A Unified Framework for Water Erosion and Deposition Equations

Abstract

Two modeling frameworks have been developed to describe and predict soil erosion and sediment deposition in recent years. The first is based on the concept of transport capacity. Deposition occurs only when the transport capacity is exceeded. This approach has been implemented in WEPP (Water Erosion Prediction Project) and several other physically based erosion prediction models. An alternative approach is based on simultaneous erosion and deposition. Net erosion or deposition is seen as a result of the dynamic interactions among all processes involved. The simultaneous erosion and deposition approach lays the foundation for GUEST (Griffith University Erosion System Template) and for recent studies of multi-size sediment deposition. This paper uses the original governing equations for WEPP and GUEST to represent the two approaches to water erosion and deposition modeling. The paper shows analytically that the two sets of governing equations, while vastly different in their appearance, share an identical structure, and thus can be reduced to a common set of equations unifying both approaches. The unified framework involves four terms: (i) sediment concentration at the transport limit, (ii) flow detachment, (iii) sedimentation because of gravity, (iv) a rainfall-driven sediment source term. The two modeling frameworks show only minor differences in how these four terms are formulated. Analytical solutions to the unified erosion and deposition equations show that the characteristic length for erosion is the ratio of maximum sediment discharge to maximum rate of detachment, and the characteristic length for deposition is the ratio of minimum sediment discharge to minimum rate of deposition, or simply the ratio of unit discharge to fall velocity. The paper clarifies and simplifies the current approaches to erosion and deposition modeling.