Deducing the USLE mathematical structure by dimensional analysis and self-similarity theory

The Universal Soil Loss Equation (USLE) was originally deduced by a statistical analysis of a large data set of soil loss measurements. The multiplicative structure of the model has been criticised due to the considerable interdependence between the variables. Using the soil erosion representative variables and the reference condition adopted in the USLE, the aim of this paper was to apply dimensional analysis and self-similarity theory to deduce the functional relationship among the selected variables. The analysis yielded a multiplicative equation, similar to the USLE. Therefore, this study suggested that the USLE has a logical structure with respect to the variables used to simulate the physical soil erosion process and the adopted reference condition.