ESTIMATION OF ORTHOMETRIC HEIGHT USING EGM2008 AND GPS OVER NAIROBI COUNTY AND ITS ENVIRONS

Abstract

Global Navigation Satellite Systems (GNSS) have been used widely in 3‐dimensional positioning globally, regionally and locally. Global Positioning System (GPS) is one of the most extensively used GNSS in Earth sciences. GPS which employs World Geodetic System adopted in 1984 (WGS84) as the reference system has extensively been used for height determination and has brought a revolution on how relative and absolute heights on earth’s surface are determined. GPS measures ellipsoidal heights above a reference ellipsoid (WGS84). Although these heights can be useful in deformation surveys, machine monitoring and guidance, they are not applicable in engineering projects (e.g. sewer lines, pipelines and road construction among others) where heights referenced to an equipotential surface (geoid) are required. The separation between the geoid and a reference ellipsoid (geoid undulation) is necessary in converting ellipsoidal height into orthometric height. In this study we determine geoid undulation from Earth Gravitational Model of 2008 (EGM2008) using freely available Alltrans EGM2008 calculator software version 3.002 at 18 GPS/levelling points. The determined geoid undulations are used to determine estimated orthometric heights from ellipsoidal heights. We then model the differences between spirit‐levelled orthometric and estimated orthometric heights by a four parameter model (first order polynomial) at 11 GPS/levelling points using least squares technique for improvement on the estimated orthometric heights. 7 GPS/levelling points are used for testing the performance of the four parameter model over Nairobi County and its environs. The standard deviations of the differences between observed and estimated orthometric heights (obtained from EGM2008 and GPS) at all GPS/levelling points (18) and 7 test points are ±0.52 and ±0.35 m respectively. When the four parameter model is applied, the standard deviations of the differences between spirit‐levelled and improved estimated orthometric heights at the 7 test points reduces to ±0.10 m, representing an improvement of 71%. The accuracy of ±0.10 m obtained at the test points may be sufficient for some engineering projects that do not require very high orthometric height accuracy.