Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology

Abstract

Steep, soil‐mantled hillslopes evolve through the downslope movement of soil, driven largely by slope‐dependent transport processes. Most landscape evolution models represent hillslope transport by linear diffusion, in which rates of sediment transport are proportional to slope, such that equilibrium hillslopes should have constant curvature between divides and channels. On many soil‐mantled hillslopes, however, curvature appears to vary systematically, such that slopes are typically convex near the divide and become increasingly planar downslope. This suggests that linear diffusion is not an adequate model to describe the entire morphology of soil‐mantled hillslopes. Here we show that the interaction between local disturbances (such as rainsplash and biogenic activity) and frictional and gravitational forces results in a diffusive transport law that depends nonlinearly on hillslope gradient. Our proposed transport law (1) approximates linear diffusion at low gradients and (2) indicates that sediment flux increases rapidly as gradient approaches a critical value. We calibrated and tested this transport law using high‐resolution topographic data from the Oregon Coast Range. These data, obtained by airborne laser altimetry, allow us to characterize hillslope morphology at ≈2 m scale. At five small basins in our study area, hillslope curvature approaches zero with increasing gradient, consistent with our proposed nonlinear diffusive transport law. Hillslope gradients tend to cluster near values for which sediment flux increases rapidly with slope, such that large changes in erosion rate will correspond to small changes in gradien. Therefore average hillslope gradient is unlikely to be a reliable indicator of rates of tectonic forcing or baselevel lowering. Where hillslope erosion is dominated by nonlinear diffusion, rates of tectonic forcing will be more reliably reflected in hillslope curvature near the divide rather than average hillslope gradient.