A generalized power law approximation for fluvial incision of bedrock channels

[1] Sediment flux is known to influence bedrock incision rates in mountain rivers. Although the widely used stream power incision model lacks any explicit representation of sediment flux, the model appears to work in a variety of real settings. We address this apparent contradiction using numerical experiments to explore the morphology of fluvial landscapes evolved with four different incision models, three of which include the influence of sediment flux on incision rate. The numerical landscapes have different spatial patterns of uplift and are at steady state. We analyze these landscape using the common “stream power” approach, which views incision rates to be primarily a function of the local channel gradient S and the upstream drainage area A. We find that incision rates I for these landscapes are well described by an empirical power law equation I = K′Am′Sn′. This equation is functionally equivalent to the widely used stream power model, with the important distinction that the parameters K′, m′, and n′ are entirely empirical. These parameters take on constant values within a single landscape, but can otherwise be quite different between landscapes mainly due to differences in the pattern of rock uplift within the drainage. In particular, the parameters m′ and n′ decrease as the rate of rock uplift becomes more focused in the upland part of a mountain belt. The parameter m′ is particularly important in that it describes the sensitivity of a tectonically active mountain belt to changes in precipitation or tectonic accretion. It also defines how incision rates will change as the discharge becomes flashier.