On the Definition and Realization of a Global Vertical Datum
A Global Vertical Datum (GVD) is naturally defined by the geoid, and there is a well-established consensus to adopt Gauss-Bessel-Listing's definition of the geoid (i.e. as being the level surface of the Earth's gravity field that best fits the undisturbed sea level). The main problem in defining the geoid is therefore to fix its constant geopotential (W00). Nevertheless, this definition can be interpreted as to fit either the geopotential of sea surface to a constant (W0), or to minimize the height of sea level with respect to the geoid. Although the two interpretations lead to apparently different solutions, we show that they are practically the same. To improve the estimation of W0, we propose to weight the included data according to their a priori error estimates.
Finally we discuss the use of GNSS/levelling data for vertical datum connections, concluding that such data, although indispensable for regional vertical datum connections, in combination with satellite altimetry over the oceans are practically useless for determining the GVD. Also, such a joint adjustment of the GVD and regional vertical datum biases yields inferior local connections vs. a separate adjustment with fixed GVD.
References
Bessel F.W. (1837): Über den Einfluss den Unregelmäıigkeiten der Figur der Erde auf Geodätische Arbeiten und ihre Vergleichung mit den Astronomischen Beschtimmungen. Astronomische Nachrichten, T. 14, 269: 329-331.Search in Google Scholar
Bursa M., Kouba J., Kumar M., Mueller A., Radej K., True S. C., et al. (1999): Geoidal geopotential and World Height System. Stud. Geophys. Geod. 43: 327-337.Search in Google Scholar
Bursa M., Groten E., Kouba J., Radej K., Vatrt V., Vojtísková M. (2002): Earth's dimension specified by Geoidal Geopotential. Stud. Geophys. Geod. 46: 1-8.Search in Google Scholar
Bursa M., Kenyon S., Kouba J., Sima Z., Vatrt V., Vitek V., et al. (2007): The geopotential value W0 for specifying the relativistic atomic time scale and a global vertical reference system. J. Geod. 81: 103-110.10.1007/s00190-006-0091-3Search in Google Scholar
Gauss F.W. (1828): Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector, Vanderschoeck und Ruprecht, Göttingen, 48-50.Search in Google Scholar
Listing J.B. (1873): Über unsere jetzige Kenntnis der Gestalt und Grösse der Erde. Nachr. d Kgl Gesellschaft d Wiss und der Georg-August-Univ, Göttingen: 33-98.Search in Google Scholar
Rummel R., Teunissen P. (1988): Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull. Geod. 62: 477-498.Search in Google Scholar
Sacerdote F., Sansó F. (2004): Geodetic boundary value problems and the height datum problem. IAG Symposia 127: 174-178, Springer.10.1007/978-3-662-10735-5_23Search in Google Scholar
Sánchez L. (2009): Strategy to establish a global vertical reference system. In H. Drewes (Ed.) Geodetic Reference Frames, IAG Symposia 134, 273-278.10.1007/978-3-642-00860-3_42Search in Google Scholar
Sjöberg L.E. (2003): A general model of modifying Stokes' formula and its least-squares solution. J Geod 77: 459-464.10.1007/s00190-003-0346-1Search in Google Scholar
Sjöberg L.E. (2004): The effect on the geoid of lateral density variations. J. Geod. 78: 34-39.Search in Google Scholar
Vaníček P. (Ed.) (1987): Four-dimensional geodetic positioning - Report of the IAG SSG 4.96. Manuscr Geod 12(4).Search in Google Scholar
This content is open access.
