MODELING THE EROSION PROCESS OVER STEEP SLOPES - APPROXIMATE ANALYTICAL SOLUTIONS

Analytical expressions are developed for the rainfall-runoff-erosion process on steep hillslopes subjected to time-varying rainfall events. The erosion equation is essentially represented as a first-order reaction with the reaction rate being represented by the soil erodibility. The analytical transient solutions are based upon the assumption that the flow and sediment discharge have a constant relationship as during steady-state conditions. The analytical solution for the sediment discharge performs well when compared with numerical and experimental results. The approximate analytical solution for the concentration profile is the asymptotic limit of the transient numerical solutions. An error analysis shows that the analytical solutions improve with increasing slope length and that the solution model presented here is applicable to a wide range of physical situations.