Abstract
No other mapping product has had widespread applications in developmental planning than the topographic map. Topographic maps represent the three-dimensional landscape by providing relief information in the form of contours in addition to plan information on which natural and man-made landmarks are quite accurately represented. Height information, extractible from topographic maps, comes in handy for most land use planning. However, generalizations during contouring and the need to interpolate between successive contours for specific grid nodes introduce errors in extracted heights. There is therefore, the necessity to use some mathematical modeling to remove discrepancies in the interpolation process to improve elevation data extracted from topographic maps. In this study, the accuracy of spot heights derived from interpolated and extracted heights from topographical maps is assessed. Two different mathematical models - a third degree polynomial regression model and the Thompson’s Multiple Variable Polynomial regression models, were respectively used to model the relationship between extracted heights and ground reduced levels. Results from the two models indicate that, the latter presents better refinements to converting extracted heights into reduced levels with a coefficient of determination value of 95.9%, although further research is recommended to investigate numerical techniques that could improve the solution to the Thompson’s polynomial. The Thompson’s model was implemented as a crude height refiner program that receives extracted heights to return corrected heights. The implication of these results for the mapping community is that, it is possible to model a correction function that can help obtain reasonably accurate heights from topographic maps. This will reduce the necessity of always going back to the field for field surveys in spite of the fact that topographic maps covering an area already exists.Keywords: Topographic maps, Interpolation, Thompson’s polynomial, Levelling, Terrain models
Highlights
Topographic maps represent the three-dimensional landscape with relief information in the form of contours, useful for Digital Elevation Modeling (DEM) and are quite indispensable in a National Geospatial data infrastructure for most development planning
Though several mathematical models were experimented with, two models stood out as best for simulating the relationship between the leveled and extracted heights. These were the polynomial regression model and a multiple regression model of the form proposed by Thompson, (1968)
This shows most values clustered around the estimated trend line with a coefficient of determination of 95.9% and the sum of square errors (SSE) of 1.29m
Summary
Topographic maps represent the three-dimensional landscape with relief information in the form of contours, useful for Digital Elevation Modeling (DEM) and are quite indispensable in a National Geospatial data infrastructure for most development planning. They further quite accurately, represent natural and man-made landmarks and allow for modeling and visualizing of areas at risk from natural hazards (McChesney and McSweeney, 2005). The process of extracting heights from contours on existing topographical maps and integrating same with leveled spot heights can be problematic due to generalizations during contouring, and the need to interpolate between contours for specific grid nodes. There is the necessity of some mathematical modeling to remove discrepancies in the interpolation results
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