Assessing Uncertainties in Derived Slope and Aspect from a Grid DEM

Digital elevation data are the most frequently used for computer-based terrain analysis and they form an integral part of today’s GIS data analysis capability. For most GIS-based environmental studies, primary topographic parameters such as slope, aspect, and drainage network are often required for specific environmental models. While derived from digital elevation data, particularly the grid-based Digital Elevation Models (DEM), the parameters often display noticeable uncertainties due to errors (a) in the data, (b) inherent to the data structure, and (c) created by algorithms that derive the parameters from the DEM. Some contradictory results have been reported in evaluating the results of various terrain analysis algorithms, largely because of the variety in the assessment methodologies and the difficulties in separating errors in data from those generated by the algorithms. This chapter reports on an approach to the assessment of the uncertainties in grid-based Digital Terrain Analysis (DTA) algorithms used for deriving slope and aspect. A quantitative methodology has been developed for objective and data-independent assessment of errors generated from the algorithms that extract morphologic parameters from grid DEMs. The generic approach is to use artificial surfaces that can be described by mathematical models; thus the ‘true’ output value can be pre-determined to avoid uncertainty caused by uncontrollable data errors. Tests were carried out on a number of algorithms for slope and aspect computation. The actual output values from these algorithms on the mathematical surfaces were compared with the theoretical ‘true’ values, and the errors were then analysed statistically. The strengths and weaknesses of the selected algorithms are also discussed.