Systematic errors in the Z-geocenter derived using satellite tracking data: a case study from SPOT-4 DORIS data in 1998

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1 J Geod (2006) 79: DOI /s ORIGINAL ARTICLE P. Willis J.-P. Berthias Y.E. Bar-Sever Systematic errors in the Z-geocenter derived using satellite tracking data: a case study from SPOT-4 DORIS data in 1998 Received: 11 May 2005 / Accepted: 20 September 2005 / Published online: 10 December 2005 Springer-Verlag 2005 Abstract Within the scope of the Global Geodetic Observing System, Doppler Orbit Determination and Radiopositioning Integrated by Satellite as a geodetic technique can provide precise and continuous monitoring of the geocenter motion related to mass redistribution in the Earth, ocean and atmosphere system. We have reanalyzed 1998 DORIS/SPOT-4 (Satellite pour l Observation de la Terre) data that were previously generating inconsistent geocenter positions ( 65 cm offset). We show here that this error is due to an incorrect phase center correction provided with the DORIS preprocessed data resulting from a +12 cm offset in the cross-track direction that has been confirmed since. We also conclude that a 1 mm error in the cross-track offset of non-yawing sun-synchronous SPOT satellites will generate a 6.5mm error in the derived Z-geocenter. Other non-yawing satellites would also be affected by a similar effect whose amplitude could be easily estimated from the orbit inclination. Keywords DORIS Terrestrial reference frame Geocenter variations Precise orbit determination Cross-track correction SPOT-4 1 Introduction Space geodesy can now precisely monitor geocenter variations directly related to exchanges of mass within the Earth, P. Willis Institut Géographique National, Direction Technique, 2, avenue Pasteur, BP 68, Saint-Mandé, France P. Willis (B) Y.E. Bar-Sever Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Ms , Pasadena CA 91109, USA Pascal.R.Willis@jpl.nasa.gov Tel.: Fax: J.-P. Berthias Centre National d Etudes Spatiales, 18 avenue Edouard Belin, Toulouse Cedex 9, France ocean and atmosphere system (Crétaux et al. 2002; Blewitt 2003; Dong et al. 2003; Tapley et al. 2004). Geodetic satellites are naturally sensitive to the center of mass of the combined Earth, ocean and atmosphere system. However, geodesists choose to define the origin of the terrestrial reference frame (TRF) in such a way that stations fixed on the Earth s crust would not be affected by global motions (secular, annual or even seasonal). It is then critical to be able to monitor any type of time evolution of the vector defining the center of mass of the geosphere and the origin of the frame, usually called geocenter motion. Geocenter motion monitoring is a significant geodetic contribution in the scope of the new Global Geodetic Observing System (GGOS) project of the International Association of Geodesy (Beutler et al. 2004). Doppler Orbit Determination and Radiopositioning Integrated by Satellite (DORIS) can also provide geocenter positioning (Bouille et al. 2000), but with a lesser precision compared to the fundamental techniques such as satellite laser ranging (SLR) (Altamimi et al. 2002; Meisel et al. 2002). In 2003, the International DORIS Service (IDS) was created (Tavernier et al. 2005). Since then, several DORISderived geocenter solutions have been processed by different groups and are available from the Crustal Dynamics Data Information System (CDDIS) (Willis et al. 2005b; Noll and Dube 2001). The Z-component of the geocenter derived from DORIS data is usually much noisier than the one derived from SLR (Altamimi et al. 2005; Meisel et al. 2005). Large systematic errors can also be found, which are usually associated with an annual signal and are not often discussed in the literature. Typically for DORIS, annual signals of 4 7 mm can be found in the X and Y-components and 16 mm in the Z-component, while SLR only shows a 2 3 mm annual signal in all three components (Altamimi et al. 2005), which is commensurate with the estimated order of magnitude of the geophysical signal. While systematic errors in X and Y tend to average with time due to the Earth s rotation effect, errors in the Z-coordinates of the stations propagate directly into the orbit estimation, often creating larger systematic effects (Morel and Willis 2003, 2005).

2 568 P. Willis et al. In particular, a large systematic effect was detected in the early IGN/JPL (Institut Géographique National/Jet Propulsion Laboratory) weekly solutions (Willis et al. 2005a; Angermann et al. 2005), and was later identified to be related to the Satellite pour l Observation de la Terre (SPOT-4) DORIS data in 1998 (Willis et al. 2004). However, this large systematic effect (around 60 cm, compared to sub-centimeter geophysical signals) could never be explained until now. After detection of the problem in the ignwd03 solution of the IGN/JPL IDS Analysis Center, it was decided to generate a new time series (ignwd05) (Willis et al. 2004), which does not use the 1998 SPOT-4 DORIS data. Such a simple solution took care of the problem, but resulted in the total exclusion of the first year of DORIS/SPOT-4 data, potentially leading to less precise geodetic results. In this paper, we will first explain the nature of the systematic errors that can be observed in the Z-geocenter when analyzing DORIS/SPOT-4 data in We will then propose a simple interpretation based on long-term residual analysis and demonstrate that it provides a full explanation of the erroneous results obtained previously. We will then use this method to extend the conclusions to other measurement types and satellites orbits, and assess possible limitations in the Z- geocenter determination related to satellite physical parameters measured before their launch. 2 Description of the problems related with the DORIS/SPOT data We have reprocessed all the available DORIS/SPOT-4 from May 1 to December 31, 1998 (SPOT-4 was launched on March 24, 1998) in a free-network approach, simultaneously estimating the orbit and the station positions (Heflin et al. 1992) as well as additional parameters such as Earth orientation parameters (EOPs) and once per revolution (1/rev) accelerations on a daily basis. Each daily solution (station positions and EOPs with full covariance matrix) was then combined into a weekly solution, projected (Sillard and Boucher 2001) and then transformed into International Terrestrial Reference Frame 2000 (ITRF2000) (Willis et al. 2004, 2005b) using a standard seven-parameter alignment technique. Figure 1 shows the DORIS-derived weekly TZ translations compared to the ITRF2000 reference (Altamimi et al. 2002). Translations have the same sign as the station Z-offset, while a geocenter variation has the same amplitude but an opposite sign. The Z-axis is close to the Earth s rotation axis. Before 1999, the estimated DORIS-derived geocenter (Fig. 1) show a large systematic offset that we will try to understand in this study. After 1999, the solutions are totally compatible with the ITRF2000 origin, showing no significant offset and a remaining annual signal of less than 150 mm amplitude that is due to typical computation artifacts (Willis et al. 2005b) when using only one DORIS satellite. However in 1998, a very large offset of 650 mm is clearly visible in the results (Fig. 1). This explains the anomalous results found Fig. 1 Weekly geocenter variations estimated using DORIS/SPOT-4 data (mm) by Angermann et al. (2005) of +200 mm offset for a multisatellite DORIS geocenter solution: ( )/3 mm because three satellites were used in 1998 and because the global mean offset is the sum of the three individual offsets. Figure 2 shows the estimated formal errors for these weekly TZ-translations, exhibiting a rather constant value with time. We can also note that this value is also very small and close to 2 mm. The effect on the geocenter parameter is then really due to a systematic bias, as the formal errors remain the same in 1998 and Furthermore, the effect discussed previously (650 mm) is extremely large compared to the formal errors (typically 2 mm), even if the formal errors are considered too optimistic by a factor of 2. It must also be noted that the major effect is really in the Z-translation of the geocenter and not in the station coordinates themselves. In the multi-satellite geocenter solutions, the station coordinates were not degraded, only the TZ Fig. 2 Weekly geocenter formal error estimated using DORIS/SPOT-4 data (mm)

3 Systematic errors in the Z-geocenter derived using satellite tracking data: a case study from SPOT-4 DORIS data in Fig. 3 Description of the SPOT-4 satellite geocenter value was offset by +200 mm. This explains why the problem was not seen in the very first DORIS weekly submissions to IDS because the quality checks were only performed on the daily DORIS doppler residuals and on the weekly station coordinates internal consistency. As such, geocenter results were not tested at that time. The problem is global, affecting all stations in the same direction (Z axis) with the same amplitude, and is not local, such as the one found for the Jason satellite while crossing the South Atlantic Anomaly (SAA) (Willis et al. 2004). We must also add that the DORIS doppler residuals were also slightly larger in 1998 than in 1999, but typically only 10% more. 3 Analytical approach The SPOT-4 is the fourth French satellite used for remote sensing applications. Figure 3 provides a schematic description of this satellite in the satellite frame. In Fig. 3, the satellite X-axis is along the satellite main direction, pointing from the imaging instrument towards the base of the satellite. The Y-axis is transverse. The Z-axis is radial pointingaway from the Earth. On Fig. 3, the DORIS antenna can be seen located close to the base plate, and pointing opposite to the Z-direction (toward the Earth). During flight, the X-axis is kept perpendicular to the orbit (cross-track), while the Z-axis is maintained along the geocentric (nadir) direction. LetusfirstdiscusshowaZ-translation (in the TRF) of all the stations can create an orbit effect similar to a cross-track error in the position of the phase center of the antenna on the satellite. Morel and Willis (2003) have demonstrated that errors in Z-coordinates of tracking stations can map in the estimated satellite orbit. We have chosen to study this parameter because recent investigations showed that the DORIS/SPOT residuals provide a yearly antenna correction map that is very different to all the other SPOT-4-derived yearly maps, or all other SPOTs maps in general (Willis et al. 2005c). To be more specific, a large asymmetry signal is visible in the cross-track direction. ( Let us) note Z as the axis of rotation of the Earth and U, V, W a reference system attached to the orbit with U in the direction of the ascending node and W perpendicular to the orbitplane, while V complements the frame (see Fig. 4). From the definition of the inclination of the satellite (i) Z = cos(i) W + sin(i) V (1) SPOT-4 is a sun-synchronous satellite with a retrograde and almost polar orbit (i = 98.9 ), so in this particular case Z and V are almost aligned. Also, let us note: β = i 90(in degrees) (2) A constant error in the body-fixed cross-track offset of the satellite will tend to shift the satellite orbit in the W direction (Fig. 4). To compensate this effect in a least squares solution, all stations will try to move as much as possible in the same direction, in order to keep the distance to the satellite constant Fig. 4 Relation between cross-track offset ( W )andtz-geocenter (geometrical interpretation)

4 570 P. Willis et al. between the non-perturbed (no offset) and the perturbed case (cross-track offset). If we look for a constant error in the geocenter (i.e., constant error in all stations coordinates) in X, Y and Z, it can be seen that X and Y will not create any effect of this type, due to a canceling effect related to the Earth s rotation in the inertial frame. However, Z can create a systematic effect that will create a constant error in W: W = sin (β) = cos(i) (3) Z This error would also create a large constant error in the V direction that we will address now, showing that it is taken into account by 1/rev empirical acceleration. Let us denote R as the radial unit vector and L as the along-track unit vector. If ω is the satellite orbital frequency and θ = ω t, the angle corresponding to the satellite position in the orbital plane, we have: R = cos (ωt) U sin (ωt) V (4) 4 Estimation of SPOT-4 cross-track corrections It is possible to test these results by fixing the station coordinates to their ITRF2000 values (Altamimi et al. 2002), while estimating the cross-track body-fixed offset for the SPOT-4 satellite. In order to really demonstrate our point, we have estimated very dynamic daily orbits (four drag parameters per day, no 1/rev empirical accelerations and no solar pressure coefficient). Figures 5 and 6 display the daily results obtained for SPOT-4 in 1998 and 1999 using 30 h arcs. Figure 5 shows that the offsets observed in 1999 are very close to zero (mean value is 9 mm), while offsets observed for 1998 show a large systematic value of 118 mm. The problem suddenly stops at the start of cycle 32 (January 10, 1999). A closer look also shows that some points in 1998 do not show such a large value. They all correspond to DORIS/SPOT-4 cycle 29 (December 15 22, 1998), which was obviously L = W R = sin (ωt) U cos (ωt) V (5) From Eqs. (4) and (5), we can derive: V = sin (ωt) R cos (ωt) L (6) This shows that a constant error in satellite position in the orbital plane can be mimicked by a 1/rev radial and along-track displacement. Such a displacement can be approximated by adjusting a set of discrete 1/rev empirical accelerations. In our case, 1/rev empirical accelerations are estimated in the along-track component. From Hill s equations (e.g., Colombo (1989)), it can be seen that the along-track 1/rev acceleration term can be used to account for much of the along-track orbit error in position, but only for some of the radial error. The remaining displacement in the radial component will directly map into the residuals (hence the 10% increase seen in the 1998 DORIS/SPOT-4 doppler residuals). From Eq. (3), we can now conclude that an error in the cross-track offset C (center of mass point of reference of the antenna) will create an erroneous TZ-geocenter offset Z that can be estimated by: Z = W (7) cos (i) It must be noted that here we only consider geodetic measurements being range measurements. In the specific case of DORIS, if this propriety is true for range measurement, it will be also true for DORIS-integrated doppler measurements as it corresponds to differences with time of such ranges. This also means that Eq. (4) remains true (at first order) for all types of satellites and all types of data: Global Positioning System (GPS) and in the future Galileo, Laser, GLONASS, or Precise RAnge and Range-rate Equipment (PRARE). In the case of SPOT-4, the TZ-geocenter offset computed from Eq. (7) is 76 cm. This value is close to what was observed in the weekly free-network solutions during Please note also the amplification effect due to the small value of the cosine in the case of a sun-synchronous satellite. Fig. 5 Daily SPOT-4 cross-track offset using DORIS data (mm) Fig. 6 Daily SPOT-4 cross-track formal error using DORIS data (mm)

5 Systematic errors in the Z-geocenter derived using satellite tracking data: a case study from SPOT-4 DORIS data in preprocessed differently (correctly) by Centre National d Etudes Spatiales (CNES). Figure 6 displays the formal errors on these results (cf. Fig. 5). Except for a few days, the precision does not change with time, showing that the estimated cross-track error correspond to a systematic bias that propagates freely from the data to the estimated parameter, rather than a change in the Doppler measurement noise itself due to possible malfunctioning of the DORIS receiver on-board SPOT-4. This demonstrates that the Z-translation that we observe on all stations using the DORIS/SPOT data is likely to be due to a possible constant error in the cross-track component of the satellite body-fixed frame. 5 New CNES preprocessed DORIS/SPOT-4 data Following this analysis, CNES confirmed that these 1998 DORIS/SPOT-4 were processed using erroneous values of the center of mass correction for SPOT-4 until early 1999 (cycle 32). The recovered errors are 13.2 cm in cross-track and 1.7 cm in radial offset (Berthias 2005). It also appears that cycle 29 was preprocessed differently using the correct offsets. It should be noted that the center of mass correction is the only corrupted field in the data files. Thus users who do not use the center of mass correction included in the file, but rather compute it by themselves, were not impacted by this problem. For test purposes, cycle 25 (November 11 20, 1998) was reprocessed using the correct values, estimating station coordinates. Figure 7 displays the results obtained for November 16, 1998 using either the regular DORIS data file available at CDDIS (Noll and Dube 2001) or the new corrected data file. Each bar in Fig. 7 represents the Z offset estimated for a specific station. Stations are ordered in increasing estimated formal errors. Stations on the right of Fig. 7 are more poorly determined in position than stations on the left for which the position is better estimated (usually more data). It can be seen that the erroneous bias has disappeared with the reprocessed data. The mean Z values decreased from 65.0 to 5.3 cm. 6 Discussion The analysis developed here is confirmed by experimental results (TZ-geocenter offset and constant cross-track error). This can be applied to all types of satellites and all types of data, as long as there is no yaw-steering of the satellite. However, in the case of sun-synchronous satellites, the ratio between the cross-track error in the position of the phase center and its effect on the geocenter Z position is amplified by a factor of 6.5 due to the cosine of the orbital inclination. In the case of SPOT, as it is difficult to measure the position of the phase center of the antenna with respect to the center of mass within 1 or 2 mm (the same is also true for the position of the ground station antenna phase center). The previous factor derived from Eq. (7) shows that the geocenter estimation could then be biased by up to 10 mm for the SPOT satellites (using the amplification factor of 6.5). In fact, this could be calibrated using ITRF2000 as a reference and estimating an additional cross-track offset for each satellite, starting with CNES nominal values and using a very long time span of observations. However, at present, several other effects alter the capacity of DORIS to properly monitor the Z-geocenter. In particular, annual signals are still visible in the geocenter time-series (annual for SPOT-4 as shown in Fig. 1, or at 120 days for TOPEX related to the period of the angle between the sun and the orbital plane). We have also pointed out some coupling between the Z-geocenter parameter and 1/rev empirical parameter. In the future, it is then important to model, as precisely as possible, all possible forces (not only gravitation, but also surface forces) to be able to get rid of any estimation of 1/rev empirical acceleration for geocenter monitoring. 7 Conclusions Fig. 7 Daily station Z-offset estimated using original (dashed) orcorrected (plain) DORIS/SPOT-4 data sets (mm) Theproblemfoundinearly (1998) DORISZ-geocenter timeseries is now understood. The simple model developed here explains how the error obtained in the geocenter estimation ( 65 cm) relates to an error in the center of mass correction provided with the data (resulting from the use of a wrong value for the position of the antenna phase center). The results obtained here have been confirmed by CNES, which identified the origin of the error in historical records. Ten days of data, reprocessed for test purposes, show that the new data give a correct geocenter position. Users who did not use the center of phase correction included in the CDDIS data files were not victims of this problem.

6 572 P. Willis et al. More generally, any error in the cross-track position of the antenna phase center of a sun-synchronous satellite will create an effect in the measured Z-geocenter that will be largely amplified (multiplied by 6.5) as long a yaw-steering is not involved. Acknowledgements Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA). References Altamimi Z, Sillard P, Boucher C (2002) ITRF2000, A new release of the International Terrestrial Reference Frame for Earth science applications. J Geophys Res 107(B10):2214 Altamimi Z, Boucher C, Willis P (2005) Terrestrial reference frame requirements within GGOS. J Geodyn 40(4-5): Angermann D, Kruger M, Meisel B et al (2005) Time evolution of the terrestrial reference frame. IAG Proc 128:9 14 Berthias J-P (2005) Answer to anomalous TZ geocenter value from DORIS/SPOT-4 data in IDS forum analysis web site, January 24, 2005 Beutler G, Drewes H, Verdun A (2004) The new structure of the International Association of Geodesy (IAG) view from the perspective of history. J Geod 77(10 11): Blewitt G (2003) Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. J Geophys Res Solid Earth 108(B2):2103 Bouille F, Cazenave A, Lemoine J-M, Crétaux J-F (2000) Geocenter motion from the DORIS space system and laser data to the LAGEOS satellites, comparison with surface loading data. Geophys J Int 143(1):71 82 Crétaux JF, Soudarin L, Davidson FJM, Gennero MC, Bergue-Nguyen, Cazenave A (2002) Seasonal and inter-annual geocenter motion from SLR and DORIS measurements, Comparison with surface loading data. J Geophys Res 107(B12):2374 Colombo OL (1989) The dynamics of Global Positioning System orbits and the determination of precise ephemeredes. J Geophys Res 94(B7): Dong D, Yunck T, Heflin M (2003) Origin of the international terrestrial reference frame. J Geophys Res Solid Earth 108(B4):2200 Heflin M, Bertiger W, Blewitt G, Freedman A, Hurst K, Lichten S, Lindqwister U, Vigure Y, Webb F, Yunck T, Zumberge J (1992) Global geodesy using GPS without fiducial sites. Geophys Res Lett 19(2): Meisel B, Angermann D, Muller H, Teismer V (2002) Comparison of DORIS site position and reference frame time series with other space techniques. IDS Workshop, Biarritz, France, June 13 14, 2002 Meisel B, Angermann D, Krugel M, Drewes H, Gerstl M, Kelm R, Muller H, Seemuller W, Tesmer V (2005) Refined approaches for terrestrial reference frame computations. Adv Space Res 36(3): Morel L, Willis P (2003) Parameter sensitivity of TOPEX orbit and derived mean sea level to DORIS station coordinates. Adv Space Res 30(2): Morel L, Willis P (2005) Terrestrial reference frame effects on mean sea level determined by TOPEX/Poseidon. Adv Space Res 36(3): Noll C, Dube M (2001) The IGS global data center at CDDIS An update. Phys Chem Earth Solid Earth Geod 26(6 8): Sillard P, Boucher C (2001) A review of algebraic constraints in Terrestrial Reference Frame datum definition. J Geod 75(2 3):63 73 Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins MM (2004) GRACE measurements of mass variability in the Earth system. Science 305(5683): Tavernier G, Fagard H, Feissel-Vernier M, Lemoine F, Noll C, Ries J, Soudarin L, Willis P (2005) The International DORIS Service (IDS). Adv Space Res 36(3): Willis P, Crétaux J-F (2004) DORIS data analysis strategies, Position Paper, paper presented at the International DORIS Service Plenary Session, Paris, France, May 3 4 Willis P, Heflin MB (2004) External validation of the GRACE GGM01C gravity field using GPS and DORIS positioning results. Geophys Res Lett 31(13):L13616 (Doi: /2004GL020038) Willis P, Haines B, Berthias JP, Sengenes P, Le Mouel JL (2004) Behavior of the DORIS/Jason oscillator over the South Atlantic Anomaly. CR Geoscience 336(9): (Doi: /j.crte.2004/01.004) Willis P, Bar-Sever YE, Tavernier G (2005a) DORIS as a potential part of a Global Geodetic Observing System. J Geodyn 40(4-5): Willis P, Boucher C, Fagard H, Altamimi Z (2005b) Geodetic applications of the DORIS system at the French Institut Géographique National. CR Geoscience 337(7): (Doi: /j.crte ) Willis P, Desai SD, Bertiger WI, Haines BJ, Auriol A (2005c) DORIS satellites antenna maps derived from long-term residuals time series. Adv Space Res 36(3):