Channelization cascade in landscape evolution

Abstract

The hierarchy of channel networks in landscapes displays features that are characteristic of nonequilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial differential equations coupling landscape evolution dynamics with a specific catchment area equation. By means of a linear stability analysis we identify the critical conditions triggering channel formation and the emergence of characteristic valley spacing. The ensuing channelization cascade, described by a dimensionless number accounting for diffusive soil creep, runoff erosion, and tectonic uplift, is reminiscent of the subsequent instabilities in fluid turbulence, while the structure of the simulated patterns is indicative of a tendency to evolve toward optimal configurations, with anomalies similar to dislocation defects observed in pattern-forming systems. The choice of specific geomorphic transport laws and boundary conditions strongly influences the channelization cascade, underlying the nonlocal and nonlinear character of its dynamics.

Environmental heterogeneity dynamics drive plant diversity on oceanic islands

“…These results indicate that whole‐island metrics successfully describe total energy (TEMPrg, HLIrg), water supply (PRECrg) and available space for species (ELEVrg), all major elements of island carrying capacity (Hui, 2006). Moving‐window metrics, in contrast, are more suitable for describing the climatic and topographic complexity of islands (Cramer & Verboom, 2017), when using roughness or standard deviation because they capture local changes in temperature and precipitation regimes and terrain complexity, for example, ridges and valleys (Bonetti, Hooshyar, Camporeale, & Porporato, 2020), found in landscapes such as the Anaga mountains on Tenerife (Figure 1), Moka in Mauritius and Koke'e in Kauai (see island maps in Figure S2.4).…”

A minimalist model for coevolving supply and drainage networks

“…A physical understanding of the feedback mechanism related to the source/sink term in equation ( 2.3 ) can be achieved by inspecting the example of an eroding overland flow in a natural landscape. The sink term used in landscape evolution models (the same as that employed in equation ( 2.3 )) implies that heavy erosion of h occurs for large values of material density a − and high magnitudes of h gradients [ 11 , 38 , 39 ]. Following the steepest descent direction of h , more accumulation of the drained material causes high erosion.…”

“…This feedback loop in carving a preferential path creates a surface instability, which tends to be inhibited by the smoothing effect of diffusion. A threshold exists, above which the instability grows and results in the formation of a complex valley network [ 11 , 40 ].…”

“…The conceptual framework developed here stems from observing the complex ridges and valleys patterns in topographic landscapes, and the related work in the fields of image processing, geomorphology and hydrology related to the duality between the interlocking network of ridges and valleys [29][30][31]. For its mathematical formulation, we draw inspiration from the landscape evolution models (LEMs), which have been successful in describing the formation of river and stream networks [11,[32][33][34][35]. Generalizing these models, we develop a simple system consisting of three nonlinear coupled PDEs with an essential parametrization.…”

Controls of the Topological Connectivity on the Structural and Functional Complexity of River Networks

“…Landscapes contain fundamental natural features such as channel networks (CNs) that exert significant control on catchment hydrology (Bonetti et al, 2020; Gupta & Mesa, 1988; Horton, 1932; Rodriguez‐Iturbe & Valdes, 1979; Snell & Sivapalan, 1994). These dendritic features are known to deliver environmental fluxes to the outlet via multiple pathways that are highly complex in structure (consisting of topology and geometry) resulting from both internal dynamics and external forcing (e.g., climate and tectonics) (Dietrich et al, 2003; Dietrich & Dunne, 1993; Hack, 1957; Hooshyar et al, 2016; Horton, 1945; Kirkby, 1976; Lashermes et al, 2007; Leopold, 1971; Marani et al, 1994; Orlandini et al, 2011; Passalacqua et al, 2010).…”