The soil production function and landscape equilibrium

Hilly and mountainous landscapes are partially to completely covered with soil under a wide range of erosion and uplift rates, bedrock type and climate. For soil to persist it must be replenished at a rate equal to or greater than that of erosion. Although it has been assumed for over 100 years that bedrock disintegration into erodable soil declines with increasing soil mantle thickness1,2,3,4,5,6,7,8,9, no field data have shown this relationship. Here we apply two independent field methods for determining soil production rates to hillslopes in northern California. First, we show that hillslope curvature (a surrogate for soil production7) varies inversely with soil depth. Second, we calculate an exponential decline of soil production rates with increasing soil depth from measurements of the in situ produced cosmogenic 10Be and 26Al concentrations in bedrock sampled under soils of different depths. Results from both methods agree well and yield the first empirical soil production function. We also illustrate how our methods can determine whether a landscape is in morphological equilibrium or not.