Data assimilation is a method to incorporate real-time measurement data into simulations for calibration and better forecast/prediction. We have developed a robust and efficient wave forecast system for the short-term prediction of water waves. In the system, to evaluate the sensitivity of the wave model to control variables, we use adjoint equations to construct the gradient field. Then we feed the gradient field into a gradient-based optimizer to minimize the difference between simulation and measurement.
With this wave forecast system, we construct the synthetic optical observations of the wave field based on the downwelling irradiation field and reconstruct the wave field in Fig. 1. The result is of high accuracy and justifies the robustness of the system. In another application, as shown in Fig. 2, we are able to assimilate observational wave height data from the X-band marine radar image, reconstruct the wave field, and reduce the measurement error in observations. Moreover, as shown in Fig. 3, the surface elevation profile can be assimilated into wind-waves using nudging.