Soil production function

Abstract: Data drawn from a global compilation of studies quantitatively confirm the long-articulated contention that erosion rates from conventionally plowed agricultural fields average 1–2 orders of magnitude greater than rates of soil production, erosion under native vegetation, and long-term geological erosion. The general equivalence of the latter indicates that, considered globally, hillslope soil production and erosion evolve to balance geologic and climate forcing, whereas conventional plow-based agriculture increases erosion rates enough to prove unsustainable. In contrast to how net soil erosion rates in conventionally plowed fields (≈1 mm/yr) can erode through a typical hillslope soil profile over time scales comparable to the longevity of major civilizations, no-till agriculture produces erosion rates much closer to soil production rates and therefore could provide a foundation for sustainable agriculture.

Abstract: A model is proposed for predicting the spatial variation in colluvial soil depth, the results of which are used in a separate model to examine the effects of root strength and vertically varying saturated conductivity on slope stability. The soil depth model solves for the mass balance between soil production from underlying bedrock and the divergence of diffusive soil transport. This model is applied using high-resolution digital elevation data of a well-studied site in northern California and the evolving soil depth is solved using a finite difference model under varying initial conditions. The field data support an exponential decline of soil production with increasing soil depth and a diffusivity of about 50 cm 2 / yr. The predicted pattern of thick and thin colluvium corresponds well with field observations. Soil thickness on ridges rapidly obtain an equilibrium depth, which suggests that detailed field observations relating soil depth to local topographic curvature could further test this model. Bedrock emerges where the curvature causes divergent transport to exceed the soil production rate, hence the spatial pattern of bedrock outcrops places constraints on the production law. The infinite slope stability model uses the predicted soil depth to estimate the effects of root cohesion and vertically varying saturated conductivity. Low cohesion soils overlying low conductivity bedrock are shown to be least stable. The model may be most useful in analyses of slope instability associated with vegetation changes from either land use or climate change, although practical applications may be limited by the need to assign values to several spatially varying parameters. Although both the soil depth and slope stability models offer local mechanistic predictions that can be applied to large areas, representation of the finest scale valleys in the digital terrain model significantly influences local model predictions. This argues for preserving fine-scale topographic detail and using relatively fine grid sizes even in analyses of large catchments.