Blending bathymetry: Combination of image-derived parametric approximations and celerity data sets for nearshore bathymetry estimation

Estimation of nearshore bathymetry is important for accurate prediction of nearshore wave conditions. However, direct bathymetry data collection is expensive and time-consuming while accurate airborne lidarbased survey is limited by breaking waves and decreased light penetration affected by water turbidity. Instead, tower-based platforms or Unmanned Aircraft System (UAS) can provide indirect video-based observations such as time -series (or videos) and time-averaged (Timex) or variance enhanced (Var) images. The timeseries imagery can provide wave celerity information for bathymetry estimation through the well-known dispersion relationship, for example the cBathy algorithm, or physics-based models. However, wave celerities and associated inverted water depths are sensitive to noise during image collection and processing stages or may not even be available over the entire area of interest. Timex or Var images can be used to identify persistent regions of wave breaking (for example over the sand bar and at the shoreline) so that one can create bathymetry profiles using simplified approximations based on parametric forms. However, the accuracy of this approach highly depends on the assumption of the chosen parametric form as well as the accuracy of detecting sandbars and shoreline. In this work, we propose a rapid and improved bathymetry estimation method that takes advantage of image-derived wave celerity from cBathy and a first-order bathymetry estimate from Parameter Beach Tool (PBT), software that fits parameterized sandbar and slope forms to the nearshore imagery. Two different sources of the data, PBT and wave celerity, are combined or blended optimally based on their assumed accuracy in a statistical (i.e., Bayesian) framework. The PBT-derived bathymetry serves as "prior"coarse-scale background information and then is updated and corrected with the cBathy-derived wave data through the dispersion relationship, which results in a better bathymetry estimate that is consistent with imagery-based wave data. To illustrate the accuracy of our proposed method, imagery data sets collected in 2017 at the US Army Engineer Research and Development Center's (ERDC) Field Research Facility (FRF) in Duck, North Carolina under different weather and wave height conditions are tested. Estimated bathymetry profiles are remarkably close to the direct survey data due to the optimal fusion of two data sets. The computational time for the estimation from PBT-based bathymetry and CBathy-derived wave celerity is only about five minutes on a free Google Cloud node with one CPU core. These promising results indicate the feasibility of reliable real -time bathymetry imaging during a single flight of UAS.