A nonparametric/parametric analysis of the Universal Soil Loss Equation.

Due to its modest data demands and transparent model structure, the Universal Soil Loss Equation (USLE) remains the most popular tool for water erosion hazard assessment. However, the model has several shortcomings, two of which are likely to have prominent implications for the model results. First, the mathematical form of the USLE, the multiplication of six factors, easily leads to large errors whenever one of the input data is misspecified. Second, the USLE has a modest correlation between observed soil losses and model calculations, even with the same data that was used for its calibration. This raises questions about its mathematical model structure and the robustness of the assumed parameter values that are implicitly assigned to the model. This paper, therefore, analyzes if the USLE could benefit from mathematical model transformations that, on one hand, mitigate the impact of incorrect input factors and, on the other hand, result in a better fit between model results and observed soil losses. For the analysis, we revisit the original data set and consider the USLE factors as variables rather than their common interpretation as parameters. We first use both nonparametric and parametric techniques to test the robustness of the implicit parameter assignments in the USLE equation. Next, we postulate alternative mathematical forms and use parametric test statistics to evaluate parameter significance and model fit. A tenfold cross-validation of the model with the best fit tests the sensitivity of the parameters for inclusion or exclusion of the data. The results show that the USLE model is not very robust, however, only slight model improvements are obtained by drastic modifications of its functional form, thereby sacrificing the simple model structure that was intended by its designers.