Skip to main content
Log in

Testing global geopotential models through comparison of a local quasi-geoid model with GPS/leveling data

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

Abstract

The satellite missions CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) provide accurate data that are routinely inverted into spherical harmonic coefficients of the geopotential forming a global geopotential model (GGM). Mean square errors of these coefficients, in some cases even entire covariance matrices, are included in the GGM. Due to estimation procedures with a large redundancy and insufficiently propagated observation errors, they often do not represent the actual accuracy of the harmonic coefficients, thus also gravity field parameters synthesized from the respective GGM. Since in most cases standard methods validating the GGMs reached their limits, new procedures and independent data are being currently sought. This article discusses an alternative validation procedure based on comparison of the GGMs with independent data represented by a set of GPS/leveling stations. Due to a different spectral content of the height anomalies synthesized from the GGMs and of those derived by combination of GPS-based ellipsoidal and leveled normal heights, the GGM-based low frequency height anomaly is enhanced for a high frequency component computed from local ground gravity and elevation data. The methodology is applied on a set of selected points of the European Vertical Reference Network and Czech trigonometric stations. In accordance with similar tests based on entirely independent data of cross-over altimetry, obtained results seem to indicate low-frequency deficiencies in the current GGMs, namely in those estimated from data of single-satellite missions.

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.

Similar content being viewed by others

References

  • Bruns H., 1878. Die Figur der Erde. Publ. des Königlichen Preussischen Geodätischen Inst., Berlin, Germany (in German).

    Google Scholar 

  • Gooding R.H., Wagner C.A., Klokočník J., Kostelecký J. and Gruber C., 2007. CHAMP and GRACE resonances, and the gravity field of the Earth. Adv. Space Res., 39, 1604–1611, doi: 10.1016/j.asr.2007.02.086.

    Article  Google Scholar 

  • Harwood N.M., Swinerd G.G. and King-Hele D.G., 1994. Individual Geopotential Harmonic Coefficients of Order 15 from 30 Resonant Satellite Orbit Analysis. Proc. R. Soc. London, Ser. A, 444, 129–147.

    Article  Google Scholar 

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

    Google Scholar 

  • Ihde J. and Sacher M. (Eds), 2002. European Vertical Reference Network, Final Documentation. EUREF Publication No. 11/I, Mittailungen des Bundesamt für Kartografie und Geodäsie, Band 25, Verlag des BKG, Frankfurt/Main (http://www.euref.eu/documentation/ EUVN/vol%20I.pdf).

  • King-Hele D.G. and Walker D.M.C., 1989. Evaluation of 15th-and 30th-order geopotential harmonic coefficients from 26 resonant satellite orbits. Planet. Space Sci., 37, 805–823.

    Article  Google Scholar 

  • Klokočník J., Wagner C.A. and Kobrle F., 1992. a Test of GEM-T2 from Geosat crossovers using latitude lumped coefficients. In: Montag H. and Reigber C. (Eds.), Geodesy and Physics of the Earth, International Association of Geodesy Symposia, 112, Springer-Verlag, Berlin, Heidelberg, 79–82.

    Google Scholar 

  • Klokočník J., Kostelecký J., Wagner C.A., Schwintzer P., Förste C. and Scharroo R., 2005. Evaluation of the accuracy of the EIGEN-1S and 2 CHAMP-derived gravity field models by satellite crossover altimetry. J. Geodesy, 78, 405–417.

    Article  Google Scholar 

  • Kostelecký J. and Klokočník J., 1983. Collocation and 30th-order resonant harmonics. Planet. Space Sci., 31, 829–841.

    Article  Google Scholar 

  • Kostelecký J. Jr., 2001. Accuracy estimates of Bouguer gravity anomalies. Geodetický a kartografický obzor, 47, 117–123 (in Czech).

    Google Scholar 

  • Kostelecký J. Jr., 2004. Elevation and Gravity Database GOP30x30. Report of the Research Institute of Geodesy, Topography and Cartography, Zdiby (in Czech).

  • Lederer M., Pálinkáš V. and Kostelecký J. Jr., 2006. Repeated absolute gravity measurements in the Czech gravimetric network. Geodetický a kartografický obzor, 52, 101–109 (in Czech).

    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. NASA Technical Report NASA/TP-1996/8-206861, NASA, Greenbelt, Maryland, USA.

    Google Scholar 

  • Lerch F.J., 1991. Optimum Data Weighting and Error Calibration for Estimation of Gravitational Parameters. NASA GSFC TM 100737.

  • Martinec Z., 1993. Effect of Lateral Density Variations of Topographical Masses in View of Improving Geoid Model Accuracy over Canada. Contract Report for the Geodetic Survey of Canada, Ottawa, Canada.

  • Martinec Z. and Vaníček P., 1996. Formulation of the boundary-value problem for the geoid determination with a higher-degree reference field. Geophys. J. Int., 126, 219–228.

    Article  Google Scholar 

  • Mayer-Gürr T., Eicker A. and Ilk K.H., 2006. ITG-GRACE02S: a GRACE Gravity Field Derived from Short Arcs of the Satellite’s Orbit. Institute for Theoretical Geodesy, University of Bonn, Bonn, Germany (http://ifen.bauv.unibw-muenchen.de/gw06/down/mayer-guerr-muenchen-2006.pdf).

    Google Scholar 

  • Molodensky M.S., Yeremeev V.F. and Yurkina M.I, 1960. Methods for Study of the External Gravitational Field and Figure of the Earth. TRUDY Ts NIIGAiK, 131, Geodezizdat, Moscow (English translat.: Israel Program for Scientific Translation, Jerusalem 1962).

    Google Scholar 

  • Novák P., 2000. Evaluation of Gravity Data for the Stokes-Helmert Solution to the Geodetic Boundary-Value Problem. PhD Thesis, Dept. of Geodesy and Geomatics Eng., Univ. of New Brunswick, Fredericton, Canada.

    Google Scholar 

  • Rabus B., Eineder M., Roth A. and Bamler R., 2003. The shuttle radar topography mission-a new class of digital elevation models acquired by spaceborne radar. ISPRS-J. Photogramm. Remote Sens., 57, 241–262.

    Article  Google Scholar 

  • Reigber C., Balmino G., Schwintzer P., Biancale R., Bode A., Lemoine J.M., König R., Loyer S., Neumayer H., Marty J.C., Barthelmes F., Perosanz F. and Zhu S.Y., 2002. a high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophys. Res. Lett., 29, doi: 10.1029/2002GL015064.

  • Reigber C., Schwintzer P., Neumayer K-H., Barthelmes F., König R., Förste C., Balmino G., Biancale R., Lemoine J-M., Loyer S., Bruinsma S., Perosanz F. and Fayard T., 2003. The CHAMP-only Earth gravity field model EIGEN-2. Adv. Space Res., 31, 1883–1888.

    Article  Google Scholar 

  • Reigber C., Schmidt R., Flechtner F., König R., Meyer U., Neumayer K.H., Schwintzer P. and Zhu S.Y., 2004a. An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J. Geodyn., 39, 1–10.

    Article  Google Scholar 

  • Reigber C., Jochmann H., Wünsch J., Petrovic S., Schwintzer P., Barthelmes F., Neumayer K.H., König R., Förste C., Balmino G., Biancale R., Lemoine J.M., Loyer S. and Perosanz F., 2004b. Earth gravity field and seasonal variability from CHAMP. In: Reigber C., Lühr H., Schwintzer P. and Wickert J. (Eds), Earth Observation with CHAMP-Results from Three Years in Orbit. Springer-Verlag, Berlin, Heidelberg, 25–30.

    Google Scholar 

  • Sjöberg L.E., 2003. A general model for modifying Stokes formula and its least-squares solution. J. Geodesy, 77, 459–464.

    Article  Google Scholar 

  • Vaníček P. and Kleusberg A., 1987. The Canadian geoid-Stokesian approach. Manuscr. Geod., 12, 86–98.

    Google Scholar 

  • Wagner C.A., Klokočník J. and Kostelecký J., 2000. Geopotential and Oceanographic Signals from Inversion of Single and Dual Satellite Altimetry. Research Institute of Geodesy, Topography and Cartography (VUGTK), Series 46, 1–39, Zdiby, Czech Republic, ISBN: 80-85881-08-X.

  • Zeman A., 2001. Central European vertical and kinematic systems. In: Drewes H., Dodson A.H., Fortes L.P.S., Sanchez L. and Sandoval P. (Eds), Vertical Reference Systems. International Association of Geodesy Symposia, 124, Springer-Verlag, Berlin, Heidelberg, 72–74.

    Google Scholar 

  • Zeman A., Kostelecký J. and Ryšavý V., 2007. Vertical component of the Earth’s surface movement in the region of Central Europe (Czech Republic) from the results of satellite geodesy methods and their comparison with the results of repeated terrestrial geodetic methods. Eos Trans. AGU, 88(52), Abstract G43B-1240.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pavel Novák.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Novák, P., Kostelecký, J. & Klokočník, J. Testing global geopotential models through comparison of a local quasi-geoid model with GPS/leveling data. Stud Geophys Geod 53, 39–60 (2009). https://doi.org/10.1007/s11200-009-0003-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-009-0003-0

Key words

Navigation