1. Introduction
Remote sensing technology offers some advantages for the continuous monitoring of nearshore environments because the sensors are removed from frequently harsh in situ conditions and often provide easier access to real-time data (Holman and Haller 2013) than provided by self-recording sensors. In addition, the larger footprints of remote sensors can be a significant benefit in areas where spatial variability is high. However, remote sensing observations often are a more indirect form of measurement of fundamental hydrodynamic parameters than obtained with most in situ sensors.
Primary drivers of the hydrodynamics in the nearshore are spatial gradients in the radiation stresses, which are functions of wave height and direction (Longuet-Higgins and Stewart 1964). The spatial wave transformation and hence, the radiation-stress gradients, are affected by refraction and shoaling, and are modulated by dissipation in and around the surfzone (Svendsen 2006). Recent in situ observations of waves and currents at the tidal inlet investigated here (Wargula et al. 2014) demonstrated that the breaking-induced gradient of the cross-shore radiation stress contributed significantly to the subtidal along-channel momentum balance, enhancing the flood flows into the inlet, particularly during storms, similar to results at other inlets (Malhadas et al. 2009; Bertin et al. 2009; Dodet et al. 2013; Orescanin et al. 2014).
Remote sensing observations (optical) of wave dissipation have been used successfully to assess the cross-shore evolution of the momentum balance in laboratory surfzones (Haller and Catalán 2009; Flores et al. 2013), and remote observations (infrared) of wave breaking have been used to assess the depth-induced dissipation over a longshore sandbar on an open beach (Carini et al. 2015, manuscript submitted to J. Geophys. Res. Oceans). Doppler radar (S band) estimates of wave orbital velocities have also been used to characterize both the nearshore wave transformation and bathymetry along a single cross-shore transect (McGregor et al. 1998).
Here, an approach based almost entirely on remote sensing observations is presented to evaluate the time and space variability of wave transformation. The observations were obtained near an energetic tidal inlet with substantial spatial variability and wave conditions that are modulated strongly by the tide. The remote sensing and in situ observations are described in section 2, and the methodology for identifying wave breaking, estimating wave breaking dissipation, and calculating wave height transformation are presented in section 3. Results are discussed, including comparisons of remote sensing with in situ observations in section 4, followed by a brief discussion of accuracy and sources of error. In addition, the remotely sensed wave height transformation results are used to estimate radiation-stress forcing, and compared with estimates from in situ measurements. Conclusions are given in section 5.
2. Field observations
Observations were obtained 7–16 May 2012 at New River Inlet (NRI), a small (1 km wide at the mouth), tide-dominated estuary located on the North Carolina Atlantic coast (Fig. 1). Abundant shoals and a complex sandbar system characterize the inlet mouth and flanking beaches. Tidal currents were as high as 1.5 m s−1 and were in phase with the ±1-m tidal amplitude. Offshore (9-m water depth) significant wave heights [Hs, 4 times the standard deviation of sea surface elevation fluctuations in the frequency (f) band from 0.05 to 0.30 Hz] ranged from 0.5 to 1.5 m, centroidal (energy weighted) frequencies fc ranged from 0.11 to 0.18 Hz, and waves approached the region from the east-southeast to southeast (Wargula et al. 2014).
Experiment site (the location of New River Inlet, North Carolina, along the U.S. Atlantic coast is shown in the inset map). Gray-shaded areas are land, and gray curves are depth contours (−2, −4, −6, and −8 m NAVD88). The plus sign near (−477, −365 m) denotes the location of the radar, and the dashed curve indicates the limit of the 1.5-km radius radar footprint. The triangle indicates the location of the meteorological station, circles are collocated buried pressure gauges (sampled at 2 Hz) and ADVs (sensors 55–68, sampled at 2 Hz), profilers (sensors 5–8, 1-min average samples), and a combination velocimeter (sensor 9, 2-Hz samples, 1024 s every half hour) and profiler (1-min average samples for 12 min every half hour). Trapezoids are the areas for which the PDF analysis was performed. Thick black lines are the cross-shore transects.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
a. Radar collections
An X-band wave imaging marine radar, consisting of a commercial SI-TEX Koden radar and an acquisition system developed by Imaging Science Research, Inc. was deployed on the southwest shore of the inlet (xNRI = −477.3 m and yNRI = −365.2 m in Fig. 1). Mounted atop of a scaffolding structure, every half hour the radar recorded 1024 images of the ocean surface over a footprint radius of 1.5 (from 7 to 9 May) or 3.0 km (from 9 to 16 May) with an angular coverage of about 300° (Fig. 1). The 9-ft-long HH-polarized antenna rotated at approximately 46.7 rpm, thus taking about 22 min to acquire the 1024 images.
b. In situ data
Waves and currents were measured along two transects across the ebb shoal and offshore (9-m water depth) (Fig. 1). Wave heights on the ebb shoal were estimated by correcting bottom pressure to sea surface elevation using linear theory. Offshore wave heights were measured with an acoustic surface-tracking beam. Wind speed and direction, in addition to standard meteorological parameters, were recorded 100 m offshore of North Topsail Beach (Fig. 1). In situ GPS-based bathymetric surveys (Fig. 1) were conducted on 16 April, and 2, 10, 17, and 25 May.
3. Methodology
a. Breaker identification and estimation of the fraction of breaking waves Qb
To identify the radar signal associated with breaking waves, histograms [which represent the probability density function (PDF); Catalán et al. 2011] of normalized radar cross section σ0 were analyzed. Recorded radar intensity, stored as a function of range, azimuth, and time, was calibrated during postprocessing to compensate for the intensity falloff with range (Gommenginger et al. 2000) and to compare σ0 values with previous studies. Calibration coefficients were estimated during a later campaign conducted at the mouth of the Columbia River in 2013, and are considered approximate. The PDFs were computed from the calibrated data extracted from four distinct regions of the radar footprint (black trapezoids in Fig. 1) where environmental conditions were expected to differ: North Topsail Beach (TB, where waves were observed to break at all times), the south ebb shoal (ES, where waves broke during low tide), the main inlet channel (CH, where waves may break as a consequence of wave–current interaction), and offshore (OS, where waves were not expected to break).
b. Cross-shore wave height transformation and wave forcing
c. Bathymetry
The bathymetric grid used for wave transformation was interpolated from bathymetry computed from radar data collected between 7 and 16 May using the cBathy algorithm with a 25-m horizontal resolution (Holman et al. 2013). The algorithm estimates spatially varying frequency (f)–wavenumber (k) pairs and inverts the linear wave dispersion relation [σ2 = gk tanh(kh)] to obtain maps of bathymetry, h(x, y), for every radar collection. To produce a smoother estimate of bathymetry, the tidal signal was removed from the h time series using the data from the tide gauge at Wrightsville Beach, North Carolina (NOAA gauge station 8658163) and the resulting time series was averaged. For the wave transformation analysis, the tidal signal was reincorporated, producing time-varying depth profiles referenced to the North American Vertical Datum of 1988 (NAVD88). Differences between wave transformation results based on the cBathy-estimated bathymetry and those based on surveyed bathymetries were small (discussed in section 4).
4. Results and discussion
The shapes of the PDFs of σ0 varied spatially (Fig. 2 compares the four panels with each other) and temporally, with a strong dependence on environmental conditions, particularly the tide. The distributions (Fig. 2) represent the mean PDFs (averages per NRCS bin) of all radar collections recorded within a 3-h period centered on the minimum (gray curves) and maximum (black curves) tide levels between 7 and 16 May, at each of the four locations (TB, CH, ES, and OS; Fig. 1) described in section 3a. Consistent with previous studies, the PDFs corresponding to nonbreaking wave conditions showed a single, well-defined peak at low NRCS, followed by a relatively smooth exponential decay toward higher radar backscatter values. For example, the PDFs corresponding to CH, ES, and OS (Fig. 1) are similar during high tide, with a single large peak in the −56- to −64-dB range and an exponential decay toward high NRCS (Figs. 2b–d). The relatively lower NRCS peak (−74 dB) corresponding to TB (Fig. 2a) is the result of a calibration procedure that is only approximate and is less accurate at very close range. In addition, portions of this analysis box were exposed (i.e., dry) during low tide, which also lead to lower returns. In contrast, in the presence of active breaking, the PDFs exhibit a secondary peak at high NRCS. For example, the high-tide PDF corresponding to TB (Fig. 2a) is bimodal, with a smooth plateau at −48 dB and a sharp peak at −4 dB. The low-tide PDFs corresponding to TB and ES (Figs. 2a and 2c) also are bimodal, with high NRCS peaks at −4 and −8 dB, respectively. The time (low or high tide) and space distributions of the breaking returns are consistent with aerial photographs and land-based video imagery. During high tide, breaking waves were observed only at the shoreline, and during low tide breakers were observed on all the tidal shoals and submerged bars. The average low- and high-tide PDFs from OS showed no significant differences (Fig. 2d). The amplitude of the σ0 = −4-dB peak is correlated with the tide, with R = 0.86 for region TB, and smaller negative correlations R = −0.67 and R = −0.57 for ES and CH, respectively, consistent with the hypothesis that high NRCS values, associated with wave breaking, occur during high tide at TB and during low tide at ES and CH. The correlation of the PDF amplitude at σ0 = −4 dB with the tide at OS was not statistically significant. However, amplitude at σ0 = −4 dB was correlated with the significant wave height (from station 9) in the OS (R = 0.75), CH (R = 0.68), and ES (R = 0.68) regions, but not in TB (R = −0.03). The wind speed u10, measured near TB (Fig. 1), was not significantly correlated with the amplitude of σ0 = −4 dB for any region.
Probability density vs normalized radar cross section for (a) North Topsail Beach, (b) main inlet channel, (c) south ebb shoal, and (d) offshore for high-tide (black curves) and low-tide (gray curves) conditions. High and low NRCS peaks are indicated as σ0hp and σ0lp, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Based on these results, the value of −4 dB was selected as a threshold σ0br to distinguish active wave breaking. This threshold value was used to mask the radar data and create maps of the fraction of breaking waves Qb (Fig. 3). Strong breaking (Qb > 0.7) occurred almost exclusively at North Topsail Beach during high tide (Fig. 3a, TB region). During low tide waves broke farther offshore (Fig. 3b, ES region), revealing the complex morphology of the tidal shoals and nearshore bar system. In addition, Qb estimates from the higher sea-state conditions observed on 13–15 May exhibit strong breaking over the shoals (not shown), approximately coinciding with the 2-m NAVD88 bathymetry contour during low tide. Breaking over the shoals persisted through the entire tidal cycle, with the higher Qb values displaced shoreward at high tide. These observations are in good agreement with results from a wave-averaged quasi-3D circulation model [Nearshore Community Model System (NearCoM-TVD)] that showed that the location of the breaker zone over the NRI ebb tidal deltas is modulated by the tides and wave intensity (Chen et al. 2014, manuscript submitted to J. Geophys. Res. Oceans).
Maps (color scale on the right) of the fraction of breaking Qb as a function of spatial coordinate corresponding to (a) high (0230 UTC 10 May) and (b) low (0900 UTC 10 May) tide. Gray curves are depth contours (see Fig. 1). The maps have been cropped to display data in the east–south (i.e., azimuth 90°–180° from true north) sector of the radar footprint only. The plus sign is the location of the radar.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Time series of the predicted and observed cross-shore wave height transformation along the south (Fig. 4) and north (Fig. 5) transects illustrate that, except for the most seaward stations (68 and 58, located offshore of the ebb shoal in approximately 5-m depth), in situ wave heights were depth limited, and thus were tidally modulated, resulting in bigger waves observed along the transects during high tide. Predicted wave heights along the south transect (Fig. 4) agree well with the in situ data (R = 0.69–0.95 and RMSE = 0.06–0.19 m). A positive bias at all five stations, ranging between 0.01 and 0.17 m, is indicative of a slight underestimation of the wave dissipation Dw derived from the radar-derived Qb values. The Hrms values along the north transect (Fig. 5) display a slightly higher level of agreement, with correlation values R = 0.77–0.96, decreasing onshore. In comparison with results from the south transect, the lower bias and RMSE values in the north suggest a more accurate estimation of Dw. Willmott skill score values (Willmott 1981) range between 0.63–0.97 and 0.82–0.88 for the south and north transects (Table 1), respectively, consistent with previous model–data comparisons at this site (Chen et al. 2014, manuscript submitted to J. Geophys. Res. Oceans).
Predicted (gray) and observed (black) Hrms vs time for locations along the south inlet transect (sensors 5–8 and 68, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Predicted (gray) and observed (black) Hrms vs time for locations along the north inlet transect (sensors 55–58, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Willmott skill scores from prior model results (Chen et al. 2014, hereafter Ch14, manuscript submitted to J. Geophys. Res. Oceans), and skill scores, correlation coefficients R, and error metrics (bias and RMSE) for the 1D wave transformation model results computed using A: surveyed bathymetry and parametric dissipation (Janssen and Battjes 2007), B: surveyed bathymetry and radar-derived dissipation, and C: radar-derived bathymetry and dissipation.
Predicted shoaling Ks (blue), refraction Kr (red), and dissipation KD (green) coefficients vs time for locations along the south inlet transect (sensors 5–8 and 68, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Predicted shoaling Ks (blue), refraction Kr (red), and dissipation KD (green) coefficients vs time for locations along the North inlet transect (sensors 55–58, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
One possible cause of the differences between the radar-based predicted and the observed wave heights is the neglect of currents in the model [Eq. (4)]. The normalized residual wave height, computed as the sum of the predicted minus the measured divided by the measured Hrms, is negatively correlated with the water level, a proxy for tidal currents, at stations 5, 6, 7, and 55 (R = −0.79, −0.61, −0.42, and −0.44, respectively), and positively correlated with currents at stations 55 and 56 (R = 0.44 and 0.35, respectively). Correlation with tidal currents along the south transect is not statistically significant. Another possible cause of differences is error in the radar-derived bathymetry. The depth profiles along the south and north transects estimated with cBathy agree reasonably well with those interpolated from the bathymetric survey of 17 May (Fig. 8; R = 0.96 and 0.95 for the south and north transects, respectively; bias = −0.26 and −0.54 m, respectively; RMSE = 0.61 and 0.89 m, respectively). Differences between weekly surveys from 27 April and 17 May were small. Although the cBathy and in situ estimates of water depth are similar, at some locations along the transects, the cBathy depths are more than 1 m deeper than the in situ depth estimates (Fig. 8). However, using the in situ–estimated bathymetry did not change the results significantly (Table 1).
Water depth vs cross-shore coordinate along the (a) south and (b) north transects estimated with radar and cBathy (gray curves) and with in situ bathymetric surveys (black curves). The radar-derived (surveyed) water depths at the along-transect locations of the in situ sensors (Fig. 1) (triangles) are h5 = 4.9 (3.7) m, h6 = 2.7 (2.7) m, h7 = 2.7 (2.3) m, h8 = 3.3 (2.9) m, h55 = 3.5 (2.6) m, h56 = 3.6 (2.2) m, h57 = 3.0 (1.7) m, h58 = 5.1 (5.1), and h68 = 5.3 (6.1) m.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
To assess the sensitivity of the wave transformation model to the breaking threshold, tests were run for −8 < σ0br < 0 dB, representing overestimation to underestimation of the breaking-induced dissipation. The agreement between the predicted and the observed wave height at stations 58 and 68 did not vary with the different threshold values, because wave breaking seldom occurred there. The correlations between predicted and observed wave heights along both the south and north transects varied by less than 7% over the range of σ0br tested, and the RMSE and bias changed by less than 0.04 m, suggesting that the breaking threshold within this range has a relatively small effect on the wave dissipation and therefore on model skill along each of the cross-shore transects.
The methodology for using radar observations to estimate wave transformation also allows spatially dense estimates of radiation stresses and their gradients along the transects (Fig. 9). The radar-derived estimates of radiation stress (south and north, Figs. 9a and 9b, respectively) are tidally modulated and increase as the wave height (Fig. 9c, blue curve) increases. Moreover, radar-derived estimates of radiation stress are similar to those estimated from in situ acoustic Doppler velocimeters (ADVs) at the offshore end of the south transect (Fig. 10, sensor 68, R = 0.93) and along the north transect (Fig. 11, sensors 55–58, 0.79 < R < 0.95), where a positive bias (108–191 kg s−2 m−1) is indicative of overprediction of radiation stress.
Predicted cross-shore radiation stress (color contours, scale on the right) as a function of cross-shore location and time for the (a) north and (b) south channels. (c) Observed offshore significant wave height (blue curve) and tidal elevation (gray curve) vs time.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Predicted (gray) and observed (black) cross-shore wave radiation stress Sxx vs time for locations along the south inlet transect (sensors 5–8 and 68, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
Predicted (gray) and observed (black) cross-shore wave radiation stress Sxx vs time for locations along the north inlet transect (sensors 55–58, Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
To assess the accuracy of the radar-derived wave forcing estimates, the along-transect gradient of the predicted cross-shore radiation stress (i.e., 
Predicted (gray) and measured (black) wave forcing, computed as the along-inlet gradient of the cross-shore radiation stress Sxx, vs time for the (a) south and (b) north inlet transects. Predictions and observations used the frequency and direction of the waves at the peak of the frequency spectrum.
Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00215.1
5. Conclusions
Radar-derived estimates of bathymetry, wave propagation direction, and the fraction of breaking waves combined with wave heights measured in 9-m water depth and a 1D wave transformation model that neglects the presence of currents, accurately predict the observed evolution of wave heights and radiation stresses across a complex ebb shoal incised by two inlet channels. Wave heights across the ebb shoal (approximately 2–5-m depth) predicted using the radar-based methodology were modulated by tidal depth changes (±1 m), consistent with observations and with previous numerical modeling results (Chen et al. 2014, manuscript submitted to J. Geophys. Res. Oceans). The modeled wave heights incorporating the radar measurements agreed better with the observations than wave heights estimated using a parametric model with default settings. Using the radar images of the ocean surface allows spatially dense estimates of radiation stresses and their gradients. During energetic waves, radar-estimated radiation-stress gradients would force water into the inlet, similar to gradients estimated from in situ observations (Wargula et al. 2014).
Acknowledgments
These data were collected as part of a joint field program, Data Assimilation and Remote Sensing for Littoral Applications (DARLA) and Rivers and Inlets (RIVET-1), both funded by the Office of Naval Research. We gratefully acknowledge D. Trizna from ISR and R. Pittman from OSU for their assistance with radar deployment and data collection; R. Holman and J. Stanley from the Coastal Imaging Lab, OSU, for the ARGUS video data; J. Thomson from APL-UW for the wind data; J. McNinch and the USACE-FRF for the bathymetric data; G. Farquharson from APL-UW for installing the scaffolding structure; and the PVLAB field crew for deploying, maintaining, and recovering the in situ sensors in less-than-pleasant conditions. Many thanks to the reviewers of this paper for their comments and suggestions. The authors were funded through the Office of Naval Research Grant N00014-10-1-0932 and the Office of the Assistant Secretary of Defense for Research and Engineering.
REFERENCES
Bertin, X., Fortunato A. , and Oliveira A. , 2009: A modeling-based analysis of processes driving wave-dominated inlets. Cont. Shelf Res., 29, 819–834, doi:10.1016/j.csr.2008.12.019.
Catalán, P. A., Haller M. C. , Holman R. A. , and Plant W. J. , 2011: Optical and wave detection of wave breaking in the surf zone. IEEE Trans. Geosci. Remote Sens., 49, 1879–1893, doi:10.1109/TGRS.2010.2095864.
Catalán, P. A., Haller M. C. , and Plant W. J. , 2014: Microwave backscattering from surf zone waves. J. Geophys. Res. Oceans,119, 3098–3120, doi:10.1002/2014JC009880.
Dodet, G., Bertin X. , Bruneau N. , Fortunato A. B. , Nahon A. , and Roland A. , 2013: Wave-current interactions in a wave-dominated tidal inlet. J. Geophys. Res. Oceans, 118, 1587–1605, doi:10.1002/jgrc.20146.
Farquharson, G., Frasier S. J. , Raubenheimer B. , and Elgar S. , 2005: Microwave radar cross sections and Doppler velocities measured in the surf zone. J. Geophys. Res., 110, C12024, doi:10.1029/2005JC003022.
Flores, R. P., Catalán P. A. , and Haller M. C. , 2013: Incorporating remotely-sensed roller properties into set-up estimations for random wave conditions. Proc. Seventh Int. Conf. on Coastal Dynamics, Arcachon, France, CNRS, 615–626.
Gommenginger, C. P., Ward N. P. , Fisher G. J. , Robinson I. S. , and Boxall S. R. , 2000: Quantitative microwave backscatter measurements from the ocean surface using digital marine radar images. J. Atmos. Oceanic Technol., 17, 665–678, doi:10.1175/1520-0426(2000)017<0665:QMBMFT>2.0.CO;2.
Haller, M. C., and Lyzenga D. R. , 2003: Comparison of radar and video observations of shallow water breaking waves. IEEE Trans. Geosci. Remote Sens., 41, 832–844, doi:10.1109/TGRS.2003.810695.
Haller, M. C., and Catalán P. A. , 2009: Remote sensing of wave roller lengths in the laboratory. J. Geophys. Res., 114, C07022, doi:10.1029/2008JC005185.
Holman, R., and Haller M. C. , 2013: Remote sensing of the nearshore. Annu. Rev. Mar. Sci., 5, 95–113, doi:10.1146/annurev-marine-121211-172408.
Holman, R., Plant N. , and Holland T. , 2013: cBathy: A robust algorithm for estimating nearshore bathymetry. J. Geophys. Res. Oceans, 118, 2595–2609, doi:10.1002/jgrc.20199.
Janssen, T. T., and Battjes J. A. , 2007: A note on wave energy dissipation over steep beaches. Coastal Eng., 54, 711–716, doi:10.1016/j.coastaleng.2007.05.006.
Kirby, J. T., 1984: A note on linear surface wave-current interaction over slowly varying topography. J. Geophys. Res., 89, 745–747, doi:10.1029/JC089iC01p00745.
Longuet-Higgins, M. S., and Stewart R. W. , 1964: Radiation stresses in water waves; A physical discussion, with applications. Deep-Sea Res. Oceanogr. Abstr., 11, 529–562, doi:10.1016/0011-7471(64)90001-4.
Malhadas, M., Leitão P. , Silva A. , and Neves R. , 2009: Effect of coastal waves on sea level in Óbidos Lagoon, Portugal. Cont. Shelf Res., 29, 1240–1250, doi:10.1016/j.csr.2009.02.007.
McGregor, J. A., Poulter E. M. , and Smith M. J. , 1998: S band Doppler radar measurements of bathymetry, wave energy fluxes, and dissipation across an offshore bar. J. Geophys. Res., 103, 18 779–18 789, doi:10.1029/98JC00447.
Orescanin, M., Raubenheimer B. , and Elgar S. , 2014: Observations of wave effects on inlet circulation. Cont. Shelf Res., 82, 37–42, doi:10.1016/j.csr.2014.04.010.
Svendsen, I. A., 2006: Introduction to Nearshore Hydrodynamics. Advanced Series on Ocean Engineering, Vol. 24, World Scientific, 722 pp.
Trizna, D., Hansen J. P. , Hwang P. , and Wu J. , 1991: Laboratory studies of sea spikes at low grazing angles. J. Geophys. Res., 96, 12 529–12 537, doi:10.1029/91JC00705.
Wargula, A., Raubenheimer B. , and Elgar S. , 2014: Wind-driven along-channel subtidal flows in a well-mixed ocean inlet. J. Geophys. Res. Oceans, 119, 2987–3001, doi:10.1002/2014JC009839.
Willmott, C. J., 1981: On the validation of models. Phys. Geogr., 2, 184–194.
Young, I. R., Rosenthal W. , and Ziemer F. , 1985: A three-dimensional analysis of marine radar images for the determination of ocean wave directionality and surface currents. J. Geophys. Res., 90, 1049–1059, doi:10.1029/JC090iC01p01049.
Zippel, S., and Thomson J. , 2015: Wave breaking and turbulence at a tidal inlet. J. Geophys. Res. Oceans, doi:10.1002/2014JC010025, in press.
