@article{MuddClubbGailletonetal.2018,
  author    = {Mudd, Simon M. and Clubb, Fiona J. and Gailleton, Boris and Hurst, Martin D.},
  title     = {How concave are river channels?},
  series = {Earth surface dynamics},
  volume    = {6},
  journal   = {Earth surface dynamics},
  number    = {2},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {2196-6311},
  doi       = {10.5194/esurf-6-505-2018},
  pages     = {505 -- 523},
  year      = {2018},
  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 k(s). However, the calculation of channel steepness requires the normalisation of channel gradient by drainage area. This normalisation requires a power law exponent that is referred to as the channel concavity index. Despite the concavity index being crucial in determining channel steepness, it is challenging to constrain. In this contribution, we compare both slope-area methods for calculating the concavity index and methods based on integrating drainage area along the length of the channel, using so-called "chi" (chi) analysis. We present a new chi-based method which directly compares chi values of tributary nodes to those on the main stem; this method allows us to constrain the concavity index in transient landscapes without assuming a linear relationship between chi and elevation. Patterns of the concavity index 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 chi-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 the concavity index varies across diverse landscapes, with the aim to improve our understanding of the physics behind bedrock channel incision.},
  language  = {en}
}
@article{GailletonMuddClubbetal.2019,
  author    = {Gailleton, Boris and Mudd, Simon M. and Clubb, Fiona J. and Peifer, Daniel and Hurst, Martin D.},
  title     = {A segmentation approach for the reproducible extraction and quantification of knickpoints from river long profiles},
  series = {Earth surface dynamics},
  volume    = {7},
  journal   = {Earth surface dynamics},
  number    = {1},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {2196-6311},
  doi       = {10.5194/esurf-7-211-2019},
  pages     = {211 -- 230},
  year      = {2019},
  abstract  = {Changes in the steepness of river profiles or abrupt vertical steps (i.e. waterfalls) are thought to be indicative of changes in erosion rates, lithology or other factors that affect landscape evolution. These changes are referred to as knickpoints or knickzones and are pervasive in bedrock river systems. Such features are thought to reveal information about landscape evolution and patterns of erosion, and therefore their locations are often reported in the geomorphic literature. It is imperative that studies reporting knickpoints and knickzones use a reproducible method of quantifying their locations, as their number and spatial distribution play an important role in interpreting tectonically active landscapes. In this contribution we introduce a reproducible knickpoint and knickzone extraction algorithm that uses river profiles transformed by integrating drainage area along channel length (the so-called integral or chi method). The profile is then statistically segmented and the differing slopes and step changes in the elevations of these segments are used to identify knickpoints, knickzones and their relative magnitudes. The output locations of identified knickpoints and knickzones compare favourably with human mapping: we test the method on Santa Cruz Island, CA, using previously reported knickzones and also test the method against a new dataset from the Quadrilatero Ferrifero in Brazil. The algorithm allows for the extraction of varying knickpoint morphologies, including stepped, positive slope-break (concave upward) and negative slope-break knickpoints. We identify parameters that most affect the resulting knickpoint and knickzone locations and provide guidance for both usage and outputs of the method to produce reproducible knickpoint datasets.},
  language  = {en}
}
@misc{MuddClubbGailletonetal.2018,
  author    = {Mudd, Simon M. and Clubb, Fiona J. and Gailleton, Boris and Hurst, Martin D.},
  title     = {How concave are river channels?},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {718},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42699},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-426998},
  pages     = {19},
  year      = {2018},
  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 k(s). However, the calculation of channel steepness requires the normalisation of channel gradient by drainage area. This normalisation requires a power law exponent that is referred to as the channel concavity index. Despite the concavity index being crucial in determining channel steepness, it is challenging to constrain. In this contribution, we compare both slope-area methods for calculating the concavity index and methods based on integrating drainage area along the length of the channel, using so-called "chi" (chi) analysis. We present a new chi-based method which directly compares chi values of tributary nodes to those on the main stem; this method allows us to constrain the concavity index in transient landscapes without assuming a linear relationship between chi and elevation. Patterns of the concavity index 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 chi-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 the concavity index varies across diverse landscapes, with the aim to improve our understanding of the physics behind bedrock channel incision.},
  language  = {en}
}