Precise geoid determination over Sweden using the Stokes-Helmert method and improved topographic corrections

Four different implementations of Stokes formula are employed for the estim ation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications: modif ied Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes kernel: and a least-squares (LS) spectral weighting proposed by Sjoberg (1991). Classic al topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formu lae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-leve lling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stat ions distributed over Sweden. The LS method is in best agreement, with a 10 .1-cm mean and +/-5.5-cm standard deviation in the differences between grav imetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. T he results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to +/-1.1 cm. For compar ison, the NKG96 geoid yields a 17-cm mean and +/-8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to t he GPS stations, the standard deviation reduces to +/-6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the a ccuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m w ith a mean value of 29.01 m. The standard errors of the computed geoid heig hts, through a simple error propagation of standard errors of mean anomalie s, are also computed. They range from +/-7.02 to +/- 13.05 cm. The global r oot-mean-square error of the LS model is the other estimation of the accura cy of the final geoid, and is computed to be +/- 28.6 cm.