Bedrock river erosion through dipping layered rocks: quantifying erodibility through kinematic wave speed

Abstract

Abstract. Landscape morphology reflects drivers such as tectonics and climate but is also modulated by underlying rock properties. While geomorphologists may attempt to quantify the influence of rock strength through direct comparisons of landscape morphology and rock strength metrics, recent work has shown that the contact migration resulting from the presence of mixed lithologies may hinder such an approach. Indeed, this work counterintuitively suggests that channel slopes within weaker units can sometimes be higher than channel slopes within stronger units. Here, we expand upon previous work with 1-D stream power numerical models in which we have created a system for quantifying contact migration over time. Although previous studies have developed theories for bedrock rivers incising through layered stratigraphy, we can now scrutinize these theories with contact migration rates measured in our models. Our results show that previously developed theory is generally robust and that contact migration rates reflect the pattern of kinematic wave speed across the profile. Furthermore, we have developed and tested a new approach for estimating kinematic wave speeds. This approach utilizes channel steepness, a known base-level fall rate, and contact dips. Importantly, we demonstrate how this new approach can be combined with previous work to estimate erodibility values. We demonstrate this approach by accurately estimating the erodibility values used in our numerical models. After this demonstration, we use our approach to estimate erodibility values for a stream near Hanksville, UT. Because we show in our numerical models that one can estimate the erodibility of the unit with lower steepness, the erodibilities we estimate for this stream in Utah are likely representative of mudstone and/or siltstone. The methods we have developed can be applied to streams with temporally constant base-level fall, opening new avenues of research within the field of geomorphology.

Tectonic advection of contacts enhances landscape transience

“…Our choice to use slope exponent n = 2 is a common approach (Darling et al, 2020; Han et al, 2014; Peifer et al, 2021) that also accounts for most data on the scaling between erosion rate and channel steepness (Harel et al, 2016; Lague, 2014). Additionally, we avoid using n = 1 because that parameterization makes a river's kinematic wave speed insensitive to changes in channel slope; this insensitivity introduces unusual behaviors when using the stream power model for bedrock river incision through dipping contacts (i.e., the development of vertical steps; Darling et al, 2020; Mitchell & Yanites, 2021; Perne et al, 2017).…”

“…A contact dip of 90° indicates a perfectly vertical contact, which prevents erosion from altering the contact's position across the landscape. Conversely, a contact dip of −30° allows both erosion and vertical rock uplift to alter the contact's position in the landscape and such contact migration can perturb both channel steepness and erosion rates (Darling et al, 2020; Mitchell & Yanites, 2021; Perne et al, 2017).…”

“…Figures 1c–1f show these landscapes after the exposure of a weaker lithology. The migration of the contact separating these units drives the development of a knickpoint in the strong unit (Darling et al, 2020; Forte et al, 2016; Mitchell & Yanites, 2021; Perne et al, 2017; Wolpert & Forte, 2021). The increased erosion within the basins draining to the right may then cause these basins to capture drainage area from the basins draining to the left (Forte & Whipple, 2018; Willett et al, 2014).…”

“…Previous work has shown that rock strength contrasts can introduce autogenic perturbations to bedrock rivers with steady climate and rock uplift (Darling et al, 2020; Forte et al, 2016; Mitchell & Yanites, 2021; Perne et al, 2017). As rock uplift carries units upwards, any nonvertical contacts will consequently move across a landscape.…”

“…As rock uplift carries units upwards, any nonvertical contacts will consequently move across a landscape. The migration of a contact separating weak and strong rock types along a river can cause dramatic variations in channel steepness because river reaches on either side of the contact must have the same horizontal retreat rate (i.e., kinematic wave speed), and maintaining a certain retreat rate requires different channel slopes in stronger or weaker rocks (Darling et al, 2020; Mitchell & Yanites, 2021). Although such work highlights the role of rock strength in landscape morphology and dynamics, research examining the impact of rock strength contrasts on river erosion has focused exclusively on landscapes without a significant horizontal component of rock motion.…”