Institute of Oceanography

University of Hamburg

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Institute of Oceanography
University of Hamburg
Bundesstraße 53
D-20146 Hamburg
Tel.: +49 40 42838-2605 / -5449
Fax: +49 40 42838-7488
E-Mail:  waltraut.domke-sommer(at)

Sea surface height and currents


A review of satellite altimetry with specific focus on TOPEX/POSEIDON results is given by Wunsch and Stammer (1998) . The purpose of satellite altimetry is to study the ocean general circulation, it's large-scale, low-frequency variability, it's turbulent eddy component, and associated transport properties, among among many other problems. We study the ocean circulation using altimeter data in various ways by using the TOPEX/POSEIDON (hereafter T/P) and JASON altimetric observations as well as numerical models, either separately or combined through state estimation ; procedures. The T/P and JASON data have been analyzed on a global scale to produce estimates of the average frequency, wavenumber, and frequency/wavenumber spectra as well as their regional forms. The outcome of those studies is important for the dynamical interpretation of ocean observations and for the improvement of present ocean general circulation models; in simulating observed circulation properties. Our methods are also intended for use with gravity data from the upcoming GRACE and GOCE missions and when combined with that data should come close to providing the optimum marine gravity field estimates.

A note on correcting aliased fast barotropic motions in the TOPEX/POSEIDON data can be found here.


The French-US altimetric satellite called TOPEX/POSEIDON (hereafter T/P)is the first altimetric spacecraft designed and flown for the purpose of observing and understanding the large scale ocean circulation and its variability through measurements of the sea surface topography. It was launched in August 1992 and is providing oceanographers, for the first time in history, with a continuing, global scale data set able to describe the oceanic general circulation. This data stream is expected to be of central importance for understanding and predicting the ocean impact on climate.

Figure 1: The TOPEX/POSEIDON satellite trans-passing the North Pacific in south-east directions at an altitude of 1300km.

An overview of the TOPEX/POSEIDON mission is given by Fu et al. (1994). The spacecraft is orbiting the earth at an altitude of 1330 km and with an inclination of 66°. Its repeat period is 9.91 days (nominally a "10-day repeat cycle") during which the satellite orbits the earth 127 times, producing a track separation of about 317 km at the equator (Fig. 2). Two altimeters are being flown on board the satellite: the operational U. S. National Aeronautics and Space Administration (NASA) dual frequency altimeter (ALT) and the French Centre National d'Etudes Spatiales (CNES) solid state single frequency altimeter (SALT) which is an experimental system. In addition, several auxiliary instruments (e.g. the TOPEX mircowave radiomenter) required to correct the altimeter observations are being carried.

Figure 2: TOPEX/POSEIDON ground-tracks which are completed every repeat cyle. The geographical range is +- 66° in latitude. The tracks separation is about 320 km at the equator and the along-resolution is 6.2 km.


The French-US altimetric satellite called JASON-1 (hereafter JASON)


Figure 3: The JASON-1 satellite at an altitude of 1300km.

Jason-1 is the first follow-on to the highly successful TOPEX/Poseidon mission that measured ocean surface topography to an accuracy of 4.2 cm, enabled scientists to forecast the 1997-1998 El Niño, and improved understanding of ocean circulation and its effect of global climate. The joint NASA-CNES program will launch a French spacecraft on an American Delta II from an American base. Like TOPEX/Poseidon, the payload will include both American and French instruments. Jason-1 altimeter data will be part of a suite of data provided by other JPL-managed ocean missions--the GRACE mission will use two satellites to accurately measure Earth's mass distribution, and the QuikSCAT scatterometer mission will measure ocean-surface winds. Jason-1 was launched 1 year ago, on 12/07/01 at 7:07AM from Vandenberg Air Force Base. The spacecraft is orbiting the earth at the same orbit TOPEX/POSEIDOn was flying, i.e., at an altitude of 1330 km and with an inclination of 66$^{\circ }$. Its repeat period is 9.91 days (nominally a "10-day repeat cycle") during which the satellite orbits the earth 127 times, producing a track separation of about 317 km at the equator (Fig. 2).

After the initial calibration phase during which TOPEX/POSEIDON and JASON flew along almost the same orbit covering exactly the same ground track, TOPEX/POSEIDON was maneward into a new orbit: Three propulsive maneuvers to move TOPEX/Poseidon to a new Tandem Mission orbit were successfully executed on August 15, 19, and 23. These maneuvers placed TOPEX/Poseidon in an orbital position halfway between that of Jason-1. In this new formation flying configuration, the two satellites will increase global data coverage twofold, bringing us that much closer to uncovering some of the ocean clues in smaller scale circulation features like eddies, and to solving the global climate puzzle.

Figure 4: The TOPEX/POSEIDON and JASON-1 satellite in tandem constellation.

Selected Results

To demonstrate the usefulness of the altimeter data, we will present here a few selected results. For a more complete overview, the reader is referred to the two JGR Oceans special TOPEX/POSEIDON issues published in December of the years 1994 and 1995, respectively. A recent review of satellite altimetry with specific focus on TOPEX/POSEIDON results is given by Wunsch and Stammer (1998) .

Absolute sea surface topography

Most generally, a satellite altimeter is providing observations of the sea surface height above a frame of reference. This surface has two components: the marine goid and the elevation of sea level due to movements in the interior ocean. The geoid is the gravitational equipotential of the earth defined, for practical purposes, as that surface to which a resting ocean would conform, and it is thus central to using altimetric data for determining absolute currents. An example of a geoid estimate is given in Fig. 5. Note the large geoid amplitudes of +- 100m as compared to oceanic signals which are of the order of 10cm.

Figure 5: The EGM-96 (Lemoine et al., 1997) geoid estimate.

An estimate of the global absolute dynamic sea surface topography (SSH) is being obtained by subtracting the EGM96 geoid model from the altimetric observations. A global map of the mean absolute SSH estimate from the repeat periods 1 through 200 of the T/P mission is given in Fig. 6 on a 2°x 2°geographical grid. A spatial low-pass filter (Shapiro, 1970) was applied to the field in order to emphasis the basin-scale structures and the geostrophic surface velocity field estimated from the related surface slopes is superimposed. Note that in the figure an extra goid error correction was applied which followed out of an ocean state estimation approach. There a global GCM was constrained by absolute and time-varying T/P data. The residual part not explained by the model was interpreted as geoid error and removed from the mean T/P field in the figure, subsequently. As compared to the uncorrected field, large-scale ocean structures appear with much improved spatial coherence and current fields are closer to conventional wisdom.

Figure 6: Mean absolute sea surface height estimated from 5 years of T/P data relative to the EGM-96 geoid.

Time dependent topography

In Fig. 7 we show an estimate of the sea surface topography anomaly relative to a 5-year mean at a specific 10-day intervals. The figure is dominated by an intense eddy field superimposed on a pronounced seasonal cycle in the steric sea level elevation and wind-driven currents. Careful inspection of figures like this reveals the propagation of individual features, which is predominantly westward remote from the equator with a phase speed close to the first mode Rossby wave phase speed. On the equator there is a pronounced eastward component due to Kelvin waves.


Figure 7: Sea surface height anomaly relative to a 5 year mean from the 10-day repeat period March 8-18, 1993. The geostrophic flow vectors corresponding to the elevation anomaly are superimposed. Wavelength shorter than about 500 km have been omitted to permit some visual clarity. The actual anomaly field i sfar more complex and visually dominated by the omitted scales.

The variation of large-scale sea surface height pattern and their spatial propagation is most readily visible in an animation of fields like the one shown in Fig. 7. An animation (9 MByte) of 5 years of T/P SSH anomalies from the period September 1992 through September 1997 can be viewed here. A larger, but substantially slower version (28 MByte) of the same animation is also available.

The purely seasonal cycle in the sea level changes is illustrated in Fig. 8 which shows the amplitudes and phases of the annual harmonic least-squares fitted to 5 years worth of 10-day averaged TOPPEX/POSEIDON maps. In mid- and high latitude, amplitudes are dominated by the effect of changes in the oceanic heat content on the water column. The tropics are dominated by the effect of changing wind fields.

Figure 8: Amplitude and phase of the annual cycle of elevation in TOPEX/POSEIDON data estimated from 4 years of data. The amplitude is in centimeters, the phase in degrees measured from January 1. Areas of extreme air/sea exchanges produce large variations in elevation due to anomalies in heat added or removed by the atmosphere. The structures apparent in the quieter oceanic interior are related to wavelike motions.

Figure 9 shows the RMS sea surface height variability observed locally by TOPEX/POSEIDON during the 5 year period December 21 1992 to December 1997 (repeat cycles 10 to XXX) and averaged in 2° by 2° geographical areas. Note that the use of the TOPEX/POSEIDON based ocean tide estimates led to a decrease in the "background" variability in quiescent subtropical areas and reveals current-related variability with an unprecedented spatial coherence.

Figure 9: Root mean square elevation anomaly from 4 years of TOPEX/POSEIDON SSH data. Units are in cm. The very great inhomogeneity in oceanic variability with space is apparent, with the quietest areas showing variability of less than 2 cm - close to the present noise level of the overall system.

An estimate of the eddy kinetic energy (KE) obtained from the cross-track velocity fields under the assumption of spatial isotropy is given in Fig. 10.

Figure 10: Equivalent slope variability .... from 5 years of TOPEX/POSEIDON data. The slope variability is computed from the local cross-track slope and its temporal changes and then averaged in 2° geographical areas before plotting. The figure is a kinetic energy field with f set to 2 omega to avoid the equatorial singularity in the geostrophic kinetic energy.

We have exploited the remarkable richness of the TOPEX/POSEIDON data in more detail to determine the nature of the oceanic general circulation with a specific emphasis on the global scales. Wunsch and Stammer (1995) were able to estimate the global average frequency/wavenumber characteristics of oceanic variability (Fig. 11). Stammer (1997) illustrated the close correlation between spatial length scales of ocean variability and the internal Rossby radius of deformation (Fig. 12) and was able to produce a first estimate of a "universal" spectral shape independent of geography. Stammer (1998) inferred e global map of eddy transfer coefficients (eddy diffusivity coefficients) from T/P data; resulting zonal averaged eddy temperature are shown in Fig. 13. Using a quasi-global data set Wunsch (1997) showed that to a good first approximation, altimeters depict the movement of the oceanic main thermocline, that is reflect strongly the deep interior flows.

Figure 11: Frequency-wavenumber sea surface height spectrum computed from a spherical harmonic fit as described in Wunsch and Stammer, 1995, but from four years of data. Wavenumbers are actually in terms of spherical harmonic order n, for which the wavelengths are approximately 40,000 km/n.
Figure 12: Scatter diagram of the eddy length scale L0estimated from the first zero-crossing of TOPEX/POSEIDON autocorrelation functions in 10° by 10° regions of the world ocean and plotted against the corresponding Rossby radii of the first baroclinic mode. The correlation coefficient between the fields is r=0.8.
Figure 13: Zonally integrated meridional eddy transports of heat as estimated from TOPEX/POSEIDON eddy statistics. Lines represent (bold solid) a global integral, (thin solid) the Atlantic Ocean, (dashed) the Pacific Ocean, and (dash-dotted) the Indian Ocean, respectively. Estimates are not obtained in the shaded low-latitude area.

As the extended mission data become available, and with further analysis of models and in situ data, we anticipate producing a full three dimensional frequency/wavenumber description of oceanic variability extending from about 1 month to order a decade.

Detlef Stammer