Modelling of Orthometric heights from Multi-Networks of GNSS/Precise Levelling in FCT, Abuja

Abstract

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 (multiquadratic 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.

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

“…A study has stated that a small area is the one that is less than 200km 2 in size (Schofield, 2007). In surface fitting methods, models adopted depend on the size and nature of the variation of the heights of the points used as opined Oluyori (2019). As such, Romans (2007) suggested that for small areas, models with four parameters or lower, be adopted for better accuracy.…”

Spatial Distribution of Survey Controls and Effect on Accuracy of Geometric Geoid Models (Multi-quadratic and Bicubic) in FCT, Abuja

“…The geographic location and size of a project area may point to the need for adoption of different polynomial interpolation surfaces used for different regions instead of single surface model to cover all. The ideal scenario is however, for a single geoid model to cover a study area which was achieved by Oluyori (2019).…”

“…However, circumstances in practical reality may make homogeneity impossible/infeasible (location of various classes of controls) and therefore the need to investigate the implication of such occurrences is desirable by computing accuracy/standard deviations (σ). Geoid modelling by Nwilo (2013), Eteje et al (2018), Oluyori (2019), and others may be applied to modernization of heights to produce orthometric heights by reference to vertical datum when adopting Global Positioning System (GPS) technology. GPS technology produces three dimensional coordinates (N, E, h) relative to earth ellipsoid.…”

“…To obtain orthometric height (H) of a point from GPS observations, a geoid undulation (N) of the point is needed. Eteje et al (2018) and Oluyori (2019) gave the model for the transformation of the GPS ellipsoidal height (h) to orthometric height (H) if the geoid height is known as:…”

“…Vertical datum is referred to as geopotential reference frame capturing gravity, geoid undulation, orthometric height and deflection of the vertical while geometric reference frame is used to replace horizontal datum to include geocentric X, Y, Z; latitude, longitude and ellipsoid height (h) according to Hansar (2016). Nwilo (2013) as well as Oluyori (2019) can fit into modern categorization of height modernization. One very important factor to be stressed in accuracy determination in geometric geoid modelling according to Kaloop et al (2008) is the spatial distribution and number of controls available within study area.…”