3.2.2. Estimation by Satellite Image

Fortunately, we got one ASAR image during the cruise. The phase speed was also estimated from the satellite image for comparison. Figure 6 shows an ASAR image acquired by the Envisat satellite at 02:17 UTC on 23 May 2011, capturing the same ISW 26.3 h after it was detected by the vessel. The image shows several bright–dark bands corresponding to wave crests–troughs near Dong-sha Atoll, indicating the first baroclinic mode depression waves. The wave we discussed above was a leading wave, and the trailing wave was also detected (Section 3). The ISW wave packet can be classified as an A-type wave. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 7 of 10

**Figure 6.** Satellite image of the Environment satellite (Envisat) taken at 02:17 UTC on 23 May 2011, 26.3 h after the ISW was measured by the shipboard ADCP. The red pentagram represents the location where the ISW was captured by the ship, the dashed line represents the propagation path, and **Figure 6.** Satellite image of the Environment satellite (Envisat) taken at 02:17 UTC on 23 May 2011, 26.3 h after the ISW was measured by the shipboard ADCP. The red pentagram represents the location where the ISW was captured by the ship, the dashed line represents the propagation path, and the red triangle represents the same ISW 26.3 h after it was detected in the satellite image.

**4. Discussion** The distance between the wave crest (shown in Figure 6) and the ship ADCP measurements location was about 150 km. Considering the distance and time difference, the

which may contribute to the horizontal velocity in ADCP measurements. When considering the influence of the barotropic tide on the observed ISW, the barotropic tide should be calculated first. With long-term and all-depth observation records, the internal wave signal could be separated via filter analysis from tidal and inertial signals [2,23,24] to investigate the influence of the barotropic tide on the observed ISW. However, the vessel cannot provide full-depth current data due to ADCP measurement limitations. Instead, here we

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 red triangle represents the same ISW 26.3 h after it was detected in the satellite image.

considered two other methods to subtract the velocity of the barotropic tide.

4.1.1. Modal Decomposition to Reconstruct the Barotropic Current

the first three vertical modes. The calculation did not go into detail here.

*4.1. Influence of Barotropic Tide*

mean phase speed of the ISW was around 1.59 m/s, which is only 0.17 m/s slower than the theoretical result of the KdV solution. The difference can be attributed to the accuracy of HYCOM data products in the SCS, and also may relate to the variations of bathymetry over a distance of 150 km and the background current.
