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We use a numerical model to investigate disequilibrium conditions in detachment-limited river networks. Erosion rates are modeled using two different equations that include sediment flux as a variable for determining incision rates into bedrock. A number of numerical simulations are performed to explore erosion patterns, channel profile shape, and network concavity after an increase in uplift rate across the network. In the case where an increase in sediment flux (relative to carrying capacity) is considered only to decrease incision rates, the main channel has a two-part response to a faster uplift rate; initially a knickpoint steepens channel slopes locally, but at later times channel slopes rise throughout the network. However, in the case where an increase in sediment flux can both enhance and suppress incision rates, the transient network response can be much more dynamic; channel slopes (and also elevations) can both rise and fall, all in response to a single increase in uplift rate. The response varies depending on the magnitude of change in uplift rate and the initial ratio of sediment flux to sediment carrying capacity. In all examples, the lower parts of the network respond quickly to an increase in uplift rates by increasing channel slopes, while the response of erosion rates in the upper parts of the network occurs later. As a result, the change in sediment flux delivered to higher order channels lags the initial changes in the slope of these channels and causes a complex response in erosion rates. These findings highlight that erosion rates at any point in the network respond to changes both downstream and upstream, and therefore variables such as sediment flux that integrate the upstream response can play an important role is shaping the transient morphology of river networks.

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