Abstract
A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m2/s2) and as such is (0.191 ± 0.003) (m) under the geoid defined by W 0 = 62636855.8 (m2/s2). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.
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References
Amiri-Simkooei AR (2007) Least-squares variance component estimation: theory and gps applications. Ph.D. thesis, Delft University of Technology, Publication on Geodesy, 64, Netherlands Geodetic Commission, Delft
Ardalan AA (2000) High-resolution regional geoid computation in the World Geodetic Datum 2000, based upon collocation of linearized observationals of the type GPS, gravity potential and gravity intensity. Ph.D. thesis, Department of geodesy and geoinfirmatics, Stuttgart University, Stuttgart
Ardalan AA, Safari A (2004) Ellipsoidal terrain correction based on multi-cylindrical equal0area map projection of the reference ellipsoid. J Geod 78: 114–123
Ardalan AA, Safari A (2005) Global height datum unification: a new approach in gravity potential space. J Geod 79: 512–523
Ardalan AA, Grafarend EW (2004) High-resolution regional geoid computation without applying Stokes’s formula: a case study of the Iranian geoid. J Geod 78: 138–156
Balasubramania N (1994) Definition and realization of a global vertical datum. Report No. 427 Department of Geodetic Science and Surveying Ohio State University, Columbus
Bursa M, Kouba J, Muller A, Radej K, True SA, Vatrt V, Vojtiskova M (2001) Determination of geopotential differences between local vertical datums and realization of a world height system. Studia Geoph. et Geod 45: 127–132
Bursa M, Kenyon S, Kouba J, Radej K, Vatrt V, Vojtiskova M, Simek J (2002) World height system specified by geopotential at tide gauge stations. In: Proceedings of IAG symposium, vertical reference system, 20–23 February 2001, Cartagena, Columbia, pp 291–296, Springer, Berlin
Colombo OL (1980) A world vertical network. Department of Geodetic Science and Surveying, Ohio State University, Columbus. Report No. 196
de Freitas SRC, Schwab SHS, Marone E, Pires AO, Dalazoana R (2002) Local effects in the Brazilian Vertical Datum. In: Proceedings of IAG symposium, vol 125. Vistas for Geodesy in the New Millennium, 2–7 September 2001, Budapest, pp 02–107, Springer, Berlin
Ekman M (1989) Impacts of geodynamic phenomena on systems for height and gravity. Bulletin Géodésique 63: 281–296
Ekman M (1999) Using mean sea surface topography for determination of height system differences across the Baltic Sea. Mar Geod 22: 31–35
Ekman M (2001) On the permanent tide in the European Vertical Reference System. In: Veröffentlichung der Bayerischen Kommission für die Internationale Erdmessung.München No 61, pp 13–114
Featherstone WE (2002) Prospects for the Australian Height Datum and geoid model. In: Proceedings of IAG symposium, vol 125. Vistas for geodesy in the new millennium, 2–7 September 2001. Budapest, pp 96–101, Springer, Berlin
Grafarend E, Ardalan AA (1997) W0: an estimate of the Finnish Height Datum N60, epoch 1993.4, from twenty-five GPS points of the Baltic Sea Level Project. J Geod 71: 673–679
Groten E (2004) Fundamental parameters and current. Best estimates of the parameters of common relevance to astronomy, geodesy, and geodynamics by Erwin Groten, IPGD, Darmstadt. J Geod 77: 724–797
Groten E (2002) Do we need a new reference system? In: Proceedings of IAG symposium, vol 125. Vistas for geodesy in the new millennium, 2–7 September 2001, Budapest, pp 108–113, Springer, Berlin
Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Sea surface topography and the geoid. Proceedings of the IAG symposia, vol 104. Springer, pp 116–127
Holota P (1983a) The altimetry gravimetry boundary value problem I: linearization, Friedrich’s inequality. Boll Geod Sci Afini XLII: 13–32
Holota P (1983b) The altimetry gravimetry boundary value problem II: weak solution, V-allipticity. Boll Geod Sci Afini XLII: 69–84
Huang J (2002) Computational methods for the discrete downward continuation of the earth gravity and effects of lateral topographical mass density variation on gravity and the geoid. A Thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in the Department of Geodesy and Geimatics Engineering, The University Of New Brunswick, May, 2002
Ihde J, Augath W (2002) The european vertical reference system (EVRS), its relation to a world height system and to the ITRS. In: Proceedings of IAG symposium, vol 125. Vistas for geodesy in the new millennium, 2–7 September 2001, Budapest, pp 78–83. Springer, Berlin
Ihde J, Sanchez L (2005) A unified global height reference systems as a basis for IGGOS. J Geodyn 40: 400–413
Jekeli C (2000) Heights, the geopotential, and vertical datums. Department of Geodetic Science and Surveying, Ohio State University, Columbus, Report No. 459
Kellogg OD (1929) Foundations of potential theory. Berlin, J Springer. Dover Publications, New York, 1953
Klees R, Tenzer R, Prutkin I, Wittwer T (2008) A data-driven approach to local gravity field modeling using spherical radial basis functions. J Geod 82: 457–471
Koch KR, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geod 76: 259–268
Kusche J (2003) A Monte-Carlo technique for weight estimation in satellite geodesy. J Geod 76: 641–652
Lelgemann D (1977) On the definition of the Listing geoid taking into consideration different height systems. Nachrichten Karten-u. Vermessungswesen, Rh.II 34: 25–47
MacMillan WD (1930) Theoretical mechanics vol 2: the theory of potential. McGraw-Hill New York. Dover Publications, New York
Marsden JE Tromba AJ (2003) Vector calculus, 5th edn. W.H. Freeman, San francisco. ISBN 0716749920
Martinec Z, Grafarend EW (1997) Construction of Green’s function to an external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution. J Geod 71: 562–570
Marti U, Schlater A, Brockmann E, Wiget A (2002) The way to a consistent national height system for Switzerland. In: Proceedings of IAG symposium, vol 125. Vistas for geodesy in the new millennium, 2–7 September 2001, Budapest, pp 90–95. Springer, Berlin
Martinec Z, Grafarend EW (1997) Construction of Green’s function to an external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution. J Geod 71: 562–570
Mather RS, Rizos C, Morrison T (1978) On the unification of geodetic levelling datums using satellite altimetry. NASA Tech. Memo. 79533, Goddard Space Flight Center, Greenbelt
Nahavandchi H, Sjöberg LE (1998) Unification of vertical datums by GPS and gravimetric geoid models using modified Stokes formula. Mar Geod 21: 261–273
Pan M, Sjöberg LE (1998) Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia. J Geod 72: 64–70
Pick M (1970) Generalization of the system of normal heights. J Geod 44: 245–255
Poutanen M (1999) Use of GPS in unification of vertical datums and detection of levelling errors. In: Lilje M (ed) Geodesy and surveying in the future—the importance of heights. Proceedings of the seminar March 15–17, 1999. Reports in geodesy and geographical information systems, 1999:3. Lantmäteriverket, Gävle. pp 301-312
Poutanen M (2000) Sea surface topography and vertical datums using space geodetic techniques. Publications of the Finnish Geodetic Institute No.128, Helsinki
Rapp RH (1994) Separation between reference surfaces of selected vertical datums. Bull Géodésique 69(1): 26–31
Rapp RH (1995) A world vertical datum proposal. Allgemeine Vermessungs-Nachrichten 8-9(95): 297–304
Rummel R (2000) Global integrated geodetic and geodynamic observing system (GIGGOS). In: Rummel R, Drewes H, Bosch W, Hornik H (eds) Towards an integrated global geodetic observing system (IGGOS), pp 253–260, IAG Symposia 120, Springer
Rummel R, Ilk KH (1995) Height datum connection—the ocean part. Allgemeine Vermessungs-Nachrichten 102: 321–330
Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Géodésique 62: 477–498
Saaranen V, Lehmuskoski P, Rouhiainen P, Takalo M, Mäkinen J, Poutanen M (2008) The new finnish height reference N2000. In: Proceedings of the IAG/FIG symposium geodetic reference frames, Munich, 9–14 October 2006 (GRF 2006). In print
Safari A, Ardalan AA, Grafarend EW (2005) A new ellipsoidal gravimetric, satellite altimetry and astronomiac boundary value problem, a case study: the geoid of Iran. J Geodyn 39: 545–568
Sanchez L (2002) A reference surface for the Unified Height System in the northern part of South America. In: Proceedings of IAG symposium, vol 125. Vistas for geodesy in the new millennium, 2–7 September 2001, Budapest, pp 84–89, Springer, Berlin
Sanso F, Usai S (1995) Height datum and local geodetic datums in the theory of geodetic boundary value problems. Allgemeine Vermessungs-Nachrichten 102: 343–355
Sanso F, Vaniček P (2006) The orthometric height and the holonomity problem. Presented at the Grafarend symposium in Stuttgart, February 18. J Geod 80: 225–232
Svensson SL (1983) Solution of the altimetry–gravimetry problem. Bull Geod 57: 332–353
Svensson SL (1988) Some remarks on the altimetry- gravimetry problem. Manuscr Geod 13: 63–74
Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geod 82: 65–82
Xu P, Rummel R (1991) A quality investigation of global vertical datum connection. Netherlands Geodetic Commission, Publications on Geodesy, new series, number 34
Xu P, Shen Y, Fukuda Y, Lio Y (2006) Variance component estimation in linear inverse Ill-posed Mpdels. J Geod 80: 69–81
Zilkoski DB, Richards JH, Young GM (1992) Results of the general adjustment of the North American Vertical Datum of 1988. Surv Land Inform Syst 52: 133–149
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Ardalan, A.A., Karimi, R. & Poutanen, M. A bias-free geodetic boundary value problem approach to height datum unification. J Geod 84, 123–134 (2010). https://doi.org/10.1007/s00190-009-0348-8
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DOI: https://doi.org/10.1007/s00190-009-0348-8