Ted Durland and Dudley Chelton provided insightful discussion on this work over a couple of years, and discussions with Durland were especially helpful in formulating the treatment surrounding Eqs. (1)–(3). Durland, Chelton, Jim Price, Bruce Warren, and two anonymous reviewers provided helpful comments on the manuscript. Discussions with Bill Smyth, Roland DeSoeke, Roger Samelson, Ken Brink, Kurt Polzin, Carl Wunsch, Joe Pedlosky, and Mike Spall also helped shape this paper. The altimeter product was produced by SSALTO/DUACS and distributed by AVISO, with support from CNES (http://www.aviso.oceanobs.com/duacs/). I appreciate the efforts of the many scientists, engineers, and others who have developed satellite altimetry over the preceding decades, to the point that I am able to use it to examine a sea level signal on the order of a centimeter. Funding for this research came from WHOI’s Tropical Research Initiative, the Charles D. Hollister Fund for Assistant Scientist Support, the John E. and Anne W. Sawyer Endowed Fund in Special Support of Scientific Staff, and Grant OCE-0845150 from the National Science Foundation.
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Results are presented here with 95% confidence intervals computed assuming there are 22 degrees of freedom in the spectral estimates. There are admittedly fewer than 22 degrees of freedom, because, for example, the time-domain tapering introduces linear dependencies in frequency. Therefore, the error estimates and significance levels given here should be regarded with some caution. If a more conservative estimate of the number of degrees of freedom is preferred, note that one would arrive at results that are quantitatively almost identical by assuming 18 degrees of freedom and examining results deemed significant at 90% confidence.
It would be understandable if the reader found Fig. 6c confusing. Note first that the phase estimate shown in Fig. 6b can be interpreted as a line of constant wave phase in latitude and longitude. (Recall that 360° of phase is one wavelength, which is 12.4° of longitude for this zonal-wavenumber–frequency band.) In other words, the phase estimate shown in Fig. 6b can be interpreted as the spatial shape of a line tracing a wave crest, a wave trough, or a zero crossing. The phase estimate shown in Fig. 6b has been rotated counterclockwise by 90° for display in Fig. 6c (i.e., latitude is the horizontal axis in Fig. 6b and it is the vertical axis in Fig. 6c). The zonal placement in Fig. 6c of one of these lines of constant phase is arbitrary, but the black lines and white lines represent opposite phases (e.g., local maxima and minima) for the zonal-wavenumber–frequency band of the coherence phase estimate (because the black lines are shifted westward from the white lines by half of a zonal wavelength).
The 10°–20°N region encompasses the westward North Equatorial Current, but the current is not expected to have a significant effect on the propagation of barotropic Rossby waves for the zonal wavenumbers and frequencies of interest here because the observed wave propagation speeds (of order 50 cm s−1) are much greater than plausible values of the mean barotropic flow speeds (a few cm s−1). A posteriori support for assuming mean-flow effects are negligible will come from the good agreement between the observed wave propagation and the dispersion relation derived under this assumption.
Topographic variations and the associated topographic β effect have been neglected. For a meridional bottom slope Hy, the topographic β effect is expected to be less important than the planetary β effect when |Hy f|/(Hβ) < 1 (e.g., LeBlond and Mysak 1978, p. 181). For the 10°–20°N region of the eastern Pacific of interest here, this ratio is mostly less than 0.1 and is unusually small compared to its value at other locations (such as near midlatitude continental slopes where other barotropic Rossby waves have been observed), because, by comparison, the bottom slope is weak, f is small, H is large, and β is large. Values in this region reach 0.5 only in isolated areas, near the Clarion Fracture Zone (near 16°N, 140°W) and isolated seamounts. Topographic effects may prove to be important in some respects, but they are left for future work.
Note that the phase convention used for the coherence phase calculations plotted in Fig. 9 (and Fig. 6b) is slightly different than the phase convention commonly used in theoretical work [including Eqs. (2) and (3) and the definition of θ given in the text]. Doing this made the cross-spectral calculations somewhat simpler to code and yields phase estimates consistent with related prior work (Lyman et al. 2005; Farrar 2008). Under the phase convention used in Fig. 9, a linear increase of phase with latitude corresponds to a negative meridional wavenumber, and the theoretical predictions (red lines) are plotted using the appropriate phase convention.
There are subtleties in estimating the number of independent spectral bands contained in the passband because of the longitude zero padding north of 15°N and the tapering performed in the space–time and wavenumber–frequency domains. All of these will tend to reduce the number of independent spectral bands contained in the passband. All of the bands in the passband are treated as independent ones here, which is the conservative choice in the context of this discussion, because including more bands will lead to a higher noise estimate.
The measurement error in the raw, 1-Hz sea surface height measurements from the TOPEX/Poseidon and Jason-1 missions is thought to be about 17 cm2 (Chelton et al. 2001; Ménard et al. 2003). The errors in the European Remote Sensing Satellite-1 (ERS-1), ERS-2, and Geosat Follow-On data are thought to be comparable after cross calibration against the Jason series altimeters (Le Traon et al. 1998, 2003). Additional errors are inevitably introduced in attempting to remove tidal and atmospheric pressure loading contributions (e.g., Ponte et al. 2007) and because of unresolved variability (e.g., eddies), but the total error should be substantially reduced by the averaging and gridding process used to make the AVISO gridded product.