Are "Physically-based" soil erosion models physically-based? Some elements from a sensitivity analysis of the Hairsine and Rose model

We study parametric uncertainty propagation and quantification for the simulation of erosion processes in the presence of rainfall and/or runoff. Uncertain input parameters of the Harisine & Rose model are treated in a probabilistic framework, considering them as independent random variables defined by prescribed probability density functions. This probabilistic modeling is based on a literature review to identify the range of variation of the main input parameters. The output statistical analysis is realized by Monte Carlo sampling and by Polynomial Chaos expansions. Our analysis aims at quantifying uncertainties in selected model outputs and establishing a hierarchy within input parameters according to their respective influence on output variability by means of global sensitivity analysis (Sobol indices). The sensitivity of the output variability to the different parameters is discussed. Furthermore, our analysis of the Harsine & Rose erosion model permits to conclude that, for the quantities of interest considered, the parametric interactions are not significant in the rainfall detachment model, but they prove to be important in the runoff detachment model