Significant wave height percentage decrease as a result of varying model parameters as indicated above each panel using SNL-SWAN Switch 1.. Mean wave direction decrease degrees as a resu
Introduction
Objectives
The objectives of the SNL-SWAN evaluation and the WEC sensitivity study were to compare SNL-SWAN against the native SWAN code and to assess how a range of WEC devices influence nearshore wave propagation through SNL-SWAN model simulations To achieve these goals, the study performed a direct comparison between SNL-SWAN and the native SWAN implementation and conducted simulations across multiple WEC configurations to quantify their impact on nearshore wave fields.
(1) Evaluate the modified wave propagation model, SNL-SWAN, which allows the incorporation of device-specific WEC characteristics to assess their effects on nearshore wave propagation
(2) Optimize SNL-SWAN model parameters to minimize model artifacts and edge effects
Perform a model sensitivity analysis using SNL-SWAN to examine how variations in incident wave height, wave period, frequency distribution spread, directional distribution spread, WEC device type and size, the number of WECs, and spacing within the WEC array affect near-field and far-field wave conditions in the lee of the devices, applying a methodology aligned with the native SWAN model as used by Chang et al.
(4) Investigate the differences in derived transmission coefficients for SNL-SWAN switch 1 and switch 2 (“switches” are described below).
SNL-SWAN Model Evaluation
SNL-SWAN Evaluation Model Set-Up
To simplify the evaluation of the SNL-SWAN model, we used a two-nested model-domain framework covering Monterey Bay and Santa Cruz The assessment employed the same model configuration described in Chang et al., ensuring consistency with prior work.
Using a previously validated SWAN model for the region, waves were propagated from deep-water offshore to shallow-water zones Local NOAA NDBC buoys provided measurements dating back to 1987, including significant wave heights, dominant wave periods, peak wave directions, wind speeds, and wind directions These observed datasets were compared with model outputs to demonstrate excellent model performance The wave model and its validation are described in Chang et al (2010, unpublished) and illustrated in 2014 (Figure 1).
Two nested SNL-SWAN model grids were used to predict the propagation of deep-water waves from offshore Monterey Bay, California, to nearshore Santa Cruz, California The coarse Monterey Bay model domain, shown in Figure 1, used a latitude-longitude grid spacing of about 0.001° (roughly 100 m in both x and y) The simulation was run as a stationary model, with offshore meteorological and hydrodynamic conditions held constant at the boundaries Directional wave energy spectra generated by the coarse-resolution Monterey Bay model were exported and used as boundary conditions for the nested, high-resolution Santa Cruz model domain, enabling refined nearshore wave predictions.
Grid resolution of the nested Santa Cruz model domain was matched to the size of the modeled wave energy converter (WEC), selecting a 25‑m floating two‑body heaving converter (F-2HB; Babarit, 2012) for the SNL-SWAN evaluation Consequently, the Santa Cruz model grid spacing was approximately 0.00025° in both latitude and longitude Wave spectrum boundary conditions were applied along the offshore boundaries of the Santa Cruz SNL-SWAN model domain The nested grid model was implemented as a stationary model.
Figure 1 Monterey Bay and Santa Cruz, CA model domains used for SNL-SWAN model evaluation
SNL-SWAN was run in three configurations—Switch 0, Switch 1, and Switch 2—with a native SWAN model included for comparison All simulations used the same initial wave conditions: 1.5 m significant wave height, a 12.5 s peak period, a mean wave direction of 205°, plus a frequency distribution spread of 3.3 and a directional distribution spread of 10.
All four model runs (three SNL-SWAN switches and one native SWAN model run) incorporated an array of 10 WEC devices with zero wave energy reflection allowed, centered on the 40 m depth contour The WEC device array was arranged in a honeycomb/diamond-shape as a representative configuration (Figure 2) WEC devices were simulated in the model with 6- diameter spacing between devices, center to center Devices were equally spaced in all directions Again, the simulated WEC device type was a floating two-body heaving converter with 25 m diameter (same as the grid spacing for the nested Santa Cruz model domain)
Figure 2 Example honeycomb geometry of a 10-WEC device array in the model
The model results were evaluated at six shoreline locations along the Santa Cruz coast on the 10 m, 20 m, and 30 m depth contours as described in
Table 2 and shown in Figure 3 The shoreline locations were, from west to east:
Table 2 Model output locations for SNL-SWAN model evaluation
1 30 m - West Santa Cruz 10 30 m – Santa Cruz Harbor
2 20 m - West Santa Cruz 11 20 m – Santa Cruz Harbor
3 10 m - West Santa Cruz 12 10 m – Santa Cruz Harbor
4 30 m - Steamer Lane 13 30 m – East 26th Ave
5 20 m - Steamer Lane 14 20 m – East 26th Ave
6 10 m - Steamer Lane 15 10 m – East 26th Ave
7 30 m – Santa Cruz Wharf 16 30 m - Pleasure Point
8 20 m – Santa Cruz Wharf 17 20 m - Pleasure Point
9 10 m – Santa Cruz Wharf 18 10 m - Pleasure Point
Figure 3 Eighteen model output locations in the Santa Cruz, CA model domain with example WEC device array shown.
SNL-SWAN Evaluation Results
SNL-SWAN was first run for Switch 2 and then for Switch 1 The computed transmission coefficient (Kt) outputs for the 10 WEC array from the Switch 2 and Switch 1 model runs nearly identical (
From Table 3, the average Kt value of 0.86 was specified as the transmission coefficient for both the SNL-SWAN Switch 0 and the native SWAN model run, and the results were evaluated for the 18 output locations described above.
With a transmission coefficient of 0.86, SNL-SWAN Switch 0 yielded results identical to the native SWAN model (Figure 4) SNL-SWAN Switch 1 and Switch 2 produced nearly identical results as well, differing only at output location 7 by 0.1 cm, demonstrating consistency across switch configurations and alignment with reference SWAN performance.
Comparing SWAN Switch 0 and native SWAN results with SNL-SWAN Switch 1 and Switch 2 shows a maximum difference in simulated wave height of 0.5 cm at locations directly in the lee of the WECs, indicating that the SNL-SWAN wave model largely aligns with the reference results Overall, these findings demonstrate that the SNL-SWAN wave model was generally operating as intended under the conditions specified for the SNL-SWAN model evaluation.
Table 3 Transmission coefficients (Kt) for 10 WEC devices computed from SNL-SWAN evaluation model runs, Switch 1 and Switch 2
Figure 4 Simulated wave height for SNL-SWAN model evaluation runs The text on the left indicates the simulated wave height at each of the 18 output locations.
SNL-SWAN Model Parameter Optimization
SNL-SWAN Optimization Model Set-Up
To evaluate the SNL-SWAN model, the nearshore study area encompassed Monterey Bay and Santa Cruz, California (Figure 1) Two nested SNL-SWAN model grids were used to predict the propagation of deep-water waves from offshore Monterey Bay to nearshore Santa Cruz The Monterey Bay model domain had a resolution of approximately 0.001° in latitude and longitude, while the nested Santa Cruz domain's computational grid was sized to match the WEC device type For model optimization runs, the device chosen was a 20‑m floating two-body heaving converter (F-2HB; Babarit, 2012).
Historical wave conditions offshore of Monterey Bay are well understood thanks to long-term wave data from several NOAA NDBC and CDIP buoys Representative data from NOAA NDBC buoy 46042 are used to characterize typical and extreme wave conditions in the Monterey Bay region The buoy is located 27 nautical miles west-northwest of Monterey, California, in water depths greater than 2,000 meters, and it has recorded data at this location continuously since 1987, making it a statistically robust source for evaluating offshore wave conditions approaching Monterey Bay.
From historical data, a wave height and wave period rose diagram was generated to evaluate the historical wave climate Significant wave height is the average of the highest one-third of recorded wave heights, while the dominant wave periods correspond to the frequencies containing the largest amount of wave energy Mean wave directions indicate the directions from which the dominant waves—those associated with the dominant period—approach.
Buoy data show a dominant wave direction from the northwest (270–360 degrees True North) toward the Monterey Bay region, with most waves arriving from this northwesterly direction The plots also reveal the most frequently occurring wave heights and wave periods, indicated by the color-band magnitudes, while the basic statistics from all available buoy data are summarized in Table 4 Figures 6, 7, and 8 display histograms of each wave property and provide a visual comparison to the model input values selected for this modeling effort Overall, the results indicate that the majority of waves approach Monterey Bay from the northwest and that more than half of recorded waves have heights of 2.0 meters or less and periods shorter than 12 seconds.
In wave data, the wave heights refer to significant wave heights, while the wave periods denote the dominant wave periods The wave directions, captured as the mean wave direction (MWD) by the buoy, indicate the directions from which the waves approach.
Figure 5 Wave height (left) and wave period (right) rose diagrams showing direction from which the waves are approaching Data collected by NOAA NDBC buoy #46042
Table 4 Statistical data analysis - NOAA NDBC buoy #46042
Parameter and Units Mean Value Median Value Mode Value
Figure 6 Wave height histogram (frequency of occurrence) - NOAA NDBC buoy #46042
Figure 7 Wave period histogram (frequency of occurrence) - NOAA NDBC buoy #46042
Figure 8 Wave direction histogram (frequency of occurrence) - NOAA NDBC buoy
To model a scenario with potential nearshore and shoreline impacts at Santa Cruz, representative offshore wave conditions were selected for their ability to modify nearshore wave properties Analysis of NOAA NDBC buoy #46042 data yielded a significant wave height (Hs) of 1.7 m and a peak period (Tp) of 12.5 s, which were adopted as the representative offshore boundary conditions (Table 5) The offshore mean wave directions applied at the boundaries were 310 degrees and 205 degrees, chosen because these directions produce wave shadowing toward the nearest shoreline, approximately 5 km away, relative to the simulated WEC deployment locations (Table 5).
To evaluate the impacts of a WEC array on nearshore wave properties, a conservative modeling approach was used The analysis accounts for directional variability at Santa Cruz, with waves arriving from a southwesterly sector (180°–270° True North) about 15% of the time and from a northwesterly direction under other conditions.
Simulations show that waves arriving from 270° to 360° True North occur about 80% of the time The results illustrate the potential effects on wave properties near the Santa Cruz shoreline if an offshore wave energy converter (WEC) array were installed off Santa Cruz, highlighting how offshore deployment could influence nearshore wave dynamics.
Offshore model boundary conditions were specified for all wet boundaries—north, west, and south—of the Monterey Bay domain Waves were propagated from offshore to onshore across the entire domain, ensuring a consistent offshore-to-onshore wave field Wave frequency and directional spectra were extracted along the domain to characterize the resulting wave conditions.
The 'wet' boundaries of the Santa Cruz domain were used as boundary conditions for the nested Santa Cruz domain Waves were then propagated from the offshore boundaries of the Santa Cruz model domain toward the shoreline.
An array of 50 wave energy converters (WECs) of the 20-m F-2HB buoy type was modeled on the 40 m depth contour, with six-diameter center-to-center spacing chosen to leverage the device’s large size for easier alignment with the model grid The WEC devices were arranged in a representative honeycomb/diamond-shaped configuration (Figure 2) and spaced six diameters apart in all directions The devices were simulated in a model parameter optimization study using this six-diameter center-to-center spacing, and the output location information is described above and shown in Table 2 and Figure 3.
SNL-SWAN Model Optimization Parameters
Based on NOAA NDBC buoy 46042 data, the incident sea state was represented by the mode wave height of 1.7 meters and the mode wave period of 12.5 seconds, establishing the incident wave height and wave period conditions The frequency-spreading coefficient gamma was kept constant at 3.3 to define the spectral broadening for the scenario.
Directional resolution was varied from 15° down to 9°, with mdc values of 24 and 40 corresponding to these resolutions, respectively A 9° angular resolution was the highest achievable given a 5 m computational grid, and resolutions finer than 9° caused model allocation errors The two mdc values (24 and 40) were each run with directional spread (dd) set between 10 and 25, with diffraction alternately turned on and off When diffraction was enabled, the SWAN‑recommended smoothing parameters were applied (a = 0.2 and n = 6) Eight model parameter optimization runs were conducted, as shown in Table 6 The results were compared to simulations using the same parameter values but without WEC devices, and percent differences were computed accordingly.
Eq 1 where InitialValue and FinalValue was H s determined from model runs without WEC devices and with WEC devices, respectively
Table 6 SNL-SWAN model parameter optimization scenarios
Model parameter optimization was performed to minimize artifacts, as indicated by linear streaks in the lee of obstacles Researchers from Delft University of Technology suggest maximizing the directional spreading coefficient (dd) to achieve a more accurate representation of wave energy in the lee of obstacles, and they recommend exploring diffraction effects to further improve model fidelity.
SNL-SWAN Model Optimization Results
Model parameter optimization results are shown in Figure 9 Linear streaks appeared when the 15° directional resolution was used, arising from averaging model results into 24 directional bins (every 15° over 360°) These streaks were reduced when a 9° directional resolution (40 directional bins) was employed Further increases in directional resolution were not possible within the present model domain due to the relatively small computational grid size for the smallest modeled WEC devices High-resolution directional binning with a small grid (8 m or less) was not feasible because of memory allocation limitations in the model.
An increased directional spread (dd = 25) concentrates the influence of the WEC array in the lee of the obstacles, as shown by results with Dirtn Spread = 25 and Dirtn bin = 15° under both diffraction ON and OFF Both figure panels illustrate a focused wave-height reduction extending all the way to the shoreline directly in the WEC array's lee By contrast, runs with dd = 10 exhibit wave-height reductions that are more spread out laterally along the shoreline.
Diffraction from the Wave Energy Converter (WEC) array produces larger wave heights at the edges of its influence, reducing the difference in significant wave height (Hs) between model runs with and without WECs and, in some cases, even increasing edge wave heights Directly in the lee of the WEC array, wave heights are smaller, while the array enhances wave-height reduction toward the shoreline Additionally, streak-like effects appear in the lee of the WEC array, visible as vertical lines in Figure 10.
Based on the model parameter optimization results, SWAN’s diffraction representation is not accurate for the study’s purposes SWAN simplifies diffraction with a phase-decoupled approach to reduce computing requirements, which can cause edge effects in optimization simulations Diffraction should be used in regions where wave-height variability occurs over a horizontal scale of only a few wavelengths, and a higher directional resolution (mdc = 40) is recommended (Delft University of Technology, pers comm., 2013) Consequently, subsequent SNL-SWAN runs will incorporate these optimization findings, and Section 4 provides further sensitivity analyses of the ‘dd’ parameter across a range of WEC device types.
Figure 9 Percent difference in Hs between model optimization with and without WECs
Figure 10 Percent difference in Hs between model optimization with and without WECs illustrating diffraction streak effects.
SNL-SWAN Sensitivity Analysis – Part 1
Sensitivity Analysis Model Set-Up – Part 1
Three nested SNL-SWAN model grids were used to predict the propagation of deep-water waves from offshore Monterey Bay, California, to near-shore Santa Cruz, California The model domains for Monterey Bay, Santa Cruz, and the WEC area are shown in Figure 11 The Monterey Bay and Santa Cruz grids follow the specifications described in Section 2.1 The Monterey Bay grid has a resolution of approximately 0.001° in latitude and longitude and is run as a stationary model Directional wave energy spectra from the coarse-resolution Monterey Bay model were exported and used as boundary conditions for the nested, higher-resolution Santa Cruz model. -**Support Pollinations.AI:**🌸 **Ad** 🌸 Get free, AI-powered wave modeling support with Pollinations.AI—[Support our mission](https://pollinations.ai/redirect/kofi) and enhance your coastal predictions today!
The nested Santa Cruz model domain used a grid resolution of approximately 0.00025 degrees in both latitude and longitude Wave spectrum boundary conditions were applied along the offshore boundaries of the Santa Cruz SNL-SWAN domain The nested grid model was implemented as a stationary model Directional wave energy spectra from the Santa Cruz model domain were exported and used as boundary conditions for the nested, finest‑resolution model, hereafter referred to as the WEC model domain.
Within the nested WEC model domain, the grid resolution was approximately 0.00010 degrees in latitude and longitude, equating to about 10 meters in both x and y This grid size was finer than the full-scale WEC devices modeled in the study, enabling more detailed representation of near-field features In SWAN and SNL-SWAN wave models, obstacles are only represented in the wave propagation simulation when they cross computational grid points, making grid-point crossing a key factor in determining their impact on the results.
A computational grid size smaller than the full-scale WEC devices for which the power matrices are provided was chosen to ensure that obstacles crossed at least one grid point Santa Cruz model wave spectrum boundary conditions were applied along the offshore boundaries of the WEC SNL-SWAN model domain, and the inner nested grid model was implemented as a stationary model.
See Section 2.1 for a description of the WEC array and model output locations
Figure 11 presents the SNL-SWAN sensitivity analysis for a three-domain nested model, illustrating how the domain configuration influences WEC simulations In this figure, NDBC buoys are shown as stars, the white dot marks the simulated WEC array, and the black dots denote the model evaluation locations This layout provides a clear visual reference for assessing model sensitivity within the nested domains.
Sensitivity Analysis Parameters – Part 1
An assessment of the near- and far-field effects of wave energy converter (WEC) devices and arrays on the near-shore environment was conducted by examining changes in wave properties at 18 model-output locations (Figure 3) and by estimating the horizontal extent of these changes A targeted sensitivity analysis near Santa Cruz, CA explored potential nearshore wave-property changes by simulating three WEC device types, two incident wave heights, two incident wave periods, and by varying three frequency distribution spreading coefficients (gamma) and three directional distribution spreading coefficients (dd) (Table 7).
Using SNL-SWAN, a total of 108 model runs were conducted for Switch 1 (36 runs per WEC device type), with an additional 108 runs evaluated for Switch 2; these results were compared against 36 model runs conducted with no obstacles The simulations kept the initial mean wave direction constant at 205°, and each run included an array of 10 WEC devices (obstacles) with zero wave energy reflection, centered on the 40 m depth contour, as depicted in Figure 2.
Sensitivity analysis parameter values are shown in Table 7 The three wave energy converter (WEC) devices examined are: a bottom-fixed oscillating flap (B-OF), a floating two-body heaving converter (F-2HB), and a floating oscillating water column (F-OWC) The devices’ characteristic diameters (maximum of length and width) are 26 m for B-OF, 20 m for F-2HB, and 50 m for F-OWC, as stated by Babarit et al (2012) The power matrix for each device was computed following the approach described by Babarit et al (2012).
Using data from NOAA NDBC buoy #46042, two incident wave conditions were defined: a modal condition with wave height 1.7 m and period 12.5 s, and a 95th percentile condition with wave height 3.5 m and period 16 s For these conditions, the frequency spreading coefficient gamma was varied among 1, 3.3, and 10, while the directional spreading coefficient Dd was set to 2, 10, or 25.
Table 7 Sensitivity analysis parameter values
WEC Device Type [‘B-OF’, ‘F-2HB’, ‘F-OWC’]
Sensitivity Analysis Results – Part 1
Model results were retained for each model run listed in Appendix A, totaling 216 runs (108 for Switch 1 and 108 for Switch 2) The retained outputs include propagated wave heights, wave periods, wave directions, and near-bottom orbital velocities at every grid point within the model domains In addition, the same wave properties were extracted at 18 distinct model output locations to enable straightforward point-to-point comparisons across runs.
Figures 12 through 22 present sensitivity-analysis results as surface-to-surface comparisons between the modeled scenario and the baseline scenario, where the baseline does not include obstacles In Figures 12–17, black indicates no (or negligible) change in the wave parameter relative to the baseline Each figure includes color bars to define the magnitude of change, with change calculated as a percentage relative to the baseline (Eq 1) A positive change indicates a decrease in the wave parameter in the presence of a WEC array, and a negative change indicates an increase Additionally, the percentage change at each of the 18 model output locations is shown as text next to the corresponding output location number in each sub-figure, enabling rapid, case-to-case comparisons.
Results of significant wave height predictions from the sensitivity analysis using Switch 1 and Switch 2 are presented in Figures 12 and 13, with additional results for Switch 2 at Tp = 16 s shown in Figure 14 The model parameters, including the WEC device type and boundary conditions, are indicated above each subplot A clear outcome from these figures is that there appears to be an issue with running the SNL-SWAN model for Switch 2 at the initial wave period.
Assessment of 16-second wave conditions for the B-OF and F-2HB device types (Figure 14) showed that wave height increased in the lee of the WEC array The resultant transmission coefficients for both the B-OF buoy and the F-2HB buoy at a 16-second wave period were unrealistically high (values above 1.0) or negative The root cause was an error in the SNL-SWAN code that incorrectly passed variables from the model to the output PRINT file This issue has been debugged and fixed in the current SNL-SWAN version (Appendix A; Figure A1).
Switch 1 and Switch 2 results for model runs with initial wave period of 12.5 sec were comparable Wave height decreases of between zero and 3% were observed at the 18 output locations when compared to the baseline scenario The largest wave height decreases directly in lee of the WEC arrays and the longest horizontal impact (i.e largest effect toward the shoreline) occurred for the B-OF WEC device type The widest horizontal (along-shore) effects were largest for the F-OWC device type, which makes intuitive sense given that these are the largest devices
Near-bottom orbital velocities, which reflect wave-driven currents, scale directly with the surface wave expression, i.e., the significant wave height When wave heights decrease, near-bottom orbital velocities decline accordingly, potentially altering ambient current patterns in near-shore environments Consequently, the percentage differences in near-bottom orbital velocities essentially mirror those calculated from the significant wave height model scenarios No separate figures for near-bottom velocity percentage differences are presented, since these differences are equivalent to Figures 12, 13, and 14.
Percentage changes in peak wave periods observed in this study were negligible (Figure 15; Switch 2 results are identical and thus not shown) This outcome arises for two reasons: first, the model’s frequency-bin resolution may be too coarse to detect small changes in wave periods, since small frequency shifts do not necessarily alter the corresponding frequency bin in model space; second, because the model obstacles are absorbing and the transmission coefficient is effectively frequency-independent, there is no shift in dominant wave energy to alternate frequencies, leading to no change in peak wave energy Consequently, no appreciable change in peak wave periods is observed Note that up to -30% differences were found in peak wave periods for Switch 2 runs with a 16 s initial wave period and the B-OF and F-2HB WEC devices; this issue is described above and has since been resolved.
Changes in mean wave directions are illustrated in Error! Reference source not found.Figure
16 and Figure 17 as degrees changed (as opposed to percentage changes) for easy interpretation Negative changes (blue) indicate clockwise (CW) rotation of wave direction Positive changes (red) indicate counter-clockwise (CCW) rotation Rotation, when it occurred, was relatively large, for the same reasons described for peak periods: the directional bin spacing was 15- degrees Any changes less than this were indeterminable by the model
Recall from Chang et al (2014) that mean wave directions were most affected by the largest WEC device array(s) (e.g., greater than 100 WEC devices), which caused the largest horizontal extent wave shadowing effects in lee of the array(s) As a result of transmission coefficient and depth contour variation, mean wave directions were altered, but changes were minor For the present study, only 10 WEC devices were modeled in an array; hence directional changes were for the most part negligible throughout the WEC model domain Up to ~-15° differences were found near the 10 m depth contour for Switches 1 and 2 and also directly in the lee of the B-OF WEC array when using Switch 1
Figure 12 shows the percentage decrease in significant wave height that results from varying model parameters (indicated above each panel) when using SNL-SWAN Switch 1 The wave energy converter (WEC) array is centered on the 40 m depth contour and consists of 10 devices, with a note that the device diameters depicted in the figure are not to scale.
Figure 13 Same caption as for Figure 12 but using Switch 2
Figure 14 Same caption as for Figure 12 but for Switch 2 and T p = 16 s, shown to illustrate the issue with particular Switch 2 model runs.
Figure 15 Peak wave period percentage decrease as a result of varying model parameters, as indicated
Figure 16 Mean wave direction decrease (degrees) as a result of varying model parameters, as indicated, for SNL-SWANSwitch 1
Figure 17 Same caption as Figure 16 but for SNL-SWAN Switch 2.
Figure 18 presents how wave properties vary with wave height boundary conditions The eight-panel figure shows that the left four panels correspond to results obtained with Switch 1, while the right four panels display results for Switch 2; this layout emphasizes the impact of boundary condition selection on the observed wave properties Notably, the y-axis scales differ between the two sets of panels, underscoring the sensitivity of wave-property measurements to the chosen boundary condition and the comparative performance of Switch 1 versus Switch 2.
Figure 19 summarizes how wave properties vary with wave-period boundary conditions across 216 model runs The eight panels are divided into two sets: the left four panels correspond to Switch 1, while the right four panels correspond to Switch 2 The comparison reveals distinct patterns between the two boundary-condition configurations, and the y-axis scales differ between the panel groups, indicating that Switch 1 and Switch 2 yield different representations of the wave-property variation under the same period changes.
Figure 20 illustrates how wave properties vary with the spread of the frequency distribution across all 216 model runs The left four panels show results for Switch 1, while the right four panels present results for Switch 2, highlighting how the two switch configurations influence the relationship between wave characteristics and frequency spread Notice the differences in the y-axes between the panel sets, which reflect how switch choice alters the observed variation in wave properties relative to the distribution spread.
Figure 21 illustrates the variation of wave properties as a function of directional distribution spread across all 216 model runs The left four panels present results obtained with Switch 1, while the right four panels show results from Switch 2 The comparison highlights notable differences in the y-axes between the two switch configurations, demonstrating how changing the directional distribution parameter alters the relationship between wave properties and spread.
Figure 22 shows how wave properties vary with the WEC device type across all 216 model runs, with the left four panels representing Switch 1 results and the right four panels representing Switch 2 results, and it highlights the differences in the y-axes between the two switch configurations.
SNL-SWAN Sensitivity Analysis – Part 2
Sensitivity Analysis Parameters – Part 2
Model sensitivity analysis was performed using SNL-SWAN to understand how a WEC array's behavior responds to variations in device type, size, spacing, and the number of devices To examine potential wave-property changes near the Santa Cruz, CA shoreline, eight WEC device types spanning seven diameters were simulated in honeycomb/diamond-shaped arrays containing 10, 50, or 100 devices with inter-device spacings of 4, 6, or 8 diameters The power matrix for each device type was computed following Babarit et al (2012).
Table 8 WEC device types and associated diameters (maximum of length and width; from Babarit et al., 2012) simulated for SNL-SWAN model sensitivity analysis
Small bottom-referenced heaving buoy Bref-HB 5*
Bottom-fixed heave-buoy array # B-HBA 5
Bottom-referenced submerged heave-buoy # Bref-SHB 7
Floating heave-buoy array % F-HBA 8
Floating three-body oscillating flap device F3 OF 9.5
Floating two-body heaving converter F-2HB 20
Bottom-fixed oscillating flap B-OF 26
Floating oscillating water column F-OWC 50
* The Bref-HB size was listed as 3 m; however it was specified as 5 m in SNL-SWAN model runs due to limitations on computational grid size
#B-HBA and Bref-SHB were modeled as obstacles that extended throughout the water column although both are devices without surface expressions
%F-HBA is a multi-body wave energy converter (WEC) composed of multiple heaving buoys linked to a submerged structure The overall dimension of %F-HBA varies with the number of buoys, so in modeling it is represented as a single obstacle with an 8-meter diameter.
Sensitivity Analysis Model Set-Up – Part 2
The nested model domains used for WEC devices larger than 15 m in diameter followed the same configuration described in Section 3.1 and illustrated in Figure 1 For these cases, the inner Santa Cruz model domain grid size was aligned with the specific WEC device being modeled, effectively treating each device as equivalent to a single model grid cell to streamline performance evaluation and assessment.
WEC devices smaller than 15 m in diameter were simulated using a triple-nested SNL-SWAN framework due to grid-cell size constraints that prevent modeling sub-15 m cells in a single domain The additional nested grid supports higher resolution in the WEC domain, encompassing Monterey Bay, WEC, and Santa Cruz, as shown in Figures 26 and 27 The coarse Monterey Bay domain used roughly 100 m grid spacing in both x and y and was run as a stationary model Directional wave energy spectra generated by the coarse-resolution domain were then exported and imposed as boundary conditions for the finer, nested WEC-domain model.
Grid resolution in the nested WEC model was set to match the modeled device diameter, with 5 m devices requiring a smaller domain due to computational limitations, while devices ranging from 6 to 10 m demanded a larger WEC domain to accommodate an array of up to 100 devices; the nested grid model was implemented as a stationary model, with wave spectrum boundary conditions applied along the southern offshore boundary of the Santa Cruz domain, and to minimize boundary effects the boundary between the WEC domain and the Santa Cruz domain was extended sufficiently to the west.
Within the innermost Santa Cruz model domain, the computational grid has a resolution of approximately 0.00025 degrees in latitude and longitude, corresponding to roughly 25 meters in the x and y directions The innermost Santa Cruz domain was also implemented as a stationary model, furnishing a fixed spatial framework for the simulations.
A total of 144 model runs were conducted, with 72 runs for each SNL-SWAN Switch 1 and Switch 2 configuration, and seven runs with no WECs representing seven distinct device sizes The initial wave conditions were Hs = 1.7 m, Tp = 12.5 s, mean wave direction 205°, frequency spread 3.3, and directional spread 25°, and these conditions were held constant across all model runs All simulations were performed with a 9° directional resolution (mdc = 40), zero wave energy reflection allowed, no diffraction, and the WEC array centered on the 40 m depth contour, as shown in Figure 2 Model sensitivity analysis parameters for each model run are summarized in Appendix B.
Figure 26 presents the SNL-SWAN model domains for devices under 6 m in diameter, covering Monterey Bay, the WEC domain bounded by solid lines, and the Santa Cruz domain bounded on the north, west, and east by dashed lines, with the 40 m depth contour indicated by a dotted line The inset provides a close-up view of the WEC and Santa Cruz domains, with the boundary between them marked by a solid line.
Figure 27 Same caption as Figure 26 but for devices between 6 m and 15 m in diameter.
Sensitivity Analysis Results – Part 2
Model results were retained for every run, including propagated wave heights, wave periods, wave directions, and near-bottom orbital velocities at all grid points in the model domains To enable direct point-to-point comparisons, the same wave properties were extracted at each of the 18 distinct model output locations.
Figures 28 through 30 show the results of sensitivity analyses as surface-to-surface comparisons between the modeled scenario and the baseline scenario, the latter lacking WEC devices Black indicates no change in the wave parameter relative to the baseline, while the color bars in each figure define the magnitude of change as a percentage relative to the baseline (as defined in Eq 1).
Figure 28 shows the results of significant wave height predictions from the sensitivity analysis for 50 F-2HB type WECs using Switch 1 and Switch 2, enabling a direct comparison of the two transmission-coefficient switches Switch 1 and Switch 2 results were similar but not identical, likely due to the interpolation of wave height and period when computing the RCW for Switch 2 Wave heights were slightly more reduced in the lee of six diameters apart 50 F-2HB WECs for Switch 1 compared with Switch 2 Switch 2 simulations yielded 0.1% more wave reduction at output locations 7, 8, 11, 12, and 18 Wave height decreases of 0 to 8% were observed at output locations northeast of the WEC array for both Switch 1 and Switch 2 Comparisons between Switch 1 and Switch 2 for the other seven WEC devices were similar.
Figure 28 depicts the percentage decrease in significant wave height resulting from varying model parameters, with panels showing the effects for SNL-SWAN Switch 1 on the left and Switch 2 on the right; the parameter variations are indicated above each panel Note that the device diameters in the figure are not drawn to scale.
Switch 1 model results for all eight WEC buoy types are shown in Figure 29 and Figure 30 Switch 2 results were similar and are not shown The model parameters (number of WECs, WEC device type, WEC spacing, and WEC diameter) are indicated above each subplot
Across eight device types, the largest reductions in wave height occurred in the lee of the WEC arrays Generally, larger devices produced greater wave-height reductions, while smaller devices had less impact Notable exceptions include the 7 m Bref-SHB buoy, whose wave-height reductions were comparable to those of the 5 m B-HBA WEC type, and the 50 m F-OWC buoy, which reduced wave height less than the 26 m B-OF device type Overall, the magnitude of wave-height reduction correlated with the WEC’s power matrix values, with larger power values yielding greater reductions and smaller values yielding smaller reductions.
Among the devices analyzed, the largest horizontal wave reduction was observed with the F-OWC, which makes intuitive sense since these were the largest devices and were spaced furthest apart, blocking a larger percentage of the propagating waves Submerged buoys (B-HBA and Bref-SHB) were modeled as obstacles extending throughout the water column, and results could differ significantly if these devices were simulated as obstacles covering only a portion of the lower water column.
Figure 31 demonstrates how model sensitivity varies with WEC buoy type, the number of devices in the array, and WEC spacing Percent differences in wave height were largest across buoy types, indicating the model is most sensitive to WEC device type—and to WEC size for all buoys except the F-OWC buoy The power matrix associated with each WEC generally scales with buoy size, so larger buoys exhibit greater power generation than smaller devices, with the F-OWC buoy as an exception Higher power generation by WECs results in greater wave height reduction Wave height reduction is highly sensitive to the number of WEC devices but relatively insensitive to WEC spacing As expected, increasing the number of WECs in the array yields a larger difference between modeled wave height with and without obstacles (Figure 31).
Figure 29 illustrates the percentage decrease in significant wave height that results from varying model parameters, using the SNL-SWAN Switch 1 configuration for four of the eight Wave Energy Converter (WEC) types The percent differences are shown for 18 output locations, with the values indicated on the left of the panels Note that device diameters are not to scale, and the figure uses variable scale bars to reflect differing data ranges.
Figure 30 Same caption as for Figure 29 for the other four WEC types
Figure 31 Variations in wave properties versus wave height reduction The left three panels are the results from using Switch 1 and the right three panels are from Switch 2
Section 4.3 shows that near-bottom orbital velocities, including wave-driven currents, scale directly with the surface wave expression, i.e., the significant wave height Decreases in wave height lead to reductions in near-bottom orbital velocities, potentially altering ambient wave-driven currents in near-shore environments Consequently, the percentage differences in near-bottom orbital velocities closely align with those calculated from the significant wave height model scenarios.
In this study, the percentage changes in peak wave periods were negligible (Figure 32) This result arises from two factors: first, the model’s frequency-bin resolution may be too coarse to register small changes in wave periods, since minor frequency shifts can remain within the same bin in model space; second, the obstacles absorb the same fraction of energy across all frequencies because the transmission coefficient is frequency-independent, leaving the peak wave energy unchanged and preventing a shift to other frequencies Consequently, in line with the prior sensitivity analysis (Section 4.3), no appreciable change was observed.
Figure 32 Variations in wave properties versus peak wave period reduction The left three panels are the results from using Switch 1 and the right three panels are from
Figure 33 shows changes in mean wave directions All percent differences correspond to changes within ±4.5%, i.e., ±9° in direction Negative changes denote clockwise (CW) rotation, while positive changes denote counterclockwise (CCW) rotation When rotation occurred in the model, it was relatively large because the directional bin spacing was 9°, making smaller changes indeterminable by the model No wave direction change was observed for modeled devices smaller than 8 m, suggesting that any direction changes caused by the WEC devices were less than 9°.
Figure 33 Variations in wave properties versus peak wave period reduction The left three panels are the results from using Switch 1 and the right three panels are from
Under the current model setup, wave heights and the associated near-bottom orbital velocities decreased by as much as 30% when comparing baseline conditions to the modeled scenarios for 100 B-OF buoy devices, with the B-OF power matrix peaking at an incident wave height of 1.7 m Other buoy types produced smaller differences, less than 15% in modeled wave height with and without obstacles, and effects diminished for buoys smaller than 10 m in diameter Although the F-OWC device is the largest model, its power matrix values at 1.7 m are still lower than those of the B-OF, reducing its wave attenuation potential; nonetheless, the F-OWC effects span a larger spatial extent due to its size and spacing, potentially creating a greater shoreline impact.
Wave directions and periods appeared largely insensitive to changes in the input parameters However, a more comprehensive sensitivity analysis is needed to fully understand how the model responds to parameter variation, particularly for the peak wave period and the mean wave direction.
West output locations (1–6) showed little to no change in wave heights compared with the baseline scenario The largest differences occurred downstream of the array near the centerline (output locations 7–12), where the most pronounced wave shadowing effects were predicted East output locations (13–18) indicated relatively small changes in wave heights.
9 m in diameter This all makes intuitive sense given that the modeled incident wave direction was from the southwest and these waves refracted toward the shoreline in a counter-clockwise manner.
SNL-SWAN Switch 1 and Switch 2 Transmission Coefficients
The SNL-SWAN computed transmission coefficients were output to the model PRINT file for all sensitivity analysis runs, as summarized in Appendix B (part 2); here we discuss only results from 10 WEC devices with six-diameter spacing Across these runs, transmission coefficients ranged from approximately 0.54 to 0.99 (Figure 34), indicating varying levels of wave energy transmission through the array The lowest coefficients, corresponding to the greatest energy absorption, were observed for the B-OF buoy (which has the largest power matrix values), while the highest coefficients were found for the Bref-HB WEC type (the smallest power matrix values) Consequently, the B-OF buoy produced the most substantial wave-height reduction in the lee of the array, with the opposite behavior for the Bref-HB device.
Within the nested model domain, RCW is computed solely as a function of wave period, which did not vary across the domain, so transmission coefficients were consistent across all WECs in the array when Switch 2 was used Switch 1 computes RCW from both wave height and wave period, leading to slight differences in transmission coefficients among WEC devices due to interpolation of the RCW Although the magnitudes were similar, the transmission coefficients from SNL-SWAN Switch 1 and Switch 2 differed slightly, likely because of the interpolation involved in Switch 2 Switch 2 coefficients were not consistently higher or lower than Switch 1 The largest differences between Switch 1 and Switch 2 occurred for the B-OF and F-HBA buoy types, about 0.04 and 0.02 respectively, while other devices showed differences under 0.01.
Figure 34 illustrates the percentage reduction in significant wave height achieved with SNL-SWAN, comparing Switch 1 (left) and Switch 2 (right) across eight different WEC device types, while the transmission coefficients computed by SNL-SWAN for each of the ten WECs in the array are shown on the left panel The figure notes that the two panels use different color bar scales, which should be considered when comparing the results.
Conclusions
The presence of WEC arrays have the potential to alter wave propagation patterns significantly and affect coastal circulation patterns, sediment transport patterns, and alter ecosystem processes
To accelerate the deployment of environmentally friendly wave energy converter (WEC) arrays, predictive modeling tools are needed to accurately capture WEC-induced changes in wave propagation and to assess potential environmental impacts This study employs a modified version of the industry-standard SWAN model, named SNL-SWAN, to evaluate WEC array deployment scenarios at a California coast site and to quantify model sensitivity, ensuring the framework can be effectively and confidently used in environmental assessments The analysis builds on a previous sensitivity study in which SWAN parameters were varied to examine their influence on model results (Chang et al., 2014).
This study evaluates a modified SWAN wave model, SNL-SWAN, against the native SWAN code and uses it to assess how different wave energy converter (WEC) devices influence near-shore wave propagation SNL-SWAN parameters were optimized for directional spread, direction resolution, and diffraction Two sensitivity analyses were conducted to explore how model choices and WEC configurations affect near-field and far-field conditions in the wake of WEC arrays: (i) variations in incident-wave height, period, and distributions (frequency and directional spreads); (ii) variations in WEC device type and size, the number of devices in an array, and inter-device spacing The goal was to better understand SNL-SWAN functionality and identify potential code issues early in development.
Sensitivity analyses show that wave direction and the WEC device type are the most sensitive to parameter variation in this study, whereas wave heights are minimally affected by changes in wave parameters In every modeled scenario, locations along the lee centerline of the arrays exhibited the largest potential changes in wave height and near-bottom orbital velocity, surpassing the changes observed at the eastern and western fringes of the shadow zone.
Significant wave height is most sensitive to changes in WEC device type and size, as well as the number of WEC devices in an array, because each device has a device-specific power matrix and associated RCW, making power outputs highly variable across configurations In all modeled scenarios, the largest potential changes in wave height—and in near-bottom orbital velocity—occur along the lee centerline of the array, with additional changes along the shadow edge in the direction of wave propagation; in these cases the shadow tends to skew to the east, consistent with a wave field that has a westerly component.
Ongoing laboratory studies and future field tests are essential to identify the most appropriate power matrix values for a specific wave energy converter (WEC) device and its configuration Until these matrix values are accurately determined or validated, including any WEC-friendly model enhancements, environmental assessments of wave energy devices should examine a broad range of WEC characteristics to define the limits of potential environmental effects associated with a WEC array.
This study establishes a baseline model understanding for evaluating a range of Wave Energy Converter (WEC) devices and systematically examines the model’s sensitivity, optimization potential, and behavior across diverse WEC configurations The resulting insights create a robust, evidence-based understanding of the model and furnish the confidence needed for reliable future WEC evaluations and technology optimization.
Note the differences in the y-axes
Figure 33 illustrates changes in mean wave directions, with all percent differences confined to ±4.5%, corresponding to about a ±9° directional change Negative changes indicate clockwise (CW) rotation, while positive changes indicate counter-clockwise (CCW) rotation When rotation occurred in the model, it tended to be relatively large because the directional bin spacing was 9°; changes smaller than this were indeterminable by the model No wave direction change was observed for modeled devices smaller than 8 m, suggesting that any direction changes caused by the WEC devices are less than 9°.
Figure 33 Variations in wave properties versus peak wave period reduction The left three panels are the results from using Switch 1 and the right three panels are from
These results ultimately illustrate, that, given the present model setup, the wave heights (and associated near-bottom orbital velocities) showed decreases of up to 30% between baseline and modeled conditions for 100 devices of the B-OF buoy type The B-OF power matrix values were largest for an incident wave height of 1.7 m Other buoy types resulted in less than 15% differences in modeled wave height with and without obstacles, with lesser influence for buoys less than 10 m in diameter Although the F-OWC device was the largest device modeled, its power matrix values for an incident wave height of 1.7 m were less than that of the B-OF device and hence its wave reduction potential was less However, the F-OWC effects extended over a larger spatial extent due to its size and spacing, thereby potentially having a greater impact on the shoreline
Wave directions and periods did not appear to be sensitive to changes in parameters However, additional analysis is required to fully explore the model sensitivity of peak wave period and mean wave direction to the varying of the parameters
West output locations 1–6 showed little to no change in wave heights compared with the baseline scenario The largest wave height differences occurred downstream of the array near the centerline (locations 7–12), where the predicted wave shadowing effects were most pronounced East output locations 13–18 indicated relatively small changes in wave heights.
9 m in diameter This all makes intuitive sense given that the modeled incident wave direction was from the southwest and these waves refracted toward the shoreline in a counter-clockwise manner.
6 SNL-SWAN SWITCH 1 AND SWITCH 2 TRANSMISSION
For all sensitivity analyses, SNL-SWAN output the transmission coefficients to the model PRINT file, as summarized in Appendix B (part 2) To keep the discussion concise, this report focuses on results from 10 WEC devices arranged with six-diameter spacing In this configuration, transmission coefficients range from about 0.54 to 0.99 (Figure 34) The lowest coefficients—indicating the greatest absorption of wave energy—occurred for the B-OF buoy (the largest power matrix values), while the highest coefficients were observed for the Bref-HB WEC (the smallest power matrix values) Consequently, the B-OF buoy produced the most substantial wave-height reduction in the lee of the WEC array, whereas the Bref-HB device showed the least reduction.
Because the RCW is computed as a function of wave period and the wave period did not vary over the nested model domain, transmission coefficients were consistent across all WECs in the array when Switch 2 was used Switch 1, which computes RCW as a function of wave height and period, led to slightly different transmission coefficients (less than 10% variation) for each WEC device in the array due to interpolation of the coefficients Although the magnitudes were similar, the transmission coefficients from SNL-SWAN Switch 1 and Switch 2 differed slightly, likely due to the interpolation involved in Switch 2’s RCW calculation Switch 2 transmission coefficients were not consistently higher or lower than Switch 1 The largest differences between Switch 1 and Switch 2 occurred for the B-OF and F-HBA buoy types (approximately 0.04 and 0.02, respectively), while all other devices showed differences of less than 0.01.
Figure 34 presents how significant wave height percentage decreases when using SNL-SWAN, comparing Switch 1 on the left with Switch 2 on the right across eight different wave energy converter (WEC) device types, and the left panel shows the transmission coefficients computed by SNL-SWAN for each of the 10 WECs in the WEC array, with note that the color bar scales differ between panels.
The presence of WEC arrays have the potential to alter wave propagation patterns significantly and affect coastal circulation patterns, sediment transport patterns, and alter ecosystem processes
To speed up the deployment of eco-friendly wave energy converter (WEC) arrays, predictive modeling tools are needed to accurately represent WEC-induced changes in wave propagation and to assess potential environmental impacts In this study, a modified version of the industry-standard SWAN model, named SNL-SWAN, is employed to explore potential WEC array deployment scenarios along a California coastline and to evaluate the model’s sensitivity, ensuring the approach can be used reliably in environmental assessments The work builds on a prior sensitivity analysis in which SWAN parameters were varied to examine their influence on results (Chang et al., 2014).
This study evaluates the modified SWAN wave model, called SNL-SWAN, against the native SWAN code and uses it to assess how different wave energy converter (WEC) devices influence near-shore wave propagation SNL-SWAN parameters were optimized for directional spread, direction resolution, and diffraction Two sensitivity analyses were conducted to examine the effects of model and WEC variations: (i) incident wave height, period, and the spreads of frequency and direction, and (ii) WEC device type and size, the number of devices in an array, and the spacing within the array, with the goal of characterizing near-field and far-field wave conditions in the lee of the devices This approach helps better understand SNL-SWAN functionality and identify potential code concerns early in the development process.
Sensitivity analyses show that wave direction and the WEC device type are the most sensitive to the parameter variations explored in this study, while wave heights are minimally affected by changes in wave parameters Across modeled scenarios, the largest potential changes in wave height and near-bottom orbital velocity occur along the lee centerline of the arrays, whereas the eastern and western fringes of the shadow zone exhibit comparatively smaller effects.
Significant wave height was most sensitive to variations in WEC device type and size and to the number of WEC devices in an array, reflecting device-specific power matrices and the highly variable RCW values In all modeled scenarios, locations in the lee centerline of the arrays showed the largest potential changes in wave height and near-bottom orbital velocity, with the edge of the shadow in the direction of wave propagation following closely behind; in these cases the shadow was skewed to the east as expected for a wave with a westerly component.
Ongoing laboratory studies and upcoming field tests are essential to determine the most suitable power matrix values for a given WEC device and its configuration Until these values are precisely established or further WEC-friendly model enhancements are validated, environmental assessments of WEC devices should focus on evaluating a range of WEC characteristics to define the limits of potential environmental effects resulting from the presence of a WEC array.
This study establishes a baseline model understanding while evaluating the effects of a range of Wave Energy Converter (WEC) devices By examining the model’s sensitivity, optimization potential, and behavioral responses across different WEC configurations, the work builds a robust framework that underpins reliable future WEC evaluations and enables meaningful comparisons among device concepts.
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Optical Variability in Dynamic Near-shore Environments: Task Completion Report #3 – Numerical Modeling and Verification 28 pp
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APPENDIX A: SNL-SWAN SENSITIVITY ANALYSIS MODELED
Figure A1 shows the significant wave height percentage decrease achieved with SNL-SWAN when using Switch 2, highlighting an error in the SNL-SWAN code related to passing variables from the model to the output PRINT file in the left panel The right panel displays the results after the code was debugged and fixed, confirming the corrected variable flow and the resulting improvements in the output.
APPENDIX B: SNL-SWAN SENSITIVITY ANALYSIS MODELED
1 MS0899 Technical Library 9536 (electronic copy)