Spatial prediction and uncertainty assessment of topographic factor for revised universal soil loss equation using digital elevation models

Revised Universal Soil Loss Equation (RUSLE) is a model to predict longtime average annual soil loss, related to rainfall-runoff, soil erodibility, slope length and steepness, cover management, and support practice, The product of slope length L and steepness S is called topographic factor LS, implying the topographic effect on soil loss. This study focuses on (a) spatially predicting the topographic factor LS for RUSLE using a Digital Elevation Model (DEM), (b) selecting the appropriate DEM spacing for predicting the LS factor, and (c) modeling the loss of spatial variability of the predicted LS factor due to DEM resampling, The results show that using the physically based topographical factor LS equation and DEMs led to a higher correlation of predicted LS values with topographical features, compared to a spatial simulation method based on LS empirical models and sample data, The appropriate DEM spacing required to achieve prediction precision and detailed spatial variability of the LS factor was not identical for both requirements and a compromise may be made depending on the application aims. By modeling the spatial variability of predicted LS values for different DEM spacing, a new method to directly measure loss of spatial variability due to data resampling was developed. Compared to measures of entropy and global variance, the new method can reveal the different losses of spatial variability in different directions when the spatial variability is anisotropic.