Video-based depth inversion techniques, a method comparison with synthetic cases

Applications of (video-based) depth inversion in the near-shore coastal environment are growing in numbers. Video-based capabilities in nearshore monitoring are improving and coastal monitoring programs are expanding due to greater availability and reduced costs. Video-derived beach (state) indicators such as beach width, bar position and wave and current parameters are supplemented by accurate depth estimations through inversion. Video-based depth inversion knows two main approaches, a spectral and temporal method of celerity estimation. The two methods have so far never been compared as video-systems are often tailored for the chosen celerity estimation method. Here, a spectral and temporal method are compared using controlled synthetic datasets obtained using the SERRE1D Boussinesq model to estimate celerity and invert depth. The assessment is carried out on a set of wave boundary conditions with over linear and barred bottom profile. Both methods invert depth with a similar accuracy for the most realistic JONSWAP cases. An evident correlation is found between wave skewness, non-linearity and depth estimation error linked to the limits of the linear dispersion relation. A residual 'sensing' error is linked to method-based parameters and a changing wave shape as incident waves propagate inshore. The inversion-error can be reduced significantly including a wave height dependent non-linear correction. Importantly, a method-based error is introduced for the temporal method to increase the suitability for data assimilation. Likewise, the spectral method has its own existing depth-error estimation to feed into the Kalman Filter. However, these method-based error estimates show very weakly or no relation to the observed error between estimated cross-shore profile and bottom profile used for the model input.