GEOSAT and ERS-1 radar altimetry over the North Atlantic

0273—1 177~3$6.00 + 0.00 Copyright ~ 1993 COSPA1~

Mv. Space Res. Vol. 13, No. 11, pp. (1 1)305—(11)314, 1993

Printed in Great Britain. All rights reserved.

GEOSAT AND ERS-1 RADAR ALTIMETRY OVER THE NORTh ATLANTIC K. F. Wakker, M. C. Naeije, E. Wisse, R. Scharroo, P. N. A .M. Visser and B. A. C. Ambrosius Deift University of Technolo,gy, Department ofAerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands

ABSTRACF ERS—1 (35-day repeat) and GEOSAT (17-day repeat) altimetric measurements over the North Atlantic have beenprocessed to study the mean sea surface andthe sea surface currents. Thispaper presents some detailson the processing techniques applied and on the results obtained. The large-scale semi-permanent circulation is determined from a least squaresparameter adjustment method in which a number ofgravity field coefficients and a low order and —degree dynamic ocean topography model are solved for simultaneously. After radial orbit error reduction by crossover difference residuals minimization, the mesoscale eddy circulation is obtained from analyzing the temporal variation of the local sea surface. In addition, mean wavenumber spectra have been computed for two areas in the North Atlantic, and some Gulfstream eddy characteristics, such as translation and rotationvelocity, have been determined. INTRODUCTION It is recognized that both the semi-permanent circulation and themesoscale eddy circulation play dominant roles in the distribution of sea water properties. Especially mesoscale eddies have the ability to transport heat and to influence mixing on a rapid base. Interesting in this respect is the Gulfstream current system in the North Atlantic. Here eddies are originated from water trapped in current meanders. Though the Gulfstream is one of the most studied current systems in the world still many questions about its dynamics remain. Altimetryalready proved to be a proper tool in studyingthe time-variable mesoscale andthe semi-permanent large scale ocean circulation /1,2,3,4,5,6/. It is also well suited to study the marine geoid, which reflects the ocean bottom topography on small to medium scales 17/. The Section of Orbital Mechanics of Delft University (DUT/SOM) has been developing altimeter processing techniques forquite some time. At first to determineradial orbit errors, but later on to study the mean sea surface and sea surface currents. Variants of the crossover adjustment technique and the collinear tracks technique have been combined optimally for determining eddy trajectories and —characteristics. To determine the long-wavelengthocean circulation DIJT/SOM adopted the integratedapproach inwhich a model for the dynamic ocean topography is estimated simultaneously with a gravity field model adjustment. In this paper these techniques will be addressed briefly, followed by some results from processing ERS—l and GEOSAT data over the North Atlantic and in particular over the Gulfstream. ALTIMETER DATA The general satellite altimeter data reduction scheme is well documented /8/. After subtracting altimeter measurements from the satellite orbital height and applying corrections for tidal and atmosphericrefraction effects, the local height of the sea surface is obtained. The difference between this height and the marine (1 1)305

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geoid is the dynamic ocean topography, which is a measure of ocean circulation. The dynamic ocean topography can be separated in a semi-permanent and a time-variable part. The latter, also referred to as relative dynamic ocean topography, reflects the meandering of large-scale currents and the motion of mesoscale eddies. However, sea height measurements are corrupted with errors due to errors in the satellite orbital height, which in turn are due to uncertainties in the available earth gravity models. This is dealt with in the processing techniques to be discussed in the DATA PROCESSING section. ERS-l On 17 July 1991, the first European Remote Sensing Satellite (ERS—l) that carries a radar altimeter instrument was launched into a 790-km altitude and 98.5°inclinationorbit. Since 2 April 1992, the satellite ground tracks are repeated every 35 days. The associated spatial resolution of the altimeter data is about 80 km at the equator and 50 km at mid latitude in cross-track direction and 6.5 km along-track. In this study mainly data from this 35-day repeat orbit is used. The earlier 3-day repeat orbit proved to be not suited for mean sea surface determination and variability mapping because of the very low spatial resolution of the data in cross-track direction. Three months of data (April to June 1992) were selected over the North Atlantic Area (lOO°Wto 20°E,12°Nto 70°N)from the NOAA Interim Geophysical Data Records (IGDRs) /9/and used for further processing. The IGDRs are based on the ESA Fast Delivery Radar Altimeter Data (URA) and the GEM-T2 operational orbits computed by DUT/SOM /10/. However, the orbits on the IGDRs were replaced bythe PGS-4591 operational orbits also computed at Delft. The latter orbits have an accuracy of about 35 to 40 cm. GEOSAT The U.S. Navy GEOdetic SATellite (GEOSAT), which was launched on 12 March 1985, into an 800 km altitude and l08°inclinationnon-repeat orbit, was maneuvered into a 17.05-day repeat orbit on 8 November 1986. More than three years (November1986 to December1989) ofsea height measurements from this Exact Repeat Mission (ERM) were selected over the North Atlantic from the NOAA GEM-T2 GDRs distributed by NOAA’s National Oceanographic Data Center (NODC). This data became available on CD-ROM only recently and contain the best atmospheric corrections and tide corrections available (TOVS-SMMII water vapor, ECMWF dry troposphere, updated Schwiderski ocean tide model, GEM-T2 satellite orbital heights). The ERM ground track has been designed to repeat exactly after 244 orbital revs (17 days) which resulted in a spatial cross-track resolution of 160 km at the equator and 115 km at mid latitude. The along-track spacing of the data is 1 second corresponding with about 7 km. DATA PROCESSING Mean Sea Surface and Mesoscale Ocean Currents In the DUT/SOM implementationof the crossover difference residuals minimization the orbit error along tracks of up to 10,000 km length is modeled by a 2nd-order Fourier series with a base frequency of 1 cycle per rev (cpr). This empirical orbit error is based on the fact that most of the radial orbit error power is clustered around 1 cpr in the frequency domain /11/. The 5 parameters of this function are considered to be constant along a track. Crossover difference residuals, primarily a measure of the orbital height error, are used as observations in the minimization process. Since there are more observations than parameters to be solved for, the parameters of each track are adjusted such that the overall RMS ofthe crossover difference residuals is minimized. The singularities that occur due to the degrees of freedom in the set of normal equations are dealt with by adopting a weighted least-squares method with a-priori information (Bayesian). The crossover difference residuals minimization has been applied to 3 years of GEOSAT data and 3 months of ERS—1 data. The data processing started with selecting and screening the data. In the case ofERS—1 the

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orbit onthe IGDRs was replaced by the POS-4591 orbit. Sea height residuals were computed by subtracting the geoid heights according to the OSU91A model /12/ and the fully corrected altimeter measurements from the orbit heights. Next, crossover residual differences were calculated. A-priori values for the parameters and their standard deviations to be used in the minimizationprocedure were computed by fitting 2nd-order Fourier functions through the residuals along each track. For short tracks (<3,000 km) a 1st-order Fourier function (1 cpr) was used. In areas of known high variability the fitting was relaxed. Subsequently, the crossover residual differences were minimized in an RMS sense byre-estimating the3 or 5 parameters forall tracks simultaneously. Crossover differences in energetic regions were less constrained. From all sea height residuals the fitted Fourier functions representing the main part of the radial orbit error were subtracted. The next step in the process deals with the transformation of all corrected sea height residuals into a set of heights at reference points. All residuals within a 4 km radius from selected locations along a reference track were interpolated (distance weighting) to these locations. The mean residual sea height was calculated at the reference points and interpolated toequidistant grid points by means of optimal estimation (objective mapping) based on the degree variances ofthe OSU9IA geoidmodel. The grid spacing was fixed at (l/5)°in longitude and (l/7)°inlatitude. On all grid points the OSU9IA geoid height (above degree and order 12) was added to obtain a model of the small to medium scale mean sea surface. Having calculated the mean sea height at a reference point the differences from this mean value could be computed by subtracting the mean from each observation in that reference point. A sea surface variability grid was computed by gridding the root mean square of these differences in each reference point to grid points (multi-step distance weighting). Additionally, grids were created, representing the relative dynamic ocean topography at a specified epoch, by interpolating the differences from the mean in time and space (decorrelation distances of 10 days and 0.5°).By studying the sequence of such grids the temporal evolution of mesoscale ocean currents can be established. The relative dynamic ocean topography grids were converted to relative surface flow velocity grids by imposing geostrophic balance. A weak background flow enables the determination of eddies and their trajectories /2/. It is in factthe z-component of the rotation of the velocity grid (relative vorticity) that was used for eddy tracking purposes. Long-Wavelength Dynamic Ocean Topography The integrated approach has been applied to 35 days of ERS—1 altimeter observations (23 May to 26 June 1992). Altimeter normal points were computed by fitting 3rd-order polynomials through 20 successive observations (20-second batches). Next, sea height residuals were computed by subtracting the normal point values, all the relevant corrections, and the geoid height from the operational PGS-459 I orbit heights. The geoid height was computed from the POS-4591 gravity field truncated at degree and order 36 and completed withthe OSU89B geoid model /13/from degree 37 to 360. Residuals larger than 4.5 m or lccated near the poles were discarded. The residuals were used to adjust the PGS-459l gravity model up to degree and order 36 (1365 unknowns) and to determine a dynamic ocean topography model complete to degree and order 10 (120 unknowns). Also a state vector (6 unknowns) was estimated for each orbital arc. Because the orbit computation dealt with 3.5-day arcs, the altimeter data set was divided into 10 separate 3.5 day intervals. The complete set of unknowns was determined from the observation equations by means of least-squares parameter adjustment with a-priori information. This information came from the covariances of the GEM-T2 gravity field model (the covariance matrix of the PGS-459l model was not available at the time), andconstraints for the dynamic ocean topography and state vectors. Constraints for thecoefficients for thedynamic ocean topography model were based on analyses of hydrographic data /14/. Additionally, from spectral analysis the magnitude of the coefficients of the dynamic ocean topography as a function of the degree can be estimated and used as constraints /5/. The elements of the state vector were constrained by adding a constant to the relevant diagonal term of the normal equations. The magnitude of this constant is proportional to the expected accuracy of the orbit determination.

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Fig. 1. Mean sea surface from 3 months ERS—l data (rel. to low degree OSU9IA geoid). RESULTS AND DISCUSSION Figure 1 shows for the North Atlantic the 3-months averaged ERS—l mean sea surface model illuminated from the Northwest. Areas with no data or data over land are coded white. That the small-scale mean sea surface features are directly related to ocean bottom topography, will be clear when this picture is compared with bathymetric maps. Because of the dense pattern of the ERS—l satellite ground tracks the spatial resolution is very high and many of the bathymetric features can be identified in more detail than from the 3-years averaged GEOSAT mean sea surface. The steep edge of the American Continental Plateau can be seen all alongthe American East Coast, from the Grand Banks of New Foundland to the Puerto Rico Trench. Evidently, islands (Bermuda, Canary Islands, Azores, Cape Verde Islands) on the tops of largely sub-marine mountains cause the sea surface to sloop. Also sub-marine mountains at large depths, such as the New England Sea Mount Chain can be seen in front of the American coast near New York. The depth of the mountain tops varies from 1500 to 2500 meters in the 5000 meter deep North American Basin. The most striking feature is the Mid-Atlantic Ridge running vertically through the picture from Iceland down. Clearly, the ridge is intersected by many fracture zones. The largest of them, the Gibbs Fracture Zone, splitting the Reykjanes Ridge from the rest of the Mid-Atlantic Ridge, runs all the way from the Labrador Sea to the edge of the European Continental Shelf. Apparently, the fracture zone is rather wide and has a U-shaped cross-section. Apart from the smaller Oceanographer and Atlantis Fracture Zones, the Cape Verde Fracture Zone is quite interesting, as it appears to have a very fine extension throughout the Cape Verde Basin. There is also a noticeable difference in the texture between the rough mountainous areas and the smooth 5000 to 6000 meter deep Canary, Cape Verde and North American Basins. Even the Bermuda Rise seems to be more rough than its deeper surroundings. Moreover, the Reykjanes Ridge seems to have a structurewhich is quite unlike the rest of the Mid-Atlantic Ridge.

Figure 2 shows for the North Atlantic the sea surface variability computed from 3 years of GEOSAT data. Though it also was computed from the ERS—l data it will be clear that for a proper variability study a longer record ofmeasurements than 3 months is preferred. Highvariability levels can be associated with the shifting positions of the core of the Gulfstream and Gulfstream Extension, and the formation and motion of

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Fig. 2. Sea surface variability from 3 years GEOSAT data (contours every 5 cm). Gulfstream eddies. These eddies are pinched offfrom Gulfstream meanders both to the north (anticyclonic: warm-core) and to the south (cyclonic: cold-core). High variability is also found where the cold waters of the Labrador Current interacts with the warmer Gulfstream water. Remarkable is the fact that almost no variability exists over the Grand Banks, which indicates that the motion of eddies in this area is confined to the deeper parts of the ocean. The variability associated with the Gulfstream seems to bifurcate southeast of the Grand Banks. One broad branch extends to the southeast, a narrower and more energetic branch of variability extends northward. This is in agreement with Krauss /15/. The southeastward branch consists of a recirculation component which flows back along the Gulfstream itself and an eastward component extending over the Mid-Atlantic Ridge south of the Azores feeding the Canary Current. The activity in this area is probably caused by the propagation of Rossby waves. The high levels of sea surface variability that occur in a band between Scotland and Iceland were at first thought to be due to the shifting positions of the thermal front between the Arctic and Atlantic waters. Analyzing time series of the differences from the mean sea surface, based on GEOSAT data, learned that a strong semi-annual signal is present in this area, which likely indicates a tide modeling problem. When the Rather ocean tide model is used instead of the standard Schwiderski model this band of variability vanishes for a great deal. More tide modeling errors are to be expected in shallow waters, for instance near the British and northern Canadian isles and in the North Sea. The GEOSAT relative vorticity grids mentioned earlier were studied in detail for the Northwest Atlantic. Figure 3 shows the observed trajectories of 6 large cyclonic and 2 large anticyclonic eddies forpart of the Northwest Atlantic. The eddy diameters range from 100 km to 300 km. Also plotted are the 2000-m and 3500-m isodepth contours. The beginning of each trajectory is indicated by the symbol 0 and the eddy locations are separated 10 days. Some important eddies have been annotated “G” through “L”. Apparently, the motion of these Gulfstream eddies is generally westward. At first sight this might look a bit strange, because the main stream flows eastward. However, it is in agreement with fluid dynamics /16/ and this behavior was already observed from drifting buoys and infrared images. The lifetime of the observed

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Fig. 3. Trajectories of 8 large eddies observed in the NW Atlantic from GEOSAT data. Gulfstream eddies is rather short. It was found that most of the eddies are absorbed again by the Gulfstream after a few months. Figure 4 presents some eddy characteristics, like translation and rotation velocity, and the correlation between the two, for anticyclonic eddy “G” and cyclonic eddy “H’. Typical translation and rotation velocities that have been found are 4 cm/s and 30 cm/s, resp. Unlike the behavior of typical Agulhas Eddies /2,1/, there is no clear decay in time; eddy ‘G” is even gaining vorticity. This is most likely caused by interaction with a Gulfstream meander. The bottom plots give no evidence for a clear correlation between eddy translation velocity and rotation velocity. This is not surprising, because the eddy propagation depends on the eddy behavior itself (vorticity rate, merging, instability, axisymmetrization, pulsation, nutation, Rossby wave generation, etc.), on the influence of the surrounding fluid, and on the presenceof bottom slopes. To study some spatial scale characteristics of the sea surface currents in the North Atlantic mean wavenumber spectra were derived from 3 months of ERS—l data. For two 15°xl5°areas,one representing an energetic area (Gulfstrcam area) and one representing a less energetic area (Azores area), an FF1’ analysis was performed on the differences from the mean sea height along each track. This was done for ascending and descending tracks separately. However, the difference between the two did not reveal any significant anisotropic effects, and the results were combined (=averaged). Figure 5 presents the spectra for the two areas. For both areas a white noise level of approximately 300 cm2/cycle/km (~5 cm) is found for wavelengths below some 50 km. Interesting differences, however, are to be found in the red part of the spectrum between 80 and 500 km wavelength. The difference in the spectrum slope indicates a difference in the mechanism of eddy energy generation /17/. In the Gulfstream area a possible mechanism is the instability ofthe mean currents causing turbulence, whereas in the Azores area a more probable mechanism is wind forcing. The plots compare well with earlier studies on GEOSAT data by Le Traon /17/. To conclude, Figure 6 presents a low order and —degree dynamic ocean topography model (also referred to as Sea Surface Topography or SST model) from 35 days of ERS—l data using the integrated approach mentioned above. The model shown combines the separate solutions from the 3.5-days data arcs. The RMS of the sea height residuals has been reduced from an initial level of approximately 80 cm to 28 30 -

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Fig. 4. Translation velocity, swirl velocity and their correlation for two eddies in the NW Atlantic.

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cm by the gravity field adjustment and the dynamic ocean topography solution. The SST model has been compared with models computed by DUT/SOM from GEOSAT data in a similar way. It was found that the RMS of the differences of sea heights computed with the GEOSAT SST model and the ERS—1 SST model over the oceans is only 17cm, while the power ofthe sea heights themselves is 60cm. This shows the good agreement between the modelsand the consistency ofthe integrated approach. The graphical representation of the ERS—l model in Figure 6 clearly reveals the expected circulation patterns; e.g. Agulhas Current, Kuroshio, Gulfstream, Circumpolar Current. This model also compares well to the Levitus SST model /14/ which is based on 50 years of hydrographic data. SUMMARY Two different altimeter data processing techniques are discussed. These techniques have been applied to ERS—l (35-day repeat) and GEOSAT (17-day repeat) data to study the mean sea surface and sea surface currents in the North Atlantic. The presented ERS—1 mean sea surface showed a clear correlation with the ocean bottom topography. The structure of several fracture zones could be distinguished. The computed variability from the GEOSAT data showed some energetic areas near the Gulfstream, its extensions and in the Gulf of Mexico, due to eddy motion and other variable currents. From an analysis of the time series of the differences from the GEOSAT mean sea surface, a number of cyclonic and anticyclonic eddies have been detected and tracked in time. It was found that the eddies have a tendency to move westward. For two eddies the translation and swirl velocity were presented. Typical values of resp. 4 cm/s and 30 cm/s were found. Mean wavenumber spectra computed from the differences from the ERS—1 mean sea surface indicated a 5 cm data noise level below wavelengths of 50 km. A clear difference was noticed in the red part of the spectrum (80-500 km) when results were compared for an area in the vicinity of the Gulfstreain and an area near the Azores. Finally, a long-wavelength semi-permanent dynamic ocean topography model has been presented based on 35 days of ERS—l data and the GEM-T2 gravity model covariances. The model showed a good correlation with hydrographic data representing the large scale ocean circulation patterns like major gyres and the western boundary currents. Acknowledgments. The results are based on the NOAAIDUT ERS—l Interim Geophysical Data Records (IGDR), which are based on the ESA URA data product. The work described in this paper was supported by the Space Research Organization Netherlands (SRON) and the Netherlands Remote Sensing Board (BCRS). REFERENCES 1. GEOSAT special issues,J. Geophys. Res. 95, # C3, # ClO (1990). 2. M.C. Naeije, K.E Wakker, R. Scharroo and B.A.C. Ambrosius, Observation of mesoscale ocean currents from GEOSAT altimeter data, ISPRS J. Photogram. Rem. Sens., in press (1992). 3. R.E. Cheney, J.G. Marsh and B.D. Beckley, Global mesoscale variability from collinear tracks of SEASAT altimeter data, J. Geophys. Res. 88, # Cl, 4343—4354 (1983). 4. K.F. Wakker, R.C.A. Zandbergen, M.C. Naeije and B.A.C. Ambrosius, GEOSAT altimeter data analysis for the oceans around South Africa, J. Geophys. Res. 95, # C3, 2991—3006(1990). 5. P.N.A.M. Visser, Theuse ofsatellites in gravity field determination and model adjustment, PhD thesis, Delft University of Technology (1992). 6. J.G. Marsh, C.J. Koblinsky, F Lerch, S.M. Kiosko, J.W. Robbins, R.G. Williamson and G.B. Patel, Dynamic sea surface topography, gravity, and improved orbit accuracies from the direct evaluation of SEASAT altimeter data, J. Geophys. Res. 95, # C8, 13129—12150(1990). 7. AD. Watts, K. Horai and N.M. Ribe, On the determination of the deflection of the vertical by satellite altimetry, Marine Geodesy 8, 85—127 (1984).

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8. D.B. Chelton, WOCE/NASA altimeter algorithm workshop, US WOCE Techn. Rep. No.2, US Planning Office for WOCE (1988). 9. R. Cheney, J. Lillibridge and D. McAdoo, Preliminary analysis of ERS—l fast delivery altimeter data, report from the Office of Ocean and Earth Sciences, NOAA National Ocean Service, Maryland (1991). 10. R. Scharroo, K.F. Wakker, B.A.C. Ambrosius, R. Noomen, W.J. van Gaalen and G.J. Mets, ERS—l precise orbit determination, ESA Report SP—359, proceedingsfrom First ERS—l Symposium in Cannes (1992). 11. R.C.A. Zandbergen, Satellite altimeter data processing: from theory to practice, PhD thesis, Delft University ofTechnology (1991). 12. R.H. Rapp, Y.M. Wang and N.K. Pavlis, The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models, Technical Report 410, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, Ohio (1991). 13. R.H. Rapp and N.K. Pavlis, The development ofgeopotential coefficient models to spherical harmonic degree 360,J. Geophys. Res. 95,#B13, 21885—21911(1990). 14. T. Engelis, Spherical harmonic expansion of theLevitus sea surface topography, Technical Report 385, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, Ohio (1987). 15. W. Krauss, R.H. Käse and H.H. Hinrichsen, The branching of the Gulfstream southeast of the Grand Banks, J. Geophys. Res. 95, 20267—20285 (1990). 16. B. Cushman-Roisin, E.P. Chassignet and B. Tang, Westward motion of mesoscale eddies, J. Phys. Ocean. 20,758—768 (1990). 17. P.Y. Le Traon, M.C. Rouquet and C. Boissier, Spatial scales of mesoscale variability in the North Atlantic as deduced from GEOSAT data, J. Geophys. Res. 95, # C8, 13089—13103 (1990).