Mathematical method for physics-based rill erosion process using detachment and transport capacities

Quantification of rill erosion processes is of great importance in both model parameter estimations for process-based rill erosion models and in model performance verification. This study presents a mathematical method to determine a physics-based rill erosion process derived from the feedback relationship of transport capacity and detachment capacity. Experimental data sets were used to determine transport capacities under steep slope gradients of 15°, 20°, and 25° and the detachment capacities. The estimated transport and detachment capacities were then used to determine the sediment delivery processes under different hydraulic regimes. The sediment concentrations along the rill determined with the mathematical method were compared with the experimental measurements to verify the methodology and the mathematics. Results showed that the mathematical model results agreed well with the experimental data in references. The predicted detachment capacity calculated by the new method was capable of predicting saturated, unsaturated, and thawed slope, but incapable of partially thawed soil. This study not only supports the analytical solution to the differential equation of rill erosion, but also verifies that the experimental method was fit well with the mathematical concept. The new method provides a useful and efficient way to quantify rill erosion processes.