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In this note, we reply to the preceding paper by Iorio: "Some considerations on the present-day results for the detection of frame-dragging after the final outcome of GP-B, Europhysics Letters", we address criticisms regarding the Lense-Thirring frame-dragging experiment results obtained from the laser ranging to the two LAGEOS satellites.

Since the official start of the International DORIS Service (IDS) in 2003, several Analysis Centers have submitted time series of station coordinates in SINEX format. We discuss here the different DORIS weekly solutions available for ITRF 2004 and for the IERS Combinationa Campaign Project.

Activities of this Working Group include the investigation of the status quo and the development of a plan for full network integration to support improvements in terrestrial reference frame establishment and maintenance, Earth orientation and gravity field monitoring, precision orbit determination, and other geodetic and gravimetric applications required for the long-term observation of global change. This integration process includes the development of a network of fundamental stations with as many co-located techniques as possible, with precisely determined intersystem vectors. This network would exploit the strengths of each technique and minimize the weaknesses where possible. This paper discusses the organization of the working group, the work done to date, and future tasks.

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10-day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1-year mean topography, produced using four of the most accurate of the marine geoid, show that the largest error in the dynamic ocean topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10-day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the El Nino. Comparison of TOPEX-determine sea surface height at points near oceanic tide gauges shows agreement at the 4 cm root-mean-square (RMS) level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is insonsistent with traditional in situ methods for the determination of sea level variations.

The TOPEX/POSEIDON mission objective requires that the radial position of the spacecraft be determined with an accuracy better than 13 cm RMS (root mean square). This stringent requirement is an order of magnitude below the accuracy achieved for any altimeter mission prior to the definition of the TOPEX/POSEIDON mission. To satislfy this objective, the TOPEX Precision Orbit determination (POD) Team was established as a joint effort between the NASA Goddard Space Flight Center and the University of Texas at Austin, with collaboration from the University of Colorado and the Jet Propulsion Laboratory. During the prelaunch development and the post launch verification phases, the POD team improved, calibrated, and validated the precision orbit determination computer software systems. The accomplishments include (1) increased accuracy of the gravity and surface force models and (2) improved peformance of both laser ranging and Doppler tracking systems. The result of these efforts led to orbit accuracies for TOPEX/POSEIDON which are significantly better than the original mission requirement. Tests based on data fits, covariance analysis, and orbit comparisons indicate that the radial component of the TOPEX/POSEIDON spacecraft is determined, relative to the Earth's mass center, with an root mean square (RMS) error in the range of 3 to 4 cm RMS. This orbit accuracy, together with the near continuous dual-frequency altimetry from this mission, provides the means to determine the ocean's dynamic topography with an unprecedented accuracy.

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being +/- 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm root mean square (RMS), a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

Follow-on missions to provide continuity in the observation of the sea surface topography once the successful TOPEX/POSEIDON (T/P) oceanographic satellite mission has ended are discussed. Candidates include orbits which follow the ground tracks of T/P GEOSAT or ERS-1. The T/P precision ephemerides, estimated to be near 3 cm root-mean-square, demonstrate the radial orbit accuracy that can be achieved at 1300 km altitude. However, the radial orbit accuracy which can be achieved for a mission at the 800 km altitudes of GEOSAT and ERS-1 has not been established, and achieving an accuracy commensurate with T/P will pose a great challenge. This investigation focuses on the radial orbit accuracy that can be achieved for a mission in the GEOSAT orbit. Emphasis is given to characterizing the effects of force model errors on the estimated radial orbit accuracy, particularly those due to gravity and drag. The importance of global, continuous tracking of the satellite for reduction in these sources of orbit error is demonstrated with simulated GPS tracking data. A gravity tuning experiment is carried out to show how the effects of gravity error may be reduced. Assuming a GPS flight receiver with a full-sky tracking capability, the simulation results indicate that a 5 cm radial orbit accuracy for an altimeter satellite in GEOSAT orbit should be achievable during low-drag atmospheric conditions and after an acceptable tuning of the gravity model.

A technique which employs dual satellite crossover measurements from ERS-1 and Topology Ocean Experiment (TOPEX)/Poseidon together with laser tracking data and single satellite crossover measurements for ERS-1 precision orbit determination is described. The accuracy assessment of the resulting ERS-1 orbit is provided. Results of global verification of the ERS-1 Ocean Products (OPR02) and the Interim Geophysical Data Records (IGDR) data products in terms of altimeter bias, time lag bias and sea state bias are presented.

Large scale dynamic ocean topography and its variations were observed using ERS-1 radar altimeter measurements. The altimeter measurements analyzed are primarily from the ESA ocean product (OPR02) and from the Interim Geophysical Data Records (IGDR) generated by NOAA from the fast delivery (FD) data during the ERS-1 35 day repeat orbit phase. The precise orbits used for the dynamic topography solution are computed using dual satellite crossover measurements from ERS-1 and TOPEX (Topology Ocean Experiment)/Poseidon (T/P) as additional tracking data, and using improved models and constants which are consistent with T/P. Analysis of the ERS-1 dynamic topography solution indicates agreement with the T/P solution at the 5 cm root mean square level, with regional differences as large as 15 cm tide gauges at the 8 to 9 cm level. There are differences between the ERS-1 OPR02 and IGDR determined dynamic topography solutions on the order of 5 cm root mean square. Mesoscale oceanic variability time series obtained using collinear analysis of the ERS-1 altimeter data show good qualitative agreement when compared with the T/P results.

The ability of the French DORIS system operating on the SPOT-2 satellite to provide absolute site positioning at the 20-30-centimeter level using 80 d of data is demonstrated. The accuracy of the vertical component is comparable to that of the horizontal components, indicating that residual troposphere error is not a limiting factor. The translation parameters indicate that the DORIS network realizes a geocentric frame to about 50 nm in each component. The considerable amount of data provided by the nearly global, all-weather DORIS network allowed this complex parameterization required to reduce the unmodeled forces acting on the low-earth satellite. Site velocities with accuracies better than 10 mm/yr should certainly be possible using the multiyear span of the SPOT series and Topex/Poseidon missions.

In most of the recent determinations of the geocentric gravitational coefficient (GM) of the earth, the laser ranging data to the Lageos satellite have had the greatest influence on the solution. These data, however, have generally been processed with a small but significant error in one of the range corrections. In a new determination of GM using the corrected center-of-mass offset, a value of 398600.4415 cu km/sq sec (including the mass of the atmosphere) has been obtained, with an estimated uncertainty (1 sigma of 0.0008 cu km/sq sec.

Precise ephemerides have been determined for the U.S. Navy Geosat Exact Repeat Mission (ERM) using an improved gravity-field model, PTGF-4A (Shum et al. 1989). The Geosat orbits were computed in a terrestrial reference system which is tied to the reference system defined by satellite laser ranging (SLR) to Lageos through a survey between the Tranet Doppler receiver and the SLR system located at Wettzell, FRG. The remaining Doppler tracking station coordinates were estimated simultaneously with the geopotential in the PTGF-4A solution. In this analysis, three continuous 17-day Geosat orbits, which were computed using the 46-station Tranet data and global altimeter crossover data, have a crossover residual rms of 20 cm, indicating that the Geosat radial orbit error is of the order of 20 cm. The orbits computed based on data collected by a 7-station OPNET tracking network and crossover data have the same level of accuracy.

Whether one uses a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of three years of laser tracking data taken on the Lageos satellite. It is demonstrated that the simpler formulation in the geocentric frame is adequate for the purpose of near-earth satellite orbit determination. A correction to the conventional barycentric equations of motion is shown to be required.

The ability of radar altimeters to measure the distance from a satellite to the ocean surface with a precision of the order of 2 cm imposes unique requirements for the orbit determination accuracy. The orbit accuracy requirements will be especially demanding for the joint NASA/CNES Ocean Topography Experiment (Topex/Poseidon). For this mission, a radial orbit accuracy of 13 centimeters will be required for a mission period of three to five years. This is an order of magnitude improvement in the accuracy achieved during any previous satellite mission. This investigation considers the factors which limit the orbit accuracy for the Topex mission. Particular error sources which are considered include the geopotential, the radiation pressure and the atmospheric drag model.

An improved model for the Earth's gravity field, TEG-1, was determined using data sets from fourteen satellites, spanning the inclination ranges from 15 to 115 deg, and global surface gravity anomaly data. The satellite measurements include laser ranging data, Doppler range-rate data, and satellite-to-ocean radar altimeter data measurements, which include the direct height measurement and the differenced measurements at ground track crossings (crossover measurements). Also determined was another gravity field model, TEG-1S, which included all the data sets in TEG-1 with the exception of direct altimeter data. The effort has included an intense scrutiny of the gravity field solution methodology. The estimated parameters included geopotential coefficients complete to degree and order 50 with selected higher order coefficients, ocean and solid Earth tide parameters, Doppler tracking station coordinates and the quasi-stationary sea surface topography. Extensive error analysis and calibration of the formal covariance matrix indicate that the gravity field model is a significant improvement over previous models and can be used for general applications in geodesy.

Laser range, Doppler, and altimeter data collected from 14 near-earth satellites have been combined to determine the value of the geocentric gravitational coefficent (GM) of the earth. A long-arc solution using three years of laser range data to Lageos was used in a separate determination in which the effects of general relativity were invetigated. The value of GM (including the mass of the atmosphere) was determined to be 398600.4405 cu km/sq sec when all corrections for general relativity are taken into account. The uncertainty (1-sigma) in the value of GM is estimated to be 0.001 cu km/sq sec.

With the development of satellite altimetry, it is possible to infer the geostrophic velocity of the surface ocean currents, if the geoid and the position of the satellite are known accurately. Errors in current geoid models and orbit computations, both due primarily to errors in the earth's gravity field model, have limited the use of altimeter data for this purpose. The objective of this investigation is to demonstrate that altimeter data can be used in a joint solution to simultaneously estimate the quasi-stationary sea surface topography, zeta, and the model for the gravity field. Satellite tracking data from twelve satellites were used along with Seasat altimeter data for the solution. The estimated model of zeta compares well at long wavelengths with the hydrographic model of zeta. Covariance analysis indicates that the geoid is separable from zeta up to degree 9, at which point geoid error is comparable to the signal of zeta.

Whether one uses a solar-system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determinations for near-Earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of real laser-tracking data. A correction to the conventional barycentric equations of motion is shown to be required.

A diffuse-earth radiation force model is presented, which includes a latitudinally varying representation of the shortwave and longwave radiation of the terrestrial sphere. Applications to various earth satellites indicate that this force, in particular the shortwave component, can materially affect the recovery of estimated parameters. Earth radiation pressure cannot explain the anomalous deceleration of LAGEOS, but can produce significant along track accelerations on satellites with highly eccentric orbits. Analyses of GEOS-1 tracking data confirm this result.

The orbit determination requirements for the Ocean Topography Experiment (Topex/Poseidon) are discussed. A radial orbit accuracy of 13 cm for a period of three to five years is required for the mission. The factors which limit the orbit accuracy for the geopotential, the solar radiation pressure, and the atmospheric drag model are examined. Also, the effects introduced by variations with aspect angle in the spacecraft area-to-mass ratio are considered.

A technique for monitoring changes in global mean sea levels using altimeter data from a well-tracked satellite is examined. The usefulness of this technique is evaluated by analyzing Seasat altimeter data obtained during July-September 1978. The effects of orbit errors, geoid errors, sampling intervals, tides, and atmosphere refraction on the calculation of the mean sea level are investigated. The data reveal that the stability of an altimeter can be determined with an accuracy of + or - 7 cm using globally averaged sea surface height measurements. The application of this procedure to the US/French Ocean Topography Experiment is discussed.