  In Wang & Pan (J. Fluid Mech., vol. 918, A19, 2021), the authors developed
the first ensemble-based data assimilation (DA) capability for the
reconstruction and forecast of ocean surface waves, namely the EnKF-HOS method
coupling an ensemble Kalman filter (EnKF) and the high-order spectral (HOS)
method. In this work, we continue to enrich the method by allowing it to
simultaneously estimate the ocean current field, which is in general not known
a priori and can (slowly) vary in both space and time. To achieve this goal, we
incorporate the effect of ocean current (as unknown parameters) on waves to
build the HOS-C method as the forward prediction model, and obtain a
simultaneous estimation of (current) parameters and (wave) states via an
iterative EnKF (IEnKF) method that is necessary to handle the complexity in
this DA problem. The new algorithm, named IEnKF-HOS-C method, is first tested
in synthetic problems with various forms (steady/unsteady, uniform/non-uniform)
of current. It is shown that the IEnKF-HOS-C method is able to not only
estimate the current field accurately, but also boost the prediction accuracy
of the wave field (even) relative to the state-of-the-art EnKF-HOS method.
Finally, using real data from a shipborne radar, we show that the IEnKF-HOS-C
method successfully recovers the current speed that matches the in situ
measurement by a floating buoy.
