Extracted GPS-Derived Orthometric Heights to Form a Geoid Model in Sudan

Abstract

The Global Positioning System (GPS) derived-heights have no relationship to the geopotential surface of the Earth’s gravity field because it is referenced to a geocentric ellipsoid. There is a need to refer heights to the gravity field, in most cases, for the determination of the fluid flows. To convert GPS-derived ellipsoidal heights (h) to orthometric heights (H), it is necessary to use a geoid model (N). This study describes the development of gravimetric geoid model referred to WGS84 reference surface for the study area. Three different approaches for geoid determination have been studied. In the first approach; a gravimetric geoid model is constructed using: the observed gravity anomaly, the Global Geopotential Models (GGM) gravity anomaly and the digital elevation models (DEM). In the second approach; the GPS-derived ellipsoidal heights (h) and precise levelling data are used together to obtain the geometric geoid. In the third approach a combination of the gravimetric method and the geometric method is used to establish the hybrid geoid.

A number of data files were compiled for this work, containing more than 25,500 gravity point data. Global geopotential models were used to determine the long wavelength effect of the geoid surface. The GGMs contributions were evaluated with GPS/levelling data to choose the best one to be used in the combined formula. Gridding algorithms (Kriging, Inverse Distance Weighting, Nearest Neighbor and Polynomial Regression) are used to obtain a regular data grid. Corrector surface (CS) for conversion of GPS height (h) to orthometric height (H) is created. EGM96 global geopotential model up to degree and order 360 and EGM08 global geopotential model up to degree and order 360 were tested to choose the best one fitting the study area. EGM96 is chosen as a reference model for the gravimetric geoid. An additive correction is calculated by the summation of four corrections, the Down Ward Continues effect (NDWC), the terrain correction (NTC), the atmospheric correction (NATM) and the ellipsoidal correction (Ne). The new gravimetric geoid (SDG2011) has been tested usig 18 GPS/levelling points. The overall accuracy is 26 cm.

From the available 128 GPS/Levelling data laid in the Northern part of the study area, 113 GPS/Levelling stations out of 128 were used to construct the geometric geoid model (Ngeom) and the remaining points used for checking purpose. The gravimetric and the geometric geoid were combined to obtain the hybrid geoid model. The results show that the hybrid geoid is best of all since it gives standard deviation about 22 cm while the gravimetric and the geometric present standard deviations about 26 cm and 24 cm respectively.

Looking for more precision, the area of study is subdivided into three zones, according to the density of the data, to overcome the ill distribution of the GPS/Levelling data. The standard deviation in the North-West (empty zone) remains the same while the accuracy in the other two zones increased. The North-East zone presents standard deviation about 12 cm and Central zone shows about 19 cm.