Abstract
Several quasigeoid models for the Czech Republic have been developed for different purposes since mid-seventies using different data sources: gravimetric, astronomical and GPS/levelling observations, as well as data gained from the territories of neighbouring countries. Two of the recent solutions, namely the VUGTK96 quasigeoid obtained from heterogeneous data and gravimetric quasigeoid CR2000 are described and compared. Accuracies of the models were estimated with the help of accuracy characteristics resulting from the processing, by comparison with GPS/levelling results available for most of the territory, and, finally, tested on a special GPS/levelling profile across the steepest slope of the quasigeoid surface in the south-eastern part of the territory. It is shown that the CR2000 gravimetric quasigeoid is suitable for transformation of ellipsoidal GPS heights to the gravity related heights with an accuracy of 3 cm.
Similar content being viewed by others
References
Buchar E., 1951. Tížnicové odchylky a geoid v ČSR. Vědecko-technické nakladatelství, Prague (in Czech).
Čepek A., 1993. Implementation of Givens Transformation in Solving Parametric Adjustment with Sparse Matrices of Observation. PhD thesis, Czech Technical University, Prague (in Czech).
Dušátko D, 1992. On the determination of European gravimetric geoid. Stud. Geophys. Geod., 36, 392–393.
Haagmans R.H.N., de Min E. and van Gelderen M., 1993. Fast evaluation of convolution integralson the sphere using 1D_FFT, and a comparison with existing methods for Stokes' integral.Manuscr. Geod., 18, 227–241.
Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. Freeman, San Francisco, 364 pp.
Ihde J., Adam J., Gurtner W., Harsson B.G., Sacher M., Schlüter W. and Wöppelmann G., 2000. The Height Solution of the European Vertical Reference Network (EUVN). Veroff. Bayer. Komm. Internation. Erdmess., Heft 61, Verl. Bayer. Akad. d. Wissenschaft, Muenchen, 132-145.
Krarup T., 1969. A Contribution to the Mathematical Foundation of Physical Geodesy. Publ. 44, Dan. Geod. Inst., Copenhagen, Denmark.
Kostelecký J. and Šimek J., 1993. Czech and Slovak geodetic control within European reference systems-some recent activities. Veroff. Bayer. Komm. Internation. Erdmess., Heft 53, Verl. Bayer. Akad. d. Wissenschaft, Muenchen, 127-135.
Kostelecký J., Šimek J., Beneš F. and Provázek J., 1999a. National Report of the Czech Republic-EUREF based development in the Czech national geodetic control. Mitteilungen des BKG, Band 6, Verlag des BKG, Frankfurt a/M, 160–164.
Kostelecký J., Šimek J., Beneš F. and Provázek J., 1999b. National Report of the Czech Republic-Development in the Czech National Control. Veroff. Bayer. Komm. Internation. Erdmess., Heft 60, Verl. Bayer. Akad. d. Wissenschaft, Muenchen, 150–156.
Kostelecký J., Kostelecký J. (Jr.), Pešek I., Šimek J., Švábenský O., Weigel J. and Zeman A., 2002. Quasigeoids for the territory of the Czech Republic and their testing. Reports on Geodesy, 61(1), Warsaw University of Technology, Warsaw, Poland,47-52.
Kühtreiber N., 2003. High precision geoid determination of Austria using heterogenous data. In: Tziavos I. N. (Ed.) Gravity and Geoid 2002, Proceedings of 3rd meeting of the Int. Gravity and Geoid Commision, Thessaloniki, Greece, August 2002, Editions ZITI, Thessaloniki, Greece, 144–149.
Lemoine F.G., Kenyon S.C., Trimmer R., Factor J., Pavlis N.K., Klosko S.M., Chinn D.S., Torrence M.H., Williamson R.G., Cox C.M., Wang Y.M., Luthcke S.B., Pavlis E.C., Rapp R.H. and Olson T.R., 1998. EGM96-The NASA GSFC and NIMA Joint Geopotential Model. NASA Technical Memorandum, NASA, 632 pp.
Lerch F.J., Putney B.H., Wagner C.A. and Klosko S.M., 1981. Goddard Earth Models for Oceanographic Applications (GEM 10B and 10C). Marine Geodesy, 5, 145-187.
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 TsNIIGAiK, Geodezizdat, Moscow (in Russian, English transl.: Israel Program for Scientific Translations, Jerusalem, 1962, 248 pp.).
Moritz H., 1973. Least-Squares Collocation. Deutsche Geodätische Kommission bei der Bayer. Akad. der Wissenschaften, Reihe A: Theoretische Geodäsie, Heft 75, Verl. Bayer. Akad. d. Wissenschaft, Muenchen, Germany, 91 pp.
Moritz H., 1980. Advanced Physical Geodesy. Herbert Wichmann Verlag, Karlsruhe; Abacus Press Tunbridge, Wells, Kent, 500 pp.
Moritz H., 1992. Geodetic Reference System 1980. Bulletin Géodésique, 66, 187-192.
Novák P., Šimek J. and Kostelecký J. (Jr.), 2003. A detailed gravimetric quasigeoid model VUGTK2002 for central Europe. In: I.N. Tziavos (Ed.), Gravity and Geoid 2002, Proceedings of 3rd meeting of the Int. Gravity and Geoid Commision, Thessaloniki, Greece, August 2002, Editions ZITI, Thessaloniki, Greece, 150–155.
Pešek I. and Šimek J., 2000. Numerické řešení detailního průběhu gravimetrického kvazigeoidu na území České republiky rychlou Fourierovou transformací. Geod. a kartogr. Obzor, 46/88, 159–164 (in Czech).
Press W.H., Teukolski S.A., Vetterling W.T. and Flannery B.P., 1992. Numerical Recipes in Fortran, Cambridge University Press, Cambridge, U.K.
Rapp R.H., Wang Y.M. and Pavlis N.K., 1991. The Ohio State 1991 Geopotential and Sea Surface Topography Harmonic Coefficient Models. Report 410, Dept. of Geod. Sci. and Surv., Ohio State University, Columbus, USA.
Sideris M.G. and She B.B., 1995. A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method. Bulletin Géodésique, 69, 92–108.
Šimek J., 1982. Methods and accuracy of determination of detailed quasigeoid for the territory of Czechoslovakia. Sborník výzkumných prací VÚGTK, 14, 49–61 (in Russian).
Šimek J., 1992. Some Investigations Related to High-Resolution Quasigeoid for Czechoslovakia. In: P. Holota and M. Vermeer (Eds), First Continental Workshop on the Geoid in Europe-Towards a Precise Pan-European Reference Geoid for the Nineties, VÚGTK, Prague, Czech Republic, 166-191.
Šimek J., 1996. GPS, Quasigeoid and Height Determination-a Case Study for the Czech Republic. Veroff. Bayer. Komm. Internation. Erdmess., Heft 57, Verl. Bayer. Akad. d. Wissenschaft, Muenchen, 190-197.
Tanni L., 1948. On the continental undulations of the geoid as determined from the present gravity material. Publ. Isost. Inst., No 18, Helsinki, Finland.
Tanni L., 1949. The regional rise of the geoid in Central Europe. Publ. Isost. Inst., No 22, Helsinki, Finland.
Torge W. and Denker H., 1998. The European Geoid. Development over More than 100 years and Present Status. In: M. Vermeer and J. Ádám J. (Eds.), Second Continental Workshop on the Geoid in Europe. Rep. Finn. Geod. Inst., 98:4, 47-52.
Tscherning C.C. and Rapp R.H., 1974. Closed Covariance Expression for Gravity Anomalies, Geoid Undulations, and Deflection of Vertical Implied by Anomal Degree Variance Models. Dep. of Geodetic Science, The Ohio State University, Columbus, Ohio, USA, 208 pp.
Tscherning C.C., 1978. Collocation and least squares methods as a tool for handling gravity field dependent data obtained through space research techniques. Bulletin Géodésique, 52, 199-212.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kostelecký, J., Kostelecký, J., Pešek, I. et al. Quasigeoids for the Territory of the Czech Republic. Studia Geophysica et Geodaetica 48, 503–518 (2004). https://doi.org/10.1023/B:SGEG.0000037469.70838.39
Published:
Issue Date:
DOI: https://doi.org/10.1023/B:SGEG.0000037469.70838.39