Abstract
The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W 0=62636855.8 m2/s2. According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.
Similar content being viewed by others
References
1. Altamimi Z, Sillard P, Boucher C (2002) ITRF2000: a new release of the International Terrestrial Reference Frame for Earth science applications. J Geophys Res 107(B10):2214, doi:10.1029/2001JB000561
Amos MJ, Featherstone WE (2003) Progress towards a gravimetric geoid for New Zealand and a single national vertical datum. In: Tziavos IN (eds). Gravity and geoid 2002-GG2002. Aristotle University of Thessaloniki, Thessaloniki, Greece, pp 395–400
Ardalan AA (1999) High resolution regional geoid computation in the World Geodetic Datum 2000, based upon collocation of linearized observational functionals of the type GPS, gravity potential and gravity intensity. Ph D thesis, Stuttgart University
Ardalan AA, Safari A (2004) Terrain correction on the multi-cylindrical equal area map projection of the surface of the reference ellipsoid. J Geod 78:114–123
Ardalan AA, Grafarend EW, Kakkuri J (2002) National height datum, the Gauss-Listing geoid level value W 0 and its time variation \(\dot{W}_0\). J Geod 76:1–28
AVISO (1998) User handbook – corrected sea surface heights (CORSSHs). Edition 3.1, AVI-NT-011–311-CN, AVISO, France
Baker C (1977) The numerical treatment of integral equations. Oxford University Press, Oxford
Burša M, Kenyon S, Kouba J, Raděj K, Vatrt V, Vojtiskova M, Simek J (2002) World height system specified by geopotential at tide gauge stations. In: Drewes et al (eds). Vertical reference system. Springer, Berlin Heidelberg New York, pp 291–296
Burša M, Kouba J, Muller A, Raděj 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
Burša M, Raděj K, Šíma Z, True SA, Vatrt V (1997) Determination of the geopotential scale factor from TOPEX/POSEIDON satellite altimetry. Stud Geoph et Geod 14:203–216
de Freitas SRC, Schwab SHS, Marone E, Pires AO, Dalazoana R (2002) Local effects in the Brazilian Vertical Datum. In: Ádám J, Schwartz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 102–107
Ekman M (1999) Using mean sea surface topography for determination of height system differences across the Baltic Sea. Mar Geod 22:31–35
Eringen AC (1962) Nonlinear theory of continuous media. McGraw-Hill, New York
Featherstone WE (2002) Prospects for the Australian Height Datum and geoid model. In: Ádám J, Schwartz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 96–101
Grafarend EW, Ardalan AA (1997) W0: an estimate of the Finnish Height Datum N60, epoch 1993.4, from 25 GPS points of the Baltic Sea Level Project. J Geod 71:673–679
Grafarend EW, Ardalan AA (2002) Time evolution of a world geodetic datum. In: Ádám J, Schwartz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 114–123
Grafarend EW, Awange JL (2000) Determination of vertical deflections by GPS/LPS measurements. Zeitschrift für Vermessungswesen 125:279–288
Grafarend EW, Ardalan AA (1999) World Geodetic Datum 2000. J Geod 73:611–623
Groten E (2002) Do we need a new reference system? In: Ádám J, Schwarz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 108–113
Hansen PC (1996) Rank-deficient and discrete Ill-posed problems. Doctoral Dissertation, Polyteknisk Forlag, Lyngby, Denmark
Hipkin RG (2002) Vertical datum defined by W0=U0: theory and practice of a modern height system. In: Tziavos IN (eds). Gravity and geoid 2002. Aristotle University of Thessaloniki, Thessaloniki, Greece, pp 367–377
Ihde J, Augath W (2002) The European vertical reference system (EVRS), its relation to a World height System and to the ITRS. In: Ádám J, Schwartz K-P (eds). Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 78–83
Jekeli C (1988) The exact transformation between ellipsoidal and spherical harmonic expansions. Manuscr Geod 13:106–113
Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96, NASA/TP-1998–206861. National Aeronautics and Space Administration, Washington, USA
Marti U, Schlater A, Brockmann E, Wiget A (2002) The way to a consistent national height system for Switzerland. In: Ádám J, Schwartz K-P (eds) Vistas for geodesy in the new millennium. Springer, Berlin Heidelberg New York, pp 90–95
Marti U (2003) Modelling of differences of height systems in Switzerland. In: Tziavos IN (eds) Gravity and geoid 2002. Aristotle University of Thessaloniki, Thessaloniki, Greece, pp 378–383
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 Maryland
Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J Ass Comput Mach 9:84–96
Poutanen M (2000) Sea surface topography and vertical datums using space geodetic techniques. Report 128, Finnish Geodetic Institute, Masala
Poutanen M (1999) Use of GPS in unification of vertical datums and detection of levelling errors. In: Lilje M (eds) Geodesy and surveying in the future – the importance of heights. Reports 1999:3. Lantmäteriverket, Gävle, Sweden, pp 301–312
Rapp RH (1998) The development of a degree 360 expansion of the dynamic ocean topography of the POCM_4B global circulation model, NASA/CR-1998–206877. NASA, Greenbelt, Maryland
Sacerdote F, Sanso F (2001) W 0, A story of the height datum problem. In: Festschrift W. Torge, Wiss. Arb. Der Fach. Verm. Der Univ. Hannover, no. 241, pp 49–56
Safari A (2004) Ellipsoidal boundary value problem for geoid computations via modulus of gravity, astronomical longitude, astronomical latitude, and satellite altimetry observations. Ph D thesis, Department of Surveying and Geomatics Engineering, University of Tehran (In Persian)
Safari A, Ardalan AA, Grafarend EW (2005) A new ellipsoidal gravimetric, satellite altimetry and astronomic boundary value problem; a case study: the geoid of Iran. J Geodyn 39:545–568
Stakgold I (1979) Green’s functions and boundary value problems. Wiley, New York
Sanchez L (2002) A reference surface for the Unified Height System in the northern part of South America. In: Ádám J, Schwartz K-P (eds) Vistas for geodesy in the new Millennium. Springer, Berlin Heidelberg New York, pp 84–89
Tikhonov AN (1963) The regularization of incorrectly posed problems. Soviet Math Doklady 4:1624–1627
Tikhonov AN, Arsenin VY (1977) Solutions of Ill-posed problems. Winston, Washington
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ardalan, A.A., Safari, A. Global height datum unification: a new approach in gravity potential space. J Geodesy 79, 512–523 (2005). https://doi.org/10.1007/s00190-005-0001-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-005-0001-0