Seamless nearshore topo-bathymetry reconstruction from lidar scanners: A Proof-of-Concept based on a dedicated field experiment at Duck, NC

Accurate observations of the nearshore bathymetry, including within the breaking wave region, are critical for the prediction of coastal hazards, and improved understanding of sandy beach morphological response to storms. In this paper, we implement the recent Boussinesq theory-based depth inversion methodology of Martins et al. (Geophys. Res. Lett., 50 (2023), Article e2022GL100498) to single- and multibeam lidar datasets collected during a dedicated field experiment on a sandy Atlantic Ocean beach near Duck, North Carolina. Compared with common approaches based on passive remote sensing technology (e.g., optical imagery), lidar scanners present several key advantages, including the capacity to directly measure the beach topography, waveforms and the cross-shore variations in mean water levels due to wave action (e.g., the wave setup), leading to the seamless reconstruction of a vertically-referenced beach topo-bathymetry. Given the potentially gappy nature of lidar data, particular attention is paid to the robust computation of surface elevation spectral and bispectral quantities, which are at the base of the proposed non-linear depth inversion methodology. Promising results on the final topo/bathymetry are obtained under contrasting wave conditions in terms of non-linearity and peak period, with an overall root-mean square error below 0.3 m obtained along a cross-shore transect covering both shoaling and breaking wave conditions. The accuracy of the final bathymetry in the shoaling and outer surf regions is generally found to be excellent, with similar skills as previously obtained in laboratory settings (relative error $<10-15\text{\%}$). Under the most energetic conditions, an underestimation of the wave phase velocity spectra is observed within the surf zone with all theoretical frameworks, potentially owing to surf zone vortical motions not yet accounted for in the present methodology. This underestimation of the wave phase velocities results in a relatively large overestimation of the mean water depth, between 30% to 100% depending on the theoretical framework. With the methodology described herein, lidars bring new perspectives for seamlessly mapping the nearshore topo/bathymetry, and its temporal evolution across a wide range of scales. Although currently limited to a single cross-shore transect, we believe that opportunities exist to integrate multiple remote sensors, which could address individual sensor limitations, such as coverage (lidar) or the incapacity to directly measure waveforms (optical imagery).