Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria

Abstract

The conversion of geometric as well as ellipsoidal heights from GNSS observations to practical heights for engineering constructions has necessitated the determination of the local geoid model of areas. Benin City is a developing area which requires a local geoid model for conversion of geometric heights to orthometric heights for physical developments in the area. This paper is on the best local geoid model of Benin City, Nigeria by comparing three gravimetric-geometric geoid models of the study area. GNSS and gravimetric observations were carried out on 49 points to respectively obtain their coordinates and absolute gravity values. The theoretical gravity values of the points were computed on the Clarke 1880 ellipsoid, subtracted from the absolute gravity values and corrected for the air (free air) to obtain the free air gravity anomalies of the points. The computed free air gravity anomalies were applied to compute the geoid heights of the points using the integration of the modified Stokes integral. Three geometric geoid surfaces (plane, second degree and third degree surfaces) were fitted to the computed gravimetric geoid heights using the least squares technique to obtain the gravimetric-geometric geoid models of the study area. The RMSE of the three gravimetric-geometric geoid models were computed to determine their (the models) accuracy. The three gravimetric-geometric geoid models were compared using their accuracy to obtain the most suitable geoid model of the study area. The results of the comparison showed that the third degree gravimetric-geometric geoid model is most suitable for application in the study area. It is recommended that ellipsoidal heights obtained from GNSS observation within Benin City, Nigeria should be converted to orthometric heights using the third degree geoid model.

Comparative Analysis of Three Plane Geometric Geoid Surfaces for Orthometric Height Modelling in Kampala, Uganda

“…So, as the results of the spirit levelling validation, as well as the test points, agree with those of the 12 points used for the geoid modelling, the three models can be applied in the study area with more reliability, as well as confidence in model 2. Also, the accuracy achieved for the three geoid models agrees with those obtained by Oduyebo et al (2019) for Benin City and for FCT, Abuja all in Nigeria. The two studies applied the same method (geometric method) in small areas as well.…”

“…In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating the size and shape of the earth in the area of the survey. The actual measurements made on the surface of the earth with certain instruments are however referred to the geoid (Oduyebo et al, 2019). The geoid may be obtained by modelling from among others to serve as a vertical reference, as well as a datum for height determination.…”

“…Different studies have determined the local geoid models of various areas with different accuracy achieved. Oduyebo et al (2019) determined the local geoid model of Benin City by comparing three gravimetric-geometric geoid models of the study area with an accuracy of 0.6746m. also determined the local geoid model of the Federal Capital Territory, Abuja, where the accuracy of 0.419m, was obtained by comparing GNSS/Levelling and EGM 2008 geoidal undulations.…”