Polynomial interpolation methods in development of local geoid model

Abstract

In geodesy three surfaces, the physical surface of the earth, the geoid and the reference ellipsoid are encountered giving rise to orthometric height (h), the ellipsoidal height (H) and the geoidal separation (N). The orthometric height and the ellipsoidal height are with reference to the geoid and the reference ellipsoid respectively. The vertical separation between the ellipsoid and the geoid is the geoidal separation. A mathematical relation depicting the surface of the geoid with regard to the reference ellipsoid is the geoid model. It relates the geoidal separation with the horizontal location.The Global Navigational Satellite System provides precise location of points on the surface of the earth. The vertical location provided is the ellipsoidal height which needs conversion to a more usable format, the orthometric height. This is done by integrating ellipsoidal heights with a geoid model. The accuracy of conversion depends on the accuracy of geoid model. Therefore, development of geoid model has become a current area of research in geodesy.Objective of this study is to develop a local geoid model by employing various polynomial models and thereafter to analyse the accuracy of these models. The test area is in Papua New Guinea. The geometric method is used for computation of the geoidal separation from ellipsoidal and orthometric heights and thereafter the horizontal coordinates and the geoidal separation are used to develop the geoid surface using second, third and fourth degree polynomials. The study shows that the third degree polynomial provided an accuracy of ±20cm.