Toward the Computation of a Geoid Model of Ghana

English Abstract:

Use of the Global Positioning System (GPS) was introduced to Ghana in the early 1990s. The widespread use of GPS in height-related surveying and mapping activities has made the computation of a geoid model a very important task. In this research, the first gravimetric geoid for Ghana is being computed using the Stokes-Helmert method, developed by the University of New Brunswick (UNB), Canada. This method utilizes a two space solving the associated boundary value problems, including the real and Helmert’s spaces. The UNB approach combines observed terrestrial gravity data with long-wavelength gravity information from a Global Gravitational Model (GGM).

All the terrestrial gravity data used in the computation was derived from the Geological Survey Department of Ghana, due to difficulties in obtaining data from BGI and GETECH. The first gravity survey was part of Ghana’s contribution to the International Geophysical Year, 1957-1958, and was linked to the gravity network of the neighboring countries and to Potsdam reference system through a connection to Pendulum House, Cambridge, United Kingdom (UK). A least squares adjustment of the gravity survey network was carried out in the UK. Since this first campaign of gravity collection, more data have been added to the gravity database, which now covers between 70 and 80 percent of the country. A GGM is used to pad those areas lacking in terrestrial gravity data.

For the computation of topographic effects on the geoid, the STRM, a Digital Elevation Model (DTM) generated by NASA and the National Geospatial Intelligence Agency (NGA), is being used. Since the terrain in Ghana is relatively flat, the topographic effect, often a major problem in geoid computation, is unlikely to be significant. This first geoid model for Ghana will be computed on a 1'1' grid over the computation area bounded by latitudes 4ºN and 12ºN, and longitudes 4ºW and 2ºE. GPS/levelling heights will be used to validate the results of the computation.

Keywords: Geoid, Stokes’ formula, Global Gravitational Model, Topographic effect, Digital Terrain Model