A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers

Abstract

This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations.