Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria (original) (raw)
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FITTING OF A TRANSFORMATION GEOID MODEL TO THE GRAVIMETRIC-GEOMETRIC GEOID MODEL OF BENIN CITY
FUDMA Journal of Sciences (FJS), 2021
The application of the transformation geoid model in Benin City has necessitated its fitting to the existing gravimetric-geometric geoid model of the study area. The transformation geoid model was determined using the Kotsakis (2008) model for the transformation of global geoid heights to local geoidal undulations. To obtain its accuracy, the root mean square error (RMSE) index was applied. The computed accuracy is 2.0172 m. To apply the determined geoid model in the study area, as well as improving on the computed accuracy, the model was fitted to the gravimetric-geometric geoid model of the study area. The fitting result shows that geoid heights can be computed using the determined geoid model with an accuracy of 1.1041 m in the study area.
International Journal of Engineering Research and Advanced Technology (IJERAT), October, 2018
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 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 modelling. 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 – h_i ) the difference in average ellipsoidal height (h_ave) and each point’s ellipsoidal height (h_i). The ∆h term is based on the assumption that the geoid varies with topography and may hence possibly lead to some improvements in 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 levelling technique for production of topographical maps, cadastral surveys, and engineering/environmental applications.
Journal of Environment and Earth Science
An important component in position determination of any point is its height. Orthometric height determination has a significant role in geodesy, and it has wide-ranging application in numerous fields and activities. Orthometric height is the height above or below the geoid along the gravity plumb line. Orthometric height system is preferred to ellipsoidal height by many because of its relationship with the mean sea level (MSL). Determination of orthometric heights for Akure environs was carried out using gravimetric approach by determining geoidal undulations via Stokes integral and ellipsoidal heights via GPS observations. A total of 59 stations within the study area were occupied for gravity observation using Lacoste and Romberg (G-512 series) and its complete accessories. South GNSS instrument was used in static mode for position and ellipsoidal height determination. In order to determine orthometric heights of the study area, the difference between the tailored geoid height (N Taylor) and the ellipsoidal heights (h GPS) were computed. The result shows that the determined orthometric heights have a standard deviation value as 10.6121m with a standard error as 1.38159m. The contour map and the 3D surface map of the computed orthometric heights were produced for the study area. The study recommends the use of gravimetric method in orthometric height determination when the tailored geoid height is computed.
FUDMA Journal of Sciences (FJS), 2020
The conversion of theoretical, as well as geometric heights to practical heights requires the application of geoidal undulations from a geoid model. The various global geopotential models that are readily available for application in any part of the world do not best-fit regions, as well as countries. As a result, there is a need to determine the local geoid models of local areas, regions and countries. This study determines the local geoid model of Kampala in Uganda for orthometric heights computation by comparing three plane geometric geoid surfaces. A total of 19 points were used in the study. The least squares adjustment technique was applied to compute the models' parameters. Microsoft Excel programs were developed for the application of the models in the study area. The Root Mean Square Index was applied to compute the accuracy of the models. The three geometric geoid models were compared using their accuracy to determine which of them is most suitable for application in the study area. The comparison results show that the three models can be applied in the study area with more reliability, with greater confidence in model 2.
Geodetski glasnik, 2021
Height is an important component in three dimensional coordinates and determination of the position of points for any meaningful development. Ellipsoidal heights from GNSS require geoid model which could be global, regional and local for transformation to orthometric height. The absence of a national geoid model in Nigeria remains a great drawback to develop local geoid for local application in place of global geoid models. The study aims to assess the accuracy of polynomial geoid models in orthometric height determination. Differential Global Positioning System (DGPS) observations were carried out to determine ellipsoidal heights of the point while nine and eleven coefficients were used for the geoid and orthometric height modelling. Model A and Model C used 2-D (x, y) positions with nine and eleven parameters while model B used 3-D (x, y, ∆h) positions with nine parameters. The least-squares method was adopted in computing the parameters of the models. Root Mean Square Error (RMSE) was used to assess the accuracy of the models with the RMSE of model A is 14.3 cm, model B is 15.7 cm and model C is 14.5 cm, respectively. The inclusion of height term (∆h) in model B does not improve the accuracy over model A and model C. Model A with the lowest RMSE is hence the better of the three models. One-way ANOVA test conducted at 95% confidence level,
International Journal of Advanced Engineering, Management and Science (IJAEMS), 2019
The geometric heights obtained from GNSS observations cannot be used for engineering works as they are not reduced to the geoid. This study presents practical local geoid modelling from gravimetric observations using the modified Stokes integral for engineering applications in Benin City. A total of 52 points were observed with GNSS receivers and a gravimeter to respectively obtain their positions and absolute gravity values. The theoretical gravity values of the points were computed on the Clarke 1880 ellipsoid to obtain their local gravity anomalies. The modified Stokes integral was applied to compute the geoid heights of the points. The combined topographic effect was applied to the computed geoid heights of the points to obtain their precise geoid heights. The mean of the precise geoid heights of the points was computed to obtain the local gravimetric geoid model of the study area. The determined geoid model was validated for its reliability as well as the accuracy using the RMSE index. It is recommended that the use of assumed, as well as handheld GPS receiver heights for engineering works should be totally abolished as this study has established the local geoid model of Benin City.
Establishment of local geometric geoid model for Busoga, Uganda
World Journal of Advanced Research and Reviews, 2020
The importance of the local geoid model for the computation of accurate geoid heights, as well as orthometric heights used for engineering constructions, necessitated its establishment in areas, regions or countries. Consequently, this study establishes the local geometric geoid model of Busoga, Uganda, using the geometric method. A total of 26 points were used in the study, 20 points for the development of the model and 6 test points. GNSS observations were acquired with Trimble GNSS dual-frequency receivers and processed with Bernese (V5.2) and Spectra Precision Survey Office (v4.1) software to obtain the coordinates and ellipsoidal heights of the points. Differences between the existing orthometric and ellipsoidal heights were computed to obtain the geoid heights. The Least squares adjustment technique was applied to determine the fit, as well as the Bicubic and Multiquadratic models' parameters. The Root Mean Squares Error (RMSE) index was used to compute the accuracy of the models. The geoid models were compared with their RMSE, as well as accuracy to determine which of them is more suitable for application in the study area. The comparison result shows that the Multiquadratic geoid model is more suitable for implementation in the study area. A Microsoft Excel program was developed for the application of the model in the study area.
A local geoid model for Evboriaria, Benin City using the geometric (GPS/Levelling) method was determined for calculation of mean sea level heights. Fifty points were established for the model and ten points were used for interpolation. The geoid heights were determined by finding the difference between the observed orthometric heights and the ellipsoidal heights. The polynomial regression model D was used for the interpolation of the orthometric heights. The computed mean standard deviation between the observed orthometric heights and the interpolated orthometric heights was ± 21cm. A mean geoidal undulation of 28.410m was computed using the gravimetric method. The computed orthometric heights using the gravimetry mean geoidal undulation were compared with the observed orthometric heights and seen to be identical. It is recommended that orthometric heights of project areas should be determined from GPS observations with the local geoid model of the area also determined.
Modelling of Orthometric heights from Multi- Networks of GNSS/Precise Levelling in FCT, Abuja
International Journal of Environment, Agriculture and Biotechnology (IJEAB), 2019
The geoid is used as a transformation linkage between ellipsoidal heights (h) determined from DGPS observations and orthometric heights (H). Widespread acceptability and adoption of GPS in local geospatial data acquisitions require the development of a local geoid model (N) for use to obtain orthometric heights in the absence of a national geoid model. Geoid model can be developed by gravimetric approach; global geopotential model (GGM); geometric technique among others. The conventional approach to GPS measurements is the use of one base reference station for field measurements. It has several drawbacks e.g. in signal range/coverage, accuracy degradation of results, etc. Based on Grashof's law of stability of triangles, this study was therefore based on dual reference base stations to improve on DGPS signal range and stability of results. Pro-online matrix solver was applied to the least squares observation equations of the two modelled FCT surfaces (multi - quadratic and bicubic) to determine polynomial coefficients. The geoid undulation was computed and orthometric height generated for production of a topographical plan at 1m contour interval for elevation data in surveying, engineering and environmental applications. Skill =1 and bias = 0 were computed to confirm the predictive capability of the models and that no bias/errors were introduced into the respective modelling exercise. Diagnostic test also confirmed the viability and feasibility of providing vertical datum surface for FCT by this approach. Standard deviation (σ) as accuracy indicator was computed and the multi-quadratic model with σ =11cm was the better geoid surface for modelling of orthometric height in the FCT by the geometric method.