  Through ensemble-based data assimilation (DA), we address one of the most
notorious difficulties in phase-resolved ocean wave forecast, regarding the
deviation of numerical solution from the true surface elevation due to the
chaotic nature of and underrepresented physics in the nonlinear wave models. In
particular, we develop a coupled approach of the high-order spectral (HOS)
method with the ensemble Kalman filter (EnKF), through which the measurement
data can be incorporated into the simulation to improve the forecast
performance. A unique feature in this coupling is the mismatch between the
predictable zone and measurement region, which is accounted for through a
special algorithm to modify the analysis equation in EnKF. We test the
performance of the new EnKF-HOS method using both synthetic data and real radar
measurements. For both cases (though differing in details), it is shown that
the new method achieves much higher accuracy than the HOS-only method, and can
retain the phase information of an irregular wave field for arbitrarily long
forecast time with sequentially assimilated data.
