Global positioning system testing of geoids computed from geopotential models and local gravity data: A case study

Abstract

Oithometric height differences obtained from a combination of global positioning system (GPS) ellipsoidal height differences and gravimetric geoid predictions have the potential of replacing costly and time‐consuming spirit leveling, especially in remote unsurveyed areas like the Canadian north. In this paper 88 GPS stations along a 900‐km‐long first‐order leveling line around the Great Slave Lake area, Northwest Territories, Canada, are used as control for intercomparison of geoid predictions which used various geopotential models and gravimetric techniques. The global spherical harmonic models tested include satellite‐only solutions, such as GEM‐9, GEM‐L2, GEM‐Tl and GEM‐T2, as well as combination solutions, such as GEMlOB, RAPP78, RAPP81, GPM2, OSU86F, OSU89A, OSU89B and OSU91 A. These models fit the geoid with standard errors of 30 to 50 cm. Local gravimetric geoid predictions based on available gravity data were carried out using various forms of Stokes integration, fast Fourier transform methods and least squares collocation. For the first two methods, gravity data were gridded on a 5 km by 5 km Cartesian grid and on a 5′ by 10′ geographical grid. No terrain reductions were applied due to the flatness of the topography. Results show that the differences between control and predicted geoid heights have standard deviations at the 20‐to 25‐cm level, with differences between methods at 2 to 8 cm (1σ). By fitting a four‐parameter model to the geoid predictions (corresponding to a GPS, leveling or geoid datum shift and scale change), long‐wavelength errors were significantly reduced, with all methods yielding geoid fits of about 7 cm (1σ). The relative accuracies achieved were of the order of 2 ppm for baselines shorter than 200 km, and of the order of 1 ppm for baselines with lengths between 200 km and 700 km. A discussion of possible error sources concludes the paper. Some errors in the original GPS data were detected in the initial phase of the project, and a GPS resurvey verifyed these errors.