Modeling the Formation of Topographic Asymmetry by Aspect‐Dependent Erosional Processes and Lateral Channel Migration

Abstract

Some landscapes exhibit the intriguing characteristic that the steepness of hillslopes varies systematically with the direction they face, even where there is no bias introduced by bedrock structure. This topographic asymmetry has inspired numerous explanations. In the simplest scenario, insolation-driven microclimatic differences lead to different erosion rates on opposing slopes and topographic asymmetry develops. Alternatively, lateral channel migration and the corresponding steepening of undercut slopes have also been suggested as a dominant cause of topographic asymmetry. To examine these proposed origins of asymmetric topography, we adapted a numerical landscape evolution model to include lateral channel migration as well as aspect-induced variations in soil creep, regolith strength, and runoff. We compared the resulting topography and erosional response produced by each mechanism and found that the model with lateral channel migration produces unique signatures in erosion rates and the ridgetop Laplacian of elevation. To further investigate lateral channel migration, we developed a model of hillslope profile evolution in which sediment fluxes from opposing slopes control lateral channel migration rate and direction. We find that topographic asymmetry in this system can be self-sustaining. All else being equal, we find that the aspect-dependent models with variable regolith strength or runoff predict that less topographic asymmetry should develop as slope length decreases. These two models also predict that weaker asymmetry should develop as rock strength increases, whereas the lateral channel migration model predicts that greater rock strength should lead to weaker asymmetry only if lateral channel migration efficiency increases faster than fluvial incision efficiency.

Unraveling the Mysteries of Asymmetric Topography at Gabilan Mesa, California

“…We measured the asymmetry in erosion rates by comparing the paired erosion rates for low‐order basins that directly oppose one another on north facing and south facing slopes. We defined this asymmetry metric as (Richardson et al, 2020) …”

“…To reproduce the maximum degree of asymmetry measured at Gabilan Mesa, the aspect-dependent regolith strength LEM required a ratio of the mean ω between the north facing and south facing slopes of~10. The findings of Richardson et al (2020) that slope asymmetry increases with hillslope width, which is the distance between bounding channels across the divide, suggests that the wider basins at Gabilan Mesa may require smaller differences in ω on north facing and south facing slopes to produce the same degree of slope asymmetry relative to narrower basins. The blue background shows the general region for the combination of the aspect-dependent runoff and the aspect-dependent regolith strength LEMs.…”

“…Understanding how microclimatic variability at the hillslope scale influences landscape evolution offers a unique opportunity to isolate climatic variability from other variables that influence landscape evolution, such as lithology and tectonic uplift. Some landscapes that exhibit microclimatic differences also exhibit substantial differences in topographic characteristics that vary with aspect, and studies have suggested that the different microclimates are directly responsible, through a variety of mechanisms, for aspect-dependent topographic variations (e.g., Ben-Asher et al, 2017;Burnett et al, 2008;Churchill, 1982;Dohrenwend, 1978;Emery, 1947;McGuire et al, 2014;Melton, 1960); see also our companion paper (Richardson et al, 2020) for a more thorough review of prior research on topographic asymmetry and its hypothesized causal mechanisms. We seek to address several potential mechanisms that may be sensitive to differences in microclimate and responsible for the development of topographic asymmetry.…”

“…We fixed the sun altitude angle for Gabilan Mesa at 70°, which is the angle that minimizes the variance between cos( ϕ ) and the annually averaged solar radiation. Richardson et al (2020) includes additional information about the weighting function.…”

“…Likewise, Wende (1995) examined asymmetric valleys of the Tertiary Hills of Lower Bavaria and suggested that microclimates may not be required for their formation, arguing instead that they may originate from lateral channel migration driven by asymmetry in initial development of the drainage network. Richardson et al (2020) showed that lateral channel migration may be a self-sustaining process and does not necessarily require the presence of microclimates if an asymmetry in sediment flux to opposite banks of a channel occurs for other reasons, such as differing slope lengths across a valley.…”