A new model for erosion of plane soil surfaces by water is developed using physical principles.Raindrop impact and overland flow remove soil from the original cohesive soil. Once eroded soil enters overland flow, either as aggregates or primary particles, a significant proportion of it returns to the soil bed, forming a cohesionless deposited layer from which it can be removed again by the same erosion processes. The action of the eroding agents will be divided between eroding the unshielded original cohesive soil and reintroducing sediment from the deposited layer. The theory recognizes that the nature of the surface is modified by the erosion and deposition processes affecting it. Solutions of the governing differential equations describing sediment concentration are developed for two distinct equilibrium cases. The first case, when the deposited layer completely shields the original soil, appears to correspond with what has been previously called a "transport-limited" situation. The second case occurs when such shielding is incomplete, and sediment concentration is affected by the cohesive strength of the soil. The resulting equations for sediment concentration at equilibrium are compared with existing equations. Firstly, the equation for the case where the soil is lacking cohesion is shown to be similar to the semiempirical equation of Yang (1973). Secondly, when the soil is cohesive the slope length relationships are shown to be in good agreement with the universal soil loss equation over a wide range of slope steepness.

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The model of soil erosion on a plane slope introduced by Hairsine and Rose (this issue) is further developed by considering rill flow. The rills are considered to be parallel and incised in a homogeneous soil mass and have sediment and water flux contributed to them orthogonally. The erosive action of water flowing down these rills is described using the concept of stream power, which is assumed to be uniformly distributed around the wetted perimeter. The apportioning of the erosion and deposition processes within a rill is then considered to be influenced by the spatial extent of a deposited layer. The theory is developed for trapezoidal rills, with triangular rills and rectangular rills as special cases. Equations describing sediment continuity are presented, and numerical and analytical solutions are described for the entrainment-limited and transport-limited situations. The experiments of Meyer and Harmon (1985) are examined using this theory, and consistency of evaluated parameters is demonstrated within this data set. ( Wt,/D + z) 0.5 U=2(l+z + Wold 2)0.• tS• lNow at CSIRO Division of Soils, Canberra. where Wt, is the base width of the rill; D, the depth of flow: and z, the side slope ratio (horizontal to vertical). Moore and Burch [1986] found the rill shape factor, U, is largely independent of the shape once the flow width to depth ratio exceeds 2. 245 Resour. Res., 22(8), 1350-1360, 1986. Mosley, M.P., Experimental study of rill erosion, Trans. ASAE, 17, 909-913, 1974. Proffitt, A. P. B., The influence of rainfall detachment, runoff entrainment and sediment deposition processes on sediment con. centration and settling velocity characteristics of eroded soil, Ph.D. dissertation, Griffith Univ., Kinematic flow approximation to runoff on a plane: An approximate analytical solution,

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