We present a bivariate model of erosion, sediment transport, and deposition by overland flow, designed for complex terrain, soil, and cover conditions. We use a Green's function Monte Carlo method to solve the underlying continuity equations, leading to improved robustness and implementation efficiency. By deriving the relationship between the terrain shape and erosion/deposition pattern, we clarify the physical interpretation of terrain curvatures and overall importance of the bivariate formulation. We explain the impact of various soil and cover properties by simulating the detachment and transport capacity limited erosion for uniform land use and by predicting the erosion/deposition distribution for a conventional, spatially variable land use at an experimental farm. We compare the results with the observed colluvial deposits and linear erosion features and illustrate the application of the model for improving the effectiveness of erosion prevention measures. ¿ 1998 American Geophysical Union