Orthometric Height Determination using GPS to Fast Track Development: a Case study of Nairobi County, Kenya

The Global Positioning System (GPS) is commonly considered a threedimensional system. However, the heights obtained from GPS are typically heights above an ellipsoidal model of the Earth. The heights are not consistent with levelled heights above mean sea level, often known as orthometric height. Orthometric heights reflect the nature of terrain and are useful in geodetic and surveying applications. Conversion from ellipsoidal heights to orthometric height requires a geoid undulation model. The objective of this study was to design a geoid undulation model of Nairobi province using geometric approach in order to facilitate transformation of ellipsoidal heights to orthometric heights. The approach is based on a simple relationship between ellipsoidal h, orthometric H and geoid undulation N heights. We used a second order polynomial to interpolate geoid undulation variation within the study area. Parameters of the polynomial were computed from a set of controls with predetermined ellipsoidal and orthometric heights using least squares indirect observation method. A designed user interface based on the approach transformed ellipsoidal heights to orthometric heights to an accuracy of cm. The accuracy level enables the use of GPS for applications like engineering feasibility studies, approximating earth works and topographic mapping. Exploiting such approach for determination of orthometric heights reduces time and cost taken in ordinary levelling surveying. Surveying takes a bigger percentage cost in most engineering projects like road construction and power line route surveys. Therefore, the designed approach will spur sustainable infrastructural development by providing fast and accurate alternative means of determining orthometric heights. Moreover, orthometric heights are significant in producing contours in topographic and thematic maps which are important sources of spatial baseline information. .