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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
05 Feb 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).
How concave are river channels?
Simon M. Mudd1, Fiona J. Clubb1,2, Boris Gailleton1, and Martin D. Hurst3 1School of GeoSciences, University of Edinburgh, Drummond Street, Edinburgh EH8 9XP, UK
2Institute of Earth and Environmental Science, University of Potsdam, 14476 Potsdam-Golm, Germany
3School of Geographical and Earth Sciences, University of Glasgow, University Avenue, Glasgow G12 8QQ, UK
Abstract. For over a century geomorphologists have attempted to unravel information about landscape evolution, and processes that drive it, using river profiles. Many studies have combined new topographic datasets with theoretical models of channel incision to infer erosion rates, identify rock types with different resistance to erosion, and detect potential regions of tectonic activity. The most common metric used to analyse river profile geometry is channel steepness, or ks. However, the calculation of channel steepness requires the normalisation of channel gradient by drainage area. This relationship between channel gradient and drainage area is referred to as channel concavity, and despite being crucial in determining channel steepness, is challenging to constrain. In this contribution we compare both slope–area methods for calculating concavity and methods based on integrating drainage area along the length of the channel, using so-called ``chi'' (χ) analysis. We present a new χ-based method which directly compares χ values of tributary nodes to those on the main stem: this method allows us to constrain channel concavity in transient landscapes without assuming a linear relationship between χ and elevation. Patterns of channel concavity have been linked to the ratio of the area and slope exponents of the stream power incision model (m/n): we therefore construct simple numerical models obeying detachment-limited stream power and test the different methods against simulations with imposed m and n. We find that χ-based methods are better than slope–area methods at reproducing imposed m/n ratios when our numerical landscapes are subject to either transient uplift or spatially varying uplift and fluvial erodibility. We also test our methods on several real landscapes, including sites with both lithological and structural heterogeneity, to provide examples of the methods' performance and limitations. These methods are made available in a new software package so that other workers can explore how concavity varies across diverse landscapes, with the aim to improve our understanding of the physics behind bedrock channel incision.
Citation: Mudd, S. M., Clubb, F. J., Gailleton, B., and Hurst, M. D.: How concave are river channels?, Earth Surf. Dynam. Discuss.,, in review, 2018.
Simon M. Mudd et al.
Simon M. Mudd et al.

Model code and software

MuddPILE the Parsimonious Integrated Landscape Evolution Model S. M. Mudd, J. Jenkinson, D. A. Valters, and F. J. Clubb The LSDTopoTools Chi Mapping Package S. M. Mudd, F. J., Clubb, D. T. Milodowski, B. Gailleton, S. W. D. Grieve, M. D. Hurst, and D. A. Valters
Simon M. Mudd et al.


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Publications Copernicus
Short summary
Rivers can reveal information about erosion rates, tectonics, and climate. In order to make meaningful inferences about these influences one must be able to compare headwaters to downstream parts of the river network. We describe new methods for normalizing river steepness for drainage area to better understand how rivers record erosion rates in eroding landscapes.
Rivers can reveal information about erosion rates, tectonics, and climate. In order to make...