1. Estimating the cost to Helmert heights of a lateral approximation of the topographical density distribution
Robert Kingdon1, Artu Ellmann1, Petr Vanicek1, Marcelo Santos1
1Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick E3B 5A3
Type B Simulations
Type A Simulations
Helmert Orthometric Heights vs
Rigorous Orthometric Heights
θ=45° B1
θ=30° B2
θ=15° B3
Helmert’s Mean Gravity:
Cone A1
Wedge A2
Slab A3 A1 B1
Rigorous Mean Gravity:
Corrections to Helmert’s Mean Gravity:
Values from 0 (red) to 5.7 (blue) cm, 1 cm contours.
Values from -1.2 (green) to 1.2 (red) cm, 1 cm contours.
=Topographical Effect A2 B2
=Non-topographical Effect
Corrections to Helmert Orthometric Height:
Test Area
Values from 0 (red) to 7.9 (blue) cm, 1 cm contours.
Values from -1.7 (green) to 1.6 (red) cm, 1 cm contours. A3 B3
Heights from 0 (green) to 2862 (white) m, 500m contours.
Results
– Corrections could potentially reach ~8 cm in mountainous areas, and are largest for regional phenomena.
– Corrections are small for local phenomena, such as cones; and are limited in extent.
– More realistic corrections reach up to ~3 cm, but are only > 1 cm (in the test area) at elevations above 1500 m.
– There do exist limited areas where these corrections are significant, in terms of rigorous orthometric heights. Effects on e.g. geoid heights have yet to be evaluated.
Acknowledgements
We would like to acknowledge NSERC and for their funding of this research.
Values from 0 (red) to 6.9 (blue) cm, 1 cm contours.
Values from -2.3 (green) to 2.6 (red) cm, 1 cm contours.