Reconstruction of horizontal tidal current fields in a shallow water with model-oriented coastal acoustic tomography

Abstract

Reciprocal acoustic transmission and coastal acoustic tomography (CAT) is a powerful tool for measuring tidal currents in shallow coastal water, especially if data assimilation is employed. In previous CAT data assimilation studies, the ensemble Kalman filter (EnKF) has been implemented to assimilate observed path-averaged velocity, but ad-hoc procedures called localization and inflation, which compensate for issues associated with using ensemble approximation, were not always implemented. In this study, EnKF is applied to assimilate the path-averaged currents obtained from a reciprocal acoustic transmission experiment conducted at Mihara-Seto in the Seto Inland Sea, Japan, with four acoustic stations in 2020 to reconstruct spatiotemporal variations of tidal currents at the observation site. We executed EnKF with several combinations of different values of the inflation, localization, and the number of ensemble members. The resulting data assimilated velocity reconstructions are compared with acoustic Doppler current profiling (ADCP) results. The results show that data assimilation with EnKF improved the velocity reproduction compared with the model prediction and that implementing covariance inflation contributed to additional improvements. The covariance localization did not improve the results in our case. The best result in terms of fractional error variance (FEV) between the ADCP velocity was obtained from the case with 980 ensemble members with a covariance inflation of 1.01; the FEV was 7.9%. The case of 98 ensemble members with a covariance inflation of 1.01 resulted in similar performance; the FEV value was 8.2%. Thus, with the covariance inflation, the number of ensemble member used in previous CAT studies are reasonable. In the study, we also clarified the reason for the high-frequency variation in the observed path-averaged currents in a preliminary experiment; the path-averaged currents had captured the spatiotemporal variation of vortex generation associated with island wakes. The reciprocal acoustic transmission with EnKF can capture short-period variation over a long period; thus, it can be used in studies of coastal physical processes with various time scales.