Network Scale Power-Law Relationships for Estimating Sediment Flux and Bedrock Incision Rates

The simplicity of the widely applied stream-power bedrock incision model makes it appealing for use in both numerical models and natural settings. However the stream-power model does not include many of the variables that control bedrock incision, including the dual role that sediment flux can play in both enhancing and hindering bedrock incision. Here we present a number of numerical realizations of landscapes evolved using two different sediment-flux bedrock incision models. The landscapes have spatially varying uplift rates, and all of the landscapes have reached steady state. We analyze the resulting distributions of incision and sediment flux rates as a function of slope and area in order to understand how the network organizes itself in response to tectonic forcing. In traditional stream-power models we tend to think of area as an independent variable but in reality a drainage network is an organized system of channels and tributaries. Our results suggest that both slope and area always organize throughout a network to conform to the boundary conditions (uplift rate) and the governing equations (sediment-flux model). In the settings that we have explored, both sediment-flux rates and incision rates can be described as power-law functions of slope and area. However, the exponents on area and slope in the incision power-law relationship may differ from the exponents traditionally used in the stream-power model.