Efficient Global Gravity Determination from Satellite-to-Satellite Tracking (SST)
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Date
2003-09
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Ohio State University. Division of Geodetic Science
Abstract
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
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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.
Description
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.
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.