Symmetry, randomness, and process in the structure of branched channel networks

Abstract

The branched structure of channel networks has a primary impact on the spatial distribution of elevation, water, and life across Earth's surface from the hillslope to the continental scale and is also observed on other planets. However, the link between this dendritic multiscale structure and the erosional processes that sculpt it has remained elusive for more than six decades. In fact, many topologic measures fail to distinguish natural networks from those generated by random walks. Here we show that a fundamental multiscale topologic symmetry is ingrained into the structure of these networks and reflects the equal elevation drop spanned by flows that split at the drainage divide and meet again downslope. We demonstrate that this symmetry distinguishes random‐walk networks from natural ones, captures the temporal evolution of these networks, and divulges information about the processes that shape them.

Modes and rates of horizontal deformation from rotated river basins: Application to the Dead Sea fault system in Lebanon

“…This periodic pattern of c differences can result from periodic variation of U and K along strike with a wavelength equal to the width of a single basin, a scenario for which there is no evidence. Hence, following previous interpretations of similar c behavior in other settings Shelef and Hilley, 2014;Yang et al, 2015), we suggest that the pattern is indicative of disequilibrium in drainage area distribution and in divide position. This view is supported by the landscape morphology showing high-c perched channels and asymmetric hillslopes that are steeper toward low-c channels (Fig.…”

“…Therefore, when c is mapped along a fluvial channel system and shows different values between two adjacent channel heads across a water divide, the assumption of U and K commonality or the assumption of steady state is violated . Such c differences can arise from variations of the tectonic history and erosivity pattern of the two channels between the divide and the channels' confluence, or they can arise from disequilibrium in the drainage area distribution such that the position of the water divide is not optimal and perhaps transient Shelef and Hilley, 2014). Figure 1 shows that within each of the central and southern basins, the value of c is systematically higher along northern tributaries with respect to southern tributaries.…”

A Cenozoic uplift history of Mexico and its surroundings from longitudinal river profiles

“…It is unclear how these issues affect the results of Willett et al . [] and Shelef and Hilley []. More widely, the extent to which drainage topologies are highly dynamic in time at regional to continental scales is unknown [e.g., Cowie et al ., ].…”

The Influence of Lithology on the Forms of Hillslopes and Drainage Basins in Soil Mantled Landscapes

“…A space-filling network was simulated within these boundaries using a modified version of the priority flood algorithm (Barnes et al, 2014) in which filling priority was randomized, starting at the current outlet location and elevation. This procedure produces network geometries that are inconsistent with the fact that elevations must be equivalent on each side of a topographic divide and within the junction of a channel to prevent drainage divide migration (Shelef and Hilley, 2014). Thus, we migrate divides by reassigning their flow directions with an iterative procedure that ensures that the watershed areas and channel slopes globally obey the area-slope scaling required by the stream-power incision rule (e.g., Howard, 1990).…”