Adjustment of the Surface of the Gravimetric Geoidal Height Model between Constrained GPS-levelling Stations

The geoid can directly be determined from the GPS ellipsoidal height and physical (orthometric) heights derived from levelling. This has increased interest in the determination of the geoid mainly from users of GPS. It replaces costly conventional levelling operations with quicker and cheaper GPS surveys, as long as the geoidal height has been computed to a high accuracy. The geoid derived with this method has high absolute and relative accuracy, especially when the GPS coordinates have been tied directly to VLBI or SLR stations. But it is not dense enough to produce a national levelling reference surface. Following two geoid models can be combined: the classical gravimetric solution, which has very high resolution and relative accuracy but poor absolute accuracy, and the GPS-levelling geoid model which has poor resolution but very high accuracy. In this study, some robust methods are used that permit us to benefit from the advantages of the two above solutions. Different fitting procedures including linear and cubic splines interpolations as well as a four-parameter solution are investigated over Norway. The computed geoid-type surface provides significant improvement in the accuracy of height transformation from GPS data. The post-fitting residuals realize this improvement.