth.
Unlike SWAN, ADCIRC is conditionally stable, and is subject to CFL criterion. While SWAN can have a computational time step of a matter of minutes, most ADCIRC models use a time step in the order of fractions of a second to a few seconds.

A.3 SWAN+ADCIRC coupling
Coupling SWAN+ADCIRC allows for computation of water levels, currents, and waves in a non-stationary timeframe. SWAN also has the ability to compute   Because of this, the boundary conditions will be created using wave and water level conditions produced by the SWAN+ADCIRC models. During computation, four different modules are used to calculate erosion. Hydrodynamics consist of a short-wave modeule, and a flow module, which both recieve boundary conditions to calulate waves, currents, and surface elevations. The Morphodynamic modules calculate sediment transport and changes in bed level based on the hydrodynamics.

B.1 Hydrodynamics
The XBeach hydrodynamic modules consist of a short wave module, and a flow module.

B.1.1 Short wave module
The stationary mode wave action balance equation used by XBeach is shown below:

B.1.2 Flow module
The flow module calculates the water elevations, and depth averaged water velocities over the domain, based on boundary conditions. It provides surface elevation and lagrangian particle velocities to the short wave and sediment transport modules.
Shallow water equations: GLM shallow water equations:

B.2 Morphodynamics
The morphodynamics in XBeach include sediment transport and morphology modules.

B.2.2 Morphology module
The bed updating equation is determined by gradient of sediment transport: To simulate erosion and collapsing of dunes, the avalanching formulation is included in XBeach formulation.
APPENDIX C An Efficient Method to Study Long-Term Sediment Transport

C.1 Introduction
In manuscript 1, a wave, surge, and sediment transport model for storm-scale analysis of beach erosion was developed, and used to analyze the feasibility of using artificial reefs for erosion mitigation. While storms pose the greatest threat to dunes and coastal communities, long-term analysis of sediment transport is needed when considering the installation of any shoreline structure, such as an artificial reef in this case. It is likely that the natural beach equilibrium will be affected, over the course of a matter of months, or years. The following methodology presents a simplified method for providing boundary forcing for the nearshore sediment transport model. A simplified sediment transport model was used to analyze beach profile response due to the installation of an artificial reef. Two parameters were adjusted to increase dissipation from the boundary to shore.
Hurricane Sandy was the second costliest storm in the U.S. history, and significantly impacted a number of cities in the northeast United States. The storm made landfall in New Jersey, more than 200 km from Rhode Island, large waves and storm surge still caused major damage to communities along the southern coast. Although the damage in Rhode Island was significant, the return period of the storm was well bellow 100 years. In this study, Hurricane Sandy was simulated in the state of Rhode Island by assuming a number of sea level rise scenarios. The purpose of this simulation was to assess the nonlinear effects of sea level rise on storm surge. In other words, is it acceptable to simply add sea level rise estimates to the simulation results (using linear superposition), or should the bathymetry be altered, and each simulation run again (nonlinearly)?

E.1 summary
The effects of Sea level rise in Narragansett bay were analyzed using a variety of methods. With both 0.91 and 2.13 m of sea level rise, little nonlinear impact of sea level rise was observed. With increasing sea level rise, water levels up Narragansett bay are damped for hurricane Sandy.