4.1.1. Modal Decomposition to Reconstruct the Barotropic Current

According to [25], full-depth barotropic currents and baroclinic currents from limited mooring observations can be obtained by combining harmonic analysis and modal decomposition. Harmonic analysis is used to calculate harmonic constants of the major constituents and predict the time series of each major tidal constituent. Modal decomposition is carried out to obtain full-depth tidal currents of each mode by using the least-squares method [26]. It was found that when more than three vertical modes were considered in the calculation, the prescribed tidal currents could be reconstructed accurately [25].

As the time series of shipboard ADCP measurement was not long enough to be frequency filtered, processes at frequencies other than barotropic tide and baroclinic tide were ignored. Thus, we focused on the modal decomposition, only taking into account the first three vertical modes. The calculation did not go into detail here.

The first three vertical modes were taken into account. The reconstructed barotropic westward velocity (u) was 2 cm/s, and the southward velocity (v) was 6.34 cm/s. Both were insignificant compared to the large velocity induced by ISW.
