Lange, Athina M.Z., Fiedler, Julia W., Merrifield, Mark A., Guza, R.T.

UAV video-based estimates of nearshore bathymetry (2023) Coastal Engineering

Nearshore bathymetry estimated from video acquired by a hovering UAV is compared with ground truth. Bathymetry estimates from the widely used cBathy algorithm are improved by crest tracking (with machine learning-aided annotations) from near breaking through the surf zone. Individual wave crests (distinguished from the breaking wave toe that can move down the wave front face) in video timestacks are determined with a deep-learning neural network and surfzone depth estimates are computed from the wave celerity. Time-2D spatial transforms (cBathy) are used to estimate wave celerity and depth between the surfzone and 10m depth. Composite profiles (cBathyCT), formed by joining cBathy and crest-tracking solutions near the surfzone seaward edge, based on a newly determined gamma(x) parameter, avoid the large cBathy errors associated with the onset of breaking. Including an additional topography survey for the foreshore region, provides full nearshore bathymetry profiles. Incident wave heights were relatively constant on each day, but varied over days between 0.55-2.15m. Averaged over all 17-minute hovers and cross-shore transects (112 total), surfzone depths errors were relatively small (average root-mean-square error < RMSE > = 0.17m, < Bias > = 0.06m) after including a heuristic nonlinear correction to the linear phase speed. Between the seaward surfzone edge and 10-m depth, errors are similar to previous cBathy studies: < RMSE > = 0.87m, < Bias > = 0.58m with the largest errors in deepest water. Beach profiles were generally similar for all 8 test days, concave up with a slight terrace (no sandbar) and small alongshore depth variations. Accuracy was lower on one transect with a shallow reef.

This code is the companion to 'UAV video-based estimates of nearshore bathymetry'. The code is set up to be self-contained once everything is downloaded/installed, and provides a number of example timestacks to run through the method. Any questions or suggestions can be emailed to Athina Lange ([email protected]).

Everything can be run from bathy_from_UAV.m

Installation:

• current GitHub repository
  • unzip all folders
• Timestack images from GoogleDrive: https://tinyurl.com/timestack
• Curve Fitting MATLAB toolbox
• Image Processing Toolbox MATLAB toolbox
• WaveCrestDetection GitHub to predict wave crests from new timestacks (https://github.com/AthinaLange/WaveCrestDetection)

Input

• ground-truth survey (minimum: subaerial survey - requires commenting out error calculations in bathy_inversion.m)
• cBathy results from same hovers (see bathy_from_UAV.m for input format)
• timestack images at (0.1m, 0.1s) resolution (anything else requires retraining neural network)
  • WaveCrestDetection neural network is currently run with Python through the terminal and is not part of bathy_from_UAV.m)

Output

Video_bathy (structure)

• date - YYYYMMDD
• location - ie. 'Torrey' (pulled from timestack name)
• flight - flight number
• mop - mop number
• x10 - [0:0.1:500]m
• survey - z - Depth pulled from survey on MOP line
• cbathy -
  • z - cBathy direct output on given transect
  • zerr - cBathy hErr
  • cbathy_hErr - cBathy with hErr > 0.5m region interpolated over
  • cbathy_gamma - cBathy with breaking region removed for given variable gamma(x)
• tide - tide level (pulled from cbathy)
• crests -
  • t - time for wave tracks (sec)
  • x - cross-shore location for wave tracks (m) (0 is offshore, 500 is onshore)
  • c - phase speed of wave tracks - interp to x10
• bp - breakpoint index of wave tracks
• xshift - cross-shore shift index to match subaerial survey with subaqueous bathymetry
• h_avg - interped to x10
  • lin - linear crest-tracking c = sqrt(gh)
  • nlin - nonlinear crest-tracking c = sqrt(gh(1+0.42))
  • bp - breakpoint transition crest-tracking c = sqrt(gh(1+gamma(x)))
• gamma - transition between 0 and 0.42 for wave tracks (interped to x10)
• gamma_mean - gamma(x) - mean of step function gamma for wave tracks
• composite - constructed bathymetry with subaerial survey with ...
  • cbathy_hErr - cBathy with hErr < 0.5m
  • cbathy_gamma - cBathy with breaking region removed
  • cbathy_nlin - cBathy_gamma with gamma(x) correction
  • cbathyCT - breakpoint transition crest-tracking surfzone bathymetry and cBathy offshore
• lims - index of [1st BP valid onshore point, onshore cutoff of breaking, offshore cutoff of breaking]
• Error -

  • RMSE - root-mean-square error

  • Skill - skill of estimated versus observed survey bathymetry

  • Bias - bias of estimated bathymetry

  • insz - inner surfzone (between shoreline and end of active wave breaking - gamma(x)=0.42)

  • break - breaking region (active wave breaking region - where gamma changes)

  • sz - full surfzone region (between shoreline and wave breaking region)

  • full - [0 500] region

  • offshore - offshore region (between beginning of wave breaking and 500m - gamma(x) = 0)

  • cb - default cBathy (no region removed)

  • cb_hErr - cBathy with hErr > 0.5m removed

  • cb_gamma - cBathy with breaking region removed

  • lin - linear crest-tracking

  • nlin - nonlinear crest-tracking

  • bp - breakpoint transition crest-tracking

  • comp_hErr - composite cBathy_hErr

  • comp_gamma - composite cBathy_gamma

  • comp_nlin - composite cBathy_nlin

  • comp_CT - composite BP + cBathy

Results

Breakpoint Detector Example

• Blue dot: Unbroken, dot at end of track
• Green dot: Breakpoint location along wave track
• Red dot: Entire wave track broken, dot at beginning of track

Example of two hovers