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

Steep, soil-mantled hillslopes evolve through the downslope movement of soi l, driven largely by slope-dependent transport processes. Most landscape ev olution models represent hillslope transport by linear diffusion, in which rates of sediment transport are proportional to slope, such that equilibriu m hillslopes should have constant curvature between divides and channels. O n many soil-mantled hillslopes, however, curvature appears to vary systemat ically, such that slopes are typically convex near the divide and become in creasingly 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 rai nsplash and biogenic activity) and frictional and gravitational forces resu lts in a diffusive transport law that depends nonlinearly on hillslope grad ient. Our proposed transport law (1) approximates linear diffusion at low g radients and (2) indicates that sediment Aux increases rapidly as gradient approaches a critical value. We calibrated and tested this transport law us ing high-resolution topographic data from the Oregon Coast Range. These dat a, obtained by airborne laser altimetry, allow us to characterize hillslope morphology at approximate to 2 m scale. At five small basins in our study area, hillslope curvature approaches zero with increasing gradient, consist ent with our proposed nonlinear diffusive transport law. Hillslope gradient s tend to cluster near values for which sediment flux increases rapidly wit h slope, such that large changes in erosion rate will correspond to small c hanges in gradient. Therefore average hillslope gradient is unlikely to be a reliable indicator of rates of tectonic forcing or baselevel lowering. Wh ere hillslope erosion is dominated by nonlinear diffusion, rates of tectoni c forcing will be more reliably reflected in hillslope curvature near the d ivide rather than average hillslope gradient.