Precise geoid determination over Sweden using the Stokes-Helmert method and improved topographic corrections
2001 (English)In: Journal of Geodesy, ISSN 0949-7714, E-ISSN 1432-1394, Vol. 75, no 3-Feb, 74-88 p.Article in journal (Refereed) Published
Four different implementations of Stokes formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications: modified 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). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations 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 gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to +/-1.1 cm. For comparison, 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 the 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 accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from +/-7.02 to +/- 13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be +/- 28.6 cm.
Place, publisher, year, edition, pages
2001. Vol. 75, no 3-Feb, 74-88 p.
geoid height, Stokes' formula, modification, topographic correction, downward continuation
IdentifiersURN: urn:nbn:se:kth:diva-20679ISI: 000169042200002OAI: oai:DiVA.org:kth-20679DiVA: diva2:339375
QC 201005252010-08-102010-08-10Bibliographically approved