A Unified Framework for Water Erosion and Deposition Equations

detachment, and sediment deposition are considered simultaneously. This approach has received experimenTwo modeling frameworks have been developed to describe and tal support (Proffitt et al., 1991; Proffitt et al., 1993; predict soil erosion and sediment deposition in recent years. The first Huang et al., 1999; Heilig et al., 2001), and lays the is based on the concept of transport capacity. Deposition occurs only when the transport capacity is exceeded. This approach has been foundation for GUEST (Misra and Rose, 1996; Rose et implemented in WEPP (Water Erosion Prediction Project) and seval., 1997). More recently, this approach has been used eral other physically based erosion prediction models. An alternative to model multi-class sediment deposition (Beuselinck approach is based on simultaneous erosion and deposition. Net eroet al., 2002; Hairsine et al., 2002; Sander et al., 2002). sion or deposition is seen as a result of the dynamic interactions The two modeling frameworks for soil erosion predicamong all processes involved. The simultaneous erosion and deposition have been reviewed in parallel (Rose, 1993; Rose, tion approach lays the foundation for GUEST (Griffith University 1998). No critical analysis of the erosion and deposition Erosion System Template) and for recent studies of multi-size sediequations has been attempted to identify and clarify the ment deposition. This paper uses the original governing equations for similarity and differences between the two frameworks. WEPP and GUEST to represent the two approaches to water erosion The objective of this paper is to distill from the two and deposition modeling. The paper shows analytically that the two sets of governing equations, while vastly different in their appearance, seemingly disparate sets of equations a unifying set of share an identical structure, and thus can be reduced to a common equations governing soil erosion and sediment deposiset of equations unifying both approaches. The unified framework tion. This paper attempts at clarifying the current situainvolves four terms: (i) sediment concentration at the transport limit, tion with different modeling frameworks, and highlights (ii) flow detachment, (iii) sedimentation because of gravity, (iv) a the challenges in formulating mathematical descriptions rainfall-driven sediment source term. The two modeling frameworks of detachment, transport, and deposition processes. show only minor differences in how these four terms are formulated. Analytical solutions to the unified erosion and deposition equations MATERIALS AND METHODS show that the characteristic length for erosion is the ratio of maximum sediment discharge to maximum rate of detachment, and the characIn this section, the two alternative sets of erosion and depoteristic length for deposition is the ratio of minimum sediment dissition equations are summarized in their original form. Equacharge to minimum rate of deposition, or simply the ratio of unit tions implemented in the current version of WEPP were condischarge to fall velocity. The paper clarifies and simplifies the current sidered to represent the transport capacity approach (Foster approaches to erosion and deposition modeling. et al., 1995), while the set of equations developed by Hairsine and Rose (1991, 1992) was used to represent the simultaneous erosion and deposition approach. T alternative approaches to water erosion and WEPP deposition modeling have been developed in recent decades to predict the rates of soil erosion and sediment The governing equation for sediment movement in a rill is deposition over the landscape. Characteristic of the first approach is the concept of sediment transport capacity dG dx Df Di [1] (Foster and Meyer, 1972; Foster, 1982). Sediment deposition occurs only when this transport capacity is exwhere G is sediment discharge per unit flow width (kg m 1 ceeded. The concept of transport capacity thus plays s ); Df, the rill erosion or deposition rate (kg m 2 s ); Di, a pivotal role in erosion and deposition models. This interrill sediment delivery rate (kg m 2 s ); and x, the distance approach to erosion and deposition modeling based on in the downslope direction (m). Note that the governing Eq. [1] is based on mass balance of sediment in rills. Net erosion sediment transport capacity was adopted for WEPP in rills is modeled in WEPP by (Nearing et al., 1989; Foster et al., 1995; Laflen et al., 1997). A very similar approach was used for other physiDf Kr( f c) 1 G Tc [2] cally based erosion prediction models such as LISEM and EUROSEM (de Roo et al., 1996; Morgan et al., where Kr is a rill erodibility parameter (m 1 s), f and c are 1998). flow shear stress and critical shear stress (Pa), respectively, Another approach to erosion and deposition modeland Tc is sediment transport capacity (kg m 1 s ). Equation ing is based on the concept of simultaneous erosion and [2] applies only when G Tc. When net deposition occurs, deposition (Rose et al., 1983; Rose, 1985; Hairsine and that is, G Tc, the Df term is given by: Rose, 1991; Hairsine and Rose, 1992). In this approach, three continuous processes of rainfall detachment, flow Df Vf q (Tc G) [3] B. Yu, Faculty of Environmental Sciences, Griffith University, Nawhere is a raindrop induced turbulence coefficient, Vf is the than, Qld 4111, Australia. Received 17 Oct. 2001. *Corresponding author ([email protected]). Abbreviations: GUEST, Griffith University Erosion System Template; WEPP, Water Erosion Prediction Project. Published in Soil Sci. Soc. Am. J. 67:251–257 (2003).