Skip to main content
Log in

GOCE Quick-Look Gravity Solution: Application of the Semianalytic Approach in the Case of Data Gaps and Non-Repeat Orbits

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

The satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), the first Core Mission of the Earth Explorer Programme funded by ESA (European Space Agency), is dedicated to the precise modelling of the Earth's gravity field, with its launch planned for 2006. The mathematical models for parameterizing the Earth's gravity field are based on a series expansion into spherical harmonics, yielding a huge number of unknown coefficients. Their computation leads to the solution of very large normal equation systems. An efficient way to handle these equation systems is the so-called semianalytic or lumped coefficients approach, which theoretically requires an uninterrupted, continuous time series of observations, recorded along an exact circular repeat orbit. In this paper the consequences of violating these conditions are analyzed. The effects of an interrupted observation stream onto the estimated spherical harmonic coefficients are demonstrated, and an iterative strategy, which reduces the negative influence depending on the characteristics of the data gaps, is proposed. Additionally, the impact of an imperfectly closing orbit (non-repeat orbit) on the gravity field model is analyzed, and a strategy to minimize the corresponding errors is presented. The applicability of the semianalytic approach also to a joint inversion of satellite-to-satellite tracking data in high-low mode (hl-SST) and satellite gravity gradiometry (SGG) observations is demonstrated, where the analysis of the former component is based on the energy conservation law. Several realistic case studies prove that the semianalytic approach is a feasible tool to generate quick-look gravity solutions, i.e. fast coefficient estimates using only partial data sets. This quick-look analysis shall be able to detect potential distortions of statistical significance (e.g. systematic errors) in the input data, and to give a fast feedback to the GOCE mission control.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arsov K., Badura T., Höck E., Pail R., Rothacher M. and Švehla D., 2002. Effect of Temporal Variations on High-low SST observations. Final Report, ESA/ESTEC Contract 14287/00/NL/DC, European Space Agency, 217-319.

  • Cesare S., 2002. Performance requirements and budgets for the gradiometric mission. Technical Note, GOC-TN-AI-0027, Alenia Spazio, Turin, Italy.

    Google Scholar 

  • ESA, 1999. Gravity Field and Steady-State Ocean Circulation Mission. Reports for Mission Selection. The four candidate Earth explorer core missions, SP-1233(1), European Space Agency.

  • Gruber T., 2001. High-resolution gravity field modeling with full variance-covariance matrices. J. Geodyn., 75, 505-514.

    Google Scholar 

  • Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. W.H. Freeman and Company, San Francisco, London.

    Google Scholar 

  • Ilk K.-H., 1999. Energieintegrale und Energieaustauschbeziehungen der Bewegungen küunstlicher Erdsatelliten. In: F. Krumm und V.S. Schwarze (Eds.), Quo vadis geodesia?, Schriftenreihe d. Inst. d. Studienganges Geodäsie und Geoinformatik, no.1999.6-1, Univ. Stuttgart, Stuttgart, 253-259.

    Google Scholar 

  • Jekeli C., 1999. The determination of gravitational potential differences from satellite-to-satellite tracking. Celest. Mech. Dyn. Astron., 75, 85-101.

    Google Scholar 

  • Kaula W.M., 1966. Theory of Satellite Geodesy. Blaisdell Publishing Company, Waltham-Massachusetts, Toronto, London.

    Google Scholar 

  • Klees R., Koop R., Visser P.N.A.M. and van den Ijssel J., 2000. Efficient gravity field recovery from GOCE gravity gradient observations. J. Geodyn., 74, 561-571.

    Google Scholar 

  • 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 NASE GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96. National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland.

    Google Scholar 

  • Pail R., Plank G. and Schuh W.-D., 2001. Spatially restricted data distribution on the sphere: the method of orthonormalized functions and applications. J. Geodyn., 75, 44-56.

    Google Scholar 

  • Pail R., 2002. In-orbit calibration and local gravity field continuation problem. Final Report, ESA/ESTEC Contract 14287/00/NL/DC, WP1, European Space Agency, Noordwijk, 9-112 (www-geomatics.tu-graz.ac.at/mggi/research/e2mgp/e2mgp.htm).

    Google Scholar 

  • Pail R. and Plank G., 2002. Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform. J. Geodyn., 76, 462-474.

    Google Scholar 

  • Plank G., 2002. Implementation of the pcgma-package on massive parallel systems. Final Report, ESA/ESTEC Contract 14287/00/NL/DC, WP 3, European Space Agency, 183-216 (wwwgeomatics.tu-graz.ac.at/mggi/research/e2mgp/e2mgp.htm).

  • Rapp R., Wang Y. and Pavlis N., 1991. The Ohio state 1991 geopotential and sea surface topography harmonic coefficient models. OSU Report, 410, Department of Geodetic Science and Surveying, The Ohio State University, Columbus.

    Google Scholar 

  • Rummel R., van Gelderen M., Koop R., Schrama E., Sanso F., Brovelli M., Miggliaccio F. and Sacerdote F., 1993. Spherical harmonic analysis of satellite gradiometry. Publications on Geodesy, 39, Neth. Geod. Comm., Delft, The Netherlands.

    Google Scholar 

  • Schrama E.J.O., 1989. The role of orbit errors in processing satellite altimeter data. Publications on Geodesy, 33, Neth. Geod. Comm., Delft, The Netherlands.

    Google Scholar 

  • Schuh W.-D., 1996. Tailored Numerical Solution Strategies for the Global Determination of the Earth's Gravity Field. Mitteilungen geod. Inst. TU Graz, no.81, Graz Univ. of Technology, Graz, Austria.

    Google Scholar 

  • Schuh W.-D., 2002. Improved modeling of SGG-data sets by advanced filter strategies. Final Report, ESA/ESTEC Contract 14287/00/NL/DC, WP2, European Space Agency, Noordwijk, 113-181.

    Google Scholar 

  • Sneeuw N., 2000. A Semi-Analytical Approach to Gravity Field Analysis from Satellite Observations. Dissertation, DGK, Reihe C, Munich, no. 527, Bayerische Akademie d. Wissenschaften, Munich.

    Google Scholar 

  • Sneeuw N. and van Gelderen M., 1997. The polar gap. In: F. Sanso and R. Rummel (Eds), Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Sciences, 65, Springer, 559-568.

  • Visser P.N.A.M., van den IJssel J., Koop R. and Klees R., 2001. Exploring gravity field determination from orbit perturbations of the European Gravity Mission GOCE. J. Geodyn., 75, 89-98.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Preimesberger, T., Pail, R. GOCE Quick-Look Gravity Solution: Application of the Semianalytic Approach in the Case of Data Gaps and Non-Repeat Orbits. Studia Geophysica et Geodaetica 47, 435–453 (2003). https://doi.org/10.1023/A:1024795030800

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024795030800

Navigation