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How concave are river channels?

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 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” (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 the
concavity index in transient landscapes without assuming a linear
relationship between χ 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 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 the concavity index varies
across diverse landscapes, with the aim to improve our understanding of the
physics behind bedrock channel incision.
