Hillslope diffusion and channel steepness in landscape evolution models

Abstract

The streampower (SP) fluvial erosion model is the basis for many landscape evolution simulations and analyses. It assumes that river incision into bedrock depends only on flow intensity and rock erodibility and is insensitive to sediment flux. In two dimensions, the SP model is often coupled with diffusion processes, which together describe the evolution of channels and hillslopes. In a widely used formulation, the SP model and hillslope diffusion are applied everywhere while tracking only topography (the SPD model). In this case channels may steepen to erode deposited hillslope material. We conduct the first systematic investigation of this effect and use a scaling analysis to demonstrate that the increase in channel steepness can be predicted from model parameters when diffusion is linear. Alternative approaches to channel-hillslope coupling include fully detachment-limited models where channels have unlimited capacity to transport hillslope sediment, as well as models where transport capacity is limited but erosion processes differ for sediment and bedrock. A model of the latter type shows that both distinguishing bedrock and sediment erodibility and allowing for some sediment retention in channels weaken or eliminate the increase in channel steepness due to hillslope diffusion. This highlights that the SPD scaling emerges from an unlikely set of circumstances in which sediment is as hard to erode as bedrock but cannot redeposit or affect conditions downslope. A test at field sites where an SPD model adequately describes the spacing of first-order valleys shows that channels steepen to transport hillslope sediment, but the SPD scaling does not hold. This suggests that the separate treatment of sediment and bedrock and the consideration of factors such as grain size that affect sediment erodibility may be essential for predicting channel steepness using coupled channel-hillslope models.