Responses of soil‐mantled hillslopes to transient channel incision rates

Abstract

Channel incision drives hillslope morphology in humid soil‐mantled landscapes. When channel incision rates change, numerous hillslope soil properties (e.g., erosion rates, soil thickness, and soil production) adjust in response to this change. Here we investigate the timescales of adjustment of hillslope soil properties when channel incision rates change in time. An idealized soil‐mantled hillslope (linear sediment flux law and soil density equal to bedrock density) is investigated, and the transient evolution of this hillslope is determined analytically. This analysis reveals two dominant adjustment timescales. The longer of these two timescales determines the rate at which the entire hillslope adjusts to a change in channel incision rates and is proportional to 4λ2/(π2D), where λ is the length of the hillslope and D is the sediment diffusivity. Numerical simulations are then used to examine responses of hillslopes that involve nonlinear behavior (e.g., hillslopes that experience nonlinear sediment transport or have soil thicknesses that respond to the soil production function). Using these numerical models, we show that the ratio between the soil density (ρs) and the density of the soil parent material (ρη) can alter the long‐term response of the hillslope such that the characteristic timescale becomes 4ρηλ2/(π2Dρs). In addition, we show that the adjustments of the soil erosion rate, the soil production rate, and the soil thickness have different characteristic response timescales. Hillslopes that experience sediment flux that is proportional to the depth slope product respond on longer timescales than hillslopes that experience a linear sediment flux law when channel incision rates increase. We illustrate how the spatial pattern of hillslope response to changes in channel incision rates can be used to constrain either channel incision histories or hillslope response timescales. If the hillslope response timescale is known, the pattern of hillslope disturbance can be used to constrain the celerity of a incision wave as it moves upstream through a channel. If the channel incision history is known, the hillslope response timescale may be evaluated on the basis of the spatial pattern of hillslope disturbance.