Abstract

On the basis of the Manning equation and basic mass conservation principles, we derive an expression for scaling the steady-state width (W) of river channels as a function of discharge (Q), channel slope (S), roughness (n), and width-to-depth ratio (α): W = [α(α + 2)2/3]3/8Q3/8S−3/16n3/8. We propose that channel width-to-depth ratio, in addition to roughness, is a function of the material in which the channel is developed, and that where a river is confined to a given material, width-to-depth ratio and roughness can be assumed constant. Given these simplifications, the expression emulates traditional width-discharge relationships for rivers incising bedrock with uniformly concave fluvial long profiles. More significantly, this relationship describes river width trends in terrain with spatially nonuniform rock uplift rates, where conventional discharge-based width scaling laws are inadequate. We suggest that much of observed channel width variability in river channels confined by bedrock is a simple consequence of the tendency for water to flow faster in steeper reaches and therefore occupy smaller channel cross sections. We demonstrate that using conventional scaling relationships for channel width can result in underestimation of stream-power variability in channels incising bedrock and that our model improves estimates of spatial patterns of bedrock incision rates.

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