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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/esurf-2019-47
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-2019-47
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 26 Sep 2019

Submitted as: research article | 26 Sep 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).

Mass balance, grade, and adjustment timescales in bedrock channels

Jens Martin Turowski Jens Martin Turowski
  • Helmholtzzentrum Potsdam, German Research Centre for Geosciences GFZ, Telegrafenberg, 14473 Potsdam, Germany

Abstract. Rivers are dynamical systems that are thought to evolve towards a steady state configuration. Then, geomorphic parameters, such as channel width and slope, are constant over time. In the mathematical description of the system, the steady state corresponds to a fixed point in the dynamic equations in which all time derivatives are equal to zero. In alluvial rivers, steady state is characterised by grade. This can be expressed as a so-called order principle: An alluvial river evolves to achieve a state in which sediment transport is constant along the river channel, and is equal to transport capacity everywhere. In bedrock rivers, steady state is thought to be achieved with a balance between erosion and uplift. The corresponding order principle is: A bedrock river evolves to achieve a vertical bedrock incision rate that is equal to the uplift rate or baselevel lowering rate. Within the present paper, considerations of process physics and of the mass balance of a bedrock channel are used to argue that bedrock rivers evolve to achieve both grade and a balance between erosion and uplift. As such, bedrock channels are governed by two order principles. As a consequence, the recognition of a steady state with respect to one of them does not necessarily imply an overall steady state. For further discussion of the bedrock channel evolution towards a steady state, expressions for adjustment timescales are sought. For this, a mechanistic model for lateral erosion of bedrock channels is developed, which allows to obtain analytical solutions for the adjustment timescales for the morphological variables of channel width, channel bed slope and alluvial bed cover. The adjustment timescale to achieve steady cover is of the order of minutes to days, while the adjustment timescales for width and slope are of the order of thousands of years. Thus, cover is adjusted quickly in response to a change in boundary conditions to achieve a graded state. The resulting change in vertical and lateral incision rates triggers a slow adjustment of width and slope, which in turn affects bed cover. As a result of these feedbacks, it can be expected that a bedrock channel is close to a graded state most of the time, even when it is transiently adjusting its bedrock channel morphology.

Jens Martin Turowski
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Jens Martin Turowski
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Latest update: 21 Oct 2019
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Short summary
Bedrock channels are the conveyor belts of mountain regions, evacuating sediment produced by erosion. Bedrock channel morphology and dynamics affects sediment transport rates, local erosion and set the baselevel for hillslope response. Here, using mechanistic considerations of the processes of fluvial erosion and transport, and considerations of the mass balance of sediment and bedrock, I discuss the principles governing steady state channel morphology and the dynamic paths to achieve it.
Bedrock channels are the conveyor belts of mountain regions, evacuating sediment produced by...
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