Nonlinear Kinematic Depth Inversion Coupled With a Spectral Wave Model

Abstract

We present a bidirectional coupling between a nonlinear kinematic depth inversion method and a phase‐averaged spectral wave model to evaluate the influence of wave nonlinearity over gently sloping nearshore bathymetry. Time‐resolved wave imagery provides spatially varying frequency–wavenumber fields, whereas the simulated significant wave height field supplies a measure of amplitude dispersion. These data are integrated to quantify an effective nonlinearity parameter across contrasting wave energy conditions, encompassing both calm and energetic states. Particular attention is given to the shoaling region and the inner surf zone under spilling type breaking, where amplitude effects and depth‐induced dissipation significantly modify the dispersion characteristics. Comparisons between the proposed nonlinear depth inversion and independently surveyed bathymetry show that neglecting nonlinearity produces a systematic depth overestimation that scales with the local nonlinearity, whereas addressing nonlinearity reduces this bias by as much as 90%. Video‐derived surface motion retains identifiable dispersive signatures after the onset of spilling type breaking, enabling depth inversion when wave nonlinearity is addressed. This remains valid until breaking‐generated foam becomes sufficiently dense that the resulting noise level becomes comparable to the wave signal. The analysis shows that video‐derived wave kinematics and bathymetry, when interpreted with a calibrated spectral wave model, provide a consistent description of the nonlinear transformation of shoaling and breaking waves. It also identifies the parameter ranges in which linear depth inversion becomes less reliable under field conditions.