Suitability of S factor algorithms for soil loss estimation at gently sloped landscapes

The reliability and the estimation technique of the S factor limit the use of the Universal Soil Loss Equation (USLE) at a regional scale. The accuracy of the S factor principally depends on the digital elevation model (DEM) accuracy and the precision of algorithms. Few studies were conducted on the accuracy of the S factor for a gently rolling landscape at a regional scale. We select a rectangular study site of 1.3 km2 in northern Germany as a case study to explore the effects of algorithm, horizontal resolution and vertical precision of DEM as well as terrain on the S factor. Horizontal resolution includes 1 m, 5 m, 10 m, 25 m, 50 m and 100 m. We use the following eight algorithms: maximum slope gradient, maximum downhill slope gradient, second-order finite difference, third-order finite difference, third-order finite difference weighted by reciprocal of squared distance, third-order finite difference weighted by reciprocal of distance, frame finite difference and simple difference. The results are as follows: (1) the algorithms affect the accuracy of the S factor at any given resolution of DEM, in particular more obvious for the lower DEM resolutions; (2) the accuracy of the S factor decreases as horizontal resolution decreases; (3) the most suitable algorithm is maximum downhill slope gradient for 1 m, and maximum slope gradient for the 5 m to 100 m resolution; (4) vertical precision also affects the accuracy of the S factor. However, vertical precision almost does not change the order of rank of the S factor with eight different algorithms at any given resolution of DEM; (5) the more complex the terrain is, the worse the accuracy of the S factor is represented. Among all the affective factors, horizontal resolution is the most important for the accuracy of the S factor. Selecting the most suitable algorithm is the best way for reducing the errors of the S factor when applying the USLE.