GRACE Gradiometer

  • M.A. Sharifi
  • W. Keller
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 129)


Improving the accuracy of the spherical harmonic coefficients of the Earth’s gravity field and its temporal variations at long and medium spatial-scales with unprecedented accuracy is the primary science objective of the GRACE mission. The line of sight (LOS) acceleration difference between the satellite pair is the most frequently utilized form of the observable. It is the simplest form of the observable which can be easily employed. Nevertheless, the observable is a two-point function and has no direct relationship with the field geometry at the evaluation point.

In this paper, as the alternative, gradiometry approach is proposed. Being a one-point function and having a direct relation with the field geometry (curvature of the field at the point) are two noteworthy achievements of the alternative formulation. Besides, using an observation quantity that is related to the second instead of the first-order derivatives of the gravitational potential amplifies the high-frequency part of the signal.

Complexity of the derived mathematical model and its proper treatment is the severe problem for the gradiometry approach. Herein, mixed gravitational acceleration-gradient model and also use of the available Earth’ gravity model as a priori information on the low-degree harmonics are addressed.

The first recently released EIGEN2 CHAMP-only Earth’s gravity model was employed for numerical analysis. Error analysis showed that the residuals of the estimated degree variances were of about 10−4 for n≤ 90. Also, the gravity anomaly residuals were less than 5 mGal for most points on the Earth.


GRACE Gradiometer Gradiometry Sequential solution 


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  1. Garcia, R. V. (2002). Local Geoid Determination from GRACE Mission. Report No. 460, Dept. of Geod. Sci., Ohio State University, Columbus.Google Scholar
  2. Hajela, D. P. (1974). Improved Procedures for the recovery of 5° mean gravity anomalies from ATS-6/GEOS-3 satellite-to-satellite range-rate observation. Report No. 276, Dept. of Geod. Sci., Ohio State University, Columbus.Google Scholar
  3. Han, S. C, Jekeli, C, Shum, C. K., (2003). Static and temporal gravity field recovery using grace potential difference observables. Advances in Geosciences, 1: 19–26.CrossRefGoogle Scholar
  4. Ilk, K. H., Visser, P., Kusche, J. (2003). Satellite Gravity Field Missions. Final Report Special Commission 7, Travaux IAG, Vol. 32, general and technical reports 1999–2003, Sapporo.Google Scholar
  5. Keller, W., Heß, D. (1998). Gradiometrie mit GRACE. ZfV 124: 137–144.Google Scholar
  6. Keller, W. Sharifi, M. A. (2004). Satellite Gradiometry Using a Satellite Pair. J. Geodesy, under review.Google Scholar
  7. Lemoine, F. G., Kenyon, S. C, Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., Cox, C. M., Klosko, S. M., Luthcke, S. B., Torrence, M. H., Wang, Y. M., Williamson, R. G., Pavlis, E. C, Rapp, R. H., Olson, T. R. (1998). The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. NASA/TP-1998-206861, National Aeronautics and Space Administration, Washington, DC.Google Scholar
  8. Reigber, C, Schwintzer, P., Neumayer, K.-H., Barthelmes, F., König, R., Förste, C, Balmino, G., Biancle, R., Lemoine, J.-M., Loyer, S., Bruinsma, S., Perosanze, F., and Fayard, T. (2003). The CHAMP-only Earth gravity field model EIGEN2. Adv. Space Res. accepted.Google Scholar
  9. Rummel R, Reigber, C., Ilk, K. H. (1978). The Use of Satellite-to-satellite Tracking for Gravity Parameter Recovery. Proc. of the European workshop on Space Oceanography, Navigation and Geodynamics, ESA SP-137, pp. 153–161.Google Scholar
  10. Rummel, R. (1980). Geoid height, Geoid height differences, and mean gravity anomalies from “low-low” satellite-to-satellite tracking-an error analysis. Report No. 306, Dept. of Geod. Sci., Ohio State University, Columbus.Google Scholar
  11. Rummel, R., Balmino, G., Johannessen, J., Visser, P., Woodworth, P. (2002). Dedicated Gravity Field Missions-Principles and Aims, J. Geodynamics 33: 3–20.CrossRefGoogle Scholar
  12. Rummel, R. (2003). How to Climb the Gravity Wall. Space Science Reviews, vol. 108: 1–14.CrossRefGoogle Scholar
  13. Wolff M (1969). Direct Measurements of the Earth’s Gravitational Potential Using a Satellite Pair. J. Geophys Res., 74: 5295–5300.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M.A. Sharifi
    • 1
  • W. Keller
    • 1
  1. 1.Department of Geodesy and GeolnformaticsUniversity of StuttgartStuttgartGermany

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