Determination of a Gravimetric Geoid Model of Greece Using the Method of KTH

Abstract

The main purpose of this study is to compute a gravimetric geoid model of Greece using the least squares modification method developed at KTH. In regional gravimetric geoid determination, the modified Stokes’ formula that combines local terrestrial data with a global geopotential model is often used nowadays. In this study, the optimum modification of Stokes’ formula, introduced by Sjöberg (2003), is employed so that the expected mean square error (MSE) of the combined geoid height is minimized. According to this stochastic method, the geoid height is first computed from modified Stokes’ formula using surface gravity data and a global geopotential model (GGM). The precise geoid height is then obtained by adding the topographic, downward continuation, atmospheric and ellipsoidal corrections to the approximate geoid height. In this study the downward continuation correction was not considered for the precise geoid height computations due to a limited DEM. The dataset used for the computations, consisted of terrestrial gravimetric measurements, a DEM model and GPS/Levelling data for the Greek region. Three global geopotential models (EGM96, EIGEN-GRACE02S, EIGEN-GL04C) were tested for choosing the best GGM to be combined into the final solution. Regarding the evaluation and refinement of the terrestrial gravity measurements, the cross-validation technique has been used for detection of outliers. The new Greek gravimetric geoid model was evaluated with 18 GPS/Levelling points of the Greek geodetic network. After using a 7-parameter model to fit the geoid model to the GPS/Levelling data, the agreement between the absolute geoid heights derived from the gravimetric method and the GPS/Levelling data, was estimated to 27 cm while the agreement for the relative geoid heights after the fitting, to 0.9 ppm. In an optimal case study, considering the accuracies of the ellipsoidal and orthometric heights as $\sigma _h \approx \pm 10\,{\textrm{cm}}$ and $\sigma _H \approx \pm 20\,{\textrm{cm}}$ respectively, the RMS fit of the model with the GPS/Levelling data was estimated to $\sigma _N \approx \pm 15\,{\textrm{cm}}$. The geoid model computed in this study was also compared with some previous Greek geoid models, yielding better external accuracy than them.