A unified framework for modeling landscape evolution by discrete flows

Abstract

Topographic features such as branched valley networks and undissected convex-up hillslopes are observed in disparate physical environments. In some cases, these features are formed by sediment transport processes that occur discretely in space and time, while in others, by transport processes that are uniformly distributed across the landscape. This paper presents an analytical framework that reconciles the basic attributes of such sediment transport processes with the topographic features that they form and casts those in terms that are likely common to different physical environments. In this framework, temporal changes in surface elevation reflect the frequency with which the landscape is traversed by geophysical flows generated discretely in time and space. This frequency depends on the distance to which flows travel downslope, which depends on the dynamics of individual flows, the lithologic and topographic properties of the underlying substrate, and the coevolution of topography, erosion, and the routing of flows over the topographic surface. To explore this framework, we postulate simple formulations for sediment transport and flow runout distance and demonstrate that the conditions for hillslope and channel network formation can be cast in terms of fundamental parameters such as distance from drainage divide and a friction-like coefficient that describes a flow's resistance to motion. The framework we propose is intentionally general, but the postulated formulas can be substituted with those that aim to describe a specific process and to capture variations in the size distribution of such flow events.

Martian gullies: a comprehensive review of observations, mechanisms and insights from Earth analogues

“…Further work is needed to ascertain whether CO2 sublimation can produce long-lived fluidisation and therefore morphologies similar to martian gullies. It has been hypothesised that the repeated action of discrete granular flows can produce connected networks (Shelef and Hilley, 2016) and complex channel geometries as seen in martian gullies and terrestrial equivalents. As stated by Hoffman (2002) "quantitative diagnostic criteria must be developed to distinguish between the morphologies produced by subaerial flows and those of density flows".…”

“…However, this approach has yet to be applied to martian gullies. Martian gullies are ripe for this application because of two recent innovations: 1) the increasing use of synthetic DEMs as a starting point for landscape evolution models (Hillier et al, 2015), allowing gullies to be simulated in undisturbed topography and 2) the recognition that landscape evolution models can be driven by stochastic discrete flow events (Shelef and Hilley, 2016), rather than flow driven by continuous variables. The use of landscape evolution models could help us to explore the age of gullies, the climate drivers and the expected sedimentary packages relevant for understanding the rock record on Mars.…”

The Generation and Scaling of Longitudinal River Profiles

“…These interactions are difficult to observe on appropriately long time scales. Nonetheless, there is tentative agreement that an empirical stream power law provides one practical means for analyzing the geometry of a river profile (e.g., Dietrich et al, ; Howard & Kerby, ; Howard & Dietrich, ; Mudd et al, ; Rosenbloom & Anderson, ; Shelef & Hilley, ; Weissel & Seidl, ; Whipple & Tucker, ). The stream power law can be written in the form where z is the height along the river channel as a function of time, t , and distance, x .…”

Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA

“…Recent work on hillslope sediment transport has highlighted the idea that sediment particle travel distance is an important component of the flux (Carretier et al, ; Lamb et al, ; Michaelides et al, ; Shelef & Hilley, ). In certain settings, transport processes may redistribute sediment over length scales that are long relative to hillslope topographic (e.g., slope) length scales.…”