Stability of creeping soil and implications for hillslope evolution

The geomorphic behavior of a soil-mantled hillslope undergoing diffusive cr eep involves a coupling between changes in land surface elevation, soil tra nsport rates, soil production, and soil thickness. A linear stability analy sis suggests that the coupled response of the soil mantle to small perturba tions in soil thickness or surface topography is influenced by two factors. The diffusive-like behavior of soil creep has a stabilizing effect wherein perturbations in land surface elevation are damped. The relation between t he soil production rate and soil thickness may be either stabilizing or des tabilizing. A monotonically decreasing production rate with soil thickness reinforces the stabilizing effect of diffusive land surface smoothing. An i ncreasing production rate with soil thickness has a destabilizing effect wh erein perturbations in soil thickness or the soil-bedrock interface are amp lified, despite the presence of diffusive land surface smoothing. This coup led behavior is insensitive to the transport relation, whether the soil flu x is proportional to the land surface gradient or to the product of the soi l thickness and land surface gradient. The latter type of relation, nonethe less, could lead to a more complex hillslope form than might otherwise be e xpected for purely diffusive transport. Moreover, the response to periodic (sinusoidal) variations in the rate of stream downcutting at the lower hill slope boundary involves upslope propagation of coupled (damped), waveforms in the land surface and the soil-bedrock interface. The distance of upslope propagation goes with the square root of the product of the transport diff usion-like coefficient and the period of the downcutting rate. The upper pa rt of the hillslope is therefore insensitive to relatively high-frequency v ariations in stream downcutting, so together with a stable behavior of the coupled soil-mantle-bedrock system, this part of the hillslope may exhibit a tendency toward uniform lowering, while the lower part behaves transientl y. Conversely, in the presence of low-frequency variations in stream downcu tting, hillslope morphology and soil thickness variations are more likely t o reflect unsteady conditions over the entirety of the hillslope.