A FINITE-ELEMENT MODEL FOR SIMULATING RUNOFF AND SOIL-EROSION FROM MECHANICALLY TREATED AGRICULTURAL LANDS .1. GOVERNING EQUATIONS AND SOLUTIONS

A finite element model simulating runoff and soil erosion from agricul tural lands is developed. The computational efficiency and stability o f various numerical schemes used for time integration are critically e xamined employing L2 and Chebycheff (Chebyshev) norms. Predictor-corre ctor and fully implicit schemes are found to give the least values of norms, thereby permitting larger time steps. A finite element solution of the one-dimensional Richards equation with a sink term simulates r ain infiltration and soil moisture balance in cropped fields. A criter ion to ensure stability and convergence of the solution is suggested. A finite element solution of the sediment continuity equation in conju nction with a fully implicit scheme for time integration and Yalin's e quation for sediment transport capacity is developed to simulate soil erosion. The potential of the model to reasonably simulate runoff and soil erosion is demonstrated by comparing the finite element solutions with the analytical solutions under simplified configurations and wit h experimental data.