The relation between rigorous and Helmert’s definitions of orthometric heights |
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| Authors: | M C Santos P Vaní?ek W E Featherstone R Kingdon A Ellmann B -A Martin M Kuhn R Tenzer |
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| Institution: | (1) Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, NB, Canada, E3B 5A3;(2) Present address: Department of Civil Engineering, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia;(3) Present address: Critchlow Associates Ltd, 61 Molesworth Street, Wellington, New Zealand;(4) Western Australian Centre for Geodesy, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia;(5) Faculty of Aerospace Engineering, Physical and Space Geodesy, Kluyverweg 1, 2629 HS Delft, P.O. Box 5058, 2600, GB, Delft, The Netherlands |
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| Abstract: | Following our earlier definition of the rigorous orthometric height J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model. |
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| Keywords: | Orthometric height Geoid Mean gravity Plumbline |
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