This thesis shows the level at which reliable geoidal mapping is possible over a small area using the Global Positioning System (GPS), geodetic levelling and appropriate interpolation strategies.
The geoid shape over an area 15kmx30km of Dunedin, New Zealand, was determined by the geometric approach (King et al, 1987) using almost 70 control points. Investigations were then made to determine the precision to which orthometric heights can be estimated within this area with various interpolation strategies. This was done by creating subsets of control points with various point densities. Experimental data sets were then generated by estimating the undulations at the points not selected as control. Quantitative analysis of the differences between estimated and known undulations was then carried out.
The investigations indicate that:
• Where average known undulation point spacing is between one and five kilometres, the mean error in the estimation using linear interpolation will vary by twenty millimetres. Any specific point may vary from the true value by up to fifty millimetres.
• Where average known undulation point spacing is between five and ten kilometres, the mean error in the estimation using linear interpolation will vary by sixty millimetres. Any specific point may vary from the true value by up to 150 millimetres.
• Low order polynomials (three to five independent variables) are not as good as linear interpolation when average known point spacing is less than ten kilometres.
