Cosmogenic nuclides, topography, and the spatial variation of soil depth

If the rate of bedrock conversion to a mobile layer of soil depends on the local thickness of soil, then hillslopes on uniform bedrock in a landscape approaching dynamic equilibrium should be mantled by a uniform thickness of soil. Conversely, if the depth of soil varies across an actively eroding landscape, then rates of soil production will also vary and, consequently the landscape will not be in morphologic equilibrium. The slow evolution of hillslopes relative to the tempo of climatic variations and tectonic adjustments would suggest that local morphologic disequilibrium may be expected in many landscapes. Here, we explore this issue of equilibrium landscapes through a previously developed model that predicts the spatial variation in thickness of soil as a consequence of the local balance between soil production and erosion. First, we confirm the assumption in the model that soil production varies inversely with the thickness of soil using two independent methods. One method uses the theoretical prediction that at local steady state (soil production equals removal), the depth of soil should vary inversely with hillslope curvature. The second method relies on direct measurements of in situ produced concentrations of cosmogenic 10Be and 26Al in bedrock at the base of the soil column. For our study site in Northern California, the two methods agree and yield the expression that the rate of soil production declines exponentially with the thickness of soil from 0.077 mm/year with no soil mantle to 0.0077 mm/year under 1 m of soil. We then use this function of soil production in a coupled production and diffusive model of sediment transport to explore the controls on the spatial variation of the depth of soil on four separate spur ridges (noses) where we measured the data for the function of soil production. Model predictions are sensitive to boundary conditions, grid scale, and run time. Nonetheless, we found good agreement between predicted and observed depths of soil as long as we used the observed function of soil production. The four noses each have spatially varying curvature and, consequently, have varying depths of soil, implying morphologic disequilibrium. We suggest that our study site has been subjected to a wave of incision and varying intensities of erosion because of tectonic and climatic oscillations that have a frequency shorter than the morphologic response time of the landscape.