Global observations of nonlinear mesoscale eddies
Introduction
High-resolution sea-surface height (SSH) fields constructed by merging measurements from two simultaneously operating altimeters (Ducet et al., 2000, Le Traon et al., 2003) have revealed that SSH variability is dominated by westward-propagating nonlinear mesoscale eddies throughout most of the World Ocean (Chelton et al., 2007). Prior to the availability of this merged dataset, interpretations of westward-propagating SSH variability were based on SSH fields constructed from TOPEX/Poseidon (T/P) data alone. The ground track spacing of the T/P orbit was too coarse to resolve the mesoscale variability that is evident in the merged altimeter dataset. The merged dataset is thus enabling observational studies of mesoscale ocean variability that were not previously possible using altimetry data. This investigation extends the global analysis of 10 years of these high-resolution SSH fields by Chelton et al. (2007) to include an additional 6 years of data, and presents a refined and more comprehensive summary of the characteristics of the observed mesoscale eddies detected using an improved eddy identification and tracking procedure.
While it is arguably a matter of semantics, the terminology adopted here refers to features that obey linear dynamics, perhaps modified by ambient conditions of mean flow or bottom topography, as Rossby waves. The term eddy is reserved for the coherent mesoscale features that are the focus of this study, which are shown in Section 6.1 to have maximum rotational fluid speeds U that exceed their translation speed c, and are therefore characterized by an advective nonlinearity ratio U/c > 1. The possible alternative terminology “nonlinear wave” for these features is purposely avoided in order to emphasize the distinction from linear waves. The mesoscale features for which U/c > 1 can advect a parcel of trapped fluid as they translate.
From an historical perspective, it is important to note that westward-propagating SSH variability could not be unambiguously identified by satellite altimetry prior to the launch of T/P. The T/P orbit was carefully designed to minimize the effects of tidal aliasing, thus allowing the detection of westward propagating features without the aliased tidal errors that contaminated SSH fields constructed from measurements from the Geosat altimeter that preceded T/P (Schlax and Chelton, 1994a, Schlax and Chelton, 1994b, Schlax and Chelton, 1996, Parke et al., 1998). It was evident from the first few years of the SSH fields from T/P that westward propagation is nearly ubiquitous in the World Ocean (Chelton and Schlax, 1996), confirming the conclusions from previous analyses of upper-ocean thermal observations in the North Pacific during the 1970s and 1980s (see Fig. 9 of Fu and Chelton, 2001). Subsequent global analyses from a 10-year T/P data record (Fig. 14 of Fu and Chelton, 2001) and from the 16-year merged dataset analyzed in this study (see Section 7.2 and Fig. 22 below) have validated the strong tendency for westward propagation of SSH variability and fine-tuned the estimates of the propagation speeds.
The qualitative similarity between the latitudinal variation of the observed westward propagation speeds and the phase speeds expected for long baroclinic Rossby waves has led to widespread interpretation of the westward propagation as linear Rossby waves. Close scrutiny reveals that the propagation speeds outside of the tropics are somewhat faster than predicted by the classical theory for Rossby waves (Chelton and Schlax, 1996, Fu and Chelton, 2001, and references therein; Osychny and Cornillon, 2004, and numerous subsequent studies; see also Section 7.2 and Fig. 22 below). This has inspired numerous theoretical studies to understand the dynamics responsible for the speedup. While the relevance of these theories to the nonlinear mesoscale features that are shown here and by Chelton et al. (2007) to dominate the SSH variability is unclear, these theoretical studies have led to important improvements in the understanding of the dynamical effects of ambient conditions on Rossby waves. In particular, it has been shown that much of the discrepancy between the observed westward propagation speeds and those predicted by the classical theory may be accounted for by the vertical shear of background mean currents (e.g., Killworth et al., 1997, Dewar, 1998, de Szoeke and Chelton, 1999, Liu, 1999, Yang, 2000, Colin de Verdière and Tailleux, 2005), small-scale bottom roughness (Tailleux and McWilliams, 2001) or the combined effects of vertical shear and variable large-scale bottom topography (Killworth and Blundell, 2004, Killworth and Blundell, 2005, Killworth and Blundell, 2007).
To date, little attention has been paid to other inconsistencies between the observations and classical Rossby wave theory. In particular,
- (1)
It was apparent even from the T/P data that the observed westward-propagating SSH over most of the ocean (especially poleward of about 20° of latitude) was dominated by “blobby” structures rather than the latitudinally β-refracted continuous crests and troughs that are expected for long Rossby waves and are sometimes evident in the altimeter data.
- (2)
The observed variability comprises a broad continuum of time and space scales, with little or no evidence in most regions of a spectral peak at the annual period that might have been expected for long Rossby waves forced by the strong annual cycles of wind and thermal forcing and has been sought in numerous past studies.
- (3)
There is little evidence in the time-longitude structure of SSH variability for the dispersion expected for linear Rossby waves; the blobby features propagate westward for long distances as coherent structures.
- (4)
There is little evidence for the meridional propagation expected for Rossby waves with the finite meridional scales of the blobby structures apparent in the SSH fields.
These characteristics are all consistent with the conclusion of Chelton et al. (2007) that the westward propagating variability consists mostly of nonlinear eddies rather than linear Rossby waves. The focus on Rossby wave interpretations in earlier studies was a consequence of the coarse resolution of SSH fields constructed from T/P data alone (see the top panel of Fig. 1 and Appendix A.1). The distinction between linear Rossby waves and nonlinear eddies is important since the latter can transport water parcels and their associated physical, chemical and biological properties, while linear Rossby waves cannot. Eddies can thus have important influences on heat and momentum fluxes and on marine ecosystem dynamics.
The SSH fields analyzed here span the 16-year period 14 October 1992 through 31 December 2008 and were constructed by SSALTO/DUACS at 7-day intervals on a Mercator grid with a nominal spacing of 1/3° using measurements from two simultaneously operating altimeters, one in a 10-day exact repeat orbit (T/P, followed by Jason-1 and presently by Jason-2) and the other in a 35-day exact repeat orbit (ERS-1 followed by ERS-2 and presently by Envisat). The SSALTO/DUACS processing (see Appendix A.2) includes removal of the 7-year mean SSH (1993–1999) to eliminate the unknown geoid. These SSH fields are distributed and referred to by AVISO as the “Reference Series.” (See the Acknowledgments for definitions of the above acronyms associated with the dataset analyzed here.) The analysis presented here is based on the version of this Reference Series that was available in early 2010 and included SSH fields for the 14 October 1992–31 December 2008 time period (see the footnote in Appendix A.2). Except in the left panels of Fig. A3 in Appendix A.3 for reasons explained in the caption, the analysis presented here is based on the anomaly SSH fields that were interpolated by SSALTO/DUACS from their 1/3° Mercator grid onto a globally uniform 1/4° latitude by 1/4° longitude grid.
It is shown in Appendix A.3 that the objective analysis procedure used to construct the SSH fields of the AVISO Reference Series has half-power filter cutoff wavelengths of about 2° in latitude by 2° in longitude. For eddies with Gaussian shape, this corresponds approximately to an e-folding radius of about 0.4°, or roughly 40 km (see Appendix A.3). Even a cursory comparison of the SSH fields of the AVISO Reference Series with the low-resolution SSH fields from T/P data alone reveals a fundamentally different perspective on the nature of SSH variability (Fig. 1). The T/P data resolve only very large scales while the SSH fields of the AVISO Reference Series are rich in mesoscale cyclonic and anticyclonic features (negative and positive SSH, respectively) with O(100 km) radius scales that are too small to be detected by the T/P sampling pattern, except when these features are near the crossovers of ascending and descending ground tracks. The eddy detection algorithm developed and applied to the AVISO dataset for this study (Appendix B.2) identifies 3291 mesoscale eddies in Fig. 1 alone, 2398 of which were trackable for 4 weeks or longer. This is typical of the number of eddies that are detectable and trackable at any given time in this dataset.
We note that AVISO also provides SSH fields with higher accuracy and potentially higher resolution than the Reference Series analyzed here. These fields, referred to by AVISO as the “Updated Series,” were constructed from measurements by all of the altimeters available at any given time. The most well-sampled time period is the 3-year period October 2002 through September 2005 during which four altimeters were operating simultaneously (Jason-1, T/P in an orbit interleaved with the Jason-1 ground tracks, Envisat and Geosat Follow-On). While three altimeters were operating simultaneously at various other times during the 16-year data record analyzed here, only two altimeters were operating most of the time, in which case the SSH fields of the Updated Series are identical to those of the Reference Series. The superiority of the SSH fields of the Updated Series when more than two altimeters were in operation has been demonstrated by Pascual et al. (2006). For the purpose of this investigation, however, the homogeneous resolution of the SSH fields of the AVISO Reference Series over the 16-year data record is preferable to the temporally varying resolution of the Updated Series. The potentially larger amplitudes and smaller scales (because of improved resolution) of eddies in the Updated Series during periods when more than two altimeters were operating could complicate the statistical analysis of mesoscale eddies presented here. A comparison of the results of this study with the eddy characteristics deduced from the Updated Series during periods of higher resolution SSH fields is deferred to a future investigation.
While it is visually apparent from the middle panel of Fig. 1 that much of the SSH variability is composed of energetic mesoscale features, there is also evidence at latitudes lower than about 20° in the Pacific for the long crests and troughs that are expected for Rossby waves, distorted into westward-pointing chevron patterns by β refraction. Although they are relatively small in amplitude and are “speckled” by much more energetic mesoscale features, these telltale chevron patterns are identifiable across much of the South Pacific, arguably to latitudes as high as 50°S in the eastern, and possibly the central, part of the basin. In the North Pacific, they are less evident in the middle panel of Fig. 1 because of an overall higher SSH in the northern hemisphere in this map, as expected from the steric effects of summertime heating of the upper ocean during the August time period of the map. Depending on the details of the filtering, the chevron patterns can become more evident in the eastern North Pacific as far north as about 50°N when the SSH fields are spatially high-pass filtered to remove the steric effects of large-scale heating and cooling (e.g., the one-dimensional zonal high-pass filtering used for Fig. 1 of Chelton et al., 2007), but they generally do not penetrate more than about 2000 km westward from the eastern boundary in the North Pacific (Fu and Qiu, 2002). These chevron patterns are mostly eliminated with the two-dimensional high-pass filtering applied to isolate the mesoscale eddies for this investigation (bottom panel of Fig. 1; see Section 2 for a description of this filtering).
The abundance of mesoscale features in the SSH fields of the AVISO Reference Series confirms globally the view of the ocean posited from regional field programs during the 1970s, referred to by Wunsch (1981) as the “decade of the mesoscale”. Observations in the western North Atlantic from the Mid-Ocean Dynamics Experiment (MODE Group, 1978) and POLYMODE (McWilliams et al., 1983) were interpreted as evidence that mid-ocean variability is dominated by mesoscale eddies (see also Robinson, 1983). Satellite altimetry has thus advanced to the point where observational studies of mesoscale dynamics that have been feasible only from regional in situ datasets can now be addressed globally from multiple satellite altimeters operating simultaneously, with the caveat that only the surface characteristics can be observed by altimetry.
This paper is organized as follows. The resolution of the SSH fields of the AVISO Reference Series and the automated eddy identification procedure developed for this study are summarized in Section 2; the details of the assessment of the resolution are given in Appendix A and the details of the eddy identification and tracking procedure and an assessment of the biases of the eddy amplitude estimates are presented in Appendix B SSH-based eddy identification and tracking procedure, Appendix C Assessment of the bias of the estimated eddy amplitudes, respectively. Census statistics for the ∼36,000 eddies with lifetimes of 16 weeks and longer identified and tracked in the 16-year data record by this automated procedure are presented in Section 3: their lifetimes, propagation distances, trajectories, geographical distributions, and polarities (cyclonic versus anticyclonic). The kinematic properties (amplitudes, scales, rotational speeds and estimated Rossby numbers) of these robust mesoscale eddies are summarized in Section 4 and the composite average eddy shape is investigated in Section 5. The nonlinearity of the mesoscale eddies is assessed in Section 6 from three different metrics, and their propagation characteristics (direction and speed) are summarized in Section 7. This wealth of information about mesoscale eddies deduced from the 16-year dataset is summarized in Section 8.
Section snippets
Feature resolution and automated eddy detection
It is shown in Appendix A.3 that features with wavelength scales shorter than 3° are attenuated in the SSH fields of the AVISO Reference Series analyzed in this study. The variance attenuation is about a factor of 2 at a wavelength of about 2°, which we interpret as the approximate half-power filter cutoff of the objective analysis procedure used to construct the AVISO fields. This filter cutoff wavelength can be expressed in terms of the approximate scales of the mesoscale features that can be
Eddy lifetimes and propagation distances
Global histograms and upper-tail cumulative histograms (i.e., the number of eddies with lifetimes greater than or equal to each particular value along the abscissa) of the eddy lifetimes are shown separately for cyclones and anticyclones in Fig. 2. In total, the automated procedure summarized in B.2 A new SSH-based automated eddy identification procedure, B.3 Definitions of eddy amplitude and scale, B.4 Automated eddy tracking detected ∼177,000 eddies with lifetimes of 4 weeks or longer over the
Kinematic properties of the observed eddies
The automated eddy identification and tracking procedure described in B.2 A new SSH-based automated eddy identification procedure, B.3 Definitions of eddy amplitude and scale, B.4 Automated eddy tracking provides estimates of eddy amplitude, scale and rotational speed as defined in Appendix B.3 at each 7-day time step along an eddy trajectory. These kinematic properties and estimates of the Rossby numbers of the tracked eddies over the 16-year data record analyzed here are summarized in this
Eddy shapes
The shapes of the mesoscale eddies were investigated from the combined cyclones and anticyclones by normalizing the SSH within each eddy by its (positive) amplitude A, and then normalizing its spatial coordinates by the speed-based scale Ls of the eddy. Specifically, if the SSH within an eddy at time step ti is h(x, y, ti), we formed the doubly normalized SSH defined byEach observation of an eddy is thus transformed to have unit amplitude and scale, allowing them
Nonlinearity
The nonlinearity of the eddies identified in the SSH fields of the AVISO Reference Series is assessed in this section from the statistics of three different nondimensional parameters.
Eddy propagation directions
A striking feature of the trajectories in Fig. 4a and b, Fig. 4c and d, Fig. 4e and f is the visual tendency for nearly due-west propagation. This can be quantified from the average azimuth of each eddy trajectory, defined here as the angle with respect to due west formed by the great circle connecting the starting and ending points of the trajectory. The eddy centroid locations are somewhat noisy, either because of noise in the SSH fields of the AVISO Reference Series or because of distortions
Summary and conclusions
The SSH fields constructed by merging the measurements from two simultaneously operating altimeters (one in a 10-day repeat orbit and the other in a 35-day repeat orbit) reveal mesoscale features with spatial scales much smaller than could be resolved from SSH fields constructed from TOPEX/Poseidon (T/P) data alone. The existence of these mesoscale features raises questions about the conclusions of numerous past studies that the strong tendency for westward propagation of SSH variability is
Acknowledgments
We thank Lee-Leung Fu, Jim McWilliams and an anonymous third reviewer for their thorough and constructive formal reviews of this paper. We are grateful to Gerald Dibarboure for clarifying the details of the AVISO objective analysis procedure that are summarized in Appendix A.2. We also thank Tom Farrar, Brian Arbic, Curt Collins and Thierry Penduff for their detailed and helpful comments on the manuscript. This research was funded as part of the NASA Ocean Surface Topography Mission through
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