Journal of Agriculture, Science and Technology

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Practical application of the geometric geoid for heighting over Nairobi county and its environs

PA Odera, SM Musyoka, MK Gachari


Geoid determination is one of the main current geodetic problems in Kenya. This is because a geoid model is required to convert ellipsoidal heights to orthometric heights that are used in practice. A local geometric geoid covering Nairobi County and its environs has been determined by a geometric approach. Nineteen points levelled by both Global Positioning System (GPS) and precise levelling techniques in the area of study have been used. Seven triangulation points have been used for the determination of transformation parameters between World Geodetic System 1984 (WGS84) and Arc‐Datum 1960 coordinates in order to express the local geoid height as a function of position. The geoid height is expressed as a function of the local plane coordinates through a biquadratic surface polynomial, using 14 GPS/levelling points. Five points have been used for testing the results. The experience with Nairobi County and its environs geometric geoid indicates that interpolation of geoid heights in a small area by a biquadratic polynomial is simple and it works well. The geoid heights obtained by biquadratic polynomial (interpolation) compare favourably on the test points with root mean square and standard deviation of ±1cm in the area of study. This accuracy is sufficient for most engineering projects.

Key words: Geoid, GPS, coordinate transformation, height determination, Nairobi County

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