Determination of a gravimetric geoid model of Sudan using the KTH method

The main objective of this study is to compute a new gravimetric geoid model of Sudan using the KTH method based on modification of Stokes’ formula for geoid determination. The modified Stokes’ formula combines regional terrestrial gravity with long-wavelength gravity information provided by the global gravitational model (GGM). The collected datasets for this study contained the terrestrial gravity measurements, digital elevation model (DEM), GPS/levelling data and four global gravitational Models (GGMs), (EGM96, EIGEN-GRACE02S, EIGEN-GL04C and GGM03S). The gravity data underwent cross validation technique for outliers detection, three gridding algorithms (Kriging, Inverse Distance Weighting and Nearest Neighbor) have been tested, thereafter the best interpolation approach has been chosen for gridding the refined gravity data. The GGMs contributions were evaluated with GPS/levelling data to choose the best one to be used in the combined formula. In this study three stochastic modification methods of Stokes’ formula (Optimum, Unbiased and Biased) were performed, hence an approximate geoid height was computed. Thereafter, some additive corrections (Topographic, Downward Continuation, Atmospheric and Ellipsoidal) were added to the approximated geoid height to get corrected geoid height. The new gravimetric geoid model (KTH-SDG08) has been determined over the whole country of Sudan at 5′ x 5′ grid for area ( 4 ). The optimum method provides the best agreement with GPS/levelling estimated to 29 cm while the agreement for the relative geoid heights to 0.493 ppm. A comparison has also been made between the new geoid model and a previous model, determined in 1991 and shows better accuracy. ≤φ ≤ 23 , 22 ≤ λ ≤ 38 Keywords: geoid model, KTH method, stochastic modification methods, modified Stokes’ formula, additive corrections