Analysis of errors of derived slope and aspect related to DEM data properties

One of the obvious sources of errors in digital terrain analysis (DTA) algorithms is that introduced by raster data structure employed by a digital elevation model (DEM). Because of its regular sample space and orientation, the DTA results often show significant octant 'bias', presenting obvious visual and numerical error patterns. Moreover, other DEM data properties may also introduce errors in slope and aspect computation, such as data precision and spatial resolution (i.e. grid interval). This paper reports an investigation on the accuracy of algorithms that derive slope and aspect measures from grid DEM. A quantitative methodology has been developed for objective and data-independent assessment of errors generated from the algorithms that extract surface morphological parameters such as slope and aspect from grid DEM. The generic approach is to use artificial surfaces that can be described by a mathematical model, thus the 'true' output value can be pre-determined to avoid uncertainty caused by uncontrollable data errors. Two mathematical surfaces were generated based on ellipsoid (representing convex slopes) and Gauss synthetic surface (representing complex slopes), and the theoretical 'true' value of the slope and aspect at any given point on the surfaces could be computed using mathematical inference. Based on these models, tests were made on the results from a number of algorithms for slope and aspect computation. Analysis has been undertaken to find out the spatial and statistical patterns of error distribution so that the influence of data precision, grid resolution, grid orientation and surface complexity can be quantified.