How concave are river channels?

Abstract

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" (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.

Clustering River Profiles to Classify Geomorphic Domains

“…We ran a detachment‐limited stream power model, based on Mudd () and Mudd et al (), where the model elevation evolves through time as where U is the uplift rate, K is channel erodibility, which is a measure of the efficiency of the incision process, and m and n are constant exponents. We solved for fluvial incision using the Fastscape algorithm of Braun and Willett ().…”

“…We ran a detachment-limited stream power model, based on Mudd (2016) and Mudd et al (2018), where the model elevation evolves through time as…”

“…As k s and θ are strongly correlated when determined from this fitting, k s is commonly normalized by a reference concavity index ( θ ref ) and referred to as k sn . Wobus et al () suggest that θ ref should be selected as the mean θ of channel segments determined to be in steady state, although recent work has shown that θ can vary significantly over small spatial scales, meaning that this is in practice challenging to determine (Mudd et al, ). Normalized channel steepness can be calculated for each point along a channel network as where the subscript i refers to a data point.…”

“…This normalized channel steepness is often used in tectonic geomorphology to infer variations in uplift rate across different catchments or orogens (e.g., Kirby & Whipple, ; ; Snyder et al, ; Wobus et al, ). Recently, additional techniques have been developed to extract channel steepness by plotting an upstream integral of drainage area, referred to as χ , against elevation along the channel, to try and avoid common problems with noise inherent in deriving slope data from digital elevation models (DEMS; e.g., Harkins et al, ; Hergarten et al, ; Mudd et al, , ; Perron & Royden, ; Whipple et al, ).…”

Base Level and Lithologic Control of Drainage Reorganization in the Sierra de las Planchadas, NW Argentina

“…Therefore, this index is commonly assumed to vary between 0.4 and 0.6, and 0.45 is the most widely used value (e.g., Kirby et al, 2003;Kirby & Whipple, 2012;Snyder et al, 2000). However, recent studies have indicated that the concavity index may be more variable (e.g., Mudd et al, 2018;Shelef et al, 2018 (3)) and allow for the comparison of channels with differing catchment areas. Therefore, k sn is the ratio between the true channel slope, S, and the expected slope due to the upstream drainage area, A −θref .…”