Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test areaThe remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification of Stokes' Formula (LSMS) technique not requiring gravity reductions is implemented here with a Residual Terrain Modelling based interpolation of gravity data. The 2-D Spherical Fast Fourier Transform (FFT) and the LSC methods applying the RCR technique and the LSMS method are tested over the Auvergne test area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs best with 3.0 cm r.m.s difference with GPS-levelling while the LSMS method gives the best agreement with GPS-levelling with 2.4 cm r.m.s after a 4-parameter fit is used. However, the quasi-geoid models derived using two techniques differed from each other up to 33 cm in the high mountains near the Alps. Comparison of quasi-geoid models with EGM2008 showed that the LSMS method agreed best in term of r.m.s.

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Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric models for Turkish territory were computed depending on OSU91 (TG-91 ) and EGM96 (TG-03 ) earth gravitational models. The release of the Earth Gravitational Model 2008 (EGM08 ), the collection of new surface gravity observations, the advanced satellite altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain Model (RTM ) reduction of the surface gravity data. Fast Fourier Transformation (FFT ) was then used to obtain the residual quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height (TQG-09 ). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model was then converted to the geoid model (TG-09 ) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09 ) (or a transformation surface) to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be  0.95 cm, which represents the internal precision of the final combination.And finally, we tested the hybrid geoid model with GPS/leveling data, which were not used in the combination, to assess the external accuracy. Results show that the external accuracy of the THG-09 model is  8.4 cm, a precision previously not achieved in Turkey until this study.

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