Skip to main content
SpringerLink
Log in

Problems in the Definition of Vertical Reference Frames

  • Conference paper
V Hotine-Marussi Symposium on Mathematical Geodesy

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 127))

Abstract

Present and future satellite-borne gravity field missions will have a major impact on the unification of regional height systems into a consistent global vertical reference frame. On the background of the high precision and quality of the expected data the scientific concepts of vertical reference frames have to be discussed, before a global frame will be implemented or before international standards and conventions can be fixed.

This paper addresses some major theoretical problems in the definition of vertical reference frames such as difficulties due to the time-dependence of the gravity field and its level surfaces, problems in assigning a geoidal potential value W0, and the consistent treatment of the permanent tidal effect. Examples from the European Vertical Reference Frame 2000 (EVRF 2000) and the draft of the IERS conventions 2000 prove that these inconsistencies are inherent in several branches of Geodesy and must be taken care of in the practical work involving height systems. Emphasis is given to the formulation of open problems rather than to the presentation of solutions.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ardalan, A, E. Grafarend, and J. Kakkuri (2002). National Height Datum, the Gauss-Listing Geoid Level Value wo and its Time Variation *0. (Baltic Sea Level Project: Epochs 1990.8, 1993.8, 1997, 4). J. Geod., 76, pp. 1–28.

    Article  Google Scholar 

  • Baarda, W. (1979). A Connection Between Geometric and Gravimetric Geodesy. A First Sketch. Netherlands Geodetic Commission, Publications on Geodesy, New Series, Vol. 6, No. 4.

    Google Scholar 

  • Bursa, M., E. Groten, S. Kenyon, J. Kouba, K. Radej, V. Vatrt, and M. Vojtiskova ( 2001 ). Earth’s Dimension Specified by Geoidal Geopotential. IAG Scientific Assembly, Sept. 2001, Budapest.

    Google Scholar 

  • Colombo, O.L. (1980). A World Vertical Network. Dept. of Geodetic Science, Ohio State University, Columbus, Ohio, Rep. No. 196.

    Google Scholar 

  • Denker, H., and W. Torge (1997). The European Gravimetric Quasigeoid EGG97–An IAG Supported Continental Enterprise. In: Forsberg R, Feissel M, Dietrich R (Eds), Geodesy on the Move. IAG Symposia, 119, Springer, pp. 249–254.

    Google Scholar 

  • Ekman, M. (1989). Impacts of Geodynamic Phenomena on Systems for Height and Gravity. Bull. Géod. 63, pp. 281296.

    Google Scholar 

  • EUREF (2000). European Vertical Reference System (EVRS). Torres JA, Hornik H (Eds), Report on the EUREF Symposium Tromso, June 2000. Veröff. Bay. Komm. f Internat. Erdmessung,Astron.-Geod. Arbeiten, Nr. 61, pp. 101–110.

    Google Scholar 

  • Grafarend, E. (1982). Six Lectures on Geodesy and Global Geodynamics. In: Geodesy and Global Geodynamics, Mitt. Geod. Inst. TU Graz, Folge 41. Moritz H Sünkel H (Eds), pp. 531–685.

    Google Scholar 

  • Grafarend, E.W., and A.A.Ardalan (1999). World Geodetic Datum 2000. J. Geod., 73, pp. 611–623.

    Article  Google Scholar 

  • Groten, E. (1980). A Remark on M. Heikkinen’s Paper „On the Honkasalo Term in Tidal Corrections to Gravimetric Observations“. Bull. Géod., 54, pp. 221–223.

    Article  Google Scholar 

  • Heck, B. (1984). Zur Bestimmung vertikaler rezenter Erdkrustenbewegungen und zeitlicher Änderungen des Schwerefeldes aus wiederholten Schweremessungen und Nivellements. Deutsche Geodätische Kommission, Reihe C, Heft Nr. 302, Munich.

    Google Scholar 

  • Heck, B. (1993). Tidal corrections in geodetic height determination. In: Linkwitz K, Eisele V, Mönicke H-J (Eds), Applications of Geodesy to Engineering. IAG Symposia, Vol 108, Springer, pp. 11–24.

    Google Scholar 

  • Heck, B. (1995). Rechenverfahren und Auswertemodelle der Landesvermessung. 2. Aufl., Wichmann Heidelberg.

    Google Scholar 

  • Heck, B., and H. Mälzer (1983). Determination of Vertical Recent Crustal Movements by Levelling and Gravity Data. Tectonophysics, 97, pp. 251–264.

    Article  Google Scholar 

  • Heck, B., and R. Rummel (1990). Strategies for Solving the Vertical Datum Problem Using Terrestrial and Satellite Data. In: Sünkel H, Baker T (Eds), Sea Surface Topography and the Geoid. Proc. of IAG Symposia. Vol 104, Springer Berlin Heidelberg New York, pp. 116–128.

    Google Scholar 

  • Heikkinen, M. (1979). On the Honkasalo Term in Tidal Corrections to Gravimetric Observations. Bull. Géod., 53, pp. 239–245.

    Article  Google Scholar 

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

    Google Scholar 

  • Heitz, S. (1980). Mechanik fester Körper. Mit Anwendungen in Geodäsie, Geophysik und Astronomie. Band 1. Dümmler, Bonn.

    Google Scholar 

  • Lemoine, F.G. et al. (1998). The Deveploment of the Joint NASA-GSFC and the NIMA Geopotential Model EGM96. NASA/TP-1998–206861.

    Google Scholar 

  • Listing, J.B. (1873). Ueber unserer jetzige Kenntnis der Gestalt und Grösse der Erde. Nachr. Königl. Gesellschaft der Wissenschaften und der G.A. Universität zu Göttingen, No. 3, pp. 33–98.

    Google Scholar 

  • Mäkinen, J. (2000). A Note on the Treatment of the Permanent Tidal Effect in the European Vertical Reference System (EVRS). Torres JA, Hornik H (Eds), Report on the EUREF Symposium Tromso, June 2000. Veröff. Bay. Komm. f Internat. Erdmessung,Astron.Geod. Arbeiten, Nr. 61, pp. 111–113.

    Google Scholar 

  • Mather, R.S. (1978). The Role of the Geoid in Four- Dimensional Geodesy. Marine Geodesy, 1, pp. 217–252.

    Article  Google Scholar 

  • McCarthy, D.D. (Ed.) (1996). IERS Conventions. IERS Technical Note 21, CB/IERS, Paris.

    Google Scholar 

  • Melchior, P. (1983). The Tides of the Planet Earth. Pergamon Press, Oxford.

    Google Scholar 

  • Moritz, H. (2000). Geodetic Reference System 1980. J. Geod., 74, pp. 128–133.

    Article  Google Scholar 

  • Poutanen, M., M. Vermeer, and J. Mäkinen (1996). The Permanent Tide in GPS Positioning. J. Geod., 70, pp. 499504.

    Google Scholar 

  • Rapp, R.H. (1983). Tidal Gravity Computations Based on Recommendations of the Standard Earth Tide Committee. Bull. Inf. Marés Terrestres, 89, pp. 5814–5819.

    Google Scholar 

  • Rapp, R.H. (1989). The Treatment of Permanent Tidal Effects in the Analysis of Satellite Altimeter Data for Sea Surface Topography. Manuscr. Geod., 14, pp. 368–372.

    Google Scholar 

  • Rapp, R.H. (1995). A World Vertical Datum Proposal. Allgemeine Vermessungs-Nachrichten, 102, pp. 297–304.

    Google Scholar 

  • Rapp, R.H., and N. Balasubramania (1992). A Conceptual Formulation of a World Height System. Dept. of Geodetic Science, Ohio State University, Columbus, Ohio, Rep. No. 421.

    Google Scholar 

  • Rummel, R. (2001). Global Unification of Height Systems and GOCE. In: Sideris M (Ed), Gravity, Geoid and Geodynamics 2000. Proc. of IAG Symposia. Vol 123, Springer Berlin Heidelberg New York, pp. 13–20.

    Google Scholar 

  • Rummel, R., and B. Heck (2000). Some Critical Remarks on the Definition and Realization of the EVRS. Tones JA, Hornik H (Eds.), Report on the EUREF Symposium Tromso, June 2000. Veröff Bay. Komm. f Internat. Erdmessung, Astron.-Geod. Arbeiten, Nr. 61, pp. 114–115.

    Google Scholar 

  • Rummel, R., and K.H. Ilk (1995). Height Datum Connection–the Ocean Part. Allgemeine Vermessungs-Nachrichten, 102, pp. 321–330.

    Google Scholar 

  • Rummel, R., and P. Teunissen (1988). Height Datum Definition, Height Datum Connection and the Role of the Geodetic Boundary Value Problem. Bull. Géod., 62, p. 477–498.

    Article  Google Scholar 

  • Sanso, F., and S. Usai (1995). Height Datum and Local Geodetic Datums in the Theory of Geodetic Boundary Value Problems. Allgemeine Vermessungs-Nachrich-ten, 102, pp. 343–355.

    Google Scholar 

  • Sanso, F. and G. Venuti (2002). The Height Datum/Geodetic Datum Problem. Geoph. J. Int., 149, pp. 768–775.

    Article  Google Scholar 

  • Schneider, M. (1981). Himmelsmechanik. Bibl. Inst.

    Google Scholar 

  • Tscherning, C.C. (Ed.) (1984). The Geodesist’s Handbook. Bull. Géod. 58, No. 3.

    Google Scholar 

  • Wenzel, H.-G. (1997). Tide-generating Potential for the Earth. In: Wilhelm H, Zürn W, Wenzel H-G (Eds), Tidal Phenomena. Lecture Notes in Earth Sciences 66, Springer-Verlag Berlin Heidelberg, pp. 9–26.

    Google Scholar 

  • Xu, P. (1992). A Quality Investigation of Global Vertical Datum Connection. Geophys. J. Im’., 110, pp. 361–370.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Geodetic Institute, University of Karlsruhe, Englerstr. 7, D-76128, Karlsruhe, Germany

    B. Heck

Authors
  1. B. Heck
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Polytechnic of Milan, D.I.I.A.R. — Surveying Section, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy

    Fernando Sansò

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Heck, B. (2004). Problems in the Definition of Vertical Reference Frames. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-10735-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-06028-1

  • Online ISBN: 978-3-662-10735-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation