Comparison of Angles from Surface Slope/Aspect Algorithms
Hodgson, Michael E., Cartography & Geographic Information Systems
ABSTRACT: Few studies have compared algorithms for mapping surface slope and aspect from digital elevation models. Those studies that have compared these algorithms treat slope and aspect angles independently. The evaluation and comparison of surface orientation algorithms may also be conducted by treating slope and aspect as characteristics of a bi-directional vector normal to the surface. Such a comparison is more appropriate for selecting an accurate surface orientation algorithm for applications that use bi-directional measurements, such as modeling solar radiation or removing the topographic effect from remotely sensed imagery. This study empirically compared the slope angle and bi-directional surface angle estimated from five slope/aspect algorithms using a synthetic terrain surface and an actual terrain surface. The most accurate algorithm is consistently that which uses only the four nearest neighboring elevations in the grid.
KEYWORDS: Slope, aspect, topographic, bi-directional angle, directional statistics, algorithm
Surface slope and aspect are two of the most important characteristics of a terrain surface and are likely the two most commonly used products of an elevation surface. It may be argued that these angles are more often used than absolute elevation. Such characteristics are important in studying the relationships between vegetation distributions and topography (Parker 1982), and mammals and topography (Pereira and Itami 1991); conducting automated drainage basin extraction (Jenson and Dominque 1988); classifying land cover in remotely sensed imagery (Dozier and Strahler 1983, Franklin et al. 1986); modeling the distribution of solar insolation (Dubayah and Rich 1995); removing the topographic effect in remotely sensed imagery (Smith et al. 1980, Colby 1991); and even in selecting algorithms for modeling error propagation (Hunter and Goodchild 1997). The use of digital elevation models for mapping the distribution of slope/aspect requires consideration of the most accurate slope/aspect algorithms.
The choice of a slope/aspect method should be based on previous empirical comparisons of the accuracy of such methods. Several different slope/aspect algorithms have been suggested, and several have been empirically evaluated for accurately estimating surface orientation characteristics. Comparisons of algorithmically derived slope/aspect angles are problematic, however, in that evaluating the accuracy of any slope/aspect algorithm requires the use of observations whose "true" surface slope and aspect are known. Most comparisons derive "truth" manually from a contour map and suffer from the inherent problem of visual interpretation and estimation of slope from contour lines (Skidmore 1989).
With one known exception (Hodgson 1995), previous studies have compared the "true" surface slope and aspect with the estimated angles in an independent manner--separate errors for slope and aspect. In many applications (e.g., incident solar radiation), the bi-directional surface normal, not the independent measurements of slope and aspect, are required and thus, the bi-directional angle from the slope/aspect algorithms should be evaluated for these applications. The bi-directional angle is a three-dimensional angle between two vectors in hemispherical space (Figure 1a), such as the normal vector of a surface element measured by two methods.
[Figure 1 ILLUSTRATION OMITTED]
In this paper both the slope angle and bi-directional surface angle determined from five different slope/aspect algorithms are compared using both a synthetic surface sampled at a range of cell sizes and an actual topographic surface. This research differs from previous work in that it 1) uses bi-directional angular measurements to assess the accuracy of each algorithm; 2) uses a mathematically defined synthetic topographic surface to compare actual and estimated surface orientations; 3) derives "truth" from a reference source of much higher resolution; and 4) includes a comparison of two algorithms not previously evaluated. …