Hillslope evolution by nonlinear, slope-dependent transport: Steady state morphology and equilibrium adjustment timescales


  • Joshua J. Roering,

  • James W. Kirchner,

  • William E. Dietrich


Soil-mantled hillslopes are typically convex near the crest and become increasingly planar downslope, consistent with nonlinear, slope-dependent sediment transport models. In contrast to the widely used linear transport model (in which sediment flux is proportional to slope angle), nonlinear models imply that sediment flux should increase rapidly as hillslope gradient approaches a critical value. Here we explore how nonlinear transport influences hillslope evolution and introduce a dimensionless parameter ΨL to express the relative importance of nonlinear transport. For steady state hillslopes, with increasing ΨL (i.e., as slope angles approach the threshold angle and the relative magnitude of nonlinear transport increases), the zone of hillslope convexity becomes focused at the hilltop and side slopes become increasingly planar. On steep slopes, rapid increases in sediment flux near the critical gradient limit further steepening, such that hillslope relief and slope angle are not sensitive indicators of erosion rate. Using a one-dimensional finite difference model, we quantify hillslope response to changes in baselevel lowering and/or climate-related transport efficiency and use an exponential decay function to describe how rapidly sediment flux and erosion rate approach equilibrium. The exponential timescale for hillslope adjustment decreases rapidly with increasing ΨL. Our results demonstrate that the adjustment timescale for hillslopes characteristic of the Oregon Coast Range and similar steep, soil-mantled landscapes is relatively rapid (≤50 kyr), less than one quarter of the timescale predicted by the linear transport model.