Bathymetry correction using an adjoint component of a coupled nearshore wave‐circulation model: Tests with synthetic velocity data

The impact of assimilation of wave‐averaged flow velocities on the bathymetric correction is studied in tests with synthetic (model‐generated) data using tangent‐linear and adjoint components of a one‐way coupled nearshore wave‐circulation model. Weakly and strongly nonlinear regimes are considered, featuring energetic unsteady along‐beach flows responding to time‐independent wave‐averaged forcing due to breaking waves. It is found that assimilation of time‐averaged velocities on a regular grid (mimicking an array of remotely sensed data) provides sensible corrections to bathymetry. Even though the wave data are not assimilated, flow velocity assimilation utilizes adjoint components of both the circulation and wave models. The representer formalism allows separating contributions of these two components to the bathymetric correction. In a test case considered, involving a beach with an alongshore varying bar, the adjoint wave model contribution was mainly to determine the cross‐shore position of the bar crest. The adjoint circulation model provided an additional contribution, mostly adding to alongshore variability in the shape of the bar. The array mode analysis reveals that there are very few modes that can be effectively corrected, given the assumed data error level. Bathymetry perturbations associated with these modes are a mixture of near‐coast intensified modes as well as modes extending their influence to deep water (along the background wave characteristics). Additional tests show the utility of different observational arrays in providing the bathymetric correction.