Hillslope diffusion and channel steepness in landscape evolution models

Abstract. The streampower fluvial erosion (SP) model is the basis for many analyses and simulations of landscape evolution. It assumes that the rate of 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 coupled evolution of channels and hillslopes (SPD models). While it is implicitly assumed that channels in the SPD models retain their detachment-limited character, this has not been extensively tested. Here we show that the deposition component of hillslope diffusion has a substantial effect on channel slope and relief in SPD models, and present a new method to predict the channel steepness index from model parameters. We contrast the results with those of a mixed bedrock-alluvial river model coupled with a hillslope diffusion model that both track sediment mass balance, and suggest that the combination of mass-conservative hillslope processes and non-mass-conservative fluvial erosion in SPD models leads to unrealistic scaling behavior. We demonstrate this by examining several field sites where an SPD model adequately describes the spacing of first-order valleys, and show that it is inadequate to predict channel steepness.