Quasi‐Steady Evolution of Hillslopes in Layered Landscapes: An Analytic Approach

Abstract

Landscapes developed in layered sedimentary or igneous rocks are common on Earth, as well as on other planets. Features such as hogbacks, exposed dikes, escarpments, and mesas exhibit resistant rock layers adjoining more erodible rock in tilted, vertical, or horizontal orientations. Hillslopes developed in the erodible rock are typically characterized by steep, linear‐to‐concave slopes or “ramps” mantled with material derived from the resistant layers, often in the form of large blocks. Previous work on hogbacks has shown that feedbacks between weathering and transport of the blocks and underlying soft rock can create relief over time and lead to the development of concave‐up slope profiles in the absence of rilling processes. Here we employ an analytic approach, informed by numerical modeling and field data, to describe the quasi‐steady state behavior of such rocky hillslopes for the full spectrum of resistant layer dip angles. We begin with a simple geometric analysis that relates structural dip to erosion rates. We then explore the mechanisms by which our numerical model of hogback evolution self‐organizes to meet these geometric expectations, including adjustment of soil depth, erosion rates, and block velocities along the ramp. Analytical solutions relate easily measurable field quantities such as ramp length, slope, block size, and resistant layer dip angle to local incision rate, block velocity, and block weathering rate. These equations provide a framework for exploring the evolution of layered landscapes and pinpoint the processes for which we require a more thorough understanding to predict their evolution over time.

Evolution of the field of ecological restoration over the last three decades: a bibliometric analysis

“…There is a great deal of interest in incorporating more traditional ecological knowledge into current research and practices in ecological restoration. Meanwhile, there are some newly emerging areas of research in ecological restoration since 2017; an example of such a new area is layered landscapes (Glade et al ; Glade & Anderson ).…”

Canyon shape and erosion dynamics governed by channel-hillslope feedbacks

“…During the early stages of canyon evolution, channel incision causes failure of the cap rock (Ward et al, 2011), which delivers large blocks to the hillslopes and channel. The presence of blocks on the hillslopes inhibits soil erosion, stalling subsequent block release from the cap rock (Glade et al, 2017;Glade and Anderson, 2018). Blocks in the channel, if they are too large to be transported, reduce the river incision rate by armoring the bed and increasing hydraulic roughness (Shobe et al, 2016(Shobe et al, , 2018.…”

“…Hillslopes make up the majority of canyon plan-view area and are often the primary source of sediment to the rivers. Steep canyon walls with substantial bare bedrock exposure and sufficient fracture density commonly release large pieces of rock (with diameters of several meters) into the channel (Howard and Selby, 1994;Glade et al, 2017;DiBiase et al, 2018;Glade and Anderson, 2018). Large grain delivery to rivers can inhibit incision over large spatial and temporal scales (Shobe et al, 2016(Shobe et al, , 2018, even damming rivers for short periods of time (Korup et al, 2006;Ouimet et al, 2007;Castleton et al, 2016).…”

Impact of vegetation on erosion: Insights from the calibration and test of a landscape evolution model in alpine badland catchments

“…Landscape evolution models are meant to describe and simulate the evolution of landforms based on mechanistic laws for erosion and other flow processes (Tucker and Hancock, 2010;Willgoose, 2005). Since the early 1960s, numerous models have been developed, with an increasing ability to incorporate and simulate various erosion processes, including linear and nonlinear hillslope transport (Anderson, 2002;Gabet, 2000), detachment-limited and transport-limited stream sediment transport (Howard, 1994;Crave and Davy, 2001), hydrodynamics (Coulthard et al, 2013), frost-induced regolith formation and entrainment (Anderson, Anderson, and Tucker, 2013), soil mantle dependent creep (Glade and Anderson, 2018), landslides (Booth, Roering, and Rempel, 2013), vegetation and hydrology coupling (Istanbulluoglu and Bras, 2006). These models are able to create realistic landforms, as demonstrated for instance by the similarity between the simulated slope-area relationships and those found in natural landscapes (Lague, 2014).…”