Poseidon, Jason, Envisat and SPOT

Acta Astronautica 60 (2007) 611 – 621 www.elsevier.com/locate/actaastro

Analysis of DORIS range-rate residuals for TOPEX/Poseidon, Jason, Envisat and SPOT Eelco Doornbosa,∗ , Pascal Willisb, c a Department of Earth-Observation and Space Systems, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1,

2629 HS Delft, The Netherlands b Institut Geographique National, Direction Technique, 2, Avenue Pasteur, BP 68, 94160 Saint-Mande, France c Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Received 31 August 2005; received in revised form 22 May 2006; accepted 18 July 2006 Available online 9 October 2006

Abstract Three currently operational radar altimeter satellites are equipped with the Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking system for precise orbit determination and two more are already foreseen. Any systematic errors in their computed orbits could possibly adversely affect scientific products used in climate change studies, such as sea level and ice sheet heights. DORIS residuals, which can be interpreted as a measure of orbit determination performance, often show systematic errors. We have therefore analyzed long time series of DORIS range-rate residuals in order to investigate possible systematic errors common to all DORIS analysis strategies and software packages, either on a satellite or on a station basis. In particular, the investigation has focused on global DORIS data of six satellites (TOPEX, Jason, Envisat and SPOT-2, -4 and -5) and station-specific data for Fairbanks, Easter Island and Syowa Base. Large measurement errors when crossing the South Atlantic Anomaly are easily detected in the DORIS residuals of Jason, while Envisat residuals show the most prominent evidence of multipath interference and the effect of a flight software update. Particularly, large errors were also found in low-elevation data. © 2006 Elsevier Ltd. All rights reserved. Keywords: DORIS; Orbit determination; Geodesy; Systematic errors; Antenna phase center variation

1. Introduction Current and future applications of satellite radar altimetry missions require a measurement precision of only a few centimeters, with measurement stability spanning multiple decades and missions. In order to accurately connect satellite radar altimeter measurements of sea and ice levels to the terrestrial reference frame (TRF), a precise tracking system is essential to ∗ Corresponding author. Tel.: +31 15 2785163; fax: +31 15 2785322. E-mail address: [email protected] (E. Doornbos).

0094-5765/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2006.07.012

guarantee the scientific objectives of such missions. Although the orbit is just one aspect of satellite altimetry measurement systems, any systematic error in the orbit determination could adversely affect the accuracy of derived geophysical results, such as long-term evolution of the mean sea level [1,2] or ice thickness. Such results could then be erroneously interpreted in climate change studies. It is therefore of great importance to investigate all possible error sources in orbit determination of these satellites in order to make improvements where possible and to be able to assess a realistic error budget that could be used by oceanographers and other scientists using the altimeter data.

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Table 1 List of available DORIS satellites through the International DORIS Service (1990.0–2005.0) Satellite

Mission type

Launch dates

Altitude (km)

Inclination (degrees)

Tracking instruments

SPOT-2 TOPEX SPOT-3 SPOT-4 Jason Envisat SPOT-5 Cryosat

Remote sensing Altimetry Remote sensing Remote sensing Altimetry Altimetry and environment Remote sensing Altimetry

830 1330 830 830 1330 780 830 717

98.8 66.0 98.8 98.8 66.0 98.5 98.8 92.0

1G DORIS 1G DORIS, SLR, GPS 1G DORIS 1G DORIS 2GM DORIS, SLR, GPS 2G DORIS, SLR 2GM DORIS 3G DORIS, SLR

Jason-2

Altimetry

January 22, 1990 August 10, 1992 September 26, 1993 March 24, 1998 December 7, 2001 March 5, 2002 May 4, 2002 Launch failure in 2005 (to be replaced by Cryosat-2 around 2009) Expected in 2008

1330

66.0

4G DORIS, SLR, GPS

1G = first generation, 2G = second generation, 2GM = second generation miniaturized.

The TOPEX/Poseidon (abbreviated to TOPEX for the remainder of this paper), Jason and Envisat altimeter satellites all make use of the Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking system [3] along with other tracking equipment such as global positioning system (GPS) or satellite laser ranging (SLR). The future Cryosat and Jason-2 altimeter satellites will carry DORIS receivers as well. In addition, DORIS is or has been used on four of the SPOT remote sensing satellites as their sole precise tracking instrument. Table 1 summarizes the main characteristics of all DORIS satellites. It must be noted that two receivers are not active anymore: SPOT-3 (since the loss of the satellite in November 1996) and TOPEX (since the failure of the DORIS receiver in November 2004). With the expansion of the number of DORIS-carrying satellites, the use of DORIS has gradually expanded from its initial task of orbit determination in support of altimetry [4] to a larger number of scientific applications [5], such as satellite geodesy and geophysics [6–8]. In 2003, the International DORIS Service (IDS) [9] has been created in order to foster the cooperation between all DORIS analysis centers (ACs) and to generate scientific products on a continuous basis. DORIS data consists of range-rates derived from the Doppler shifts of radio signals transmitted by approximately 50 beacons. The system provides an almost continuous ground tracking of low Earth orbiting satellites. Fig. 1 shows the visibility of the permanent DORIS tracking network for the future Cryosat satellite [10,11], including four-letter beacon identifiers. Satellites at higher altitudes, such as TOPEX and Jason, benefit from an even more continuous ground tracking. The DORIS network is continuously maintained by the IGN/SIMB group [12], which often involves the

replacement of the beacon and/or antenna. In such cases, a new four-letter identifier is issued, of which the first two letters are identical to the previous identifier, and on which the third letter is incremented, if necessary. The last letter of the identifier, which is “A” or “B”, identifies the version of the beacon hardware. Most first generation beacons have been gradually replaced by second or third generation versions in recent years [12]. The range-rate measurements, as distributed by the IDS through the IDS data center [13], are provided over 7 or 10 s Doppler count intervals, combined with their time tag and corrections for the antenna center-of-mass offset (vector between the center of mass of the satellite and the 2 GHz center of phase of the antenna) and estimated ionospheric and tropospheric corrections. Orbit determination is performed by collecting data over a certain time-span (the orbit arc, typically spanning from 1 to 10 days) and minimizing the differences between the observed DORIS range-rate measurements and range-rates derived from a computed orbit. The final differences correspond to the DORIS residuals that will be further analyzed here. A satellite’s orbit can be computed by integrating its equations of motion using detailed force models. The residuals are then minimized by iteratively adjusting a number of force and measurement model parameters and thereby improving the computed orbit accuracy. The tracking residuals are an important quality indicator in orbit determination. After each orbit analysis, the root mean square (RMS) of the residuals of all valid measurements is calculated and checked. An RMS DORIS residual at a level of around 0.5 mm/s is generally deemed acceptable. However, after the launch of Jason and Envisat in late 2001 and early 2002, several inconsistencies in residual levels between satellites

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Fig. 1. Simulation of the Cryosat satellite visibility from the DORIS tracking network (as of January 2005). Ground stations are identified by their four-character acronym. An elevation cut-off angle of 10◦ was used.

and stations have become quite apparent. Fortunately, DORIS residuals contain a wealth of information beyond what is represented by RMS figures per arc. A closer look at the DORIS residuals might therefore be helpful in identifying any problems in the DORIS system or in the processing of its data. The purpose of this paper is to investigate and compare DORIS residuals of different satellites or different stations, and computed by different orbit analysis groups, using different software packages and analysis strategies. The paper will start with a description of the different types of error sources that could affect the DORIS residuals, the DORIS data considered in this analysis, and the analysis methods in Section 2. The actual analysis is performed in two different ways: per station pass on a global scale, and for individual beacons in an Azimuthelevation frame. These analyses will be described in more detail in Sections 3 and 4. Discussion and recommendations for further research will be presented in Section 5. 2. Description of the study 2.1. Information content of the DORIS residuals DORIS residuals contain a mixture of measurement noise and model noise. While measurement noise can be

linked to measurement accuracy as well as short-term oscillator stability, model noise depends on the selection of model parameters, force and measurement models, and an a priori hypothesis on measurement noise stochastic behavior. So basically some errors are inherent in the technique itself, while some others are related to the analysis and could later be improved by a refined reprocessing. It is well known that systematic errors are very likely to be found in satellite geodesy analysis. For example, errors in the gravity field could appear as geographically correlated errors in tracking residuals [14–17]. Recent studies have also shown that systematic errors in station coordinates [18] as well as in TRF realizations [2] could generate systematic errors in the orbit itself. All such systematic errors can also degrade the accuracy of the geodetic products based on the processing of this data. By analyzing satellite geodesy residuals and looking for specific signals or patterns in the residuals, we may have a valuable indication of the type of model or correction that is creating these artifacts. This is a first important step in improving such models because it could provide some clues about the origin of the errors. As a matter of fact, there are so many corrections and models involved in satellite geodesy that it would be close to impossible to test them all on a systematic basis. Nevertheless, by analyzing residuals from

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different groups and different software packages and by considering these residuals by satellite or by station we will show what valuable lessons we can learn concerning possible errors in the observations or in the models. Looking at residual patterns is often an easier approach to develop than a more complex but exhaustive analytical approach. In practice, both approaches complement each other. Some examples of possible mis-modeling errors that could be potentially detected in the residuals are: (a) force model errors, such as errors in the models for the gravity field, drag or solar radiation pressure; (b) errors in station coordinates or velocities; (c) phase center offsets and variations or antenna patterns [19–23]; (d) timing errors, such as measurement time tagging errors or on-board oscillator biases, drifts or accelerations [24,25]; (e) poorly modeled propagation effects (troposphere or ionosphere) and (f) errors in the processing software, such as software bugs, typing errors in configuration files or over-simplifications in the modeling of some effects. In the specific case for DORIS, it must be noted that all analysis groups estimate a constant range-rate bias per pass (corresponding to an unknown drift between the frequency realized on the ground by the transmitter oscillator and the frequency realized on-board the satellite by the receiver oscillator). Consequently, by construction, all DORIS residuals always possess a zero mean value per pass. Furthermore, all Doppler-like systematic errors that would be constant during a pass would not be visible in the residuals. Only the time evolution of the DORIS residuals within the same pass is really meaningful and can help us understand the true nature of the errors.

supply some of their residual data. Fortunately, this request was answered by many groups to whom we are grateful: CLS/LEGOS, France [6,7], CSR, USA [26], ESOC, Germany [27], IGN/JPL, France and USA [28,29], TU Delft, The Netherlands [30] and University of Newcastle, UK [31]. In preparing this paper, we only considered results from CSR, ESOC, IGN/JPL and TU Delft, who provided the longest time series of residuals, which are really needed to provide meaningful results. Software packages used and satellites processed by these centers are presented in Table 2. All groups used the same DORIS data for POD. Station coordinates were fixed to their original ITRF2000 values [32] or to newly derived ITRF2000 coordinates in the case of recently installed stations [33]. Each group used their own latest orbit determination strategy in terms of data editing, relative weighting and selection of adjustment parameters, such as once-per-revolution empirical accelerations, drag coefficients and solar radiation pressure coefficients. Most groups used a gravity field derived using recent data from the GRACE mission: GGM01C [34] and EIGEN-GRACE01S [35] or the slightly older GRIM5-S1 model [36]. Each group provided us with time series of residuals, in their own specific format consisting at least of the epoch of the measurement, the station and satellite name and the Doppler residual, which we could refer for data stacking, either to the satellite position on its ground track or to the satellite elevation and Azimuth as seen by the tracking beacon. Table 3 lists a series of important satellite events, which need to be taken into account for a careful interpretation of the DORIS data. 2.3. Method used

2.2. Data used In order to be able to identify possible software errors or differences, and effects due to the choices made at orbit analysis groups, a request was made to these precise orbit determination (POD) groups to

In this study we have used two different approaches. In a first step, called the global approach, we have made use of the fact that the altimetry satellites are in repeat orbits. This means that the satellite orbit is operationally maintained to insure that the same ground-track pattern

Table 2 List of analyzed DORIS residuals submitted by POD groups Analysis center

Country

Software

TOPEX

Jason

CSR, J.C. Ries ESOC, M. Otten IGN/JPL, P. Willis TU Delft, E. Doornbos

USA Germany France/USA The Netherlands

Utopia NAPEOS Gipsy/Oasis II Geodyn II

X

X

X X

X X

Precise orbit determination results by satellite.

Envisat

SPOTs

X X X

X

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Table 3 List of satellite events that could possibly affect the DORIS processing and results for this study Date

Satellite

Event

15 August 2002 16 September 2002 14 June 2004 28 June 2004 12 October 2004 1 November 2004

TOPEX TOPEX Envisat Jason Envisat TOPEX

Start of maneuvers to interleaving ground track End of maneuvers to interleaving ground track Switch to back-up DORIS chain, because of failure of primary chain Switch to back-up DORIS chain, because of oscillator instability over SAA on the primary chain New flight software, switch from waiting mode to self-programming mode End of DORIS operations, because of failure of back-up chain

Sources: TOPEX attitude event file and DORISmails #323, #326 and #366.

is covered again and again after a specified number of days (the repeat cycle). For instance, TOPEX and Jason make exactly 127 orbital revolutions in a cycle of almost 10 days, while Envisat makes exactly 501 revolutions in 35 days. A certain pass (period of satellite visibility from a specific station) is therefore also repeated with the exact same station–satellite geometry after this exact period. For every specific repeat pass of such altimeter satellites, we have computed a simple RMS of all the residuals considered over a large number of repeat cycles. The results were then sorted so that higher RMS values, potentially representing problematic passes, appear prominently on the global plots. We have also looked at the evolution with time of residuals, to see if some patterns can be linked to specific events or epochs or are present during only short or long periods of time. In a second step, a much more detailed picture was created for some individual station–satellite combinations. We collected all residuals in azimuth-elevation bins (from a station point of view), and then computed RMS and mean values for each bin. Since the repeat orbits imply a limited spatial resolution of the ground-track coverage, the azimuth-elevation coverage can sometimes be sparse. The track spacing and therefore the coverage is generally more dense for longer repeat periods and high latitudes. Ground tracks converge close to the maximum latitude of the satellite tracks, defined by the orbit inclination. Because of this varying coverage and for ease of plotting, the binned RMS and mean values have been interpolated and regridded before plotting, in order to obtain a more uniform picture. 3. Global views of DORIS residuals per satellite The global comparison of DORIS residuals starts with the three SPOT satellites in Fig. 2. These satellites are identical to a large degree, as are their orbits. It is clear that the global patterns in the residuals per pass in Fig. 2 are also nearly identical. The receiver on SPOT-5

is of a newer generation, which allows it to acquire data from two beacons simultaneously. In order to make better use of this feature, the minimum elevation is set to a lower value than on the previous SPOT satellites. The better coverage due to larger circles around the beacons in the plot is a direct result of this. For all three SPOTs, large errors (darker colors) seem to be confined mostly to the circular areas, corresponding to specific tracking stations, while often adjacent stations show much lower residuals. This indicates that station-specific influences such as coordinates, multipath and the generation and performance of the beacon are much more strongly represented in the SPOT residuals than global and general effects such as force model or propagation model errors. Fig. 3 provides the RMS value of the DORIS residuals for all passes of the three altimeter satellites and for three different analysis groups per satellite. For TOPEX and Jason, due to their inclination (66◦ ), no DORIS data can be obtained over the polar areas. In this figure, results from all three groups show similar patterns for TOPEX (left column). The TOPEX results are also similar to those for SPOT. Among the stations that stand out most in the TOPEX and SPOT data are: ROTA (Rothera Base, Antarctic Peninsula), HELB (St. Helena Island, South Atlantic), EVEB (Mount Everest, Nepal) and MSOB (Mount Stromlo Observatory, Australia). All these stations, except EVEB, have in recent years had beacon and antenna replacements (ROTB, HEMB and MSPB), after which residuals have decreased significantly. A comparison of TOPEX and Jason residuals is interesting, because these satellites are in nearly identical orbits. Jason carries a more advanced and miniaturized DORIS receiver. TU Delft/DEOS uses all available DORIS data, and a large area of extremely high residuals covering South America and surrounding areas is apparent in its plot in Fig. 3. These residuals are related to satellite oscillator instabilities when crossing the South Atlantic Anomaly (SAA) due to sensitivity

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Fig. 2. RMS values of SPOT DORIS residuals, computed by IGN/JPL, over multiple repeat cycles and binned by satellite pass. Data used are from June 11, 2002 to January 1, 2004.

Fig. 3. RMS values of DORIS residuals over multiple repeat cycles, binned by satellite pass. Data used are from January 15, 2002 to January 1, 2004 for TOPEX (left column) and Jason (center) and from October 4, 2002 to January 1, 2004 for Envisat (right). POD residuals were supplied by UT/CSR or ESOC (top row), IGN/JPL (center) and TU Delft/DEOS (bottom).

to radiations [24,37]. The amplitude of the DORIS residuals for Jason depends on the way the analysis groups are handling this problem. Best results are ob-

tained by UT/CSR, who have devised and implemented a data editing and down-weighting strategy as well as an empirical correction to address this issue. In their

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computation, SLR data were also used to estimate the orbit. The IGN/JPL group rejects the data for stations inside and around the SAA in a preprocessing phase, creating a large gap in the map. It is striking that outside the stations affected by the SAA, the Jason residuals are significantly lower compared to TOPEX, an indication that the new receiver is performing much better, except for the large instability due to increased sensitivity to radiations over this area. The time evolution of the Jason and TOPEX DORIS residuals is represented in Animation 1 (available online), on a cycle-by-cycle basis. Several important features are clearly visible in the animation, including the growth of the SAA-affected region for Jason (both in terms of residual amplitude and in terms of the geographical area affected), the rejection of data in the center of the SAA in the later cycles and the drop in the amplitude of the SAA effect after the switch to the backup DORIS receiver chain at the end of June 2004 (see Table 3). The animation can also be used to quickly identify short-term problems with a single station, such as GOMB (Goldstone, California), which only appears in Jason data from cycles 92 to 98 (July 5–September 12, 2004), creating larger residuals during this period of time. During this period a small degradation of the IGN/JPL weekly station coordinates was also observed for this station, indicating a possible malfunctioning of this beacon that stopped functioning between September 2003 and July 2004 as well as after September 2004. Looking at these results, it seems that the temporary reactivation of the GOMB station between July and September 2004 was perhaps performed with not completely functional equipment.

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Animation 1 also shows improvements in the DORIS residuals after replacing hardware. This is the case with the switch from KOKA to KOLB (Kauai, Hawaii) on November 12, 2002 (cycle 32), replacing a first generation ground beacon with a third generation ground beacon. As discussed by other authors [38], this upgrade also led to improved geodetic results. The DORIS residuals of the Envisat satellite over this period are much higher than for the two other altimeter satellites (TOPEX and Jason). There are several possible explanations for this. First of all, Envisat has a lower altitude (780 versus 1330 km) and due to the higher uncertainties in the gravity and atmospheric drag models, orbit computations are somewhat more difficult to handle. Secondly, Envisat is an extremely large satellite and complex mission [39,40] carrying seven major instruments besides those intended for radar altimetry. This complexity has resulted in relatively long commissioning, calibration and validation phases, during which the DORIS receiver has not been able to operate in its nominal mode. A major DORIS flight software update was required. This update was performed on October 12, 2004 and has significantly improved the DORIS residuals, as can be seen in Animation 2, which shows the evolution of the residuals over time. Fig. 4 shows a comparison of residuals before and after this update (October 12, 2004). The update has resulted in a better coverage but also, more surprisingly, in considerably lower DORIS residuals. Still, some interesting artifacts are visible in the residuals, both before and after the update. Stations such as FAIB (Fairbanks, Alaska) show higher residuals on overhead passes, i.e. those that cross the center of the visibility circle. Other beacons, such as ROTA (Rothera Base,

Fig. 4. RMS values of Envisat DORIS residuals, computed by TU Delft/DEOS, over multiple repeat cycles, binned by satellite pass. The figure shows that the situation before (left = August 2002–October 2004) and after (right = October 2004–March 30, 2005) the DORIS flight software update performed on October 12, 2004.

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Antarctica Peninsula), and EASB (Easter Island, SouthEast Pacific Ocean) show higher residuals at lowelevation passes, at the edges of the visibility circles in the plot. The residuals of several of these beacons will now be investigated more closely in the following section. 4. DORIS residuals per ground station 4.1. Results In order to investigate station-related problems, we are now analyzing the DORIS residuals as viewed by the ground station (in an Azimuth and elevation frame) instead of the global view of the previous section.

The FAIB beacon showed high residuals on overhead tracks for Envisat, as previously shown in Figs. 3 and 4. A more detailed view of the residuals of this station is now available in Fig. 5. The latitude of this station is almost equal to the inclination of TOPEX and Jason. Therefore, there is no data to the North of the station for these satellites. There are many converging ground tracks to the South however, which allow for a highly detailed view of the residuals. The plots in Fig. 4 show an intriguing circular rippling effect at around 90◦ elevation in the mean residuals, which is clearly the source of the high residuals on the high-elevation passes of Figs. 3 and 4. The corresponding RMS maps show lowresidual RMS at an axis perpendicular to the flight direction. The effect is present for all satellites, but strongest

Fig. 5. Mean and RMS residuals for the FAIB (Fairbanks, Alaska) beacon, in an Azimuth versus elevation frame (North-up, horizon = 0◦ elevation on the edge, zenith = 90◦ at the center). DORIS data were used from January 15, 2002 to January 1, 2004.

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Fig. 6. Mean and RMS residuals for the EASB (Easter Island, South-East Pacific Ocean) and SYPB (Syowa Base, Antarctica) beacons, in an Azimuth versus elevation frame (North-up, horizon = 0◦ elevation on the edge, zenith = 90◦ at center). DORIS data were used from January 15, 2002 to January 1, 2004. Only ascending tracks are considered.

for Envisat. In addition, for low elevations (at the edges of the plots) the mean and RMS have higher values. Similar mean and RMS residual plots for other beacons are available in Fig. 6. Only ascending tracks are displayed here. The selected beacons are EASB (Easter Island, South-East Pacific Ocean), which shows high residuals for low-elevation passes in Figs. 3 and 4, and SYPB (Syowa Base, Antarctica), which was chosen as an example of a beacon providing much lower residuals in Figs. 3 and 4. The EASB results for Jason clearly show the impact of the SAA problem. Low-elevation extremes are visible in the residuals of all combinations. The circular rippling effect is much less pronounced for

these stations than on FAIB, and it is barely visible in the Jason residuals for SYPB. 4.2. Discussion The high residuals at the edges of the plots (corresponding to satellites at low elevations) can indicate errors in the ionospheric and tropospheric path delay corrections at low elevations. Ionospheric path delays can be quite accurately determined from the difference between the two transmitted frequencies (we assume here that higher order corrections are sufficiently small). Tropospheric path delays however can be

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derived from meteorological data collected near the beacon, from which an estimate of the zenithal correction is derived. The zenithal correction is then subsequently transformed into the line-of-sight correction, by using an elevation-dependent mapping function [41]. In order to be independent of errors in the collection and processing of the meteorological data, most analysis groups estimate the zenithal correction from the DORIS data, as a parameter during the orbit determination [8]. The low-elevation residuals could therefore point at inaccuracy in the mapping function for low elevations. Further investigations should therefore determine whether the mapping function could be improved or if science results improve when low-elevation measurements are removed from the DORIS processing altogether. An explanation for the rippling effect is more difficult to find. Multipath interference, which is the interference caused by reflected signals near the antenna, is a likely candidate. Such a possibility was already demonstrated in analysis of long-term DORIS residuals [22]. However, the question then remains whether the interference takes place at the beacon or at the receiver on the satellite (most likely), and why the pattern is not equally strong on all beacons or all satellites. It is difficult to assess what influence timing and station coordinate errors have on these detailed views of the residuals. This could be the subject of a follow-on study, in which such errors could be knowingly introduced into the data processing, in order to see the effect on the residuals, and compare these results with the current patterns. These types of simulations, for example, using a Monte-Carlo method, are usually quite efficient to investigate the impact of perturbations on some considered parameters [2,18]. If this hypothesis would be confirmed then DORIS analysis groups could investigate the possibility to correct this effect using empirically derived models. 5. Conclusions In conclusion, we were able to analyze DORIS range-rate residuals from different analysis groups using analysis software packages for POD. Fortunately, no large software or configuration errors could be found in the comparison of residuals from different centers. Most differences could be explained by differences in the processing or the data editing strategies. The SPOT and TOPEX residuals show that station-specific issues such as beacon performance and accuracy of antenna geodetic coordinates dominate over global error sources, such as force or measurement model errors. The DORIS residuals of Jason are clearly dominated

by a mis-modeling error due to a rapid acceleration of the satellite clock when crossing the SAA due to an unexpected sensitivity to radiations. The DORIS residuals and coverage for Envisat was greatly improved after a flight software update in October 2004, although significantly higher residuals for low- and high-elevation passes remain for some stations. A detailed look at mean and RMS residuals as a function of Azimuth and elevation for several station–satellite combinations revealed two main features. The first feature, high residuals at low elevations, could be explained from errors in the elevation mapping function for tropospheric path delays. It should be investigated whether improvements of this mapping function are possible, or whether low-elevation DORIS measurements should be omitted from processing. The second feature, the presence of a circular pattern consisting of multiple rings in the mean residuals, also requires further study. Multipath interference is a likely explanation, although other explanations such as timing errors or station coordinate errors can presently not be excluded. Acknowledgments The realization of some the DORIS residual time series was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. At the TU Delft, DORIS analysis for the Envisat and Cryosat missions is supported by the European Space Agency. We would like to thank all groups who submitted DORIS residuals for this study, specifically John Ries of UT/CSR and Michiel Otten of ESA/ESOC, for the data used in Fig. 3. Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at 10.1016/j.actaastro. 2006.07.012. References [1] P. Vincent, M. Costes, A. Auriol, et al., Impact of the DORIS precise orbit determination system on climate change studies, Acta Astronautica 51 (1–9) (2002) 275–283. [2] L. Morel, P. Willis, Terrestrial reference frame effects on mean sea level determined by TOPEX/Poseidon, Advances in Space Research 36 (3) (2005) 358–368. [3] M. Dorrer, B. Laborde, P. Deschamps, DORIS (Doppler orbitography and radiopositioning integrated from space) system assessment results with DORIS on SPOT2, Acta Astronautica 25 (8–9) (1991) 497–504.

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