Equilibrium Form of Horizontally Retreating, Soil-Mantled Hillslopes: Model Development and Application to a Groundwater Sapping Landscape

Abstract

We present analytical solutions for the steady state topographic profile of a soil-mantled hillslope retreating into a level plain in response to a horizontally migrating base level. This model applies to several scenarios that commonly arise in landscapes, including widening valleys, eroding channel banks, and retreating scarps. For a sediment transport law in which sediment flux is linearly proportional to the topographic slope, the steady state profile is exponential, with an e-folding length, L, proportional to the ratio of the sediment transport coefficient to the base level migration speed. For the case in which sediment flux increases nonlinearly with slope, the solution has a similar form that converges to the linear case as L increases. We use a numerical model to explore the effects of different base level geometries and find that the one-dimensional analytical solution is a close approximation for the hillslope profile above an advancing channel tip. We then compare the analytical model with hillslope profiles above the tips of a groundwater sapping channel network in the Florida Panhandle. The model agrees closely with hillslope profiles measured from airborne laser altimetry, and we use a predicted log linear relationship between topographic slope and horizontal distance to estimate L for the measured profiles. Mapping 1/L over channel tips throughout the landscape reveals that adjacent channel networks may be growing at different rates and that south facing slopes experience more efficient hillslope transport.