Adaptation of a Global Orthometric Height Model to Local Height Datum using 'Satlevel' Collocation.
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Three-dimensional (3D) maps are of immense value in the planning and execution of engineering and other projects aimed at harmonious environmental development. In many real-life situations, the knowledge of heights is crucial for understanding the relative vertical positions of neighboring entities in a common reference system called datum - an important reference surface for elevations of terrain points. In many countries, the reference surface for heights is the geoid which is approximated by the Mean Sea Level (MSL). Conceptually, two approaches are used to determine the geoid - deterministic and empirical; and can also be determined in absolute or in relative terms. The recent success in the determination of reliable global geoid gave opportunities and preferences to the relative geoid determination using the global Geopotential Earth Model (GEM-XX), as platform. The latest edition named GEM2008 defines the global geoid to submeter accuracy. The global model generalizes the geoid in any locality; and therefore, it is not the best fit for any country or place. The fitness of the global geoid is always tested in the locality for its adequacy by comparing the GNSS derived Orthometric Heights with those obtained by direct geodetic levelling. In practice, the discrepancies are usually attributed to the imperfection of the global geoid model. The direct methods of determining Orthometric Heights by geodetic leveling is physically demanding and even almost impossible in some areas such as the rain forested areas and Niger Delta region of Nigeria due to the presence of swamp and the nature of the terrain. Thus, it is preferable to develop a mathematical model for the global model imperfections with the hope of obtaining Orthometric Heights by applying the geoidal error model to GNSS heights (which are easier to acquire) in other to obtain the Orthometric Heights. The challenge in this approach is to get the appropriate geoidal error model and this is the focus of this research. In this study, an empirical error models code named ‘Satlevel’ Collocation model is developed, and compared with other existing predictive models developed and used by researchers in other countries. The ‘Satlevel’ uses an optimal numerical model which transforms the global model to local datum using geoid modelling techniques aided by GNSS measurements. GNSS is used to obtain ellipsoidal heights at some selected control points, while the Orthometric Heights of those points were determined by geodetic levelling. Orthometric and ellipsoidal Heights were related by Geoidal Undulation (N) for which empirical error model was sought. Spherical and Rectangular ‘Satlevel’ models were explored. GEM2008 Orthometric Heights were computed in the two selected study areas (Port Harcourt, Rivers State and Lagos State of Nigeria). The results show that the geoidal undulation determination with Spherical ‘Satlevel’ models gave average values of 18.946m and 22.854m for Port Harcourt and Lagos State respectively, while Rectangular ‘Satlevel’ models gave average values of 18.948m and 22.857m for the two areas. The Mean Square Error (MSE) for Spherical ‘Satlevel’ were 6.151mm and 0.0033mm; while Rectangular ‘Satlevel’ gave 1.728mm and 0.00032mm for Port Harcourt and Lagos State respectively. The statistics show that there are no significant differences between the observed Geoidal Undulations and the computed Geoidal Undulations from ‘Satlevel’ collocation models. Also, the goodness of fit of the model was checked and satisfied 95% significant level. The geoidal map and 3D surface models of the areas were produced. ‘Orthometric height on the fly’, a user-friendly interactive program was developed to compute the local Geoidal Undulation and Orthometric Height from “Satlevel’ collocation model. Although, all the models considered give comparable accuracy of the orders of millimeters, Spherical ‘Satlevel’ model is more preferable than the Rectangular ‘Satlevel’ because of its advantage of accepting data format that is most common on maps and GNSS devices over other models. GEM2008 fits perfectly in the Port Harcourt Coastal area of Nigeria and therefore adapted for Orthometric Height with the use of ‘Satlevel’ Collocation Models developed in this research. The study recommends re-observation of the Nigerian Vertical control network and its integration with GNSS observations so that a general model applicable to the entire country can be determined.
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos.
Local Height Datum , Global Orthometric Heigh , Satlevel Collocation model , Research Subject Categories::TECHNOLOGY::Civil engineering and architecture::Surveying
Aleem, K.F (2014), Adaptation of a Global Orthometric Height Model to Local Height Datum using 'Satlevel' Collocation. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 316pp.