Regional Geoid Determination

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Abstract
78With the advent of the satellite Global Positioning System (GPS), geoid determination enjoys a renewed popularity. In many positioning, mapping, and exploration applications, conventional spirit leveling is being replaced by orthometric height determination using GPS and the geoid. 1 The geoid, loosely defined as the equipotential surface of the earth’s gravity field at mean sea level, is the reference surface above which orthometric heights are measured. By using GPS, three-dimensional coordinates or coordinate differences are obtained in a Cartesian X, Y, Z system. To approximate the shape and the gravity field of the earth, a reference ellipsoid of revolution is introduced, which can be used to transform the X, Y, Z GPS coordinates to geodetic latitude and longitude, φ, λ, and ellipsoidal height, h. Using relative GPS positioning between two points, orthometric height differences can be obtained as ΔH = Δh – ΔN. Since GPS provides only h or Δh, the required geoid undulations N or ΔN must be computed from gravimetric data. If this is not done, errors exceeding several meters may result. To achieve ΔH accuracies which are comparable to Δh, the ΔN component must be of the same quality. Typical accuracies of the GPS component are currently of the order of 1 to 2 parts per million (ppm) over distances less than 100 km. Various studies have shown that ΔN can also be obtained with the same accuracy. 2–7 Consequently, ΔH accuracies of 1 to 2 ppm are also possible, rendering leveling by GPS and the geoid a very good, and much faster and cheaper, alternative to the traditional spirit leveling.

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