Local Geoid Modelling of Lagos Island Area Using Geometrical Interpolation Method

Abstract

The geoid as an equipotential surface which coincides on the average with the mean sea level has significant relevance in geodesy, surveying and other earth related disciplines. It finds applications in geographic information systems (GIS), engineering, the transformation of ellipsoidal heights of points to the orthometric heights, etc. This paper focuses on the geoid modelling technique based on geometrical interpolation approach by fitting a surface that depends on the reference points that are chosen in the critical and characteristic locations of the field to represent the trend of the geoid surface. Using the orthometric heights and the ellipsoidal heights, empirical geoidal undulations for all the points were computed. A multiple regression model was formulated as the required geometrical model to further adjust the derived geoid undulations from observation. Using a surface interpolation (kriging) approach, the coordinate and the computed geoidal heights of some well selected points were utilized in Surfer8 for gridding. This was used as a model for generating the geoidal heights of any other arbitrary points whose coordinates are known. From the analysis, it was observed that the use of the lower order polynomial (regression) to further model the geoid surface gave the mean square errors of 0.36cm and 5.58cm in self and cross validations respectively, with a smoothened geoid terrain, while the fundamental equation that relates the trio (orthometric, ellipsoidal and geoidal heights) gave the mean square errors of 7.35cm and 187.831cm in self and cross validations respectively. The modelled surface was generated at contour intervals of 0.5m for the two equations, while the digital terrain models were also generated in both cases.