Figure 2 . Zonal wavenumber-frequency power spectral density (PSD) averaged over 0°–7°N for (a) Farrar SSH, and numerically simulated (b) SSH and (c, d) velocity components at 3992-m depth from GLORYS12V1. White box is the range of frequency and wavenumber for the typical TIWs which has periods of 25–40 days and zonal wavelengths of 9°–20°.
To extend the coherence analysis shown in Figure 1c, we calculated the coherences and phases between gridded Farrar SSH and in-situ near-bottom velocity components (Uobs, Vobs), and mapped them by averaging over the frequency range of periods 25–40 days (Figures 3a–d). The coherence map between the SSH and Uobs (Vobs) exhibits high values larger than 0.6 (0.4) especially south (southwest) of the mooring observation site. These high coherences strongly suggest that both the SSH and the observed near-bottom current are related with TIW (see also Farrar, 2011; Holmes & Thomas, 2016; Farrar et al., 2021). The significant coherence also exists to the north of the mooring observation site except along the latitude around 10°N.
The positive phase relationship in the region of high coherence (> 0.6) between SSH and Uobs suggests that the SSH which reflects the TIWs in this region leads Uobs. In contrast, the negative phase relationship in the same region between SSH and Vobs suggests that Vobs leads the SSH. These results about the phase relationship strongly indicate a southwestward phase propagation at periods 25–40 days. There is an abrupt change in phase across the latitude 10°N consistently with the cross-spectral phase estimated in the previous study where satellite-measured gridded SSH data relative to 5°N are used (Farrar, 2011). The speculation by Farrar (2011) is that this abrupt change is probably caused by a coherent superposition of TIWs with barotropic Rossby waves (BTRWs).
To verify the distribution of this BTRWs from numerically simulated barotropic velocity fields, we assume that TIW and BTRW have the same frequency and zonal wavenumber, because the TIWs will induce the BTRWs (Farrar, 2011). We would expect that the filtered barotropic velocity exhibits the BTRW induced by TIW. Further argument regarding whether the filtered barotropic velocity is BTRW induced by TIW is shown in the discussion section using the dispersion relation of BTRW.
The CEOF analysis of the filtered barotropic velocity from GLORYS12V1 clearly supports the speculation by Farrar (2011) as follows. The four maps in Figures 3e–h exhibit the first-mode CEOF phase, and the amplitude of the filtered barotropic velocity fields (Ubt, Vbt) obtained the GLORYS12V1. The phase progresses southwestward almost uniformly. The amplitude maps also show high values in the west of 115°W with slightly low values along the equator and 7°N in Figure 3g (along 4°N in Figure 3h). These tolerably uniform phase and amplitude indicate that barotropic signal with the wavelengths and periods of TIW exists over the entire study domain. The SSH data include both signal of TIW located on 0°–10°N and this barotropic signal verified from the CEOF analysis. This coexistence induces a node, which explains the non-significant coherence along approximately 10°N in Figure 3a-b.
In addition, TIWs are known to strengthen during the La Niña periods when the sea surface temperature is lower and sea surface pressure is higher than those in normal years in the equatorial eastern Pacific (Wang & Fiedler, 2006). The time series of the amplitude of the principal component of the first CEOF mode for the filtered barotropic velocity exhibits an inter-annual variation similar to that of the TIWs (Figure 3i). Large amplitudes are seen around La Niña periods (blue shades in Figure 3i). The largest amplitude occurs during the most intense La Niña periods (2007 and 2010).