Advertisement

Upward Continuation of Ground Data for GOCE Calibration/Validation Purposes

  • K.I. Wolf
  • H. Denker
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 129)

Abstract

With the upcoming ESA satellite mission GOCE, gravitational gradients (2nd derivatives of the Earth’s gravitational potential) will be measured globally, except for the polar gaps. An accuracy of a few mE (1 mE = 10−3 Eötvös, 1 E = 10−9s−2) is required to derive, in combination with satellite-to-satellite tracking (SST) measurements, a global geopotential model up to about spherical harmonic degree 200 with an accuracy of 1 … 2 cm in terms of geoid undulations and 1 mgal for gravity anomalies, respectively.

To meet these requirements, the gradiometer will be calibrated and validated internally as well as externally. One strategy for an external calibration or validation includes the use of ground data upward continued to satellite altitude. This strategy can only be applied regionally, because sufficiently accurate ground data are only available for selected areas.

In this study, gravity anomalies over Europe are upward continued to gravitational gradients at GOCE altitude. The computations are done with synthetic data in a closed-loop simulation. Two upward continuation methods are considered, namely least-squares collocation and integral formulas based on the spectral combination technique. Both methods are described and the results are compared numerically with the ground-truth data.

Keywords

gradiometry upward continuation least-squares collocation spectral combination GOCE calibration validation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arabelos, D. and Tscherning, C. C. (1998). Calibration of Satellite Gradiometer Data Aided by Ground Gravity Data. Journal of Geodesy, (72):617–625.CrossRefGoogle Scholar
  2. Brenner, P., Mehrmann, V., Sima, V, Van Huffel, S., and Varga, A. (1999). SLICOT — A Subroutine Library in Systems and Control Theory. Report 97-3, NICONET.Google Scholar
  3. de Min, E. (1995). A Comparison of Stokes’ Numerical Integration and Collocation, and a new Combination Technique. Bulletin Géodésique, (69):223–232.CrossRefGoogle Scholar
  4. Denker, H. (2003). Computation of Gravity Gradients Over Europe For Calibration/Validation of GOCE Data. In Proceedings of the Gravity and Geoid Meeting of the IAG, Thessaloniki, August 26–30, 2002, pages 287–292.Google Scholar
  5. Ditmar, P. and Klees, R. (2002). A Method to Compute the Earth’s Gravity Field from SGG/STT Data to be Acquired by the GOCE Satellite. Delft university press, Delft.Google Scholar
  6. Haagmans, R., de Min, E., and van Gelderen, M. (1993). Fast Evaluation of Convolution Integrals on the Sphere Using 1D FFT, and a Comparison With Existing Methods for Stokes’ Integral, manuscripta geodaetica, 18(5):227–241.Google Scholar
  7. JPL (2003). JPL — GRACE Homepage, Jet Propulsion Laboratory. http://podaac.jpl.nasa.gov/grace/.Google Scholar
  8. 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., and Olson, T. R. (1998). The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96. Technical Paper NASA/TP-1998-206861, NASA.Google Scholar
  9. Moritz, H. (1971). Kinematical Geodesy II. Department of Geodetic Science, Ohio State University, Report 165.Google Scholar
  10. Moritz, H. (1976). Integral Formulas and Collocation. manuscripta geodaetica, 1(1): 1–40.Google Scholar
  11. Moritz, H. (1980). Advanced Physical Geodesy. Herbert Wichmarm Verlag, Karlsruhe.Google Scholar
  12. Pail, R. (2002). In-orbit Calibration and Local Gravity Field Continuation Problem. In ESA From Eötvös to Milligal+ Final Report, Contract 14287/00/NL/GD, pages 9–112. ESA/ESTEC.Google Scholar
  13. Thalhammer, M. (1994). The Geographical Truncation Error in Satellite Gravity Gradiometer Measurements. manuscripta geodaetica, (19):45–54.Google Scholar
  14. Tscherning, C. C. (1976a). Computation of the Second-Order Derivatives of the Normal Potential Based on der Representation by Legendre Series. manuscripta geodaetica, l(2):71–92.Google Scholar
  15. Tscherning, C. C. (1976b). Covariance Expressions for Second and Lower Order Derivatives of the Anomalous Potential. Department of Geodetic Science, Ohio State University, Report 225.Google Scholar
  16. Tscherning, C. C. and Rapp, R. H. (1974). Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models. Department of Geodetic Science, Ohio State University, Report 208.Google Scholar
  17. Wenzel, H.-G. (1982). Geoid Computation by Least-Squares Spectral Combination Using Integral Kernels. In Proceedings of the General Meeting of the IAG, Tokyo, May 7–15, 1982, IAG Symposia, pages 438–453. Springer Verlag.Google Scholar
  18. Wenzel, H.-G. (1985). Hochauflösende Kugelfunktionsmodelle für das Gravitationspotential der Erde. Wiss. Arb. der Fachr. Verm.wesen der Univ. Hannover 137.Google Scholar
  19. Wenzel, H.-G. (1999). Schwerefeldmodellierung durch ultra hochauflösende Kugelfunktionsmodelle. Zeitschrift für Vermessungswesen, 124(5):144–154.Google Scholar
  20. Wolf, K. I. and Müller, J. (2004). Prediction of Gravitational Gradients Using Simulated Terrestrial Data for GOCE Calibration. In Meurers, B. and Pail, R., editors, Österreichische Beiträge zu Meteorologie und Geophysik, Proceedings of the 1st Workshop on International Gravity Field Research, Graz, May 8–9 2003, volume 31, pages 31–36. Zentralanstalt für Meteorologie und Geodynamik.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • K.I. Wolf
    • 1
  • H. Denker
    • 1
  1. 1.Institut für ErdmessungUniversity of HannoverHannoverGermany

Personalised recommendations