Addendum to unsteady soil erosion model

A simple analytical approximation is obtained for erosion on a hillslope involving sediment transport when rainfall is the only source of water. The solution extends an earlier study requiring some numerical evaluation. Owing to its simplicity, the solution gives a clear understanding on the influence of the physical processes involved. Fundamentally, there is a very short time behavior associated with rainfall impact and a longer time behavior controlled by convection. It is this time decoupling which permits the solution to be expressed in simple terms. The short time analytical results can be used to simplify greatly numerical procedures.