A mathematical model of soil erosion and deposition processes: I. Theory for a plane land element

The paper describes a new mathematical model of soil erosion and deposition on a plane land element. The model makes use of an approximate analytic theory of runoff on a plane assuming kinematic flow. Rates of the following simultaneously occurring erosion/deposition processes are represented mathematically: rainfall detachment, sediment deposition, and soil entrainment by overland flow. The concept of stream power is used in representing the entrainment process. The form of analysis reduces the first- order partial differential equation expressing conservation of mass of sediment to an ordinary differential equation, which can thus be solved analytically. This solution gives sediment concentration at any time as a function of distance down the plane in terms of four defined soil factors, the slope of the land, two separate cover factors, and the rainfall and runoff rates. The product of water flux and sediment concentration gives sediment flux at any time and position on the plane.