A Conceptual Formulation Of a World Height System
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Date
1992-08
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
Height systems are typically based on a reference surface related to mean sea level at one or more stations in a region. Because mean sea level at different locations does not lie on the same equipotential surface vertical datums of the world have inconsistent reference surfaces at the ±2 m discrepancy level. This report discusses ways in which precise space positioning techniques combined with potential coefficient models and surface gravity data in a 2° cap about a station can be used to determine consistent heights. After a review of the vertical datum inconsistency problem, a discussion is given on ideal reference surfaces and the type (orthometric or normal) of heights that are associated with the reference surface. The relationship between the ellipsoidal height, orthometric height and geoid undulation is described. These relationships lead to the first procedure that could be used to determine consistent heights from space positioning techniques. In this procedure the ellipsoidal height and geoid undulation is used to define an orthometric height with respect to an ideal reference surface. This height is then compared to the height in a specific vertical datum to develop a bias model. Such a bias model could then be used with ellipsoidal height and geoid undulation information to obtain orthometric (or other) height in the local vertical datum. A disadvantage of this procedure is the lack of precise ellipsoidal heights from inexpensive satellite positioning procedures. An advantage of the procedure is that it could be used in a relative mode to define orthometric height differences. The second procedure analyzed took data from many vertical datums which was combined in a model that would define the fundamental reference surface of the World Height System as well as the connection of the individual vertical datums to the new fundamental surface. The information required would be the ellipsoidal and orthometric heights at one or more stations in a vertical datum, a high degree potential coefficient model, and terrestrial gravity data in a 2° cap about the benchmark. Several simulation studies were carried out with different tracking station networks. These networks included SLR/VLBI stations, a DORIS tracking network, and finally, an 85 station combined network. The accuracy of the determination of the fundamental reference surface was found to be ±3 kgal cm while the accuracy of the vertical datum connection to this surface varied from 4 to 20 kgal cm. A simplified world height system (SWHS) was discussed. Such a system could be defined given station ellipsoidal heights transformed into a geocentric reference frame, and geoid undulation information. Such data would yield an orthometric height referred to the ideally defined geoid. This geoid would not be tied, directly, to a mean sea level. The accuracy of the determination of orthometric heights in the SWHS will be very dependent on the accuracy of the determination of geoid undulations. The report concludes with some specific recommendations on computations that can be made with real data that could yield information helpful for the future recommendation on the operational development of the ideal World Height System.