Precise geoid determination over Sweden using the Stokes–Helmert method and improved topographic corrections |
| |
| Authors: | H Nahavandchi L E Sjöberg |
| |
| Institution: | (1) National Cartographic Center, Meraj Ave, Azadi Square, P.O. Box 13185-1684, Tehran, Iran, e-mail: h-nahav@ncc.neda.net.ir; Tel.: +98 21 6033566; Fax: +98 21 6008477, IR;(2) Royal Institute of Technology, Department of Geodesy and Photogrammetry, 100 44 Stockholm, Sweden, SE |
| |
| Abstract: | 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 Sj?berg (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.
Received: 15 September 1999 / Accepted: 6 November 2000 |
| |
| Keywords: | : Geoid height Stokes' formula Modification Topographic correction Downward continuation |
| 本文献已被 SpringerLink 等数据库收录！ |
|
