An optimum way to determine a precise gravimetric geoid model based on the least-squares modification of Stokes’ formula — A case study of Sweden

The modification of Stokes’ formula allows the user to compensate the lack of a global coverage of gravity data by a combination of terrestrial gravity and a global geopotential model. The minimization of the errors of truncation gravity data and potential coefficients could be treated in a least-squares sense as is the basic ingredient in the Royal Institute of Technology (KTH) approach as proposed by Sjöberg in 1984. This article presents the results from a joint project between KTH and the National Land Survey of Sweden, whose main purpose is to evaluate the KTH approach numerically and to compute a gravimetric geoid model for Sweden. The new geoid model (KTH06) was computed based on the least-squares modification of Stokes’ formula, the GRACE global geopotential model, a high-resolution digital terrain model and the NKG gravity anomaly database. The KTH06 was fitted to 1162 GPS/levelling points by a 7-parameter transformation, yielding an all-over fit of 19 mm and 0.17 ppm. The fit is even smaller than the estimated internal accuracy for the geoid model (28 mm). If we assume that the accuracy of the GPS and levelling heights are 10 mm and 5 mm, respectively, it follows that the accuracy of the expected gravimetric geoid heights are of the order of 11 mm. Also, we found a significant expected difference between the KTH06 and NKG2004 models in rough topographic areas (up to 36 cm). As the major ground data and global geopotential model were almost same in the two models, we believe that there are different reasons that come into play for interpreting the discrepancies between them, as the method for eliminating outliers from the gravity database, the interpolated denser gravity observations using the high-resolution digital elevation model before Stokes’ integration, the potential of the LSM kernel, which matches the errors of the terrestrial gravity data, GGM and the truncation error in an optimum way, and the effect of applying more precise correction terms in the KTH approach compared to the remove-compute-restore method. It is concluded that the least-squares modification method with additive corrections is a very promising alternative for geoid computation