HOW SATELLITES HAVE IMPROVED OUR KNOWLEDGE

OF EXTRATROPICAL PLANETARY WAVES IN THE OCEAN

Paolo Cipollini, Peter G. Challenor, David Cromwell, Ian S. Robinson, Graham D. Quartly

National Oceanography Centre, Southampton, European Way, SO14 3ZH Southampton, United Kingdom

ABSTRACT

In the past 15 years, oceanic planetary waves have changed from a theoretical concept supported by a few limited observations to a phenomenon recorded in many different parameters in all ocean basins. Though some of this understanding comes from reanalysis of old data and model output, the greatest impetus has been the wide availability of high accuracy satellite datasets, especially altimetric ones. This paper points to the key leaps in understanding during these 15 years, and summarises the questions challenging observers and theoreticians today.

1. INTRODUCTION

What the oceanographic community knew about oceanic planetary waves in the 1980s is nicely summed up in textbooks such as [1] and [2]. When asked about these long-wavelength, westward-travelling internal waves, a physical oceanographer would have claimed a fairly good theoretical knowledge of both the basic principles underlying the existence of planetary waves in the ocean and the expected dispersion characteristics of the waves. He or she would also have stressed that they were known to be important for ocean circulation, causing the east-west asymmetric response to the wind [3]. But anything more than that would have been speculative, as in any case there was scarce observational evidence for the waves (however valiant the efforts had been – see [4] for a detailed review) due to the intrinsic difficulties in detecting them from in situ measurements. The accepted description was still in essence the classic theory inherited from Hough [5] and Rossby [6], although in some of the few sparse observations a hint of ‘faster than expected’ waves could be noticed. The theory of equatorial planetary waves had also been developed – however, equatorial waves are not dealt with in this review.

The above picture was due to change dramatically with the advances in satellite altimetry during the 1990s. The

present paper summarizes the advances in our observational and theoretical knowledge of oceanic planetary waves made possible by the availability of high-quality global observation of sea surface height (SSH) from the altimetric missions, and also presents some of the current paths of investigation. In section 2 we review the satellite-based observations. In section 3 we describe the ensuing theoretical advances. Finally, in section 4 we describe the status of current research on oceanic planetary waves and discuss some as yet unresolved issues.

2. SATELLITE OBSERVATIONS OF EXTRA-TROPICAL PLANETARY WAVES

2.1. Early studies with Geosat

The availability of Geosat data over 1986-1989 prompted a number of studies trying to detect baroclinic planetary waves and assess their characteristics over specific regions (see [4]). These achieved a qualitative success, by demonstrating that planetary waves could be observed in longitude/time sections of SSH data, although they were hampered quantitatively by the large orbit errors and by the aliasing of the M2 tide (due to the orbital configuration of the Geosat mission) which ended up at periods and wavelengths similar to those of annual planetary waves, confounding the interpretation of the results. A combination of modelling and Geosat altimetry also provided the first evidence for barotropic planetary waves [7].

2.2. The modern altimeter age

The launch of ERS-1 in 1991 and TOPEX/Poseidon (T/P) in 1992 gave new impetus to the study of planetary waves by providing high-quality global time series of SSH, which are nowadays continued by the Jason-1, ERS-2, Envisat and GFO missions. The accuracy of T/P, in particular, was instrumental to the observational quantum leap during the 1990s, as can be ascertained from the many papers published on the topic

(see [4] for an extensive list). Chelton and Schlax [8], using T/P data, presented the first global study of extra-tropical planetary waves, confirming the ubiquity of the waves and their faster speed with respect to the classic theory. Soon after, some studies proved the potential of ERS for the detection of planetary waves [9] and observed their signature in sea surface temperature (SST) data, first in a waveguide of enhanced propagation in the North Atlantic [10] and then globally [11].

References [9] and [10] also noted the phase-locked relationship between propagating signals in SSH and SST in the North Atlantic. In the South Indian Ocean, the SSH signal was found to lag the SST by π/2 [12].

In recent years, the availability of merged fields from T/P and ERS (and then Jason-1 and Envisat), made possible by both the remarkable improvement in ERS orbits [13][14], and careful intercalibration and optimal interpolation techniques [15][16], has further improved the quality of the observations of planetary waves, and constitutes an excellent example of synergy between different altimetric missions. Fig. 1 summarizes the satellite observations of planetary wave speeds and compares them to the speed predicted by the classic theory, showing that at mid-latitudes they can be more than twice as fast as expected.

3. THEORETICAL ADVANCES

The observations described above, and in particular the discrepancy between satellite-derived planetary wave speeds and the speeds predicted by the classic theory, prompted revisions of the theory. The most natural approach was to remove some of the assumptions of the classic theory, such as the assumption of flat bottom and the absence of mean flow. The inclusion of mean flow effects, first examined in [17], greatly reduced the discrepancy between observed and predicted speeds. It is worth noting that the mean flow affects the wave propagation mainly through the induced modification of the potential vorticity field, while Doppler effects are negligible except where the barotropic component of the flow is of a magnitude comparable with the wave speed, such as in the Antarctic Circumpolar Current. Other papers, such as [18][19][20] have dealt with the effects of bottom topography, finding that it can change the speed locally, but cannot result in the systematic speed-up seen in the observations.

Finally, the combination of mean flow and variable topography, examined in [21][22][23][24], resulted in a further, albeit small, reduction of the difference between predicted speeds and observed ones in several places.

Figure 1. Upper panel: phase speed cp of planetary waves from different satellite observations. The

TOPEX/Poseidon observations are an updated version of those presented in [4]; the T/P- ERS speed data are

from [25]. The solid line represents the zonally-averaged speed from the classic theory. Bottom panel: ratio of the observed speeds to the classic theory speed. Figure courtesy of Dudley Chelton and Michael Schlax

Fig. 2, from [26], presents a longitude/time plot of merged T/P and ERS SSH at 28°S in the Indian Ocean, showing clear evidence of westward-propagating features, and the corresponding 2-D Fourier transform (wavenumber/frequency spectrum). The nature of these propagating features has been the subject of much investigation [27]. In fig. 2, the dispersion curve from the linear theory, and a line corresponding to the first-

Figure 2- left panel: longitude/time plot of merged T/P and ERS SSH anomalies (m) at 28°S in the Indian Ocean; right panel: amplitude of the 2D-FFT of the longitude/time plot (wavenumber/frequency spectrum). The diagram has been

flipped horizontally so that westward-propagating signals are in the left quadrant. Contours start from 100 metre·degree·day (dark blue contour) and increase in steps of 100 metre·degree·day. The magenta curve is the

dispersion characteristic for the classic planetary wave theory; the red dashed line corresponds to a speed of 4.7 cm/s, which is the median speed from the extended theory in [17] over the area. Figure from [26].

mode baroclinic speed over the same area from the extended theory in [17], are superimposed on the spectrum; it is apparent that the speed associated with each of the spectral peaks, which can be readily computed as the ratio frequency/wavenumber, agree rather well with the speed predicted by the extended

theory, over the range of wavelengths corresponding to long waves (wavelengths greater than a few hundred km). It can be concluded that for long waves the speed issue seems to be resolved, essentially owing to the formidable theoretical effort sparked by the altimetric observations.

4. CURRENT RESEARCH AND UNRESOLVED ISSUES

A number of issues in planetary wave research are still not completely resolved and are subject of ongoing investigation. In this section we review some of them.

4.1. Generation mechanisms

An issue of particular importance for our understanding of ocean dynamics concerns the generation mechanisms for the observed westward propagation. In principle, any low-frequency large-scale phenomenon forcing the ocean can be responsible for the generation of planetary waves, including wind stress, buoyancy forcing, eastern boundary current variations and coastally-trapped waves propagating from the equator towards the poles, for instance as a result of El Niño. Even major topographic features can amplify planetary waves [28], as a result of coupling between the baroclinic and barotropic modes.

One intriguing feature of planetary wave spectra is that they are broad-banded and only rarely show clear peaks at the annual or semiannual period; this suggests that a combination of mechanisms at different frequencies may be implied in the generation process, and calls for further observational and modelling studies on this topic.

4.2. Short features: waves or eddies?

The focus of some research has recently been extended to include ‘non-long’ westward-propagating features, that is those spatial scales (wavelengths ≤ 500 km) at which waves are expected to become significantly dispersive. Fig. 3 presents a sample plot of energy versus speed, from a Radon transform-based analysis of planetary waves in the South Pacific [29]. The authors found that at latitudes poleward of 20° features propagate at speeds greater than predicted by the theory in [21][22]. Their analysis also shows various effects related to bottom topography. Further scrutiny indicates that a significant part of the energy is at wavelengths ≤ 500 km (‘short’ planetary waves). The most recent extension of the planetary wave theory [24] fits the observations of these short and fast waves better.

Another intriguing hypothesis is that shorter features such as those described above could be non linear eddies, as suggested by the authors of a recent global study [25], who notice that the distribution of energy in the wavenumber /frequency spectra tends to remain non-dispersive towards the upper range of wavenumbers resolved by the altimetric dataset and therefore features tend to be faster than expected at shorter wavelengths (see, for instance, the right panel of fig. 2).

.

Figure 3- Distribution of westward-propagating energy vs latitude and speed along a 20°-wide meridional (north-south) band centered at 250°E in the South Pacific ocean, as obtained by Radon transform analysis [29]. The upper

panel shows the position of the meridional band on a bathymetric map

Reference [27] noted the eddy-like nature of features at 25˚S in the Indian Ocean, comparing SSH and SST data with output from OCCAM, a high-resolution numerical model. this is in accordance with the suggestion in [30] that Rossby waves may 'break' forming eddies in association with a Rossby wave field

4.3. Meridional component of propagation

The various theories of planetary wave propagation do not explicitly forbid the presence of a non-zero meridional (north-south) phase speed, which in turn implies that the propagation is not purely westward, but previous studies (e.g. a study of North Atlantic data using the 3-D Radon transform [31]) did not find evidence for significant meridional propagation. This seems confirmed by an eddy-tracking technique [32] used globally in [25].

However a recent study [33], employing a technique based on autocorrelation of ungridded data, presents some results showing a significant meridional phase speed. This would undoubtedly have implications when wave characteristics are estimated from 2-D (longitude/time) sections; further investigations seem to be required in order to resolve this apparent discrepancy.

4.4 Tracking of single wave events

The assumption of periodicity of planetary waves, which is implicit in wave analysis by means of Fourier techniques, can be relaxed by developing techniques to detect and track the single-wave event, similar in scope to those developed for eddies (such as [32]). A wave-tracking technique has been built for the 2-D (longitude/time) case by fitting a ‘single wave’ shape model to sub-windows of data, then reconstructing the full wave events by joining single waves [34]. Fig. 4 shows a longitude/time plot of SSH at 34°N in the Atlantic and the track of the waves fitted by this technique. Its extension to 3-D could be the answer to finding the meridional component; moreover, the single-wave characteristics obtained with such techniques can be employed to propagate planetary waves in time (forecasts).

4.5 Other unresolved issues

Of the remaining issues in planetary wave studies, a few are worth mentioning in virtue of the interest that they have attracted amongst researchers.

One important dynamical problem is why there appear to be distinctive waveguides of enhanced westward propagation in the oceans, as noted by several observational studies. Ray tracing [22] does yield zonal waveguides of enhanced propagation, but sometimes at different latitudes from those observed in the data.

Figure 4 –Longitude/time plot of merged T/P and ERS data at 34°N; b) tracks of waves detected by wave

model fitting, superimposed on the filtered longitude/time plot. The width of the dark red (crests) and dark blue (troughs) track lines is proportional to the maximum amplitude of each single wave. Figure

from [34]

Another remarkable issue relates to the relative importance and observability of the different modes of propagation. A few studies have suggested that it is possible to observe distinct baroclinic modes, while [35] has shown a significant presence of ‘fast’ westward-propagating barotropic energy in some oceanic basins.

Finally, the presence of an indisputable signature of planetary waves in ocean colour fields [36][37] has come as a surprise and has sparked a number of studies on its causes and on whether planetary waves can affect the carbon cycle. This issue is reviewed in detail in another paper in the present volume [38].

5. CONCLUSIONS

Planetary waves can certainly be considered a success story for altimetry, given the quantum leap in the quality of the observational evidence made possible by the availability of high-quality SSH fields, and the substantial revision of our theoretical understanding of planetary waves sparked by those observations.

A number of issues remain, and are being investigated by a lively community of scientists. And there is still much more to come: the forthcoming synergies between altimetry and ARGO data should allow a full 3-D characterization of the modal structure of planetary waves, and the combination of altimetry with the gravity fields from the GRACE and GOCE satellite missions hopefully allow the study of the impacts of planetary waves on absolute oceanic transport in a changing climate scenario. The study of oceanic planetary waves is therefore still a very intriguing field of research that promises further enlightening repercussions on our knowledge of oceans and climate.

6. ACKNOWLEDGEMENTS

We thank Peter Killworth and Jeff Blundell for their invaluable theoretical support, and Dudley Chelton, Lee-Lueng Fu, Neil Holbrook, Angela Maharaj and Michael Schlax for providing data and ideas.

7. REFERENCES 1. Pedlosky J., Geophysical Fluid Dynamics, 2nd Ed.,

Springer-Verlag, 710 pp., 1987. 2. Gill A. E., Atmosphere-Ocean Dynamics, Academic

Press, San Diego, 1982. 3. Anderson D. L. T., and Gill A. E., Spin-up of a

stratified ocean, with application to upwelling, Deep-Sea Res., Vol. 22, 583–596, 1975.

4. Fu L.-L. and Chelton D. B., Large Scale Ocean circulation, in Satellite Altimetry and Earth sciences, eds. L.-L. Fu and A. Cazenave, Academic Press, 2001.

5. Hough S., On the application of harmonic analysis to the dynamical theory of the tides, Part I. On Laplace’s ‘oscillations of the first species’, and on the dynamics of ocean currents. Phil. Trans. Royal Soc., A, Vol. 189, 201–257, 1897.

6. Rossby C. G., et al., Relations between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Mar. Res., Vol. 2, 38–55, 1939.

7. Gaspar P., and Wunsch C. Estimates from altimeter data of barotropic Rossby waves in the northwestern Atlantic Ocean, J. Phys. Oceanogr., Vol. 19, 1821–1844, 1989.

8. Chelton D. B. and Schlax M. G., Global observa-tions of oceanic Rossby waves, Science, Vol. 272, 234–238, 1996.

9. Cipollini P., Cromwell D., Jones M. S., Quartly G. D. and Challenor P. G., The potential of ERS for the detection of Rossby waves in the Northeast Atlantic, ESA SP-414, Proc. of 3rd ERS Symposium Florence (Italy), Vol. 3, 1473–1478, 1997.

10. Cipollini, P., Cromwell D., Jones M. S., Quartly G. D. and Challenor P. G., Concurrent altimeter and infrared observations of Rossby wave propagation near 34° N in the Northeast Atlantic, Geophysical Research Letters,. 24 ,. 889-892, 1997.

11. Hill, K. L., Robinson I. S. and Cipollini P., Propagation characteristics of extratropical planetary waves observed in the ATSR global sea surface temperature record, J. Geophys. Res., Vol 105(C9), 21,927–21.945, 2000.

12. Quartly, G.D., P. Cipollini, D. Cromwell and P.G. Challenor, Rossby waves: Synergy in action, Phil. Trans. Royal Soc., A, Vol. 361, 57–63, 2003.

13. Scharroo R. and Visser P., Precise Orbit Determination and Gravity Field Improvement for the ERS Satellites, J. Geophys. Res., Vol. 103. 8113–8127, 1998.

14. Scharroo R., Schrama E., Naeije M. and Benveniste J., A recipe for upgrading ERS altimeter data, ESA SP-461, Proc. of the ERS-ENVISAT Symposium, Gothenburg, Sweden, 2000.

15. Le Traon P. Y., Nadal F., Ducet N., An improved mapping method of multisatellite altimeter data. J. Atmos. Oceanic Tech., Vol. 15, 522–533, 1998.

16. Ducet N., Le Traon P. Y., Reverdin G., Global high-resolution mapping of ocean circulation from the combination of T/P and ERS-1/2. J. Geophys. Res., Vol. 105, 19,477–19,498, 2000.

17. Killworth P. D., Chelton D. B. and de Szoeke R., The speed of observed and theoretical long extra-tropical planetary waves. J. Phys. Oceanogr., Vol. 27, 1946–1966, 1997.

18. Killworth P. D., and Blundell J. R., The effect of bottom topography on the speed of long extratropical planetary waves. J. Phys. Oceanogr., Vol. 29, 2689–2710, 1999.

19. Tailleux R., and McWilliams J. C., Acceleration, creation, and depletion of wind-driven, baroclinic Rossby waves over an ocean ridge. J. Phys. Oceanogr., Vol. 30, 2186-2213, 2000.

20. Tailleux R., and McWilliams J. C., The effect of bottom pressure decoupling on the speed of extratropical, baroclinic Rossby waves. J. Phys. Oceanogr., Vol. 31, 1461–1476, 2001.

21. Killworth P. D. and Blundell J. R., Long extra-tropical planetary wave propagation in the presence of slowly varying mean flow and bottom topography. I: the local problem. J. Phys. Oceanogr., Vol. 33, 784–801, 2003.

22. Killworth P. D. and Blundell J. R., Long extra-tropical planetary wave propagation in the presence of slowly varying mean flow and bottom topography. II: ray propagation and comparison with observations. J. Phys. Oceanogr., Vol. 33, 802–821, 2003.

23. Killworth, P. D. and Blundell J. R., The dispersion relation for planetary waves in the presence of mean flow and topography: I. Analytical theory and one-dimensional examples. J. Phys. Oceanogr., Vol. 34, 2692–2711, 2004.

24. Killworth, P. D. and Blundell J. R., The dispersion relation for planetary waves in the presence of mean flow and topography: II. Two-dimensional examples and global results. J. Phys. Oceanogr., Vol. 35, 2110–2133, 2005.

25. Chelton D. B., Schlax M. G., Samelson R. M. and de Szoeke R. A., Global observations of westward energy propagation in the ocean: Rossby waves or eddies?, submitted to Science, 2006.

26. Cipollini P., Quartly G. D., Challenor P. G, Cromwell D. and Robinson I. S., Remote Sensing of Extra-equatorial Planetary Waves, Manual of Remote Sensing, volume 6: Remote Sensing of Marine Environment, chapter 3, 61–84, American Society for Photogrammetry and Remote Sensing, Bethesda, MD (USA), 2006.

27. Quartly G. D., Buck J. J. H., Srokosz M. A. and Coward A. C., Eddies around Madagascar — The retroflection re-considered, submitted to J. Marine Systems, 2006.

28. Barnier B., A numerical study on the influence of the Mid-Atlantic Ridge on nonlinear first-mode baroclinic Rossby waves generated by seasonal winds, J. Phys. Oceanogr., Vol. 18, 417–433, 1988.

29. Maharaj A. M., Cipollini P. and Holbrook N. J., Observed variability of the South Pacific westward sea level anomaly signal in the presence of bottom topography, Geophys. Res. Lett., Vol. 32, L04611, doi:10.1029/2004GL020966, 2005.

30. LaCasce J. H., and Pedlosky J.. The instability of Rossby basin modes and the oceanic eddy field. J. Phys. Oceanogr., Vol. 34, 2027–2041, 2004

31. Challenor P. G., Cipollini P., Cromwell D., Use of the 3-D Radon Transform to examine the properties of oceanic Rossby waves, J. Atmosph. Ocean. Tech., Vol. 18, 1558–1566, 2001. See also: Corrigendum, ibidem, Vol. 19, 828, 2002.

32. Isern-Fontanet J., Garcia-Ladona E., and Font J., Identification of marine eddies from altimetric maps. J. Atmosph. Ocean. Tech., Vol. 20, 772-778, 2003.

33. Glazman R. E., and Weichman P. B., Meridional component of oceanic Rossby wave propagation. Dyn. Atm. & Oceans, Vol. 38, 173–193, 2005.

34. Cipollini P., Challenor P. G. and Colombo S., A method for tracking individual planetary waves in remotely sensed data, IEEE Trans. Geosc. Rem. Sens., Vol. 44, 159–166, 2006.

35. Fu L.-L., Latitudinal and frequency characteristics of the westward propagation of large-scale oceanic variability, J. Phys. Oceanogr., Vol. 34, 1907–1921, 2004.

36. Cipollini P., Cromwell D., Challenor P. G. and Raffaglio S., Rossby waves detected in global ocean colour data, Geophys. Res. Lett., Vol. 28, 323–326, 2001.

37. Uz B. M., Yoder, J. A. and Osychny, V. Pumping of nutrients to ocean surface waters by the action of propagating planetary waves, Nature, Vol. 409, 597–600, 2001.

38. Cipollini P., Altimetry, SST and ocean colour unveil the effects of planetary waves on phytoplankton, this volume, 2006.