Spatial uncertainty in prediction of the topographical factor for the revised universal soil loss equation (RUSLE)
The Revised Universal Soil Loss Equation (RUSLE) is a model widely used to predict soil loss. An important 
component of RUSLE is the combined topographical factor (LS), which is the product of the slope length factor (L) and the 
slope steepness factor (S). It is important to identify the main sources of uncertainty in the LS factor and reduce the uncertainty 
where practical. Moreover, the uncertainty of the LS factor may vary across space, and this spatial uncertainty may require 
error management. For this reason, the spatial effects of slope steepness and slope length should be quantified, and their 
uncertainty propagation should be modeled. This article presents a general methodology for spatial uncertainty assessment 
of the RUSLE and its application results to the uncertainty analysis of LS as an example. A sequential indicator simulation 
was used to develop spatial prediction maps of slope steepness and slope length based on collected field data. The uncertainty 
due to slope steepness, slope length, and model parameters were propagated through topographical factor LS using the 
Fourier Amplitude Sensitivity Test (FAST). Spatial variance partitioning was performed to generate error budgets, and 
uncertainty sources were identified. Slope steepness contributed the largest variance in predicting topographical factor LS, 
followed by slope length. The variance contributions from the model parameters and measurement errors were relatively 
small. The results provide modelers and decision–makers with spatial uncertainty information for the purpose of error 
management.