A gravity field solution based on unified ERS-1 and TOPEX/Poseidon altimetry

Abstract

If the altimetry data sets of ERS-1 and TOPEX/Poseidon are used simultaneously to compute a gravity field model, the total amount of data and the global resolution are increased with respect to solutions based on a single mission only. With radial orbit precision of ERS-1 approaching that of TOPEX/Poseidon it has become realistic to employ dual satellite crossover analysis for simultaneous adjustment of both orbits, to globally correlate the two. Unlike single satellite crossovers the dual satellite crossovers show the radial orbit perturbation of the satellites thereby helping to decouple the radial perturbation from the geoid height perturbation in the altimetry data. To take full advantage of the crossovers the crossover density is substantially increased by not only solving for two parallel orbits of the satellites but also including the orbit arcs just before and after the studied arc within a single solution process. Only the central arc with the highest crossover density is then used to generate the gravity field normal equations. From a combination of successive 10-day periods a gravity field solution is computed on the basis of the altimetry data sets of ERS-1 and TOPEX/Poseidon. Other data included in the solution comprises the dual satellite crossover data, SLR data for the two satellites, and DORIS data for TOPEX/Poseidon. The JGM-3 normal matrix is included to constrain the solution.

Keywords: Gravity field, radar altimetry, Crossover analysis

Orbit solutions

A solution period was selected from 16/08/1993 (MJD 49215) to 25/09/1993 (MJD 49286) which is within the multidisciplinary phase for ERS-1. The main criteria for the selection of this period, apart from a dense ERS-1 groundtrack, were related to good data continuity for both altimeter datasets (almost continuous ERS-1 and TOPEX altimetry, no Poseidon cycles) in combination with minimal disruption by orbit maintenance manoeuvres for ERS-1. This paper relates to the first 35-day cycle covered by the chosen solution period, while work on the full 70-day period is progressing. The present solution interval is covered by seven ERS-1 arcs versus four TOPEX/Poseidon arcs. Precise orbits were computed for these arcs using a simultaneous solution method that will be briefly introduced first.

Solutions for the 11 orbit arcs are converged on the basis of SLR data for both satellites, DORIS data for TOPEX, single satellite crossovers for both satellites and dual crossovers between the two. Altimetry data is not used in the orbit determination stage, in order to avoid unnecessary correlations between the orbital parameters and a subsequent gravity field solution based upon these orbits. The three crossover datasets were generated with an upper limit of five days to the interval between crossings, in order to keep the level of sea surface variability noise sufficiently low while still obtaining adequate data density.

In the past, dual crossovers between TOPEX/Poseidon and ERS-1 have been used mainly for refinement of the 'weaker' orbit of ERS-1, without adjusting the TOPEX orbits at the same time (Carnochan et al, 1994; Le Traon et al. 1993). The radial orbit precision of ERS-1 has come much closer to that of TOPEX/Poseidon in recent times (e.g. Zandbergen et al. 1995; ERS page), which implies that it has become unrealistic to assume that the TOPEX orbit is sufficiently more precise than that of ERS-1 to subscribe the entire dual crossover residual error to radial orbit error of ERS-1 only. Instead, dual crossovers are applied here for the simultaneous adjustment of both orbits. The parameter estimation software has been set up in such a way that it can handle all crossovers within the solution period, even if the two crossings are not part of the same arc. As a result the orbital parameters of all arcs in the solution process become correlated with each other during the iterative orbit determination process : a change in one arc will directly affect each adjacent arc by means of single crossovers between the two. The same is true for crossovers between parallel or consecutive ERS-1 arcs and TOPEX arcs.

This technique for handling crossovers between different arcs was implemented for three distinct reasons. At first, it substantially increases the crossover data density - both for the single crossovers and for the dual crossovers - in comparison to solutions in which crossovers can only be used within a single arc ( Figure 1). Furthermore, the introduced correlations help to suppress orbit discontinuities between consecutive arcs, and increase the observability of drag coefficients and empirical accelerations at the start and end of arcs, which improves the overall quality of the orbit solutions (Figure 2). Finally, it allows the required application of dual satellite crossovers in two directions without a reduction in crossover density, turning the solution process into a true simultaneous solution for ERS-1 and TOPEX/Poseidon.

Table 1 gives a survey of the orbital parameters solved for. The altimetry bias parameters are determined per arc rather than using one parameter for the entire period. In this way these parameters can be used to monitor solution consistency. If a value obtained from an individual arc differs significantly from the nominal value, this is an indication of unintended correlations between orbital parameters. The present solution showed good agreement between arcs, with for example a time tag bias for ERS-1 of -1.19 ms RMS, while values from individual arcs varied between -1.06 ms and -1.27 ms.

Figure 1 : Increased crossover density with respect to single-arc solutions. The shaded areas give the crossover density per 6 hrs for single-arc solutions. The solid lines show the density if crossovers between different arcs are also included. Gaps are related to orbit maintenance manoeuvres.

Figure 2 : Reduction of discontinuities between consecutive arcs. The shaded bars give the discontinuities between orbits integrated in single-arc solutions. The white bars show the discontinuities if crossovers between successive arcs are also included to correlate consecutive orbit solutions.

Gravity field solution

The solution process was organised in such a way that the normal matrices are generated per datatype, so that in a later stage these data types may be included in various inversions with different relative weights, without the need to regenerate all normal equations. Data used in the gravity field solution includes the SLR and altimetry datasets for the two satellites, the DORIS data for TOPEX/Poseidon and the dual crossovers between the two satellites. The single satellite crossovers are left out of the gravity runs. The elimination of the geographically correlated error from crossovers implies that little gain can be expected from generating gravity field normal equations for the single satellite crossovers. The gravity field is mainly observed from the related satellite orbit perturbations, and only the altimeter data will provide additional direct observations of the marine geoid. The gravity related radial orbit perturbations for satellites at different heights and with different orbital inclinations will not be the same, which means that effects of gravity field mismodelling will still be observable from the dual crossovers. The dual crossovers will then help to decouple the radial orbit error from the geoid height error in the altimetry data, and are therefore also included in the gravity runs. A survey of all data is given in Table 2.

The six normal matrices produced by this process are added to the JGM-3 normal matrix, with weights that are determined empirically in such a way that they result in a realistic influence of the new data upon the final solution. The relative weights used in the final solution are also given in Table 2, for each data set, and the pre- and post-solution residuals are listed as an RMS value over the 35-day period. The resulting gravity field solution is illustrated in Figure 3 by means of geoid height differences in comparison to JGM-3. Figure 4 shows the same differences separated in contributions for degree up to 10 (top) and the contributions from degree 11 to 70.

Figure 3 : Height differences between a geoid based upon the described gravity field solution and one derived from the JGM-3 model.

Figure 4 : The differences from Figure 3 separated between contributions below L = 10 and above L = 10.

Results and conclusions

The main difference between the followed solution technique and the JGM-3 model is the inclusion of ERS-1 altimetry data and dual crossovers with TOPEX. The effect of the additional altimetry data is visible in Figure 3, as the predominant changes are related to the world's oceans. Some distinct features are an apparent uplift of the Indian Ocean basin, small height reductions of the Northern oceans, but at the same time very good agreement with JGM-3 in the South Pacific. The relatively large corrections around the North Pole and South Pole are unreliable because of the lack of tracking data in these areas, although they might also suggest an offset between the Centre of Figure for the JGM-3 terrestrial reference frame and the UT-CSR station coordinate set (Eanes R.J. and Watkins M.M., 1993) that was used in the present solution.

As a logical consequence of the lower inclination of TOPEX/Poseidon, the areas with heighest dual crossover density are for TOPEX also those with the heighest altimetry density, while the heighest density for ERS altimeter measurements occurs at slightly larger latitudes where no dual crossovers exist. This implies that, if both altimeter datasets as well as the dual crossovers are included in a solution, by natural cause the dual crossovers will tend to constrain the ERS orbits to the TOPEX altimetry data, rather than introduce possible ERS altimetry noise components in the TOPEX orbits. This hypothesys is supported by the current gravity solution, because the band of maximum crossover density on the Southern hemisphere (roughly between 50 and 65 degrees South) shows very little change with respect to the JGM-3 model, which contains TOPEX data but no ERS-1 altimetry (Tapley et al., 1996). This also suggests that in future solutions it could be tolerated to slightly increase the weights of the ERS data with respect to the TOPEX data, also to compensate for the differences in dataset sizes.

The post-solution RMS of residuals listed in Table 2 were determined by regenerating all orbits using the obtained parameters as initial values, and using the new tidal model and sea surface topography for the preprocessing stages of the altimetry data. As could be expected, improvements are modest but noticeable, and more significant for ERS-1 than for TOPEX/Poseidon. Most interesting are a small reduction in the TOPEX altimetry residuals and the reduction in the crossover residuals.

The separation in low degree and high degree terms in Figure 4 shows that the low degree corrections still dominate the gravity solution. If high degree terms would be more pronounced, the feasibility of the simultaneous gravity field solution technique would have been demonstrated more convincingly, although the domination of low degree corrections does not necessarily imply absorption of ERS-1 orbit error in the solution. More likely it could confirm the suspected Centre of Figure offset between the terrestrial reference frames, which will be investigated further in the future.

The simultaneous solution technique used in this gravity field model implies that two different altimetry datasets are allowed to interfere with each other, and each satellite orbit is influenced by altimetry data from the other satellite in the process. There are inherent risks to such practice, especially if the quality of one altimeter dataset is substantially better than the other and therefore risks being corrupted by the less accurate signal. The present solution provides improvements especially for ERS-1 orbit determination. It also brings some modest reductions in TOPEX/Poseidon data residuals, despite of the fact that the dual frequency altimeter of TOPEX/Poseidon can be considered superior to that of ERS-1. For future parallel altimeter platforms - likely to have altimeters that are more compatible - simultaneous altimetry analysis can offer a valuable tool for further improvement of the marine geoid.

Acknowledgements

References

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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry