In 1985 the USDA - Agricultural Research Service initiated a national project called Water Erosion Prediction Project (WEPP) to develop a new generation water erosion prediction technology which will replace the USLE by 1992, the most widely used technology for estimating soil erosion by water. For simplicity, the WEPP model was developed assuming quasi-steady state conditions. An evaluation of the effects of formulating the unsteady state sediment continuity equation by assuming quasi-steady state conditions is presented. A methodology was developed to study soil erosion process in rainfall simulator plots treated as a microwatersheds. This was achieved by explicitly separating interrill and rill areas in the rainfall simulator plots using areal photographs and microtopographic data. A detailed analysis was conducted using response surface plots on the model structure of both formulations of the sediment continuity equation. The shape of the response surface plots indicated for each formulation whether the soil erosion parameter estimates were successfully identified. As an additional information, the sediment concentration graphs and the total sediment yield were used to determine major differences between the two formulations of the sediment continuity equation. Rainfall simulator plot data collected in five locations of the US were used for the calibration and validation of the model WESP. The unsteady state approach yielded lower values of the objective function than the quasi-steady state formulation. Using the unsteady state approach, physical interpretation may be associated with the soil erosion parameter values Kᵣ, T(cr), and Vₑ. The quasi-steady state soil erosion estimates showed a weak and unclear physical association. The shape of the sediment concentration graphs were similar for both formulations of the sediment continuity equation. The benefit obtained by using the more complicated unsteady state approach was a more accurate estimation of the peak, or maximum, sediment concentration. Total sediment yield estimates from both formulations were similar. Thus, insignificant benefit was obtained from using the unsteady state approach. In this study hydrographs reached equilibrium due to the long duration of simulated rainfall. The two model formulations might perform far differently under experimental conditions where steady state runoff is not reached.

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A physically based, distributed parameter, event oriented, nonlinear, numerical model of watershed response is developed to accommodate the spatial changes in topography, surface roughness, soil properties, concentrated flow patterns and geometry, and land use conditions. The Green and Ampt equation with the ponding time calculation for an unsteady rain is used to compute rainfall excess rates. The kinematic wave equations are used to describe the unsteady one-dimensional overland and channel flow. The unsteady and spatially varying erosion/deposition process on hillslopes and channel systems is described dynamically using simultaneous rates of sediment entrainment and deposition rather than the conventional approach using steady state sediment transport functions. To apply the model the watershed is represented by a simplified geometry consisting of discrete overland flow planes and channel elements. Each plane or channel is characterized by a length, width, and a roughness parameter. For channel elements, a cross-section geometry is also needed. A modular computer program called WESP (Watershed Erosion Simulation Program) is developed to provide the vehicle for performing the computer simulations. Rainfall simulator plots are used to estimate infiltration parameters, hydraulic roughness, and soil erodibility parameters for raindrop impact and overland flow. The ability of the model to simulate watershed response (hydrograph and sedigraph) to a variety of rainfall inputs and antecedent soil moisture conditions is verified using data collected on two small watersheds. The good agreement between the simulated watershed response and the observed watershed response indicates that the governing equations, initial and upper boundary conditions, and structural framework of the model can describe satisfactorily the physical processes controlling watershed response.