Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja

Abstract

Ellipsoidal heights from GNSS require geoid model for conversion to orthometric height. The geoid model could be global, regional or local. The lack of national geoid model in Nigeria makes the development of local geoid very critical to local applications in place of integrated global geoid models. This study compares two polynomial geoid models for terrain representation in the FCT, Abuja. Nine coefficients were used to model the FCT surface for geoid interpolation and orthometric height modeling. Model A involved the use of the 2-D (x, y) positions while model B used 3-D (x, y, ∆h) where ∆h= (h ave – hi) the difference in average ellipsoidal height (h ave ) and each point’s ellipsoidal height (hi). The ∆h term is based on the assumption that the geoid varies with topography and may hence possibly lead to some improvements in the accuracy of orthometric height determination. DGPS observations were carried out to determine ellipsoid heights. Least squares adjustment was performed to compute the coefficients of the models. Model A achieved standard deviation of σ = 11 cm while Model B achieved σ = 13cm. Though Model B has a term that included highly accurate ellipsoidal height differences (∆h), it has not resulted into any accuracy improvement over the model A. Model A based on 2-D positions is hence the better of the two models. The t-test and hypothesis test at 95% confidence limit, however, showed that the two models did not differ significantly. Model A having lower standard deviation is recommended with GNSS determined ellipsoidal heights to determine orthometric heights within the FCT. This becomes an easy alternative to conventional spirit leveling technique for production of topographical maps, cadastral surveys, and engineering/environmental applications.