12 Oceanic Planetary Waves and Eddies
199
have scales of 100–300 km (the finer diagonal stripes in the diagram) but these
are superimposed on “bands” of larger longitudinal scale, of the order of 1,000–
2,000 km. Similar diagrams have been built for all latitudes in the world’s ocean,
and westward propagation at many scales is clearly seen almost everywhere. Such
diagrams lend themselves to be analyzed with a number of statistical and signal processing techniques, in order to derive objective estimates of the main characteristics
of the waves. The two most used analysis tools are the 2-D Fourier Transform, which
decomposes the signal into its spectral components, providing an estimation of the
zonal wavenumber and frequency for each of those components, and the Radon
Transform, a particular image projection that directly offers an objective measure of
the main propagation speed of the features. For a detailed description of these two
analysis techniques see Cipollini et al. (2006b).
With the build-up of longer altimetric time series, made possible by the various
missions that followed (ERS-2, Geosat Follow-On, Jason-1, Envisat and Jason-2,
the last three still fully operative at the time of writing in November 2009), the
amount of observational studies on planetary waves has increased considerably,
giving rise to some important questions for the theoreticians. The most evident discrepancy was the mismatch between the observed propagation speed of the waves
and the speeds predicted by the standard (or classic) linear theory of Rossby waves.
The observed speeds were up to 2 times faster than the classic theory ones in several
regions at mid-latitude, a disagreement already spotted by the early satellite-based
studies. This resulted in a formidable amount of work on extending and improving the theoretical models by removing some of the assumptions of the classic
one (Killworth et al., 1997; Killworth and Blundell, 1999, 2003a, b; Tailleux and
McWilliams, 2000, 2001).
The discrepancy between theoretical and observed speeds is now much reduced
with the latest theoretical models (Tailleux and McWilliams, 2001; Killworth and
Blundell, 2004, 2005). Figure 12.2 illustrates this concept by showing the comparison of the observed speeds with the speeds predicted by the extended theory by
Killworth and Blundell. The observed speeds, displayed in Fig. 12.2a, have been
computed over more than 16 years (October 1992–February 2009) of multi-mission
SSH anomaly data. The technique employed, which is completely automated, is
based on the Radon Transform of longitude/time plots as explained by Cipollini
et al. (2006b) using a moving longitude window of 30 ◦ and removing the mean
value of each longitude-time plot prior to the analysis, as suggested by de la Rosa
et al. (2007). Areas within 15 ◦ longitude from the coast, where land enters the longitude/time plots, have been blanked out. The theoretical speeds in Fig. 12.2b are
from Killworth and Blundell’s extended theory (Killworth and Blundell, 2003a, b,
2004, 2005), recomputed with the updated temperature and salinity climatologies
of the 2005 World Ocean Atlas (Locarnini et al., 2006; Antonov et al., 2006). A 5 ◦
latitudinal band both sides of the equator has been left out of the calculations as the
extended theory does not hold for equatorial dynamics; this band is blanked out in
Fig. 12.2b.
199
have scales of 100–300 km (the finer diagonal stripes in the diagram) but these
are superimposed on “bands” of larger longitudinal scale, of the order of 1,000–
2,000 km. Similar diagrams have been built for all latitudes in the world’s ocean,
and westward propagation at many scales is clearly seen almost everywhere. Such
diagrams lend themselves to be analyzed with a number of statistical and signal processing techniques, in order to derive objective estimates of the main characteristics
of the waves. The two most used analysis tools are the 2-D Fourier Transform, which
decomposes the signal into its spectral components, providing an estimation of the
zonal wavenumber and frequency for each of those components, and the Radon
Transform, a particular image projection that directly offers an objective measure of
the main propagation speed of the features. For a detailed description of these two
analysis techniques see Cipollini et al. (2006b).
With the build-up of longer altimetric time series, made possible by the various
missions that followed (ERS-2, Geosat Follow-On, Jason-1, Envisat and Jason-2,
the last three still fully operative at the time of writing in November 2009), the
amount of observational studies on planetary waves has increased considerably,
giving rise to some important questions for the theoreticians. The most evident discrepancy was the mismatch between the observed propagation speed of the waves
and the speeds predicted by the standard (or classic) linear theory of Rossby waves.
The observed speeds were up to 2 times faster than the classic theory ones in several
regions at mid-latitude, a disagreement already spotted by the early satellite-based
studies. This resulted in a formidable amount of work on extending and improving the theoretical models by removing some of the assumptions of the classic
one (Killworth et al., 1997; Killworth and Blundell, 1999, 2003a, b; Tailleux and
McWilliams, 2000, 2001).
The discrepancy between theoretical and observed speeds is now much reduced
with the latest theoretical models (Tailleux and McWilliams, 2001; Killworth and
Blundell, 2004, 2005). Figure 12.2 illustrates this concept by showing the comparison of the observed speeds with the speeds predicted by the extended theory by
Killworth and Blundell. The observed speeds, displayed in Fig. 12.2a, have been
computed over more than 16 years (October 1992–February 2009) of multi-mission
SSH anomaly data. The technique employed, which is completely automated, is
based on the Radon Transform of longitude/time plots as explained by Cipollini
et al. (2006b) using a moving longitude window of 30 ◦ and removing the mean
value of each longitude-time plot prior to the analysis, as suggested by de la Rosa
et al. (2007). Areas within 15 ◦ longitude from the coast, where land enters the longitude/time plots, have been blanked out. The theoretical speeds in Fig. 12.2b are
from Killworth and Blundell’s extended theory (Killworth and Blundell, 2003a, b,
2004, 2005), recomputed with the updated temperature and salinity climatologies
of the 2005 World Ocean Atlas (Locarnini et al., 2006; Antonov et al., 2006). A 5 ◦
latitudinal band both sides of the equator has been left out of the calculations as the
extended theory does not hold for equatorial dynamics; this band is blanked out in
Fig. 12.2b.