An evaluation of methods to determine slope using digital elevation data

Variation in the computation of slope from digital elevation data can result in significantly different slope values and can, in turn, lead to widely varying estimates of environmental phenomena such as soil erosion that are highly dependent on slope. Ten methods of computing slope from distributed elevation data, utilizing capabilities inherent in five different geographic information systems (GIS), were compared with field measurements of slope. The methods were compared based on (1) overall estimation performance, (2) estimation accuracy, (3) estimation precision, and (4) independence of estimation errors and the magnitude of field measured slopes. A method utilizing a very high resolution digital elevation model (DEM) (1 m) produced slightly better estimates of slope than approaches utilizing somewhat lower resolution DEMs (2-5.2 m), and significantly better estimates than a method utilizing a 12.5 m DEM. The more accurate method was significantly biased, however, frequently underestimating actual slope. Methods that averaged or smoothed high resolution DEMs over larger areas also produced good estimates of slope, but these were somewhat less accurate in areas of shallow slopes. Methods utilizing differential geometry to compute percent slope from DEMs outperformed methods utilizing trigonometric functions. Errors in slope computation are exaggerated in soil erosion prediction models because erosion typically increases as a power function of slope.