Lateral migration of hillcrests in response to channel incision in soil-mantled landscapes

[1] We investigate lateral migration of hillcrests in response to vertical offsets or transient incision rates of channels bordering these hillcrests in soil-mantled landscapes. For hillslopes undergoing sediment transport that is linearly proportional to the slope, the hillcrest offset distance is one quarter of the ratio of the vertical offset between the channels to the relief of the symmetric hillslope. If channels are downcutting at different rates, the speed of hillcrest migration will depend on the ratio of the downcutting rates and the density ratio, which is the ratio of the bulk density of the bedrock to the bulk density of the soil. The density ratio plays a fundamental role in determining the transient response of the hillcrest; lower-density ratios lead to faster transient responses to changes in channel downcutting rates. Other parameters that affect the transient response of the hillcrest are the magnitude of transient differences in downcutting between the two channels, the time-averaged incision rate, and a ratio of the elevation of the hillslope to a length that characterizes the decay in soil production with increasing soil thickness; different parameters will be important for different sediment flux laws. The profile of soil thickness reacts to transient changes in downcutting at a different rate than surface topography. Hillslopes experiencing transient channel downcutting may have surface topography that is symmetric about the hillcrest but will at the same time have a soil thickness profile that is asymmetric.