COMPARATIVE ANALYSIS OF THREE PLANE GEOMETRIC GEOID SURFACES FOR ORTHOMETRIC HEIGHT MODELLING IN KAMPALA, UGANDA (original) (raw)
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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.
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.
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 Research and Science (IJAERS), 2019
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.
Comparison of local geoid height surfaces, in the province of Trabzon
Arabian Journal of Geosciences, 2016
In this study, the estimation of a local geoid model in the area of Trabzon by using geometric methods is presented. The geometric method used in this study interpolates Global Positioning System-derived ellipsoidal and orthometric heights by using the weighted average interpolation, polynomial surface regression, and multiquadratic interpolation. The orthometric and ellipsoidal heights measured at 600 C3 order control stations within a reference benchmark network covering the entire area of Trabzon in Turkey were used in this study. From the existing orthometric and ellipsoidal heights at control stations, the geoid heights were determined. Control stations were divided into two sets, namely, Breference stations^and Btesting stations,^to test the estimated geoid height surface. The three methods are compared from a practical point of view by using the descriptive statistics of the root mean square error, mean absolute error, maximum error, and minimum error of the geoid height residuals.
A Geometric Approach for Determination of Geoidal Height in Akure Environs, Ondo State, Nigeria
International Journal of Scientific and Research Publications (IJSRP)
The study attempts to carry out the determination of geoidal height using a geometric approach. This approach involves the use of GPS/levelling to determine the ellipsoidal and orthometric heights. South DGPS was used in acquiring GPS data, which were processed using South GNSS processor software for deriving ellipsoidal heights, while Leica Jogger modern automatic level instrument was used in acquiring leveling data, which were processed to produce orthometric heights. A total of fifty nine (59) points were occupied for both GPS and levelling observations. The geoidal height was determined by computing the difference between the ellipsoidal and orthometric heights. The geoidal map and the geoidal model (3D) were created using Surfer 11 software. The chart for geoidal, ellipsoidal and orthometric heights show the same pattern, which is an indication that all show a true representation of the terrain. The profile produced for geoidal map and the digital geoidal model follows the same slope, which is an indication that both are natural height systems. The geometric approach was successfully used for geoidal height determination 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.
ACCURACY OF GLOBAL GEOID HEIGHT MODELS IN LOCAL AREA: TESTS ON CAMPANIA REGION (ITALY)
Nowadays GPS technology permits to reach millimeter or sub-millimeter horizontal relative accuracy levels over very long distances (up to hundreds of kilometers). The vertical GPS accuracy is more difficult to obtain. In addition, because GPS heights are referred to ellipsoid, their transformation into orthometric heights requires the use of a geoid model that influences with its accuracy the quality of the results. Usually a local geoid model is characterized by a high level of accuracy, but often it has a fee. Global geoid models are free available and their accuracy is to test in the local area where they are to use so to evaluate their suitability for the user purposes. This paper is aimed to compare different Global Geoid Models testing their accuracy on Campania region (Italy). Particularly, models respectively named EGM84, EGM96 and EGM2008, are considered and tested on 18 points corresponding to GNSS Permanent Stations in Campania. For the best resulting model, the EGM2008, a solution to improve further its performance is adopted.
EVALUATION OF GEOPOTENTIAL MODELS EIGEN-6C4 AND EGM2008 USING GNSS AND LEVELLING DATA IN UGANDA
The determination of heights above mean sea level by spirit-leveling is known to be a difficult task as it is time-consuming, tedious and expensive. Knowledge of a reliable geoid model for transformation of heights in a particular region is therefore vital. The published quality estimates of Global Geopotential Models are presented as a global average and thus not representative of its performance in a particular region. Evaluation of EIGEN-6C4 and EGM2008 has been performed to ascertain its quality in determination of orthometric heights in Uganda. The evaluation of EIGEN-6C4 and EGM2008 geoid models involved the determination of their accuracy in obtaining geoid heights and therefore orthometric heights. This provided a validation of the quality of both geoid models in transformation of heights that was done by using GNSS and levelling data at seven fundamental benchmarks in Uganda. Also, a test for the suitability of EIGEN-6C4 in determination of heights with physical meaning is performed for a road section from Lira to Abim. This was done by relative evaluation of the geoid model with respect to a reference control station. The determination of the accuracy of the geoid models using GNSS and levelling data provided a smaller Standard Deviation of 0.158m and mean of -0.774m for EIGEN-6C4 compared to that of EGM2008 representing a better fit to the reference surface due to the GNSS and levelling data. While testing for suitability of EIGEN-6C4 for geodetic applications, the Root Mean Square Error per kilometer of 5.3mm for a baseline length of approximately 9km in the test for suitability of EIGEN-6C4 for orthometric height determination shows an acceptable levelling misclosure. The potential of EIGEN-6C4 geoid model has been demonstrated in determination of heights with physical meaning and as such plausible results to provide confidence in its adoption for geodetic and engineering applications. The quality of EIGEN-6C4 for practical applications is dependent on the quality of datasets used in its development and evaluation. It is recommended that further tests for applicability be performed in other regions of Uganda.
Journal of Geodetic Science, 2022
The use of orthometric height in geodetic applications provides elevations on the physical topographic surface of the earth rather than ellipsoidal heights that are not in conformity with the physical topography. Global positioning system (GPS)/levelling produces ellipsoidal heights that are not consistent with levelled heights above mean sea level. The study provides a practical solution of using the GPS levelling approach or the geoidal heights aimed at providing local orthometric height. Many research studies were conducted with a view of finding a viable solution to the derived orthometric heights. It was revealed that the research studies conducted were found lacking in the use of only lower order numerical solutions models, which limit the accuracy derived from the model, the use of online post-processing, RTKlib, and other non-precise software to obtain the coordinates of the stations used in the derivation of orthometric. Finally, the use of gravimetric data, with its temporal variation problem, poses a threat to the derivation of orthometric height, so also to the accuracy of the developed model. Considering factors while developing models for orthometric heights improves the accuracy in achieving required heights for geodetic applications and aids in fast-tracking mapping.