Right for the wrong reasons? On hillslope sediment and the streampower model

The streampower law is widely used to model the detachment-limited endmember of bedrock channel evolution, in which rivers set their slope mainly to abrade or pluck material from the channel bed. The model suggests a strong sensitivity of river long profiles to tectonic forcing, local bedrock strength, and climate. This has made it a tool of choice for interpreting these signatures in landscapes, regardless of the applicability of detachment limited erosion. For instance, sediment flux can be a major control on channel slope, as channels steepen to evacuate sediment and maintain their bed elevation, which is neglected by the streampower law.

While this is a well understood limitation, the implications become slightly murkier when the streampower law is used in 2D landscape evolution models that add a diffusion law to capture hillslope processes. We find that channel steepness increases with hillslope length, as channels have to steepen in order to erode the hillslope material added to the valley floor by diffusion processes. We show that this approximates some aspects of a transport-limited fluvial erosion model, but neglects others. Importantly, here channel steepening scales exactly with local hillslope properties, rather than those of the entire upstream watershed that would theoretically supply sediment. This has implications for interpretations of river profiles using chi-analysis and model inversion that rely on a version of the streampower law, especially when working between one-dimensional and two-dimensional approaches. We conclude with some extension of the physical significance of our findings, specifically related to constraints on the relationships between streampower erosivity, hillslope diffusivity, and grainsize.