Equilibrium form of horizontally retreating, soil‐mantled hillslopes: Model development and application to a groundwater sapping landscape

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.