Structured Abstract

Introduction River networks, the backbone of most landscapes on Earth, collect and transport water, sediment, organic matter, and nutrients from upland mountain regions to the oceans. Dynamic aspects of these networks include channels that shift laterally or expand upstream, ridges that migrate across Earth’s surface, and river capture events whereby flow from one branch of the network is rerouted in a new direction. These processes result in a constantly changing map of the network with implications for mass transport and the geographic connectivity between species or ecosystems. Ultimately, this dynamic system strives to establish equilibrium between tectonic uplift and river erosion. Determining whether or not a river network is in equilibrium, and, if not, what changes are required to bring it to equilibrium, will help us understand the processes underlying landscape evolution and the implications for river ecosystems.

Maps of χ for two river networks. (A) Part of the Loess Plateau, China. The values of χ are nearly equal across drainage divides at all scales, indicating that the river is in topologic and geometric equilibrium. Map is centered on 37°4' N 109°35' E. (B) Part of the coastal plain of North Carolina, southeastern United States. Large discontinuities in χ across divides indicate that the network is not in geometric equilibrium. Water divides generally move in the direction of higher χ to achieve equilibrium, so subbasins with prominent high values of χ are inferred to be shrinking and will eventually disappear. Map is centered on 35°10' N 79°8' W.

Methods We developed the use of a proxy, referred to as χ, for steady-state river channel elevation. This proxy is based on the current geometry of the river network and provides a snapshot of the dynamic state of river basins. Geometric equilibrium in planform requires that a network map of χ exhibit equal values across all water divides (the ridges separating river basins). Disequilibrium river networks adjust their drainage area through divide migration (geometric change) or river capture (topologic change) until this condition is met. We constructed a numerical model to demonstrate that this is a fundamental characteristic of a stable river network. We applied this principle to natural landscapes using digital elevation models to calculate χ for three, very different, systems: the Loess Plateau in China, the eastern Central Range of Taiwan, and the southeastern United States.

Results The Loess Plateau is close to geometric equilibrium, with χ exhibiting nearly equal values across water divides. By contrast, the young and tectonically active Taiwan mountain belt is not in equilibrium, with numerous examples of actively migrating water divides and river network reorganization. The southeastern United States also appears to be far from equilibrium, with the Blue Ridge escarpment migrating to the northwest and the coastal plain rivers reorganizing in response to this change in boundary geometry. Major reorganization events, such as the capture of the headwaters of the Apalachicola River by the Savannah River, are readily identifiable in our maps.