Global accuracy estimates of point and mean undulation differences obtained from gravity disturbances, gravity anomalies and potential coefficients
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Date
1979-05
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Ohio State University. Division of Geodetic Science
Abstract
Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap, and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled on the assumption that the coefficients are determined from a global distribution of 1° x 1° mean anomalies. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone. The two methods exhibit analogous error characteristics, the estimated errors of the gravity disturbance method being only slightly better. For continuous and errorless gravity data inside a spherical cap having a radius of 10° and with potential coefficients derived to degree 180 from a global set of 1° x 1° mean anomalies given to an accuracy of ± 10 mgal (± 1 mgal), the typical error in the difference of undulations is 30 cm to 40 cm (5 cm to 10 cm), depending on their separation. In the absence of more detailed cap data, the error is as high as 160 cm ( 70 cm). In the latter case, the corresponding error for 1° x 1° mean undulation differences is about 140cm (30cm).
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Prepared for National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland: Grant NGR 36-008-161