The phase-resolved prediction of ocean waves is crucial for the safety of offshore operations. With the development of the remote sensing technology, it is now possible to reconstruct the phase-resolved ocean surface from radar measurements in real time. Using the reconstructed ocean surface as the initial condition, nonlinear wave models such as the high-order spectral (HOS) method can be applied to predict the evolution of the ocean waves. However, due to the error in the initial condition (associated with the radar measurements and reconstruction algorithm) and the chaotic nature of the nonlinear wave equations, the prediction by HOS can deviate quickly from the true surface evolution (in order of one minute). To solve this problem, the capability to regularly incorporate measured data into the HOS simulation through data assimilation is desirable. In this work, we develop the data assimilation capability for nonlinear wave models, through the coupling of an ensemble Kalman filter (EnKF) with HOS. The developed algorithm is validated and tested using a synthetic problem on the simulation of a propagating Stokes wave with random initial errors. We show that the EnKF-HOS method achieves much higher accuracy in the long-term simulation of nonlinear waves compared to the HOS-only method.

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