[1] 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 frequencydependent 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.Citation: Holman, R., N. Plant, and T. Holland (2013), cBathy: A robust algorithm for estimating nearshore bathymetry, J. Geophys.

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A method is proposed for estimating approximate 2DH bathymetry including longshore variable shoreline and sand bar systems. The method is based on, but extends, a previous 1DH model of Holman et al [2014] by assuming that this 1DH equilibrium barred bathymetry can be applied for any offshore location if the corresponding mean shoreline orientation is taken to be the local average over a longshore span that is K times the offshore distance. Thus locations close to the beach are sensitive to shoreline and bar details while more seaward locations are steadily less sensitive. The model was tested against 14 ground truth surveys, collected over two years and under widely ranging environmental condition, spanning a 500 by 1000 m region. Models inputs for the shoreline and sand bar positions were extracted from measured bathymetries for these tests (but would be derived from other sources in real applications) while deep-water inputs were found from a single deep-water survey. The model yielded complete 2DH bathymetry maps that were a very good approximation of ground truth. The mean bias and rms error over the full region and data set were 0.27 m and 0.49 m respectively and proxy bathymetries were visually very similar to ground truth. The largest source of error was occasional cross-shore misplacements of otherwise realistic looking sand bars. Results were only weakly dependent on the value of K when tested over a factor of four and the default value of 1.0 is recommended. Performance statistics using input locations for the shoreline and bar crest that were manually digitized from breaking patterns in rectified optical time exposure images were no worse than bathymetry-based inputs. Hydrodynamic predictions using these bathymetries would be a substantial improvement over those from monotonic or even barred 1DH equilibrium proxy bathymetries.

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