Abstract
Spectral analysis of data noise is performed in the context of gravity field recovery from inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. The motivation of the study is two-fold: (i) to promote a further improvement of GRACE data processing techniques and (ii) to assist designing GRACE follow-on missions. The analyzed noise realizations are produced as the difference between the actual GRACE inter-satellite range measurements and the predictions based on state-of-the-art force models. The exploited functional model is based on the so-called “range combinations,” which can be understood as a finite-difference analog of inter-satellite accelerations projected onto the line-of-sight connecting the satellites. It is shown that low-frequency noise is caused by limited accuracy of the computed GRACE orbits. In the first instance, it leads to an inaccurate estimation of the radial component of the inter-satellite velocities. A large impact of this component stems from the fact that it is directly related to centrifugal accelerations, which have to be taken into account when the measured range-accelerations are linked with inter-satellite accelerations. Another effect of orbit inaccuracies is a miscalculation of forces acting on the satellites (particularly, the one described by the zero-degree term of the Earth’s gravitational field). The major contributors to the noise budget at high frequencies (above 9 mHz) are (i) ranging sensor errors and (ii) limited knowledge of the Earth’s static gravity field at high degrees. Importantly, we show that updating the model of the static field on the basis of the available data must be performed with a caution as the result may not be physical due to a non-unique recovery of high-degree coefficients. The source of noise in the range of intermediate frequencies (1–9 mHz), which is particularly critical for an accurate gravity field recovery, is not fully understood yet. We show, however, that it cannot be explained by inaccuracies in background models of time-varying gravity field. It is stressed that most of the obtained results can be treated as sufficiently general (i.e., applicable in the context of a statistically optimal estimation based on any functional model).
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Acknowledgments
High-precision kinematic orbits of GRACE satellites used as an input in the presented study were computed by Dr. Qile Zhao. The script for a spline approximation of piece-wise constant monthly solutions in the time domain was written by Dr. Christian Siemes. We thank also the GNSS Research and Engineering Center of Wuhan University for providing us with the PANDA software for satellite orbit integration. In addition, we thank three anonymous reviewers and prof. Jürgen Kusche, the handling editor, for the help in improving the manuscript. The work was sponsored by the Stichting Nationale Computerfaciliteiten (National Computing Facilities Foundation, NCF) for the use of supercomputer facilities, with financial support from the Nederlandse organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research, NWO).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ditmar, P., Teixeira da Encarnação, J. & Hashemi Farahani, H. Understanding data noise in gravity field recovery on the basis of inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. J Geod 86, 441–465 (2012). https://doi.org/10.1007/s00190-011-0531-6
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DOI: https://doi.org/10.1007/s00190-011-0531-6