Fig. 1. The latitudinal structures of sea surface height h (which can be equated with pressure), meridional velocity v, and zonal velocity u for the first (solid lines) and second (dashed lines) meridional modes of the classical theory that neglects the effects of background mean currents.

Fig. 6. Geographical variation of the mean value and the standard deviation of the 3°×2°×150-day filtered ECMWF wind stress curl from 1993–2000.

Fig. 7. Time-longitude plots of fully filtered SSH along 5.5° N (left, which is the same as the upper right panel of Fig. 3) and 3°×2° smoothed and 150–500-day band-pass filtered ECMWF wind stress curl along 5.5° N (right).

Fig. 9. The dominant Hilbert transform complex empirical orthogonal function (CEOF) of fully filtered SSH over the 6-year time period January 1994 through December 1999. This CEOF accounts for 67% of the variance summed over all grid points. The local percent variance accounted for by this mode at each grid point is shown in the top panel. The spatial amplitude and phase of the CEOF are shown in the second and third panels, respectively, and the longitudinal variations of the phase along 5.5° N and 5.5° S are shown in the bottom panel. The vertical solid and dashed white lines in the second panel indicate the longitudinal sections along which the EOFs were computed in Fig. 12, Fig. 14 and Fig. 15. The theoretical eigenfunctions are determined along the white solid lines in 6.3 and 6.4 and along the white dashed lines in Section 6.5.

Fig. 2. Geographical variation of the standard deviation of SSH after each of the three levels of filtering indicated at the tops of the panels (see text for details). Note the different color scale for the bottom panel. The white box in the bottom panel delineates the region in which equatorially trapped Rossby waves are investigated in 4 and 5.

Fig. 12. The dominant empirical orthogonal functions (EOFs) (heavy solid lines in the left panels) and the associated amplitude time series (right panels) of fully filtered SSH computed separately along the longitudes indicated in the upper left corners of the right panels. The percentage of total variance along each longitude accounted for by the EOF is also labeled. The thin lines in the left panels (often indistinguishable from the heavy lines) are cross-sections of the CEOF amplitude adjusted for phase variation along the vertical solid and dashed white lines in the second panel of Fig. 9.

Fig. 3. Time-longitude plots of SSH along 5.5° N (upper panels) and 5.5° S (lower panels). The 15°×2°×150-day smoothed SSH obtained after the first level of filtering is shown in the left panels. The results obtained after additionally applying the latitudinally varying zonal high-pass filter described in the text are shown in the middle panels. The final results after also high-pass filtering the time series at each location to attenuate signals with periods longer than 500 days are shown in the right panels (note the different color scale). The vertical white lines in the right panels delineate the longitudinal range over which equatorially trapped Rossby waves are investigated in 4 and 5.

Fig. 4. Time series of the Southern Oscillation Index, low-pass filtered with a half-power cutoff of 300 days (top panel), SSH at 5.5° N, 140° W (second panel), SSH at 5.5° S, 140° W (third panel) and the wind stress curl at 5.5° N, 140° W computed from the analyzed surface wind fields from the European Centre for Medium-range Weather Forecasts numerical weather prediction model (bottom panel). The thin lines in the middle two panels are the 15°×2°×150-day smoothed and zonally high-pass filtered SSH and the thin line in the bottom panel is the 3°×2°×150-day smoothed wind stress curl. The heavy lines in all three bottom panels are the 500-day low-pass filtered variability of each time series. Note that the y axis is inverted in the top panel.

Fig. 5. Time series of fully filtered SSH at 5.5° N, 140° W (heavy solid line) and 5.5° S, 140° W (thin solid line), and 3°×2° smoothed and 150–500-day band-pass filtered ECMWF wind stress curl at 5.5° N, 140° W (dashed line). The wind stress curl is inverted (see the axis labels on the right side of the plot).

Fig. 8. Longitudinal variation of the lagged correlations between the negative of the wind stress curl at 5.5° N at time t and SSH at 5.5° N (heavy lines) and 5.5° S (thin lines) at time t+τ. Positive lags τ thus correspond to SSH lagging the negative of the wind stress curl. The maximum correlation and the lag of maximum correlation are shown in the top and bottom panels, respectively.

Fig. 10. Longitudinal variation of the cross-equatorial correlation between fully filtered SSH along 5.5° N and 5.5° S.

Fig. 11. The amplitude and phase time series (top and middle panels, respectively) of the dominant CEOF of fully filtered SSH shown in Fig. 9. The Southern Oscillation Index is shown in the bottom panel (note the inverted y axis).

Fig. 13. Geographical variation of the standard deviations of the zonal and meridional components of geostrophic velocity computed from the fully filtered SSH fields as described in the text.

Fig. 14. As in Fig. 12, except for the dominant EOFs (left panels) and the associated amplitude time series (right panels) of zonal geostrophic velocity computed from SSH as described in the text.

Fig. 15. As in Fig. 12, except for the dominant EOFs (left panels) and the associated amplitude time series (right panels) of meridional geostrophic velocity computed from SSH as described in the text.

Fig. 16. The lag of maximum cross correlation between the amplitude time series of the EOFs (right panels of Fig. 12, Fig. 14 and Fig. 15) of SSH (top) zonal geostrophic velocity (middle) and meridional geostrophic velocity (bottom), displayed as a function of the zonal separation of the longitudes along which the EOFs were computed. The straight line constrained to pass through the origin in each panel was fit to the data by least squares. The corresponding westward phase speeds are labeled in each panel.

Fig. 17. The longitudinal variations of the phase speed of westward propagation along 5.5° N (heavy solid line) and 5.5° S (thin solid line) computed from the CEOF spatial and temporal phase variations as described in the text (upper panel). The lower panel shows the longitudinal variation of the first internal gravity wave phase speed c₁ from Chelton, de Szoeke, Schlax, El Naggar and Siwertz (1998) along the same latitudes.

Fig. 18. Vertical section of the mean zonal velocity estimated from ADCP/CTD data along 140° W (top). The contour interval is 10 cm s⁻¹. The zonal velocity profiles U(y) are shown in the middle panel for vertical averages over the upper 150 m (dashed line), 250 m (heavy solid line) and 400 m (dotted line). The planetary and relative vorticity contributions (f/H)_y and (U_y/H)_y to the meridional gradient of potential vorticity for the 250-m average U(y) are shown in the bottom panel by the dashed and solid lines, respectively.

Fig. 23. The meridional gradient of potential vorticity, Q_y, computed from U(y) and H(y) in the 1.5-layer model along the four eastern longitudes (upper panel) and the three western longitudes (lower panel) considered in this study. The heavy solid, thin solid, dashed and dotted lines in the upper panel represent the Q_y profiles along 140° W, 110° W, 125° W and 155° W, respectively. The thin solid, dashed and dotted lines in the lower panel represent the Q_y profiles along 170° W, 180° and 165° E, respectively. The heavy dashed line in both panels is the potential vorticity gradient β/H₁ in the 1.5-layer model with U(y)=0 and a constant upper-layer thickness of H₁=250 m.

Fig. 22. Vertical sections of the mean zonal velocity estimated from ADCP/CTD data along the four eastern longitudes considered in this study (top row). The contour interval is 15 cm s⁻¹. The zonal velocity profiles along each longitude obtained by averaging vertically over the upper 250 m are shown in the middle row. The number of ADCP/CTD samples at a depth of 150 m summed over the central longitude and the nearest neighboring longitudes to the east and west are shown as functions of latitude in the bottom row.

Fig. 25. The same as Fig. 22, except for the three western longitudes considered in this study.

Fig. 19. The eigenfunctions for h, v and u computed from the 1.5 layer β-plane (4), (5) and (6) linearized about the vertically averaged mean zonal velocity along 140° W. The heavy dotted lines represent the Hermite function solutions of the classical theory. The thin dashed, heavy solid and thin dotted lines are the shear-modified eigenfunctions computed from mean zonal velocity averaged over the upper 150, 250 and 400 m, respectively. The two thin solid lines are the shear-modified eigenfunctions computed from latitudinal shifts of the 250-m vertically averaged zonal velocity by 0.2° north (the eigenfunction with the larger southern amplitude) and 0.2° south.

Fig. 24. The eigenfunctions for h, v and u computed from the 1.5 layer β-plane Eqs. ((4), (5) and (6)) linearized about the mean zonal velocities averaged over the upper 250 m along the four eastern longitudes considered in this study (thin solid lines). The dotted lines are the Hermite function solutions of the classical theory. The heavy solid lines are the observed latitudinal structures of h, v and u from the EOFs shown in the left panels of Fig. 12, Fig. 14 and Fig. 15, respectively. The v EOF along 110° W is omitted because it is not representative of equatorially trapped Rossby waves (see the discussion of Fig. 15).

Fig. 20. The wavenumber dependence of the latitudinal structure of the h eigenfunction from the 1.5 layer β-plane Eqs. ((4), (5) and (6)) linearized about the mean zonal velocity averaged over the upper 250 m along 140° W (upper panel) and from the classical theory (lower panel). The vertical line in the upper panel is the wavenumber at which the latitudinal structures of the eigenfunctions are shown by the heavy solid lines in Fig. 19. This wavenumber corresponds to annual variability in the dispersion relation shown in Fig. 21.

Fig. 21. The dispersion relations for eigensolutions computed from the 1.5 layer β-plane Eqs. ((4), (5) and (6)) linearized about the mean zonal velocities averaged over the upper 250 m along 140° W (solid line) and from the classical theory (dashed line). The horizontal lines indicate the half-power points of the 150–500-day band-pass filter applied to the TOPEX/POSEIDON data as described in Section 3.1. The short vertical line in the lower right corner indicates the wavenumber that corresponds to annual variability in the shear-modified dispersion relation.

Fig. 26. The same as Fig. 24, except for the three western longitudes considered in this study.

Fig. 27. Superpositions of the observed latitudinal structures characterized by the EOFs (colored lines), and the theoretical eigenfunctions (thin solid black lines) for h, v and u along the seven longitudes considered in this study. The results for the four eastern longitudes and the three western longitudes are shown in the right and left panels, respectively. The two red lines in the left panels are the EOFs along 170° W and 180° and the green line is the EOF along the westernmost longitude of 165° E. Note the similarities of the latitudinal structures along 170° W and 180° to those of the EOFs along the four eastern longitudes.