Comparison and Contrast in Soil Depth Evolution for Steady State and Stochastic Erosion Processes: Possible Implications for Landslide Prediction

Abstract

AbstractThe importance of gradual erosion relative to landsliding depends predominantly on the slope angle. One factor of critical influence in landsliding along with slope angle and slope shape is the soil depth. Understanding soil depth development on steep topography is fundamental for understanding and predicting the occurrence of landsliding at threshold landscapes. We develop a model to predict soil depth that addresses both threshold and gradual processes. If erosion is a gradual process, soil depth increases until the soil production rate no longer exceeds the erosion rate, and steady state is reached. The predicted soil depth (x) is proportional to the ratio of the infiltration to the erosion rate. Identifying a predictive result for erosion as a function of slope angle (S) allows a test of both the erosion and soil production models with field observations. The same theoretical approach to soil production should be applicable when the principal erosion process is shallow landsliding. After landslides, soil recovery initially follows our predicted power law increase in time, though with increasing time background erosion processes become important. At a time equal to a landslide recurrence interval, the soil depth can exceed the steady state depth by as much as a factor 2. By comparing predicted and observed x(S) results, we show that the accessed result for erosion as a function of slope angle is accurate. Soils deeper than the depth predicted at the landslide recurrence interval are beyond the stability limit. This result suggests an important practical relevance of the new soil production function.