Prediction of Orthometric Heights of Points for Topographic Mapping

Heights are determined based on a particular reference surface for the purpose of controlling vertical coordinates of points during mapping. These heights are usually presented in various countries as orthometric heights which has geoid as its reference surface. Orthometric height is the geometric distance from a point on the earth’s surface measured along the curved plumbline to the geoid. In practice, orthometric heights are determined by conventional precise levelling combined with gravity observations along the levelling routes. They have conceptual importance in surveying as they provide the needed heights for controlling other height measurements in surveying. However, its determination seems to be time consuming, laborious and less economical of project cost. Where the density of the available orthometric heights in a study area is not enough, more heights can be measured. In some cases, where observations are not possible, probably due to inaccessibility of the stations needed for measurement or logistic problems, the required orthometric heights can be estimated (predicted). Therefore, this paper attempts the prediction of orthometric heights for unknown stations in a study area using least squares collocation technique. Data used for the study are the rectangular coordinates and orthometric heights of thirty known stations within the study area. Analyzing the results obtained, it was observed that the least squares collocation technique used for the prediction did not introduce significant distortion into the results obtained at 5% level of significance. Also, it was observed that the predicted heights satisfactory. That is, the difference between the observed and the predicted orthometric heights of the same station was found to be within the tolerant error limit.