DEVELOPMENT OF MATHEMATICAL MODELS FOR DENSIFICATION OF ORTHOMETRIC HEIGHTS

Abstract

The global positioning system (GPS) relative observations would provide a powerful and fast tool for obtaining an accurate relative three dimensional position of a point (X,Y and ellipsoidal height h). The required orthometric height values for most of surveying and engineering applications are not directly provided by GPS observations. Orthometric heights are normally derived using spirit leveling with standard observation and computation procedures .This requires the spirit level equipment to be setup from point to point along a leveling line which is a time consuming and a tedious task. The conversion from ellipsoidal to orthometric heights requires a geoid height which can be obtained from a geoid model. This research presents accurate, relatively simple, and reliable mathematical models for densification of orthometric hights (H) to densify the number of spot heights for contour maps and for the densification of geoidal heights in case of geoid contours when it is needed to draw the contour maps .Also can be used for densification of geoidal heights . To check the reliability of the model a dense test network was designed. Both precise leveling and GPS observations were carried out and adjusted for common stations to establish precise vertical control networks and it gave a good result of analysis of variance , with standard error not more than 3 Cm.