Updates to and Performance of the cBathy Algorithm for Estimating Nearshore Bathymetry from Remote Sensing Imagery

Abstract

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.

Video-Based Nearshore Bathymetric Inversion on a Geologically Constrained Mesotidal Beach during Storm Events

“…Nowadays, the increasing proliferation of low-cost and flexible new platforms such as UAVs [82,83], swift cameras, CoastSnap [84] and online-streaming webcams [31,85,86] offer an attractive option to collect image products and derive measurements of the nearshore. In addition to image-processing techniques that allow estimating the nearshore bathymetry (e.g., cBathy [19,43]), recent works have opened up the possibility to remotely estimate 2D surface currents by tracking the drifting foam, left after the passage of breaking waves, from video imagery (e.g., optical flow-based algorithms [73,87,88]). Future work could be to apply both remote sensing techniques to provide fresh insight into the coupled (hydrodynamic/morphology) morphodynamic system, which is key to the validation of process-based morphodynamic models.…”

“…The cBathy algorithm, developed by Holman et al [19], is a spectral depth inversion method that is nowadays the most popular algorithm to obtain two-dimensional bathymetries from video stations [6,25,[32][33][34][35][36][37][38][39][40][41][42][43][44]. cBathy is based on the linear wave dispersion relationship, and therefore, its validity is inherently bounded to the increasing degree of wave non-linearity (finite amplitude effects) as waves approach the shore, leading to larger propagation speeds for higher waves [45,46].…”

Depth Inversion from Wave Frequencies in Temporally Augmented Satellite Video

“…Such frequency-based depth inversion algorithms are used on imagery of shore-based cameras [15,23,24], UAVs [25,26] and Xband-radars [27][28][29][30] and have been broadly applied over the past decades. These algorithms have matured with typical accuracies of 0.5-2 m [13,31,32] and are well-embedded in the coastal remote-sensing community. In addition, recent efforts have aimed to make these algorithms easy to access and use.…”

“…In addition, recent efforts have aimed to make these algorithms easy to access and use. Accessibility and use of this algorithms is facilitated by increased robustness, selfadaptation to the data, computational speed, and open availability [13,32,33]. Connecting the collection and analysis of satellite imagery to these depth inversion algorithms and their users remains an open challenge.…”

New Perspectives for Nonlinear Depth‐Inversion of the Nearshore Using Boussinesq Theory

“…• A new depth-inversion approach for the nearshore is proposed, based on a Boussinesq theory for quantifying nonlinear dispersion effects • Unprecedented levels of accuracy (typically within 10%) are obtained in the surf zone over both planar and barred beaches • Improvement over the linear wave theory method, which overestimates depths by 40% or more in surf zones (up to 80% at the shoreline) from optical imagery (e.g., see Holman & Bergsma, 2021;Plant et al, 2008;Stockdon & Holman, 2000). In intermediate water depths, Equation 1 accurately describes the dispersive properties of low-amplitude wave fields so that typical errors on the water depth estimated with an algorithm like cBathy can be as low as 10% (e.g., see Brodie et al, 2018;Dugan et al, 2001;Holland, 2001).…”