Modeling Long-Period Swell in Southern California: Practical Boundary Conditions from Buoy Observations and Global Wave Model Predictions

a. Study region

Southern California (SC) extends from Point Conception to the United States–Mexico border (Fig. 1), and is exposed to distant North and South Pacific storms as well as local wind swell (Adams et al. 2008). Complex coastal bathymetry and shadowing from offshore islands create a spatially variable nearshore wave field that is extremely sensitive to the offshore wave direction. Directional inaccuracies of the waves specified at the offshore boundary are believed to be the dominant source of wave model prediction error in Southern California (O’Reilly and Guza 1993; Rogers et al. 2007).

b. Swell wave model

Modern third-generation wave models [e.g., WaveWatch III (WW3) and Simulating Waves Nearshore (SWAN)] solve the spectral wave action equation (Hayes 1970), which includes refraction, shoaling, wind generation, nonlinear wave interactions, wave–current interactions, whitecapping, bottom dissipation, and depth-limited breaking. These commonly used state-of-the-art models are computationally expensive with high spatial resolution and long duration. In SC, the transformation of low-frequency (0.04–0.09 Hz) swell is dominated by island sheltering, and bathymetry-controlled shoaling and refraction (O’Reilly and Guza 1993; O’Reilly et al. 2016). Our SC swell wave model, limited to 0.04–0.09-Hz frequencies, captures these effects using frequency–direction-dependent transfer coefficients derived from backward ray-tracing methods (see appendix A; Longuet-Higgins 1957; Dorrestein 1960; Mehaute and Wang 1982). The transfer coefficients represent a linear relation between the offshore and nearshore wave field. Because energy travel time across SC can be significant, 10+ hours, frequency–direction-dependent time lags are included by assuming energy propagation at the theoretical group velocity (Fig. A1), following O’Reilly and Guza (1998) and O’Reilly et al. (2016). This methodology significantly reduces computation expense, but it requires the assumption that offshore wave conditions are spatially homogenous (with time lags) in the along-crest direction (Fig. A1). This contrasts with typical modern wave models that accept heterogeneous boundary conditions offshore. However, offshore GWM predictions confirm along-crest spatial homogeneity over the few 100-km scales of SC for the remotely generated waves that dominate the swell band (<0.09 Hz); details are in appendix A. Our swell model predictions are therefore a linear function of offshore energy with an appropriate time lag .

The swell model captures approximately 60% of offshore energy flux (Fig. 2b). Model transfer coefficients are created at a 0.005-Hz frequency resolution, typical of buoy hourly records, and 1° directional resolution that is higher than commonly used but desired for directionally sensitive SC. The linear framework allowed for relatively rapid testing of different boundary conditions from 2000 to 2009. All wave properties discussed in the following are swell band averaged such that some property is

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c. Buoy observations

Quality-controlled, hourly, Datawell directional buoy observations (energy and low-order directional moments) from the Coastal Data Information Program (CDIP; http://cdip.ucsd.edu/) were smoothed with a 3-h running mean. The reduction of statistical uncertainty with 3-h smoothing is particularly important for low-frequency narrow-banded swell, where the effective degrees of freedom (EDOF) are low (Elgar 1987). In extreme cases (e.g., 20-s southwest swell), the EDOF of a 1-h buoy record can be less than 100 for the entire swell band spectrum, corresponding to approximately a ±25% uncertainty (90th percentile) in measured energy. Swell conditions are often stationary for 3 h, and minimal temporal resolution is lost. The regional wave model is initialized with the exposed offshore buoy, 071, in 550-m water depth. The model is tested with nine coastal deep-water buoys in depths ranging from 180 to 500 m, and eight local shallow-water buoys in 20-m depth (Fig. 1). Buoy site occupation duration varied (Table 1). Shallow buoys were typically deployed for the shortest times, approximately one year.

Table 1.

Wave buoy names, depths, and site occupation dates.

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d. Boundary conditions

Estimates of offshore were specified from buoy 071 observations and from GWM predictions. Buoy 071 has wide directional exposure and a 10-yr time series of energy and directional moments . For hindcast GWM predictions, we use the National Oceanic and Atmospheric Administration (NOAA) WW3 reanalysis (Tolman 2009; Chawla et al 2011, 2013). The U.S. West Coast reanalysis has a 4-arc-min (7 km) spatial resolution, 3-h temporal resolution, 10° directional resolution, and logarithmic frequency spacing. Complete WW3 energy-directional spectra predictions, , and collocated buoy 071 observations from 2000 to 2009 are used to specify boundary conditions. WW3 energy is rebanded in frequency to match typical buoy spectral output (0.005-Hz bandwidth from 0.04 to 0.09 Hz) and interpolated by nearest neighbor to 1-h temporal and 1° directional resolution. Excluded are the less-than-6-months’ total when buoy 071 observations were unavailable. Boundary conditions tested are divided into three categories:

• GWM only: is used exclusively, hereafter WW3.

• Buoy only: is created with buoy 071 observations. Three different methods—MEM, MRM, and BDM (see section 2)—are tested to estimate the discrete directional spectrum from directional buoy observations [(2)].

• Combined (CMB): Buoy 071 observations are combined with GWM predictions of the normalized directional distribution in three different ways.

The first CMB method, CMB-E, multiplies the buoy by , after the discussion of Rogers et al. (2007). Buoy directional information is not used. The second CMB method, CMB-LH, combines with both and (Long and Hasselmann 1979). The optimal directional spectrum minimizes

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while satisfying [(2)] and constraints (3) and (4). The computationally efficient iterative method developed by Long and Hasselmann (1979) terminates when constraints are met within the expected statistical uncertainty (Lawson and Long 1983; Long 1980). We tested this iterative method and found that fitting constraints exactly yielded unbiased spectra with comparatively better nearshore predictive skill. Additionally, we compared the iterative method solutions to those from a modern optimization numerical solver, CVX, a package for specifying and solving convex problems [CVX (MATLAB), CVXPY (Python), and Convex.jl (Julia); Boyd and Vandenberghe 2004; Grant and Boyd 2013]. Both solutions were robust for most conditions; however, the iterative method occasionally failed to converge for very low-energy spectra. We ultimately used CVX to solve the minimization; however, we continue to refer to the solution as CMB-LH. Once found, is multiplied by to construct , as in the CMB-E method.

The third CMB method, CMB-ADJ, is not formally optimal but relies instead on physically meaningful adjustments to , including a series of shifts and smoothings to minimize misfit to constraints [(2)] with . Initial testing showed the ideal simultaneous optimization was computationally burdensome and provided marginal improvement over the simpler sequential adjustment process used below at each frequency bin for each hour record.

1. Time lag/leads in are corrected for each 1-h time step by considering the optimal time lag correlation between GWM predicted energy, , and inside a ±36-h window. Typically, time lag/lead corrections were small (<3 h) and consistent across wave events.

2. Significant peaks in are found (using MATLAB’s Signal Processing toolbox) that meet the following criteria:

   1. Each peak contains at least 2% of primary peak energy.

   2. Peaks spaced less than 55° are considered a single peak.

3. If is unimodal (49% of records), then

   1. Rotate to match measured by buoy 071.

   2. Estimate for from (2) and (5). Smooth by convolving with a simple boxcar repeatedly until for is approximately equal to measured by buoy 071. Here, is used to sometimes avoid oversmoothing due to buoy-observed coastal reflection.

4. If is bimodal (49% of records), then

   1. Use brute force to find the shift of energy between the two D_WW3 peaks such that the misfit to , weighted by the uncertainty in (Long 1980), is minimized.

   2. Simultaneously and independently shift both peak directions (with a maximum shift of 25°) to minimize misfit to .

5. If contains three or more peaks (2% of records), then make no directional adjustments to the WW3 spectrum as buoy directional information is too limited.

Last, as in the previous methods, the adjusted is multiplied by to form . These adjustments to include some threshold values that may be region specific. Additionally, the performance of the methods is dependent on the accuracy of the GWM; statistical chatter in buoy observations can only degrade the predictions of a theoretically error-free GWM. However, here we show that buoy-based adjustments with these thresholds do detectably improve the GWM-only, WW3, and boundary condition method skill.

a. Significant wave height, direction, and spread

Model predictions (using the boundary conditions described above) are compared with observations at sheltered deep buoys using standard metrics [root-mean-square error (RMSE), bias, model skill , and squared correlation ; see appendix B for definitions]. Model skill varies across boundary condition, buoy validation site, and metric. Comprehensive skill results for significant wave height , mean direction , and directional spread for all boundary conditions at all buoy validation sites are in Tables S1 and S2 in the online supplementary material. Simple averages at deep buoy validation sites (Table 2) are used to rank boundary condition skill in Table 3, where the lowest score is best. Bias magnitude was averaged for and to avoid canceling errors. CMB-ADJ and MEM have the highest skill, while MRM and BDM have the highest skill. WW3 has overall the lowest skill followed by CMB-E. CMB-ADJ has the highest overall skill followed by BDM. Models using buoy observations in the boundary condition (buoy only and CMB) outperform WW3 alone. However, directional bias is lowest for WW3 and CMB boundary conditions at local deep buoys. Bias in predictions is negative for all boundary conditions and largest at low frequencies (not shown), suggesting weak coastal reflection (section 5c).

Table 2.

Mean model skill at local deep buoys.

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Table 3.

Model skill rankings averaged across deep local buoys for various boundary conditions and select metrics (low ranking indicates higher skill).

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The spatial distribution of model skill for a subset of boundary conditions shows that WW3 initialization consistently has relatively large RMSE and bias; in Fig. 4 the upper-left quadrant is large and dark at most buoys, for both and . The term from WW3 is biased high at the initialization offshore buoy 071 (+23 cm), and WW3 is correspondingly high in the southern half of the model domain. In contrast, WW3 initializations are biased low for in the Santa Barbara Channel (SBC), closest to the initialization buoy (Fig. 4a), and directional errors and biases are also large. Boundary condition MRM shows particularly large positive (northward) directional bias in the southern end of the SBC. A ranking of buoy site skill, averaged across select boundary conditions (Table 4), indicates the poorest model performance at buoy site 107 (in SBC) and at the southernmost buoy site, 093.

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Model performance at each SC nearshore buoy location for (a) wave height and (b) wave direction . Each circle quadrant shows a different boundary condition (key, upper right). Circle quadrant size shows RMSE (key, lower left), and color shows bias (color bar, above). Normalized error metrics [%RMSE and %bias, in (B1)] are used in (a). A small quadrant indicates small RMSE, and a pale color indicates small bias. GWM (NOAA-WW3) initialization (upper-left quadrant), in all regions and for both and , is relatively large and dark, indicating relatively high RMSE and bias. Gray contours show 20-, 50-, 100-, and 500-m isobaths.

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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Table 4.

Mean skill for best models (CMB-ADJ, MEM, BDM) ranked across local deep buoys for select metrics (low ranking indicates higher skill). Buoys are listed from north to south.

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b. Alongshore radiation stress

Mean (time averaged) model predictions and shallow (20-m depth) buoy observations are compared in the local shore-normal reference frame estimated from depth contours onshore of each buoy; positive indicates northward up-coast transport (Fig. 5). Modeled and observed usually agree, at least qualitatively. Boundary conditions using offshore buoy observations generally outperform WW3 alone. No buoy-based method clearly performs best. Uncertainty bars on correspond to ±2.5° shifts of the local shore normal. At buoy 155, mean is near zero, and the results are relatively sensitive to the definition of beach normal. At buoy 043 (Oceanside Harbor), different offshore boundary conditions yield the widest range of with WW3 biased high and MRM biased low.

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Observed (black, local buoy observations) and predicted (using methods in legend) mean at local shallow (20-m depth) buoy sites (arranged south to north on the x axis). Positive values indicate northward up-coast transport. Bars indicate range for ±2.5° local shore-normal rotation. Predictions are offset horizontally for clarity.

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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Depth contours offshore of Oceanside Harbor (gray, Fig. 6a) were used to estimate local shore normals (dark magenta, Fig. 6a) that were alongshore averaged (excluding the harbor area) to avoid the influence of slight shore-normal changes on . Predicted , , and on the 10-m-depth contour (bright green) show similar alongshore variation about constant offsets (Figs. 6b–d). WW3 predicts the highest wave heights and the most oblique waves, resulting in the highest . These are compared to buoy 043 observations of (Fig. 6d; conserved assuming depth contours are parallel). Alongshore sediment transport estimated using the CERC formula² [(7)] with constant (Fig. 6e) yields estimates between 2 and 9 × 10⁵ m³ yr⁻¹. Shaded regions show transport estimates for a typical range of CERC constant K (), smoothed by 1.5-km alongshore locally weighted scatterplot smoothing (lowess) filter. Longshore transport gradients, estimated from smoothed transport estimates, are similar for all predictions (Fig. 6f). Note this gradient estimate ignores the effect of the harbor and small-scale (<1.5 km) alongshore variations in .

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(a) Plan view of Oceanside Harbor with buoy 043 (black diamond) and depth contours (gray curves; 20-m intervals). Local beach normal (magenta) are based on the nearest distance from the backshore point to 10-m depth contour (green curve). Predicted and observed time-averaged (b) and (c) in 10-m depth vs alongshore distance for different boundary conditions (see legend). (d) Predicted mean at 10-m depth vs alongshore distance is estimated using the alongshore mean shore normal (magenta) that excludes the harbor region, where shore normals are poorly defined [light magenta in (a)]. Buoy-measured mean in 20-m depth is also shown (black diamond). (e) Predicted sediment transport using CERC formula, , vs alongshore distance. Shaded colors show alongshore-smoothed (lowess 1.5-km alongshore filter) transport estimates for the range of K values . (f) Gradient of lowess-filtered transport alongshore (e.g., the divergence of the drift) vs alongshore distance.

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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a. Optimal boundary condition

Offshore buoy observations improve WW3 nearshore wave prediction skill for most metrics at most buoy validation sites. However, improvement is lowest for CMB-E, where the buoy-measured energy is combined with . Model skill further increases when buoy energy and directional information are used, and CMB-ADJ outperforms CMB-LH (Table 3). Detailed examination of CMB-LH reveals that the least squares constraint in (8) often adds spurious directional peaks to the directional distribution. For example in Fig. 3a, CMB-LH creates a third peak at 100° and adds energy in the gap between the peaks. In contrast, CMB-ADJ more physically adjusts peak amplitude, direction, and width. While mathematically convenient and theoretically elegant, the CMB-LH squared difference constraint is not effective. CMB-ADJ, though crude, outperforms CMB-LH.

While buoy observations improved the WW3 boundary condition, the skill of CMB-ADJ is similar to buoy-only methods; CMB-ADJ skill is lower, but the direction skill is higher, yielding an overall higher skill ranking (Table 3). Given the directional ambiguity in buoy observations (e.g., Fig. 3), we expected that offshore GWM directional spectra predictions offshore, informed by global wind fields and sophisticated model physics, would provide a powerful additional constraint. However, we were surprised to find that our combinations of offshore GWM spectra and buoy observations in the offshore boundary condition parameterization were similarly skilled to buoy-only methods. We show below that CMB-ADJ and buoy-only methods have similar skill because details in GWM directional spectra are often well represented by the first four low-order moments [(2)], nonnegativity, and a smoothness constraint. In other words, the present GWM directional resolution is roughly comparable to a directional wave buoy.

GWM (NOAA-WW3 hindcast) frequency–directional spectra for 1 yr were used to estimate the first four low-order directional moments [(2)] in each frequency–time bin. Using MRM, MEM, and BDM (section 2), reconstructions of the GWM directional spectra were generated, and misfit of the reconstructed spectra to the original GWM spectra were computed. An example unimodal reconstruction by MRM and BDM is very good (); however, performance declines as spectra complexity increases in the bimodal and trimodal cases (Fig. 7, left panels). Mean misfit values of MRM reconstructions for the entire year of GWM predictions show that high-energy events tend to have high across all frequencies (red in Fig. 8). Reconstructions of lower-energy directional spectra have lower skill, suggesting that spectra are more complex (green/blue in Fig. 8). The presented skills, with the exception of normalized skill in Fig. 4a, are more strongly influence by moderate to high energy events that are well represented by buoy directional moments. During these events GWM directional spectra provides little additional information, and therefore the combined (CMB-ADJ) and buoy-only methods have similar nearshore predictive skill.

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Offshore wave energy vs direction for three cases: (a) and (b) unimodal, (c) and (d) bimodal, and (e) and (f) multimodal. (left) GWM (NOAA-WW3) directional spectra (blue) and recreations using various smoothness methods (see section 2) and low-order moments [ in (2)] integrated from the GWM spectrum. (right) GWM spectrum with an added isotropic signal equal to 10% of the total spectrum energy simulating diffuse wave reflection and corresponding smooth recreation. The (see tables) of the recreation and the original spectrum (GWM or GWM plus isotropic reflection) show that simple unimodal distributions are better recreated than multimodal shapes. The varies substantially in the presence of isotropic noise and between recreation methods.

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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Mean between GWM directional spectrum compared and recreation with second-order moments [ in (2)] and the MRM smoothness method (section 2) vs frequency (x axis) and offshore GWM energy (y axis). Black text is the number of 3-h GWM predictions in each frequency–energy bin for the 1 year (2006) of GWM predictions used. Note log scale for energy (y-axis).

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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The overall skill for buoy-only methods is comparable; however, we observed differences across metrics. MRM has lower RMSE, MEM has lower directional bias, and BDM is a compromise of the two. No buoy-only method is the overall best performer, and likely the ability of each method to recreate the true directional spectra depends on frequency band, wave age, and region. GWM directional spectra predictions, used as a proxy for true spectra, yield insight into method differences and the importance of diffuse reflections and scattering (Fig. 7). Reconstructions of GWM directional spectra from the first four low-order moments using each buoy-only method (left panels) are contrasted with the addition of a small (10% of the total energy) isotropic background energy added to the GWM spectra (right panels). Constant background energy (Snodgrass et al. 1966) crudely mimics diffuse shoreline reflections and scattering. Elgar et al. (1994) observed low levels of reflection from a natural beach, and Ardhuin and Roland (2012) found that constant reflection on the order of 10% improved GWM prediction along the coast (GWM predictions used here do not include reflection). The addition of background energy reduces MRM and BDM reconstruction skill but improves dramatically MEM reconstruction skill. MEM is designed to identify peak directions in the presence of background energy, its roots in astronomy, and image processing (Gull and Skilling 1984); however, peaks are too sharp when background energy is lacking. In contrast, MRM and BDM are both smoother than MEM, and background energy tends to overbroaden peaks. Additionally, in the bimodal case (Fig. 7d), the MRM and BDM peaks are slightly biased away from the overall mean. MEM better resolves incoming directional peaks in the presence of background energy, but BDM and MRM better resolve broader directional peaks with low background energy; no method is optimal. Buoy observations are fundamentally limited: these three methods are drawn from an infinite set (Ochoa and Delgado-González 1990), and each will perform only as well as their smoothness constraint represents the true underlying directional spectra.

b. Alongshore radiation stress and transport

For most boundary condition methods, at most buoys, bias is <10°, relatively small for most practical applications. However, at some buoy sites estimates varied significantly (Fig. 5); at buoy sites 043 and 172, estimates varied by more than a factor of 2, substantial given that is directly proportional to alongshore transport estimates based on the CERC formula. This variation in from different boundary conditions exceeds the uncertainty in the CERC constant K (Fig. 6f). Though boundary conditions utilizing offshore buoys yield better estimates of than WW3, there is no overall best performer. The positive mean at buoy 043, indicating northward transport, is contrary to expectations for the region (Inman and Frautschy 1965); however, this estimate is integrated only for swell energy (0.04–0.09 Hz). Mean for the entire wave energy spectrum is typically negative (O’Reilly et al. 2016), indicating southward transport in the region.

Alongshore transport estimates from different boundary conditions differ primarily by a constant offset (Fig. 6e). Thus, the alongshore transport gradient—that is, divergence of the drift, indicating regions of accretion and erosion—is relatively consistent (Fig. 6f). Typically, the gradients of uncertain quantities are increasingly uncertain; however, in this case the bias between predictions in terms of contributing to , , and is constant alongshore (Figs. 6b,c). Therefore, accretion and erosion zones [(4)] may be determined confidently. We suspect that at these spatial scales [O(1) km], gradients in alongshore transport gradients are dominated by local bathymetry and high-order details of the offshore directional spectrum are insignificant. Note a single offshore normal is used to estimate , and small-scale variations in beach orientation are not included.

c. Coastal reflection

Weak coastal reflection (<10%) has small effects on and mean direction; even obliquely incident wave conditions yield little change to and observations, less than 4° and 2°, respectively. Alternatively, first-order directional spread () observations are highly sensitive to coastal reflection. Including simple reflection parameterizations in GWMs significantly improves predicted skill (Ardhuin and Roland 2012). While not included in our linear wave model, strong negative biases in predictions across all model boundary conditions are consistent with weak coastal reflection (Table 2). Strong (>10°) tidal modulation of is observed at local shallow buoy 172 offshore of Huntington Beach during a low-frequency event arriving from a high incident angle, 20°–30° southward of the local shore normal (Fig. 9b). At high tide, this convex beach has relatively high slope, and enhanced reflection, similar to Duck, North Carolina (Elgar et al. 1994). A buoy also senses the effect of directional narrowing due to increased refraction as the tide falls; however, these effects (estimated assuming plane-parallel contours; Herbers et al. 1999) are small in 20-m depth for the local tidal amplitude (<2°; black line in Fig. 9b) and vanishingly small in more than roughly 100-m depth. The observed modulation in at buoy 172 corresponds roughly to a 3%–10% change in reflected energy, equivalent to a 2%–5% change in ; similar levels of reflection are observed in Elgar et al. (1994). Owing to the high incident swell angle, tidal modulation of is also observed, though at less than half the variance observed in . Coherence at tidal frequencies M₂ and K₂ between the local tidal elevation and observed (estimated independently at each observed frequency) is high in the swell band (0.04–0.09 Hz), peaking around 0.06 Hz and falling off at higher frequencies, where reflection is weaker (Fig. 9c). As expected for a nearby reflector, at local shallow buoys close to shore the phase lag for K₁ and M₂ frequencies is near zero (<±0.1 h). At local deep buoys, the phase lags at K₁ and M₂ are scattered between ±0.5 h (not shown).

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The (a) and (b) directional spread () vs time (UTC) for a low-frequency swell event ( Hz) at buoy 172 in 20-m depth. Predicted tidal elevation in gray. The tidal modulation of (solid blue), likely caused by coastal reflection, is not parameterized in modeled predictions (dashed blue, CMB-ADJ boundary condition). Modulation due to increased refraction at lower tidal levels (directional narrowing) is small, as shown for a constant σ of 22.5° (black). (c) Coherence between tidal elevation and at M₂ and K₂ tidal frequencies (see legend) for one complete year of buoy observations is significantly high for wave energy, where (x axis). Black dashed line shows the 95% coherence confidence level.

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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Steep coastline slopes reflect more incoming wave energy. The SC coastline is a mix of dissipative (fine to coarse sand), intermediate (gravel), and reflective (riprap, seawall, rocky cliffs) regions shown in Fig. 10 (NOAA 2006). The magnitude of prediction bias (left half of colored square) at local buoy sites appears lower in regions with larger amounts of dissipative coastline, for example, San Diego (Fig. 10). Conversely prediction bias is larger where coastlines are steeper, for example, Santa Barbara and Los Angeles. This evidence is admittedly qualitative, and some observations suggest the opposite, e.g., buoy 092. Coherence of tidal elevation and (colored right rectangle) is higher at shallow buoy sites and is significant at all buoys except 093 (Fig. 10). Coherence is lower further from the coastline because the travel times of reflected waves varies. At even larger distances (not shown), buoys are exposed to a large array of diffuse reflectors (coastline and islands), and tidal effects are blurred in direction and time (Snodgrass et al. 1966; Herbers et al. 1999).

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Model (CMB-ADJ boundary condition) directional spread () prediction bias at local buoy sites shown in color (see color bar) in left half of square. Right half of square shows coherence at the M₂ tidal frequency (1.9 cycles per day) of buoy-observed and local tidal elevation (see color bar). Hatched colors indicate insignificant coherence levels at 95% confidence. The coastline is classified as dissipative (fine to coarse sand), intermediate (gravel), and reflective (riprap, rocky cliffs, seawall) types shown in color (see legend at bottom left).

Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0038.1

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d. Santa Barbara Channel

Our results confirm the previously observed large prediction errors in the SBC (Rogers et al. 2007; O’Reilly et al. 2016). The extreme sheltering by Point Conception and the Channel Islands (Fig. 1) amplifies the significance of high-order details of the offshore directional wave spectra. For example, during northwest wave events the SBC is often sheltered to the dominant swell direction by Point Conception, making critical the accurate description of the peak shoulder (e.g., Fig. S1 in the supplementary material). A higher-resolution boundary condition than provided by the WW3 predictions and buoy observations may be needed. Missing model physics likely partially explain these prediction errors; reflection from the steep cliff faces of the Channel Islands could help explain the low bias. Also supporting reflection, the positive (northward) directional bias at buoy 107 suggests additional wave energy coming from a more southerly direction. However, further eastward in the SBC (buoys 111, 130, 131) model directional bias suggests the opposite. It is not clear whether wave reflection contributes significantly to the large model errors in the SBC. Diffraction, surface current–induced refraction, and bathymetry inaccuracies may also contribute to prediction errors.