An improved adjoint-based ocean wave reconstruction and prediction method

We propose a method for the reconstruction and prediction of nonlinear wave field from coarse-resolution measurement data. We adopt the data assimilation framework using the adjoint equation to search for the optimal initial wave field to match the given measurement data. Compared with the conventional approach where the surface elevation and velocity potential are independent, our method features an additional constraint to dynamically connect these two control variables based on the dispersion relation of waves. The performance of our new method and the conventional method is assessed with the synthetic nonlinear wave data generated from phase-resolved nonlinear wave simulations using the high-order spectral method. We consider a variety of wave steepness and noise levels for the nonlinear irregular wave fields. It is found that the conventional method tends to overestimate the surface elevation in the high-frequency region and underestimate the velocity potential. In comparison, our new method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential, and high-order wave statistics including the skewness and kurtosis.