Efficient Global Gravity Determination from Satellite-to-Satellite Tracking (SST)

• Main Author: Han, Shin-Chan
• Format: Report
• Language: English
• Published: Ohio State University. Division of Geodetic Science 2003
• Subjects: Arctic
• Online Access: http://hdl.handle.net/1811/78648

This report was prepared by Shin-Chan Han, a graduate student, Department Civil and Environmental Engineering and Geodetic Science, under the supervision of Professors C. Jekeli and C.K. Shum. This research is supported by grants from the Center for Space Research, University of Texas under a prime contract from NASA (CSR/GRACE #735367), and from NASA's Solid Earth and Natural Hazards Program (NASA/GRACE #736312). This report was also submitted to the Graduate School of Ohio State University as a thesis in partial fulfillment of the requirements for the degree Doctor of Philosophy. By the middle of this decade, measurements from the CHAMP (CHAllenging of Minisatellite Payload) and GRACE (Gravity Recovery And Climate Experiment) gravity mapping satellite missions are expected to provide a significant improvement in our knowledge of the Earth's mean gravity field and its temporal variation. For this research, new observation equations and efficient inversion method were developed and implemented for determination of the Earth’s global gravity field using satellite measurements. On the basis of the energy conservation principle, in situ (on-orbit) and along track disturbing potential and potential difference observations were computed using data from accelerometer- and GPS receiver-equipped satellites, such as CHAMP and GRACE. The efficient iterative inversion method provided the exact estimates as well as an approximate, but very accurate error variance-covariance matrix of the least squares system for both satellite missions. The global disturbing potential observable computed using 16-days of CHAMP data was used to determine a 50´50 test gravity field solution (OSU02A) by employing a computationally efficient inversion technique based on conjugate gradient. An evaluation of the model using independent GPS/leveling heights and Arctic gravity data, and comparisons with existing gravity models, EGM96 and GRIM5C1, and new models, EIGEN1S and TEG4 which include CHAMP data, indicate that OSU02A is commensurate in geoid accuracy and, like other new models, it yields some improvement (10% better fit) in the polar region at wavelengths longer than 800 km. The annual variation of Earth’s gravitational field was estimated from 1.5 years of CHAMP data and compared with other solutions from satellite laser ranging (SLR) analysis. Except the second zonal and third tesseral harmonics, others second and third degree coefficients were comparable to SLR solutions in terms of both phase and magnitude. The annual geoid change of 1 mm would be expected mostly due to atmosphere, continental surface water, and ocean mass redistribution. The correlation between CHAMP and SLR solutions was 0.6~0.8 with 0.7 mm of RMS difference. Although the result should be investigated by analyzing more data for longer time span, it indicates the significant contribution of CHAMP SST data to the time-variable gravity study. Considering the energy relationship between the kinetic and frictional energy of the satellite and the gravitational potential energy, the disturbing potential difference observations can be computed from the orbital state vector, using high-low GPS tracking data, low-low satellite-to-satellite GRACE measurements, and data from 3-axis accelerometers. Based on the monthly GRACE simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 6~7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The temporal gravity field, representing the monthly mean continental water mass redistribution, was recovered in the presence of measurement noise and high iii frequency temporal variation. The resulting recovered temporal gravity fields have about 0.2 mm errors in terms of geoid height with a resolution of 670 km. It was quantified that how significant the effects due to the inherent modeling errors and temporal aliasing caused by ocean tides, atmosphere, and ground surface water mass are on monthly mean GRACE gravity estimates. The results are based on simulations of GRACE range-rate perturbations due to modeling error along the orbit; and, their effects and temporal aliasing on the estimated gravitational coefficients were analyzed by fully inverting monthly simulated GRACE data. For ocean tides, the study based on the model difference, CSR4.0–NAO99, indicates that some residual constituents like in S2 may cause errors 3 times larger than the measurements noise at harmonic degrees less than 15 in the monthly mean estimates. On the other hand, residual constituents in K1, O1, and M2 are reduced by monthly averaging below the measurement noise level. For the atmosphere, the difference in models, ECMWF–NCEP, produces errors in GRACE range-rate measurements as strong as the measurement noise. They corrupt all recovered coefficients and introduce 30 % more error in the global monthly geoid estimates up to maximum degree 120. However, the analysis based on daily CDAS-1 data for continental surface water mass redistribution indicates that the daily soil moisture and snow depth variations affect the monthly mean GRACE recovery less than the measurement noise.