Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments

Diffusive processes such as creep, rain splash, and biogenic transport play a major role in controlling the development of convex hilltops on soil-mantled landscapes. Although many diffusion-based models have been proposed, little attention has been given to the effects of changing transport rates and boundary conditions. We use numerical and analytical solutions of the one-dimensional diffusion equation to explore whether hilltop convexities can be in equilibrium with contemporary climate and local channel incision rates. The results show that the timescale of such morphological adjustments varies substantially depending on whether the hillslope is tending to increase or decrease its convexity through time. By comparing the relaxation times estimated here with the frequency of the climatic oscillations observed in the last few million years, we argue that most of the convex hilltops observed in the field today are likely to be far from time-independent morphological features.