A Comparison of Geoid and Quasigeoid Modeling Methods in Rough Topography

Abstract

Geoid models covering regions as large as Canada, the United States, Europe and Scandinavia have been successfully computed with relative precision of a few centimetres over distances up to 1000 km. While this precision is proven using GPS measurements taken along levelling lines, it is a challenge to obtain the same precision in areas of rugged topography, especially since there are very few levelling lines which run up to the top of mountains. Here, geoid and quasigeoid models are computed along levelling lines with stations as high as 1500 metres, crossing the southern part of the Canadian Province of British Columbia where heights range from sea level to about 3500 metres. Various mathematical modeling techniques have been tested. They all involve the use of a global geopotential model and local gravity anomalies, and differ with regard to the way they treat the topography. The first one is the straightforward application of Stokes’ integral using the condensation technique. It consists of removing the effect of the topography according to Helmert’s condensation reduction from gravity anomalies and restoring the corresponding effect, i.e., the indirect effect, to the geoid heights. The second technique applied is called the residual terrain model (RTM) technique. In this case, the effect of the topography with respect to an average height surface is removed and restored. Height anomalies are here computed. They are transformed to geoid height for comparison with the other technique. Both techniques agree and provide a precision of 7 cm along a profile of 900 km. In most of the region, the average gravity data spacing is 10 – 15 km. Since parts of the region had a dense data coverage, a 5 km-grid was used as the most dense grid in the test computation. The denser grids did not statistically agree better with GPS than the wider grids but, in general, produce a better resolution geoid in regions of rugged topography. Graphical display will be required in following studies to show the difference between the two techniques. A close look to the correlation with topography may identify the route to improvement.