Faculty: Environmental Sciences
Department: Surveying & Geo-informatics


Oluyori, D. P.
Ono, M. N.


Orthometric heights based on GNSS require a geoid model to convert highly accurate ellipsoidal height (h) to the much desired orthometric height (H) critical to many cadastral, surveying, mapping , engineering and environmental applications. The GNSS uses the default integrated global geoid models (EGM96/EGM2008) for ellipsoidal height conversion to orthometric but for local applications, global model is inadequate and hence development of local geoid models in the absence of a national geoid becomes very critical. The aim of this research is to model orthometric heights from multi-networks of GNSS/Precise levelling in Federal Capital Territory, Abuja by using ellipsoid heights (h) and the existing orthometric heights (H)from the relationship N= (h-H) for geoid modelling. The objectives are to : i) investigate the physical status/stability of the existing orthometric heights in the FCT, ii) to carry out GNSS observations on existing controls for ellipsoidal height determination by relative technique, iii) determine geoid undulation of existing controls using N= (h – H), iv) develop Microsoft excel program for interpolation of geoid undulation and hence model orthometric heights, v) to compare height obtained from model with existing orthometric height by statistical t test. This research adopted the dual-base reference stations approach, static 2 hours DGPS mode for data capture The polynomial models used to represent the FCT surface are i) multi-quadratic model and ii) bi-cubic model. For each point, observation equation of the form AX=L was derived. The least squares equation was solved using the online matrix solver ( for (X) to determine the model coefficient parameters used to develop the geometric geoid model program using the Microsoft Excel 2010. The standard deviations of the geoid model determined orthometric height Hare: = 11cm and =14cm. Computation of t from formula and compared with value of t from t table distribution revealed and the possibility of coincidence/fit of the two surfaces though based on different vertical datum (geoid and MSL). From computed test statistics and using the standard deviation, no other surface than multi-quadratic is needed to model orthometric heights. Coefficient of correlation (R) and coefficient of Determination ( ) values of 0.995m and 99% respectively indicate the multi-quadratic model has a high predictive ability. Diagnostic tests confirmed that multi-quadratic model at 95% confidence limits can be sufficiently adequate for geoid modelling. Also computing N and comparing with 1.98/ √N (N is no of controls=24) at 95% confirmed the validity of using the models for orthometric heights determination. The bias value of zero and skill parameter of one implies total agreement between technique, observations, processing and the model results. The developed model will serve as reliable alternative for orthometric height acquisition at centimeter level accuracy which is adequate for producing topographic maps (at 1m contour interval), base maps for planning and production of large scale engineering plans. Kriging interpolation method was used to generate contour maps, geoidal maps and the digital elevation models. It is hereby recommended that the developed model (multi-quadratic) be adopted for elevation data acquisition for day to day geospatial data needs in cadastral, mapping, engineering/environmental applications.