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

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.