Performance evaluation of the Earth Gravitational Model 2008 (EGM2008) – a case study

Abstract

Ghana’s local geodetic reference network which is based on the War Office 1926 ellipsoid was established using astro-geodetic observations during the British Colonial era with data in latitude, longitude and orthometric height (?,?,?) without the existence of ellipsoidal height. The Global Positioning System (GPS) observations which is an example of the Global Navigation Satellite System (GNSS) is being referenced to the World Geodetic System 1984 (WGS84) ellipsoid with data in latitude, longitude and ellipsoidal heights (?,?,ℎ). This prevalent situation makes it difficult to apply standard forward transformation equation for direct conversion of ellipsoidal heights (h) which is global to a practical height (H) within Ghana local geodetic reference network. In order to overcome such a challenge, many researchers resort to various methods of determining the geoidal undulations for a local and national geodetic network and improving the recent New Earth Gravitational Model accuracies and its performances. This present study therefore seeks to evaluate such method of estimating geoidal heights using the Earth Gravitational Model 2008 (EGM08) in a part of the University of Mines and Technology, UMaT, Tarkwa. The estimated geoid heights obtained by the EGM08 model were compared with 328 discrete geometrical heights from co-located GPS and Total station orthometric heights of the University Primary Levelling Networks. The methods applied include estimating the geoidal heights using the EGM08 model, a geometric method and a polynomial mathematical model for improving the estimated EGM08 geoid heights values. The statistics of the differences between derived geoid heights by the geometric approach and corresponding geoid heights obtained from the geoid model (EGM08) suggests that, the EGM08 model is most suitable at this moment. The RMSE, Mean Error, and the Standard deviation of their geoidal height differences are 0.120825 m, 2.18823 m, and 3.47678 m, which is better in the area of interest. The study concluded that, the recent geoid model can be applied in UMaT and the polynomial mathematical model is the best model for modelling EGM08 geoid heights values for a local geoid model.

Keywords: GPS/levelling, Earth Gravitational Model, Polynomial mathematical model, Geoid undulations