SLR POD modeling improvements for Jason-1 and Jason-2

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Advances in Space Research 46 (2010) 1541–1558 www.elsevier.com/locate/asr

DORIS/SLR POD modeling improvements for Jason-1 and Jason-2 Nikita P. Zelensky b,a,*, Frank G. Lemoine a, Marek Ziebart c, Ant Sibthorpe d, Pascal Willis e,f, Brian D. Beckley b,a, Steven M. Klosko b,a, Douglas S. Chinn b,a, David D. Rowlands a, Scott B. Luthcke a, Despina E. Pavlis b,a, Vincenza Luceri g a

NASA Goddard Space Flight Center, Planetary Geodynamics Laboratory, Code 698, Greenbelt, MD 20771, USA b SGT Inc., 7701 Greenbelt Road, Greenbelt, MD 20770, USA c University College London, Department of Civil, Environmental and Geomatic Engineering, Gower Street, London WC1E 6BT, UK d Jet Propulsion Laboratory, California Institute of Technology, MS 238-600, 4800 Oak Grove Drive, Pasadena, CA 91109, USA e Institut Ge´ographique National, Direction Technique, 2, avenue Pasteur, 94165 Saint-Mande´, France f Institut de Physique du Globe de Paris (IPGP, Univ. Paris 7, CNRS), 35 rue He´le`ne Brion, 75013 Paris, France g E-GEOS S.P.A, ASI/CGS, Centro di Geodesia Spaziale “G. Colombo”, P.O. Box ADP, 75100 Matera, Italy Received 1 October 2009; received in revised form 7 May 2010; accepted 10 May 2010

Abstract The long-term stability and the precision of the satellite orbit is a critical component of the Jason-1 and Jason-2 (OSTM) Missions, providing the reference frame for ocean mapping using altimeter data. DORIS tracking in combination with SLR has provided orbits, which are both highly accurate and consistent across missions using the latest and most accurate POD models. These models include GRACE-derived static and time varying gravity fields and a refined Terrestrial Reference Frame based on SLR and DORIS data yielding a uniform station complement. Additional improvements have been achieved based on advances in modeling the satellite surface forces and the tropospheric path delay for DORIS measurements. This paper presents these model improvements for Jason-1 and Jason-2, including a description of DORIS sensitivity to error in tropospheric path delay. We show that the detailed University College London (UCL) radiation pressure model for Jason-1, which includes self-shadowing and thermal re-radiation, is superior to the use of a macromodel for radiation pressure surface force modeling. Improvements in SLR residuals are seen over all Beta-prime angles for both Jason-1 and Jason-2 using the UCL model, with the greatest improvement found over regimes of low Beta-prime where orbit Earth shadowing is maximum. The overall radial orbit improvement for Jason-1 using the UCL model is 3 mm RMS, as corroborated by the improvement in the independent altimeter crossover data. Special attention is paid to Jason-2 POD to assess improvements gained with the latest advances in DORIS receiver technology. Tests using SLR and altimeter crossover residuals suggest the Jason-2 reduced-dynamic DORIS-only, SLR/DORIS, and GPS orbits have all achieved 1-cm radial accuracy. Tests using independent SLR data acquired at high elevation show an average fit value of 1.02 cm for the DORIS-only and 0.94 cm for the GPS reduced-dynamic orbits. Orbit differences suggest that the largest remaining errors in the Jason-2 dynamic orbit solutions are due to radiation pressure mis-modeling and variations in the geopotential not captured in the GRACE-derived annual terms. Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: SLR; DORIS; Precision orbit determination; Jason-1; Jason-2

1. Introduction Accurate orbit determination lies at the core of the altimeter-derived sea surface height observation. The orbit *

Corresponding author at: NASA Goddard Space Flight Center, Planetary Geodynamics Laboratory, Code 698, Greenbelt, MD 20771, USA. E-mail address: [email protected] (N.P. Zelensky).

serves as a reference frame for the altimeter measurement. The stability and accuracy of the orbit time series is affected by errors in the force models, the terrestrial reference frame (TRF), and error in the tracking data and measurement models. Altimeter satellite orbit accuracy requirements have become more stringent given improved modeling and tracking system capabilities, so it is not surprising that

0273-1177/$36.00 Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2010.05.008

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orbit error remains a major focus in the error budget for both Jason-1 and Jason-2. Both spatial and temporal components of radial orbit error will directly affect the altimeter observable. Although the Jason-1 and Jason-2 orbits computed at GSFC using the latest precision orbit determination (POD) standards (Table 1) have shown very high consistency and accuracy (Lemoine et al., 2010), the improved tracking capabilities and growing interest in using altimeter data to recover small ocean signals, such as the mean sea level trends, places increasingly stringent requirements on orbit accuracy and in characterizing orbit error (Beckley et al., 2004, 2007, in press; Morel et al., 2005). A precise orbit is essential for altimeter instrument calibration, and for the proper calculation of orbit-related altimeter corrections, such as the sea-state bias. In addition, precise orbits and their stability and consistency through time are essential to properly intercalibrate altimeter data from different missions, particularly during the tandem mission periods (Beckley et al., 2004, in press). Table 1 GSFC POD model standards May 2009: std0905. Reference frame and displacement of reference points SLR SLRF2005 + LPOD2005 (version 11) DORIS DPOD2005 (version 1.4) Earth tide IERS2003 Ocean loading GOT4.7 all stations Tidal CoM and GOT4.7; VLBI high frequency terms EOP EOP IERS Bulletin A daily (consistent with ITRF2005) Precession/ IAU2000 nutation Gravity Static Time varying Atmospheric Tides

EIGEN-GL04S Linear C20-dot, C21-dot, S21-dot (IERS2003) + 20  20 annual terms from GRACE ECMWF 50  50 at 6 h; tides (Ray and Ponte, 2003) GOT4.7 20  020 (ocean); IERS2003 (Earth)

Satellite surface forces and attitude Albedo/IR Knocke–Ries–Tapley (1988) Atmospheric MSIS86 (Hedin, 1987) drag Radiation Jason-1 pressure UCL Radiation scale coefficient Attitude Tracking data and Tracking data Troposphere model Parameterization Antenna reference SLR DORIS SLR/DORIS weight

CR = 1.0 Nominal Yaw

2. Evaluation of surface force model improvements Jason-2 Jason-1 8panel CR = 0.916 (tuned) Quaternions

parameterization SLR/DORIS (Jason-1 DORIS corrected for SAA) SLR: Mendes (Hulley et al., 2007) DORIS: Hopfield/ Niell + GPT Drag/8 h + OPR along & cross-track/24 h + DORIS time bias/arc; 10-day arc dynamic solution Jason-1 Jason-2 Tuned offset Pre-launch 10-cm/3-mm/s; down-weight 10 SAA stations to 8-mm/s and 4 SAA stations to 5-mm/s

The latest GSFC Jason-1 and Jason-2 orbits have been computed with GEODYN (Pavlis et al., 2009) processing SLR (Pearlman et al., 2002) and DORIS (Tavernier et al., 2006; Willis et al., 2010) data, and using the latest POD standards outlined in Table 1. These standards include the GRACE-derived static gravity field EIGENGL04S1 (Lemoine et al., 2007), the GOT4.7 (Goddard Ocean Tide model) dynamic tide model (update to Ray, 1999), forward modeling of atmospheric mass flux using ECMWF pressure data (Klinker et al., 2000), a GRACEderived time varying gravity model capturing the annual variation (Luthcke et al., 2006), and updated ITRF2005 SLR and DORIS station coordinates using LPOD2005 (Ries, 2008; Luceri and Bianco, 2007) and DPOD2005 (Willis et al., 2009). These standards also include improved surface force modeling for Jason-1 and improved DORIS tropospheric path delay modeling. TOPEX/Poseidon (TP) was the heritage mission (Fu et al., 1994) for the Jason-1 follow-on. Many of the improvements to Jason POD presented in this paper rest on the shoulders of the earlier TP POD development and analysis (Tapley et al.; 1994; Nouel et al., 1994; Marshall et al., 1994a; Bertiger et al., 1994). This paper describes surface force modeling improvements for Jason-1, analysis performed to improve the Jason-2 modeling, improved DORIS tropospheric path delay modeling and DORIS data sensitivity to tropospheric path delay error coupled with oscillator health. The GSFC operational modeling of time varying gravity (TVG) is tested for completeness and residual error. This paper also evaluates the efficacy of the reduced-dynamic approach for removing orbit error, and presents the enhanced Jason-2 DORIS POD capability reflecting the latest advance in DORIS receiver technology. The latest Jason-2 orbits from GSFC, CNES, and JPL are compared to evaluate remaining error.

Pre-launch Pre-launch 10-cm/2mm/s

With the advances in accuracy achieved with GRACEderived gravity fields, surface force mis-modeling has emerged as the largest source of error for TOPEX/Jason dynamic orbit solutions (Ries, 2007). The non-conservative forces acting on the satellite surface are primarily due to radiation pressure and to a much lesser extent, atmospheric drag. Table 2 illustrates the relative magnitude of the surface forces acting on TP, Jason-1 and Jason-2. The effects of drag at the 1300 km altitude are typically between 1 and 2 orders of magnitude smaller than the effects due to radiation. During periods of high solar activity (indicated by the large F10.7 solar flux indices) the forces due to drag increase by about 1 order of magnitude (Table 2). Such perturbations are visible in geodetic results derived from LEO satellite data (Willis et al., 2005). The forces due to radiation pressure include direct solar radiation, Earth Albedo and infra-red re-radiation (IR), and satellite thermal radiation. Thermal radiation represents effects due to

N.P. Zelensky et al. / Advances in Space Research 46 (2010) 1541–1558 Table 2 Surface forces acting on TOPEX/Poseidon (TP), Jason-1, Jason-2 satellites. Acting force computed over one cycle in sinusoidal yaw at 1300 km altitude Solar radiation pressure Albedo + IR Thermal Drag (F10.7 = 103, 80 for J2) Drag (F10.7 = 224)

Total RMS acceleration (109 m/s2) TP

Jason-1

Jason-2

53.0 8.0 2.0 0.2 2.5

124.0 16.0 – 1.0 –

133.0 16.0 0.6

heating/cooling of the satellite while in sunlight/shadow, and internal heat dissipation. Such thermal forces are only directly modeled for TP, but not for Jason-1 or Jason-2. The Jason-1/2 Multi-Layer Insulation (MLI) covering is considered to have an emissivity of zero, and so will not contribute to the heating up of the satellite (Berthias et al., 2002). The difficulty in modeling the effects of radiation forces acting on the satellite is largely due to the complex satellite geometry and incomplete knowledge of the reflective and thermal properties of the satellite surfaces, and of the internal heat dissipation driven by component duty cycles. Most of the orbit error due to radiation pressure is characterized by a once-per-revolution (OPR) signal. This error is largely removed upon the estimation of empirical OPR acceleration parameters in the orbit solution (Colombo, 1986). The estimation of OPR parameters every 24 h is included in the GSFC dynamic orbit strategy (Table 1). However, complex errors in the radiation pressure model are believed to interact with the estimated empirical OPR parameters to create errors in Z component of the orbit with a Beta-prime period (approximately 120-days for Jason) (Haines et al., 2004; Ries, 2007; Gobinddass et al.,

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2009). Beta-prime is the angle between the orbit plane and the direction to the sun. Over each Beta-prime cycle both the attitude regimes and the satellite surface orientations with respect to the sun repeat. The Jason satellites follow a yaw steering attitude with several regimes depending on Beta-prime, much as with TP (Marshall and Luthcke, 1994b). It has been shown that a 7% error in the solar radiation pressure scale results in a systematic orbit error in Z of about 1-cm (Haines et al., 2004). Error in orbital Z-centering directly maps into a radial error having a north– south geographical distribution with maximum absolute errors found at the poles. Fig. 1a shows the geographic distribution of the 120-day amplitude for radial differences between state-of-the-art Jason-1 GSFC dynamic SLR/ DORIS (Lemoine et al., 2006) and JPL GPS reduceddynamic orbits (Bertiger et al., 2006). For Fig. 1 120-day amplitude and phase terms were estimated for orbit differences binned in 5°  5° grids every 10-days over a four year orbit time series, from 2002 to 2005. The prominent 120-day signature in the mean Z differences between state-of-the-art Jason-2 orbits computed at the three analysis centers – GSFC (Lemoine et al., 2010), CNES (Cerri et al., 2010), and JPL (Bertiger et al, 2010), suggests the presence of considerable radiation pressure model error in the latest Jason-2 orbits (Fig. 2). For the Jason-1/2 orbits shown here, all three centers use a series of flat plates and their orientations to approximate the satellite geometry and surface properties for modeling the radiation pressure. This is the macromodel approach. The macromodel approach was established through analysis efforts undertaken on TP (Marshall and Luthcke, 1994b). The analysis included finite element modeling of the satellite reflective and thermal properties and satellite self-shadowing to produce accelerations used to initially define the macromodel (Antreasian and Rosborough,

Fig. 1. Jason-1 5°  5° bin radial orbit difference 120-day amplitudes. (a) SLR/DORIS orbit (CR = 1) – JPL GPS orbit and (b) SLR/DORIS orbit (CR = 1) – SLR/DORIS orbit (CR = 0.914).

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Fig. 2. Jason-2 mean Z orbit differences. Cycles 1–30 (July 2008–April 2009).

1992). The TP macromodel was then tuned using tracking data, and is believed to accurately model over 95% of the radiation forces (Marshall and Luthcke, 1994c). The Jason-1 macromodel was constructed, much as TP, initially from finite element modeling accelerations of radiation pressure, thermal re-radiation and self-shadowing, and whose effects were averaged for each of the macromodel 8 plates over the 120-day attitude regime in a least-squares fit of the optical properties (Berthias et al., 2002). The TP macromodel includes thermal re-radiation modeling due to sun/shadow heating/cooling. The Jason macromodels do not directly model the thermal component, and neither the TP nor the Jason macromodels directly model self-shadowing. This effect occurs when different spacecraft components shadow each other as observed in a particular direction (e.g. towards the Sun for solar radiation pressure and along-track for atmospheric drag). The cross-sectional area can be effectively reduced in different ways for these two perturbations (Mazarico et al., 2009). This phenomenon is explicitly accounted for in the University of College London (UCL) model for Jason-1, but not explicitly in the standard macromodels for altimeter satellite orbit determination. The GSFC Jason-1 eight-plate macromodel uses the prelaunch CNES supplied values (Cerri et al., 2010), with the radiation scale factor (CR) tuned to 0.926 from the a priori (un-tuned) value of 1.0. It should be noted other estimates of this scale factor have been much closer to 1.0 (Cerri et al., 2010). However, Fig. 1b suggests simply tuning the CR scale as a constant for the Jason macromodel falls short in eliminating radiation pressure mis-modeling. The much smaller 120-day signal observed between using the tuned/ un-tuned CR (Fig. 1b) does not explain the large, 6-mm amplitude signal observed between the SLR/DORIS and JPL GPS orbits (Fig. 1a). Both the SLR/DORIS and GPS orbits are of comparable high accuracy (Lemoine et al., 2006). For the initial Jason-2 radiation pressure modeling GSFC has adopted the Jason-1 pre-launch macromodel

after tuning CR to a value of 0.916 (std0905). In addition, we have tested this macromodel further by including a solar array (SA) thermal re-radiation component using the TP SA thermal properties (Marshall and Luthcke, 1994b) and tuning CR to a value of 0.948 (std0905_Cr_tuned). Although tracking data residuals and the radial orbits show little change between std0905 and std0905_Cr_tuned (Table 3), the std0905_Cr_tuned recovered along-track once-per-revolution (OPR) acceleration amplitudes do show improvement with the thermal component included (Fig. 3). A smaller recovered acceleration value suggests greater accuracy in the surface force modeling with less residual signal needing accommodation. A new approach in modeling the radiation forces acting on the satellite is provided by a model for Jason-1, developed by the University College London (UCL). The foundation of the technique is to account fully for complexity in the surface geometry and properties of the spacecraft, and also to deal with complexity in the incident radiation flux and its interaction with the spacecraft. The surface geometry of the spacecraft is constructed in a computer simulation using geometric primitives such as cones, paraboloids, cylinders and flat plates. The advantage here is that the native geometry of the surface is retained in the modeling without any simplification or tessellation. Incident radiation fluxes are modeled using a pixel array, and numerically intensive ray-tracing algorithms are used to compute the insolation of the spacecraft, also accountTable 3 Jason-2 SLR/DORIS radiation pressure model tests, cycles 1–30 (July 2008–April 2009). Radiation pressure model

Residuals DORIS (mm/s)

SLR (cm)

Orbit differences RMS (cm) Radial

Crosstrack

Alongtrack

std0905 std0905_Cr_tuned UCL

0.3658 0.3647 0.3648

1.180 1.184 1.113

– 0.09 0.28

– 0.40 0.59

– 0.28 0.74

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Fig. 3. Daily estimation of along-track empirical accelerations using different Jason-2 macomodels. July 2008–March 2009.

ing for any inter-component shadowing and the subsequent path (and intersection with the structure) of radiation after reflection. The resultant forcing is computed on a pixel by pixel basis and summed together. The method is described in Ziebart (2004). Additional thermal forcing effects are modeled by consideration of the thermal response of the surface multi-layered insulation (MLI) (Adhya et al., 2005) and the thermal imbalance force caused by the temperature differences between the front and back of the solar panels (Ziebart et al., 2003). Each of these model runs determines the response of the spacecraft to a particular flux direction and energy. Finally simulated radiation fluxes are projected onto the spacecraft model from multiple directions and a continuous acceleration field model is fitted to the computation output. The continuous model is then implemented within orbit determination software. Developed specifically for Jason-1, the UCL model explicitly includes sun/shadow thermal re-radiation of the solar array (SA) and self-shadowing modeling, in contrast to the macromodel which does not. In addition the UCL model attempts to account for the subtleties of the interaction of the incident radiation fluxes with the detailed geometry of the spacecraft surface, such as the cylindrical shapes of the star cameras and the parabolic surfaces of the JMR and the altimetry dish. This represents a step change in the handling of structural complexity in such modeling. UCL shows improvement in the Jason-1 SLR residuals across all Beta-prime angles, but especially every sixty days over low Beta-prime fixed-yaw regimes (Table 4 and Fig. 4). This is the period over which most changes in attitude Table 4 Jason-1 SLR/DORIS radiation pressure model tests, cycles 1–235 (January 2002–May 2008). Radiation pressure model

Macromodel UCL

Residuals

Orbit differences RMS (cm)

DORIS (mm/s)

SLR (cm)

Xover (cm)

Radial

Crosstrack

Alongtrack

0.3837 0.3856

1.187 1.163

5.584 5.575

– 0.28

– 0.53

– 0.78

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regime occur, and also where the sun/shadow heating/cooling re-radiation will be at its peak. Since the Jason-2 satellite is similar in orbit and somewhat similar in design to Jason-1 (Cerri, 2008), the Jason-1 UCL model was tested for Jason-2. Even though there are some notable differences between the Jason-1/ Jason-2 body surface reflective properties (Cerri, 2008), the Jason-1 UCL model also significantly improves the Jason-2 orbit, especially every 60-days over periods of low Beta-prime (Table 3, Fig. 5). The Jason-2 orbit improvements using UCL are very encouraging and suggest the complicated self-shadowing and thermal re-radiation accounted in the UCL model are needed for correctly modeling surface forces due to solar radiation pressure, Earth albedo and infra-red radiation pressure (planetary radiation pressure), and satellite re-radiation. Attempts at tuning the UCL CR scale have shown that a value of 1.0 is preferred for both Jason-1 and Jason-2. 3. DORIS sensitivity to tropospheric path delay error and oscillator health DORIS is a powerful and highly accurate satellite tracking system. It is used to determine precise orbits for the SPOT, Jason, and Envisat satellites, to contribute to the ITRF realizations (Altamimi et al., 2006; Altamimi et al., 2007; Willis et al., 2006; Le Bail et al., 2010), and to contribute to determination of geocenter motion (Feissel-Vernier et al., 2006; Gobinddass et al., 2009). During the first Jason-2 OSTST/IDS meetings, an unusually large 14-cm adjustment was reported by our group in the estimated DORIS antenna Z-offset (Zelensky et al., 2008). The result was quite surprising since the prelaunch antenna offset measurements were believed to have sub-centimeter accuracy. The Z-offset estimates were computed from SLR/DORIS orbit solutions, although tests showed that the Z-offset estimates from DORIS-only solutions were almost identical. Analyses were undertaken to explain this large Z-offset. Four composite models were tested which compute the delay imparted by the troposphere on the DORIS radiofrequency signal (Table 5). The Hopfield (Hopfield, 1971) and VLBI (Chao, 1974) models compute the zenith path delay of both wet and dry components using ground meteorological pressure, temperature and relative humidity data. The meteorological data is collected at the DORIS ground beacons, or the temperature and pressure are computed with the GPT model (Boehm et al., 2007). The relative humidity data are always provided by the DORIS beacons in these tests. The Goad (Goad and Goodman, 1974), CFAF2.2 (Davis et al., 1985), and Niell (Niell, 1996) mapping functions are the final component of the composite models tested. Tests indicated the large adjustment to the a priori antenna Z-offset value was due to tropospheric path delay model error (Fig. 6), and that the better the troposphere model employed, judging by residual fits (Table 5), the least adjustment in the estimated

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Fig. 4. Comparison of Jason-1 macromodel/UCL solar radiation pressure models. Positive values show improvement in residuals for UCL model toward the tuned macromodel.

Fig. 5. Comparison of Jason-2 macromodel/UCL solar radiation pressure models. Positive values show improvement in residuals for UCL model toward the tuned macromodel. Table 5 Jason-2 DORIS-only tropospheric delay model tests, cycles 1–20 (June 2008–January 2009). Troposphere delay modeling: zenith delay/mapping function/meteorological data

Residuals DORIS (mm/s)

SLR (cm)

Radial

Orbit differences RMS (cm) Cross-track

Along-track

(a) Hopfield/Goad/DORIS (b) Hopfield/Goad/GPT (c) VLBI/CFA2.2/GPT (d) Hopfield/Niell/GPT

0.3726 0.3656 0.3666 0.3653

3.235 2.645 2.247 2.433

– 0.06 0.15 0.13

– 1.58 4.25 2.68

– 0.27 0.74 0.59

Z-offset from the pre-launch a priori value is seen (Fig. 6).The GSFC solutions use an elevation cutoff of 10° and estimate a single zenith scale for the combined wet + dry troposphere components per DORIS pass. Tests also show that GM estimated with DORIS is likewise highly sensitive to tropospheric path delay error (Fig. 7),

and that using the better tropospheric path delay model gives GM estimates closest to the SLR-derived IERS standard of 398600.4415 km3/s2 (McCarthy and Petit, 2004). These tests imply, and as analyses have shown (Le Bail et al., 2010), that the recovered DORIS TRF scale will be highly sensitive to error in tropospheric path delay

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Fig. 6. Sensitivity of Jason-2 DORIS antenna Z-offset estimation toward different tropospheric modeling.

Fig. 7. Sensitivity of Jason-2 DORIS GM estimation toward different tropospheric modeling.

modeling. Such sensitivity suggests tropospheric path delay error may prove to be a limiting factor to state-of-the-art DORIS recovery of station positions and geocenter motion, although orbit sensitivity to such error is largely in the cross-track direction with only small perturbations to the radial (Table 5). Previously GSFC had employed the Hopfield zenith delay refraction (Hopfield, 1971) and Goad mapping (Goad and Goodman, 1974) models together with the meteorological values supplied with the DORIS data as the initial conditions for solving for a pass-by-pass DORIS tropospheric scale parameter. The largest improvement in the Jason-2 DORIS and independent SLR residuals is seen when switching pressure/temperature values available with DORIS data to the GPT model (Boehm et al., 2007) (Table 5). Comparison of the DORIS pressure/temperature/relative humidity meteorological values for the Greenbelt station (GREB) to measurements collected at the

adjacent Goddard SLR station, and to GPT values shows significantly stronger agreement between the GPT and SLR values than with the DORIS values (Figs. 8–10). The DORIS (GREB) and SLR (7105) stations at GSFC are 62 m apart, with a difference in height of only 1.4 m. All these tests suggest the DORIS-supplied meteorological values are not reliable. The lack of reliability of the DORIS meteorological sensors has been known for some time, and other analysis centers make different accommodations in their analyses. We then used the sensitivity seen between tropospheric modeling error and the Z-antenna offset adjustment to test tropospheric model performance. Consideration of the Zoffset estimates and the data residual statistics (Table 5) narrows the selection for the POD standards between (b) Hopfield zenith delay (Hopfield, 1971)/Niell mapping (Niell, 1996)/GPT met data, and (c) VLBI zenith delay (Chao, 1974)/CFA2.2 mapping (Davis et al., 1985)/GPT

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Fig. 8. DORIS Greenbelt station (GREB) pressure (January 2009–May 2009).

Fig. 9. DORIS Greenbelt station (GREB) dry temperature (January 2009–May 2009).

Fig. 10. DORIS Greenbelt station (GREB) relative humidity (January 2009–May 2009).

met data. Although Table 5 (c) VLBI/CFA2.2/GPT shows the smallest SLR residuals, we have selected (b) Hopfield

troposphere zenith delay model/Niell mapping function/ GPT pressure/temperature values for the new POD

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standards (Table 1) since that combination shows the least adjustment to the a priori Z-offset (Fig. 6). In the GEODYN implementation, the Hopfield zenith delay refraction model uses surface pressure and temperature for computing the dry component, and surface temperature and the unreliable DORIS relative humidity for computing the wet component. The accuracy of the computed wet component zenith path delay is questionable. Unfortunately it is not clear what can be used in place of the DORIS supplied station relative humidity values. The Niell mapping function has been shown to perform very well in an experiment using ray tracing (Hobiger et al., 2008; Mendes and Langley, 1994). The Niell mapping function is also independent of surface meteorology and is preferred in the absence of reliable meteorological data. We plan to test the more recent mapping functions such as the GMF (Boehm et al., 2006a) and VMF1 (Boehm et al., 2006b), to estimate just the wet component, and possibly to evaluate using the ECMWF-derived zenith path delay product when it becomes available (Soudarin et al., 2008). The Jason-1 estimated DORIS antenna Z-offset time series describes the same interesting pattern for two tropospheric path delay models: Hopfield/DORIS met and Hopfield/Niell/GPT (Fig. 11). There is a steep linear trend leading to cycle 91 (June 25, 2004); with cycle 91 there is a jump followed by an even, flat series which is close to zero for the Hopfield/Niell/GPT modeling (Fig. 11). The Jason1 DORIS oscillator had progressively degraded due to increased radiation experienced in transit over the South Atlantic Anomaly (SAA) region until cycle 91 at which time operation was switched to the second on-board oscillator which has shown to have much greater stability (Willis et al., 2004; Lemoine and Capdeville, 2006). Fig. 11 suggests that trends in the estimated DORIS antenna Z-offset can also serve as a predictor of oscillator health. The Z-offset estimates shown in Fig. 11 were computed from SLR/DORIS orbit solutions, although tests show the Z-offset estimates from DORIS-only solutions are almost identical. Applica-

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tion of the Z-offset slightly improves the orbit as shown by the DORIS and SLR residuals, although the effect on the orbit radial component is very small (Table 6). 4. Modeling time varying gravity Most of the variability in the gravity field is caused by redistribution of mass within the oceans and atmosphere, water stored on land, and by the deformation of the solid Earth in response to these mass variations. The periodic effects include tides, atmospheric pressure variations over land, seasonal changes in hydrology, and the seasonal changes in ocean topography due to wind forcing. There are also secular gravity changes as the earth returns to isostatic equilibrium (Glacial Isostatic Adjustment (GIA)) from the melting of the ice sheets since the last glacial maximum, which is modeled as a linear change in the C20, C21, and S21 gravity coefficients (Table 1). In our naming convention, tidal and GIA terms are individually and separately modeled and are not included in the operational time varying gravity (TVG) model implementation (Table 1).The GSFC operational TVG modeling thereby represents atmospheric gravity, changes in hydrology, and wind-forcing changes in ocean mass. This is accomplished by:  forward modeling atmospheric gravity with a 50  50 time series of fields based on ECMWF-6 hour data, Table 6 Jason-1 SLR/DORIS orbit sensitivity to DORIS antenna Z-offset, cycles 1–235 (January 2002–May 2008). DORIS antenna Z-offset

Residuals DORIS (mm/s)

SLR (cm)

Xover (cm)

Orbit differences RMS (cm) Radial

Crosstrack

Alongtrack

Not applied Applied

0.3856 0.3849

1.163 1.156

5.575 5.575

– 0.13

– 0.16

– 0.38

Fig. 11. 10-day estimation of Jason-1 DORIS antenna Z-offset. Cycles 1–235. From January 2002 to May 2008.

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 modeling atmospheric tides (discussed below), and  employing a model of the annual variation in the gravity field determined from 4-years of GRACE data complete to degree and order 20 in spherical harmonics (Luthcke et al., 2006). This model is intended to implicitly represent changes in hydrology and wind-forcing changes in ocean mass. In preparation of the 50  50 atmospheric gravity fields the ECMWF-6 hour atmosphere grids have both the mean pressure as well as the modeled air tide signal removed. The air tide model, derived from 13 years of ECMWF-6 hour data, consists of a 20  20 S1 field with 10  10 S2, P1, K1, T2, and R2 fields (Ray and Ponte, 2003). The advantage of the operational TVG model is that it can extend back to 1982 which is the start of ECMWF6 hour data availability, and can move forward with a 1month lag time. The contribution of the operational TVG is critical to realizing the current state-of-the-art POD, showing significant orbit improvement (Table 7). We also believe that the 4-year averaged annual model developed from GRACE can fairly characterize these changes over time since this model is driven largely by continental hydrology which has distinct and fairly repeatable annual variations. The TVG model effectively removes a long-term systematic radial signature with an annual period having 5-mm amplitudes and distributed by hemisphere (Fig. 12). The largest contributor in the composite TVG model comes from the largely annual mass motion Table 7 Jason-1 performance towards Time Varying Gravity (TVG) model. Jason-1 SLR/DORIS cycles 1–135 (January 2002– September 2005)

RMS residuals DORIS (mm/s)

SLR (cm)

(a) No TVG (b) With TVG

0.4151 0.4071

1.546 1.481

of the atmosphere, and weakly followed by the hydrosphere as shown by Lemoine et al. (2010). We now address both the completeness and performance of the 20  20 time gravity model for annual variations. It has been reported that possible long-term non-linear gravity field variations not included in current POD standards can lead to apparent large trends in the measured ocean surface (1.5 mm/yr) on a basin scale (Cerri et al., 2009), although the 2002–2008 analysis period is too short for reliable recovery of any linear trends. In a test to address this question a more complete model, but one confined to GRACE data coverage and not operationally viable, was constructed. Jason-1 SLR/ DORIS dynamic orbits computed using this model over 2004–2005 are compared to respective orbits computed using the operational TVG model. The more complete TVG_test model was constructed by estimating 60  60 monthly fields using GRACE data on top of the following background models (cf. Luthcke et al., 2006) over the span of the Jason mission. The background models consist of forward modeling the atmosphere using 50  50 3-h fields based on ECMWF-3 hour data, using GLDAS (Rodell et al., 2004) to model the hydrology, and MOG2D (Carre`re and Lyard, 2003) to model the barotropic ocean. In preparation of the 50  50 atmospheric gravity fields the ECMWF-3 hour atmosphere grids have the mean pressure removed. The Jason-1 radial differences are small between orbits using TVG_operational and TVG_test, with an RMS of 3-mm over 2004–2005. However, the radial differences show a prominent annual signal having a 2.5 mm amplitude (Fig. 13). There are no other significant periodic signals or trends in the orbit differences. These results suggest about 1/3 of the TVG signal is not represented in the operational model, and likely arises from interannual variability. Consideration should be given to future improvements based on GRACE, but these will likely be restricted to mission intervals that are coincident with GRACE operations.

Fig. 12. Jason-1 operational time varying gravity model annual radial orbit signal.

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Fig. 13. Jason-1 residual radial orbit signal between operational time varying gravity model and the more complete test model.

5. DORIS and Jason-2 precise orbit determination With the first flight on-board Jason-2 of a DGXX generation receiver (Auriol and Tourain, 2010), DORIS has entered a new era of POD capability. The new DORIS capability of simultaneously observing transmission from up to seven ground beacons significantly improves tracking coverage/geometry and opens the door to new POD strategies, such as using the DORIS phase measurement (Mercier and Cerri, 2010). Previously the Jason-1 receiver could simultaneously observe only two DORIS beacons. Comparing DORIS Doppler observations over the same 10-days for Jason-1 and Jason-2 (Fig. 14), not only shows that Jason-2 has the greater number of observations over all elevation angles, but that Jason-2 data is collected below 10° elevation, whereas it is not for Jason-1. In fact about 35% of the Jason-2 data is from 10° and below. Such a distribution for Jason-2 increases data processing sensitivity to tropospheric delay model error. Conversely improved tropospheric delay modeling should significantly enhance

the Jason-2 DORIS POD capability, and possibly allow data from below 10° elevation to enter the solution. The initial GSFC solutions had used the DORIS supplied station meteorological data and the Hopfield zenith delay refraction model and Hopfield mapping function. As shown in Section 3, a significant improvement to POD is achieved with the empirically derived GPT station temperature/pressure values and with the Niell mapping function. However, the apparently unreliable DORIS relative humidity values are used by the Hopfield zenith delay model augmenting the uncertainty of the wet-troposphere delay accuracy. We plan to continue testing the more recent and improved troposphere propagation delay models. It has been known that for TOPEX, Jason-1 and Envisat that the DORIS data have a time-tag bias with respect to the time-system of the Satellite Laser Ranging (SLR) network (Zelensky et al., 2006). For TOPEX, Jason-1, and Envisat, this DORIS time-tag bias ranges to ±5– 10 ls. A DORIS time-tag bias can be estimated over a

Fig. 14. Jason-1 and Jason-2 DORIS data availability as a function of satellite elevation.

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SLR/DORIS 10-day arc with an accuracy of about 2 ls using the SLR tracking data as a reference. Since DORIS data are time tagged with a reported accuracy of 1–2 ls relative to UTC (Zaouche, 2009), these estimates should fall within a ±4 ls envelope. Indeed, the DORIS time biases so estimated for both Jason-2 and Jason-1 over the first 36 Jason-2 cycles fall inside this window (Fig. 15). Fig. 15 shows similar time bias series based on three orbits, where on average we see 1.4 ± 1.3 ls for Jason-2 dynamic orbits, 1.1 ± 1.2 ls for Jason-2 RD orbits, and 1.7 ± 1.3 ls for Jason-1 dynamic orbits. Could this signal reflect an error in the DORIS preprocessing common to both satellites, or could there be a common mean alongtrack error in the three orbits that is interpreted as a time tag error? Spectral analysis of the Jason-2 dynamic orbit time bias series shows the 118-day term is dominant and accounts for 91% of the variance. This is the precise draconitic (Beta-prime) period for the Jason satellites and suggests orbit error due to radiation pressure mis-modeling is one possible explanation for the signal. The 1.8 ls amplitude of the 118-day term could also represent about 12 mm of mean along-track orbit error. As discussed below, one can expect a reduction in orbit error with the reduced-dynamic (RD) solution. Spectral analysis of the Jason-2 RD series shows the dominant 115-day term to have amplitude of 1.0 ls. Considering the short and somewhat noisy series, 115-days appears close to the 118-days discussed, and suggests a reduction in Jason-2 radiation pressure orbit error. These tests may suggest the estimated Jason-2 DORIS time tag offset can be used as a reference to identify orbit error at the level of 1 ls or better. However, spectral analysis of the Jason-1 dynamic orbit time bias series shows the dominant term accounting for 79% of the variance to have an 86-day period, and which does not correspond to the draconitic period. Clearly further analysis is warranted using longer time series which may yield better resolution of Jason-1/2 time bias signatures. The dense and highly precise Jason-2 DORIS tracking promises significant improvement for POD capability. To

better evaluate this, a reduced-dynamic technique is applied to process the SLR/DORIS data and the DORIS data alone. In the SLR/DORIS processing, DORIS data is given more prominence than in the dynamic solution by changing the DORIS sigma-weight from 2 mm/s to 1 mm/s. In contrast to the dynamic solution, the reduceddynamic (RD) approach places greater emphasis on the accuracy of the tracking data rather than force model accuracy by estimating a closely spaced series of time-correlated empirical acceleration parameters (Bertiger et al., 1994; Luthcke et al., 2003). This approach can remove much of the residual force model error, but relies on the highly accurate modeling of the tracking measurement. Deficiencies in the tracking data are accommodated by suitably constraining the parameter adjustments. The GEODYN implementation is through the least-squares adjustment of a time series of OPR empirical acceleration parameters, which have explicitly correlated constraining equations forcing greater continuity between the adjacent OPR amplitude and phase terms. The weight used in the constraint equation between two parameters at time Tj and at time Tk, is computed as follows: weightðj; kÞ ¼ ðe=r2 ÞeðjTjTkj=sÞ

ð1Þ

where Tj is the mid-point of the jth acceleration parameter interval; r is the process noise input by user; and s is the correlation time input by user. In this implementation, OPR along-track and crosstrack accelerations are estimated every 28 min, with r = 1  109 m/s2 and s = 45 min. These values were determined empirically for optimal TP and Jason-1 performance (Luthcke et al., 2003), but with the much more dense and precise DORIS tracking available, a more aggressive approach may even further improve the Jason2 reduced-dynamic orbits. As indicated by independent crossover residuals, the reduced-dynamic orbits show greater radial accuracy over the 10-day arcs (Table 8). Indeed the reduced-dynamic

Fig. 15. Jason-1 and Jason-2 estimated DORIS time bias.

N.P. Zelensky et al. / Advances in Space Research 46 (2010) 1541–1558 Table 8 Jason-2 orbit performance residual summary cycles 1–30 (July 2008–April 2009). Orbit solution

DORIS (mm/s)

SLR (cm)

Crossover (cm) cycles 1–16, 18, 19

GSFC dynamic doris GSFC dynamic slr+doris CNES dynamic slr+doris+gps GSFC RD doris GSFC RD slr+doris JPL RD gps

0.3637 0.3557 – 0.3529 0.3550 –

1.997 1.220 1.147 1.808 1.170 1.250

5.517 5.512 5.523 5.496 5.460 5.362

radial orbits also compare best – the RD SLR/DORIS and DORIS-only radial components are closest to the RD GPS (Table 9, Fig. 16). All orbits compare radially to within 1cm of the RD GPS (Table 9) which show the lowest crossover residuals of 5.362 cm (Table 8). The much larger cross-track differences seen for the obits (Table 9), suggests considerable troposphere error still remains in the DORISonly solutions after taking into account orbit sensitivity to such error (Table 5), and underlines the importance of tropospheric delay models and modeling strategy. Presently the troposphere zenith scale correction is estimated as an independent pass-by-pass parameter. It has been shown,

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for example, that properly constraining the troposphere zenith scale correction estimates over the same geographic region and time window may yield improvement (Zelensky et al., 2000). SLR is a slant range measurement to the satellite capable of sub-centimeter accuracy (Pearlman et al., 2002). Independent high elevation SLR ranges are the only absolute test of radial orbit accuracy at the 1-cm level and have been used to verify the 1-cm Jason-1 GPS POD capability (Luthcke et al., 2003; Haines et al., 2004). In addition to radial orbit error, high elevation SLR residuals will include station position and range bias error. For this reason only the historically well performing baseline SLR stations are selected in order to minimize non-orbit error in the SLR residuals and isolate the radial orbit component accuracy. A globally well distributed set of 9 baseline stations have been selected for two high elevation SLR residual tests of radial accuracy. In the first test, a range bias is estimated for each pass of residuals and summarized by station (Table 10). For this test the previously employed criteria of 60° minimum elevation (Luthcke et al., 2003; Haines et al., 2004) has been relaxed to 50° minimum per pass to allow a significant sampling of high elevation passes

Table 9 Jason-2 RMS orbit differences (cm) cycles 1–30 (July 2008–April 2009).

Table 10 Jason-2 reduced dynamics solution estimated SLR bias/pass RMS (cm) for 9 well distributed stations (minimum elevation >50°; cycles 1–30 (July 2008–April 2009)).

JPL GPS RD -minus-

Radial

Cross-track

Along-track

SLR station

Passes

SLR/DORIS

GPS

DORIS

Dynamic doris (panel) Dynamic slr/doris (panel) Dynamic slr/doris (ucl) Dynamic slr/doris/gps gdrc RD doris RD slr/doris

0.94 0.96 0.95 0.89 0.85 0.70

3.15 2.11 2.17 1.47 3.29 2.00

3.20 3.06 3.02 2.50 2.98 2.54

Haleakala 7119 Hartebeeshoek 7501 Monument peak 7110 Graz 7839 GSFC 7105 Potsdam3 7841 Yarragadee 7090 RGO 7840 Mt Stromlo 7825 Average

5 7 8 22 22 43 59 67 70 34

0.50 1.10 1.12 0.98 1.03 1.17 0.62 0.62 1.01 0.90

1.00 0.85 1.41 0.79 0.93 1.17 0.97 0.74 0.58 0.94

0.60 0.61 1.10 1.10 1.55 1.48 0.83 0.76 1.18 1.02

SLR/DORIS RD -minus-

Radial

Cross-track

Along-track

Dynamic slr/doris (panel) Dynamic slr/doris (ucl)

0.55 0.55

1.06 1.18

1.99 2.03

Fig. 16. Jason-2 radial orbit differences.

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collected over the 30 cycles. Table 10 shows the station statistics are almost all below 1-cm for the GPS orbits, strongly suggesting that GPS POD has achieved 1-cm accuracy. Although the DORIS orbits show more variation in the station statistics the overall average of just over 1-cm suggests DORIS POD is close to that goal. In the second test, SLR residuals are binned by elevation angle using the same nine stations and 4849 points displayed for elevations of 60° and higher (Fig. 17). Fig. 17 shows the DORIS orbit residuals approach 1-cm with the increase in elevation angle, indicating the radial orbit component may be accurate to 1-cm but with the horizontal components having larger error. The number of SLR points rapidly drops off to zero for elevations of 85° and higher. Both tests suggest GPS POD has achieved 1-cm accuracy and DORIS POD may have achieved 1-cm accuracy. Although SLR residuals are not an independent metric for the SLR/DORIS reduced-dynamic orbits, crossover residuals indicate these orbits are more accurate than the DORIS-only (Table 8), and thus are likely to have achieved 1-cm radial accuracy. DORIS POD can be further refined with improved radiation pressure, TVG, and DORIS tropospheric delay models, as well as using a more aggressive reduced-dynamic approach. The RSS crossover residual differences between the dynamic and reduced-dynamic orbits can account for the observed radial orbit differences indicating the orbit differences should largely reflect error in the dynamic orbit. Below we attempt to characterize the orbit error found within the dynamic orbits. Clearly the radial differences between state-of-the-art orbits computed at the three analysis centers – GSFC (Lemoine et al., 2010), CNES (Cerri et al., 2010), and JPL (Bertiger et al, 2010), show the reduced-dynamic orbits agree best and show little signal structure (Fig. 16). The 60-day signal otherwise shown by the RMS of the radial differences (Fig. 16) suggests the dominance of radiation pressure error. Taking the largest orbit differences, which are

between the dynamic SLR-DORIS-GPS CNES and the dynamic SLR-DORIS GSFC orbits (Fig. 16), spectral analysis is performed over two 10-day cycles, over cycle 13 (November 7, 2008) at a peak of the 60-day signal and over cycle 16 (December 7, 2008) in the valley (i.e. a low and high Beta-prime). The periodogram shows similar structure for the prominent signal frequencies for both cycles, and with the peak cycle 13 just having larger amplitudes for the same terms (Fig. 18). What is surprising is the dominance of the m = 1 m-daily terms which are characteristic of gravity short-period gravity perturbations (Kaula, 1966; Goad, 1977). Analysis has shown that non-conservative force perturbations are filtered into an OPR position error term, whereas gravity model error produces a rich spectrum of orbit error signals including the m-daily terms (Colombo, 1986; Marshall et al., 1994a; Lemoine et al., 2006). Both CNES (Cerri et al., 2010) and GSFC (Lemoine et al., 2010) use the EIGEN-GL04S1 static gravity model (Lemoine et al., 2006), however, gravity field variability (including ocean tides) is modeled differently at each center. The m = 1 m-daily terms account for 26% of the orbit difference variance over cycle 13 (Fig. 18). Spectral analysis between the GSFC dynamic, GSFC reduced-dynamic, and JPL reduced-dynamic orbits also show signal structure which includes several m-daily terms, but which is dominated by the OPR term (Fig. 19). The m = 1 m-daily 3-mm amplitude terms indicate the reduced-dynamic technique accommodates some TVG model error (Fig. 19), and especially considering the 3mm RMS magnitude of the residual TVG signal (Section 4). The capability of the RD filter to accommodate error in TVG has also been recently tested (Bertiger et al., 2010), and it is important to note the RMS difference in orbits between modeling/not-modeling TVG is almost an order of magnitude smaller for the JPL GPS RD orbits (Bertiger et al., 2010) than for the SLR/DORIS dynamic orbits (Fig. 12). Since the orbit filter will turn most acting perturbations into a 1/rev orbit signal (Colombo, 1986) it

Fig. 17. Jason-2 SLR residuals for 9 well distributed stations. Cycles 1–30 (July 2008–April 2009).

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Fig. 18. Periodogram of dynamic Jason-2 radial orbit differences (GSFC SLR/DORIS – CNES SLR/DORIS/GPS).

Fig. 19. Periodogram of dynamic/reduced-dynamic Jason-2 radial orbit differences. Cycle 26 (March 2009).

is not possible to identify the perturbation(s) responsible for the 1/rev term. In all likelihood the 1/rev shown in Fig. 19 largely reflects error both in the time varying gravity and radiation pressure models.

Simulations have shown that error in the orbit Z component due to error in the CR scale is poorly removed with the RD filter (Haines et al., 2004). However, examination of the orbit differences between SLR/DORIS dynamic and

Fig. 20. Jason-2 120-day amplitude from dynamic vs. reduced dynamics SLR/DORIS radial orbit differences.

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reduced-dynamic orbits over 36 cycles largely reveals a 120day term of about 4–5 mm amplitude indicating considerable radiation pressure error present in the SLR/DORIS dynamic orbits is removed using the RD filter (Fig. 20). 6. Conclusion The analysis of altimeter data from Jason-1 and Jason-2 requires that the orbits for both missions be in a consistent reference frame, and calculated with the best possible standards to minimize error and maximize the data return from the 7+ year time series, particularly with respect to the demanding application of consistently measuring global sea level change. This paper presents SLR/DORIS orbit modeling improvements for Jason-1/2 and characterizes dominant error remaining in the Jason-2 dynamic orbits. Understanding the nature of remaining orbit error is invaluable in refining the estimates of the mean sea level and its trend and error budget. Analysis shows considerable radiation pressure error signal remains with a period of 120-days coincident with Beta-prime in both the Jason-1 and Jason-2 orbits even after macromodel tuning. The UCL radiation pressure model developed specifically for Jason-1 performs better than the macromodels for both Jason-1 and Jason-2, especially over the low Beta-prime regimes where orbit shadowing is maximum. The 3-mm RMS radial orbit improvement for Jason-1 using UCL is corroborated by improvement in independent altimeter crossover data. The Jason-2 orbit improvements using UCL are very encouraging and suggest the complicated self-shadowing and thermal re-radiation accounted in the UCL model, but not directly so in the macromodels, are required for correctly modeling surface forces due to radiation and radiation pressure. We plan to collaborate with UCL to refine a radiation pressure model designed for Jason-2. Also given the current level of POD accuracy, it may be necessary to consider modeling planetary radiation pressure with more detail than the simple model of Knocke et al. (1988). The operational Time Varying Gravity model represents atmospheric gravity, changes in hydrology, and wind-forcing changes in ocean mass. It was developed by forward modeling the atmospheric gravity, using a model of the air tides, and a 20  20 field estimated with four years of GRACE data to capture the remaining annual variations. Jason-1 tests show such an operational TVG model is critical to achieving state-of-the-art POD, however, it may not be complete. A more complete, but not operationally viable model was constructed by including the background hydrology and barotropic ocean models before estimating 60  60 monthly fields using GRACE data. The difference in Jason-1 orbits between using these two models shows a prominent annual signal having a 2.5 mm amplitude, and suggests about 1/3 of the TVG signal is not represented in the operational model. We plan to test improving the operational model by including all available and possibly improved background models, including a longer time ser-

ies of GRACE data, and possibly expanding the 20  20 GRACE-derived field. This paper also addresses DORIS sensitivity to error in tropospheric path delay and the enhanced performance of the DGXX DORIS receiver on-board Jason-2. We show estimates of the DORIS antenna Z-offset and of GM are very sensitive to tropospheric path delay error. Although orbit sensitivity to such error is largely in the cross-track direction with only small perturbations to the radial, such sensitivity suggests tropospheric path delay error may prove to be a limiting factor to state-of-the-art DORIS recovery of station positions and TRF scale. The concern is not having the ability to compute the wet component of the path delay to suitable accuracy. Our tests suggest the DORIS-supplied meteorological data are not reliable. This is an issue that is known in the DORIS community and is likely due to infrequent calibration of the met sensors due to cost and the remote location of many DORIS sites. We plan to test the more recent tropospheric path delay models, and to refine our troposphere scale estimation strategy. We have also shown that trends in the Jason-1 estimated DORIS antenna Z-offset can also serve as an indicator of deteriorating oscillator health. The latest DORIS DGXX receiver on-board Jason-2 can simultaneously observe transmissions from up to seven beacons, significantly improving the tracking coverage and the satellite observing geometry. Indeed, tests using SLR and altimeter crossover residuals suggest the Jason-2 reduced-dynamic GPS, SLR/DORIS, and DORIS-only orbits have all achieved 1-cm radial accuracy. Tests using independent SLR data acquired at high elevation over 30 cycles show an average fit value of 0.94 cm for the GPS and 1.02 cm for the DORIS-only reduced-dynamic orbits. Evaluation of the Jason-2 orbit differences shows the reduced-dynamic filter removes considerable radiation pressure and TVG model error, and that these two sources of error dominate the dynamic orbits. Over 25 years of modern satellite altimetry, improvements in orbit accuracy and altimeter data analysis have occurred concurrently, from the detailed mapping of sea mounts with 35 cm GEOSAT orbits, to mm/yr sea level change determination with 2 cm TP orbits. The empirically determined sea-state bias correction for the altimeter data depends directly on the quality of the altimeter satellite orbits. Today, Jason-1 and Jason-2 orbits produced by different analysis centers, that employ different tracking systems and use different orbit determination software packages, and apply different analysis strategies, all agree radially at 1 cm. The new orbits will permit the derivation of improved sea-state bias correction models and ocean tide models, and will reveal new information about the subtleties of satellite radar altimeter tracking algorithms. Acknowledgements This work is based on SLR, DORIS, and GPS observations of the Jason-1 and Jason-2 satellites. We acknowledge

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the International Laser Ranging Service (ILRS) the International GNSS Service (IGS), and the International DORIS Service (IDS), for providing such data. This work was supported by the US National Aeronautics and Space Administration under the auspices of the Ocean Surface Topography Science Team and the IDS Program in Mean Sea Level. Part of this work was supported by the Centre National d’Etudes Spatiales (CNES) using DORIS data. A. Sibthorpe’s contribution, supported by NERC (Natural Environment Research Council) Grant #NE/C519138/1, was performed while at University College London, UK. This paper is IPGP contribution number 2565. The authors are grateful for the long standing collaboration with the OSTST POD Team members, CNES, JPL, and UT CSR. References Adhya, S., Ziebart, M., Cross, P. Thermal force modeling for precise prediction and determination of spacecraft orbits. Navigation 52 (3), 131–144, 2005. Altamimi, Z., Collilieux, X., Boucher, C. DORIS contribution to ITRF2005. J. Geod. 80 (8–11), 625–635, doi:10.1007/s00190-0060065-5, 2006. Altamimi, Z.ITRF2005, Collilieux, X., Legrand, J., et al. A new release of the International Terrestrial Reference Frame based on time series of station positions and earth orientation parameters. J. Geophys. Res. 112 (B9), B09401, 2007. Antreasian, P.G., Rosborough, G.W. Prediction of radiant energy forces on the TOPEX/Poseidon spacecraft. J. Spacecraft Rockets 29 (1), 81– 90, 1992. Auriol, A., Tourain, C. DORIS system: the new age. Adv. Space Res. 46 (12), 1484–1496, doi:10.1016/j.asr.2010.05.015, 2010. Beckley, B.D., Zelensky, N.P., Luthcke, S.B., et al. Towards a seamless transition from TOPEX/POSEIDON to Jason-1. Mar. Geod. 27 (3–4), 373–389, 2004. Beckley, B.D., Lemoine, F.G., Luthcke, S.B., Ray, R.D., Zelensky, N.P. A reassessment of TOPEX and Jason-1 altimetry based on revised reference frame and orbits. Geophys. Res. Lett. 34, L14608, doi:10.1029/2007GL030002, 2007. Beckley, B.D., Zelensky, N.P., Holmes, S.A., et al. Assessment of the Jason-2 extension to the TOPEX/Poseidon, Jason-1 sea-surface height time series for global mean sea level monitoring. Part 1. Mar. Geod., 33 (Suppl.) Special issue on the Jason-2 calibration/validation, in press, doi:10.1080/01490419.2010.491029. Berthias, J.P., Broca, P., Ferrier, C., et al. JASON-1: a new reference for precise orbit determination, in: IAF Abstracts, 34th COSPAR Scientific Assembly, The Second World Space Congress, Houston, TX, USA, October 2002. Bertiger, W.I., Bar-sever, Y.E., Christensen, E.J., et al. GPS precise tracking of TOPEX/Poseidon: results and implications. J. Geophys. Res. 99 (C12), 24449–24464, 1994. Bertiger, W.I., Haines B, Desai S., et al. GPS based precise orbit determination: Jason-1 status, in: Presentation, OSTST Venice, March 2006. Bertiger, W.I., Desai, S., Dorsey, A., et al. Sub-centimeter precision orbit determination with GPS for ocean altimetry. Part 1, Mar. Geod. 33 (Suppl.) Special issue on the Jason-2 calibration/validation, doi:10.1080/01490419.2010.487800, 2010. Boehm, J., Niell, A., Tregoning, P., et al. Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys. Res. Lett. 33 (7), L07304, 2006a. Boehm, J., Werl, B., Schuh, H. Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. J. Geophys. Res. 111, B02406, doi:10.1029/2005JB003629, 2006b.

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