Application of coastal acoustic tomography: calibration of open boundary conditions on a numerical ocean model for tidal currents

Coastal acoustic tomography (CAT), which measures path-averaged currents from reciprocal acoustic transmission experiments and reconstructs velocity fields from the multiple path-averaged current data, is useful for monitoring tidal currents in coastal shallow water, especially if data assimilation is employed. Previous CAT data assimilation studies have focused on state estimation problems, i.e., the reconstruction of tidal currents and following dynamical discussion. In this study, we investigate the use of path-averaged currents in a boundary control problem. Specifically, we aim to use the observed path-averaged currents to determine the parameters of a numerical ocean model, which were tidal amplitudes and phases as the open boundary conditions in this study. We investigate two methods: using the ensemble Kalman filter (EnKF) results and a linearization approach called model Green's function method. Both calibration methods decreased the amplitudes of tidal constituents at the open boundaries. We compare the model performance between the model predictions with and without the calibration of the open boundary conditions. The model predictions with the calibrated open boundary conditions improved the agreement with the observed path-averaged current. We also implemented the sequential updates of EnKF with the two calibrated open boundary conditions. The EnKF results with the independently calibrated two open boundary conditions improved the agreement with the comparison data obtained by acoustic Doppler current profiler measurement compared with the original EnKF result with the initial open boundary conditions.