A three‐part algorithm is described and tested to provide robust bathymetry maps based solely on long time series observations of surface wave motions. The first phase consists of frequency‐dependent characterization of the wave field in which dominant frequencies are estimated by Fourier transform while corresponding wave numbers are derived from spatial gradients in cross‐spectral phase over analysis tiles that can be small, allowing high‐spatial resolution. Coherent spatial structures at each frequency are extracted by frequency‐dependent empirical orthogonal function (EOF). In phase two, depths are found that best fit weighted sets of frequency‐wave number pairs. These are subsequently smoothed in time in phase 3 using a Kalman filter that fills gaps in coverage and objectively averages new estimates of variable quality with prior estimates. Objective confidence intervals are returned. Tests at Duck, NC, using 16 surveys collected over 2 years showed a bias and root‐mean‐square (RMS) error of 0.19 and 0.51 m, respectively but were largest near the offshore limits of analysis (roughly 500 m from the camera) and near the steep shoreline where analysis tiles mix information from waves, swash and static dry sand. Performance was excellent for small waves but degraded somewhat with increasing wave height. Sand bars and their small‐scale alongshore variability were well resolved. A single ground truth survey from a dissipative, low‐sloping beach (Agate Beach, OR) showed similar errors over a region that extended several kilometers from the camera and reached depths of 14 m. Vector wave number estimates can also be incorporated into data assimilation models of nearshore dynamics.

The shallow waters of the nearshore ocean are popular, dynamic, and often hostile. Prediction in this domain is usually limited less by our understanding of the physics or by the power of our models than by the availability of input data, such as bathymetry and wave conditions. It is a challenge for traditional in situ instruments to provide these inputs with the appropriate temporal or spatial density or at reasonable logistical or financial costs. Remote sensing provides an attractive alternative. We discuss the range of different sensors that are available and the differing physical manifestations of their interactions with the ocean surface. We then present existing algorithms by which the most important geophysical variables can be estimated from remote sensing measurements. Future directions and opportunities will depend on expected developments in sensors and platforms and on improving processing algorithms, including data assimilation formalisms.

We explore the potential for using a small unmanned aerial vehicle (UAV) quadcopter to collect long-dwell imagery of the nearshore from which important measurements can be made at low cost and with flexibility. This paper extends the existing topographic imaging approaches that rely on having plentiful ground control spread across the image, to the nearshore case where the bulk of the image is water with no control point and vehicle metadata must be used. The UAV autopilot was found to be capable of excellent station-keeping with the positional errors of 0.20 and 0.53 m (horizontal and vertical) and the viewing angle errors of 0.25° (tilt and roll) and 0.38° (azimuth). The ground position of imaged objects could be found with 0.21-m accuracy. Metadata returned by the UAV on camera position was accurate at 5 m, and the camera roll could be assumed to be 0°, reducing the ground control requirements to two, or even one location. Even under this extreme simplification, ground position errors averaged only 10 m but were worse for cases when only control points near to the UAV were used. A model for the visual contrast of waves when viewed from different angles found that large tilts are important but, in contrast to theory, that there was little dependence on the viewing azimuthal angle. Derived Argus products agreed well with the same products collected using a traditional fixed Argus station. UAVs appear to be a very promising alternate to fixed camera systems if limited duration sampling is adequate.

This manuscript describes and tests a set of improvements to the cBathy algorithm, published in 2013 by Holman et al. [hereafter HPH13], for the estimation of bathymetry based on optical observations of propagating nearshore waves. Three versions are considered, the original HPH13 algorithm (now labeled V1.0), an intermediate version that has seen moderate use but limited testing (V1.2), and a substantially updated version (V2.0). Important improvements from V1.0 include a new deep-water weighting scheme, removal of a spurious variable in the nonlinear fitting, an adaptive scheme for determining the optimum tile size based on the approximate wavelength, and a much-improved search seed algorithm. While V1.2 was tested and results listed, the primary interest is in comparing V1.0, the original code, with the new version V2.0. The three versions were tested against an updated dataset of 39 ground-truth surveys collected from 2015 to 2019 at the Field Research Facility in Duck, NC. In all, 624 cBathy collections were processed spanning a four-day period up to and including each survey date. Both the unfiltered phase 2 and the Kalman-filtered phase 3 bathymetry estimates were tested. For the Kalman-filtered estimates, only the estimate from mid-afternoon on the survey date was used for statistical measures. Of those 39 Kalman products, the bias, rms error, and 95% exceedance for V1.0 were 0.15, 0.47, and 0.96 m, respectively, while for V2.0, they were 0.08, 0.38, and 0.78 m. The mean observed coverage, the percentage of successful estimate locations in the map, were 99.1% for V1.0 and 99.9% for V2.0. Phase 2 (unfiltered) bathymetry estimates were also compared to ground truth for the 624 available data runs. The mean bias, rms error, and 95% exceedance statistics for V1.0 were 0.19, 0.64, and 1.27 m, respectively, and for V2.0 were 0.16, 0.56, and 1.19 m, an improvement in all cases. The coverage also increased from 78.8% for V1.0 to 84.7% for V2.0, about a 27% reduction in the number of failed estimates. The largest errors were associated with both large waves and poor imaging conditions such as fog, rain, or darkness that greatly reduced the percentage of successful coverage. As a practical mitigation of large errors, data runs for which the significant wave height was greater than 1.2 m or the coverage was less than 50% were omitted from the analysis, reducing the number of runs from 624 to 563. For this reduced dataset, the bias, rms error, and 95% exceedance errors for V1.0 were 0.15, 0.58, and 1.16 m and for V2.0 were 0.09, 0.41, and 0.85 m, respectively. Successful coverage for V1.0 was 82.8%, while for V2.0, it was 90.0%, a roughly 42% reduction in the number of failed estimates. Performance for V2.0 individual (non-filtered) estimates is slightly better than the Kalman results in the original HPH13 paper, and it is recommended that version 2.0 becomes the new standard algorithm.

This paper presents optical measurements of debris movement and tsunami inundation over an unobstructed beach in a laboratory wave basin. The debris consisted of rectangular boxes and was placed unconstrained on a flat section raised above the basin floor with no still water on the raised section. Debris movement was measured using two overhead video cameras and a novel object-tracking algorithm. Two standard optical techniques, wave edge detection and particle image velocimetry, were used to compare optical and in situ measurements of fluid velocity. The debris motion (position, velocity) in the onshore direction was found to be repeatable, but the offshore motion varied between trials because of the irregular nature of the flow field during the return. For debris in free translation, as the number of debris specimens increased, the peak average velocity decreased and the onset of the peak was delayed in the onshore direction. In the offshore direction, the velocity was lower by a factor 4–6 and was independent of the quantity of debris. The decrease in the peak onshore velocity with increasing amount of debris was observed for debris that undergoes an initial rotation. The peak onshore velocity was nearly independent of whether the initial motion was purely translational or a combination of rotation and translation.

Complex two-dimensional nearshore current patterns are generated by feedbacks between sub-aqueous morphology and momentum imparted on the water column by breaking waves, winds, and tides. These non-stationary features, such as rip currents and circulation cells, respond to changing environmental conditions and underlying morphology. However, using fixed instruments to observe nearshore currents is limiting due to the high costs and logistics necessary to achieve adequate spatial sampling resolution. A new technique for processing surf-zone imagery, WAMFlow, quantifies fluid velocities to reveal complex, multi-scale (10 s–1000 s meters) nearshore surface circulation patterns. We apply the concept of a wave-averaged movie (WAM) to measure surf-zone circulation patterns on spatial scales of kilometers in the alongshore and 100 s of meters in the cross-shore. The approach uses a rolling average of 2 Hz optical imagery, removing the dominant optical clutter of incident waves, to leave the residual foam or water turbidity features carried by the flow. These residual features are tracked as quasi-passive tracers in space and time using optical flow, which solves for u and v as a function of image intensity gradients in x, y, and t. Surf zone drifters were deployed over multiple days with varying nearshore circulations to validate the optically derived flow patterns. Root mean square error are reduced to 0.1 m per second after filtering based on image attributes. The optically derived patterns captured longshore currents, rip currents, and gyres within the surf zone. Quantifying nearshore circulation patterns using low-cost image platforms and open-source computer vision algorithms presents the potential to further our understanding of fundamental surf zone dynamics.