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The illusion of diffusion: Field evidence for depth-dependent sediment transport

¹ Department of Earth Sciences, Dartmouth College, Hanover, New Hampshire 03755, USA
² Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, Tennessee 37235, USA
³ Department of Earth and Planetary Sciences, University of California, Berkeley, California 94720, USA

Soil-covered upland landscapes are common in much of the habitable world, and our understanding of their evolution as a function of different climatic, tectonic, and geologic regimes is important across a wide range of disciplines. Erosion laws direct quantitative study of the processes shaping Earth's surface and form the basis of landscape evolution modeling, but are based on limited field data. Here we use in situ–produced cosmogenic ¹⁰Be and ²⁶Al concentrations from granitic saprolite to quantify an exponential decline in soil production with increasing soil thickness for a new field site in Point Reyes, California. Results are similar to soil production functions from two different, previously studied field sites, and are used with extensive measurements of soil thickness to quantify depth-integrated sediment transport flux. Plots of calculated sediment fluxes against the product of soil depth and hillslope gradient provide the first field-based evidence that soil transport is a nonlinear, depth-dependent function. Data from all sites suggest that the widely used linear diffusion equation is only appropriate for shallow gradient, convex-up regions, while the depth-dependent transport law is more broadly applicable. Quantifying both the mobile soil thickness and landscape morphology is therefore critical to understanding how landscapes evolve.

Key Words: erosion • geomorphology • cosmogenic nuclides • landscape evolution • soil transport

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