Developing local geoid model to assess accuracy of orthometric heights from GPS-based ellipsoidal heights in Botswana

Abstract

The Global Navigational Satellite Systems, particularly the Global Positioning System has emerged as state of the art technology for providing precise horizontal and vertical location of points on surface of the earth. The vertical location is with respect to the Reference spheroid and known as ellipsoidal height. However in most of the application areas the heights considered are the orthometric heights (Mean Sea Level heights) with respect to the Geoid. The GPS-derived ellipsoidal heights are converted to corresponding orthometric heights using either a global or a local geoid model. Geoid model is a mathematical relation between the geoidal separation (N) and the horizontal location of a point. The accuracy of the conversion of ellipsoidal heights to orthometric heights depends on the accuracy of the geoid model. The objective of this study is to develop a local geoid model for a region of about 100 × 100 km2 area in Botswana in order to assess the accuracy of orthometric heights obtained from ellipsoidal heights. The geometric method is used for computation of the geoidal separation of control points from available orthometric heights and thereafter these points are used along with their horizontal coordinates and the geoidal separation to develop a surface model using a second degree polynomial as well as a TIN model. From the study it appears that an accuracy of about 20 cm in orthometric heights can be achieved by employing suitable number of well planned control points and an appropriate mathematical model in development of the geoid model.