River deltas are giant landforms that display a wide array of channel network shapes. The study demonstrates the close similarities in growth laws between river deltas over hundreds of square miles and bacterial colonies that growth across a petri dish.

When viewed from space, the shapes of river deltas are defined by their channel networks. In addition to water and sediment, these channels also form transportation corridors for millions of tons of amounts of cargo annually, and cities from Cairo to Rotterdam to New Orleans have grown on their banks. In some parts of large deltas such as the Mississippi Delta, the flow through channel networks, diversions, and spillways are intensely managed. In order to improve Louisiana’s resiliency, large sediment diversion projects are planned that will build new coastal land. Predicting such land growth requires understanding how channel networks work.

River deltas are not the only things that exhibit branching networks. Bacterial colonies tend to form branches as they grow outward in into a petri dish of nutrients. Lightning, as it moves through air, branches depending on the electrical charge of the air. Water, when injected into oil, also produces branching fingers. The bacterial, lightning, and water injection cases have been studies for decades as a family of similar growth process that depend primarily on the distribution of a key quantity outside of the network itself. The bacteria grow as a function of the food concentration. Lightning (and Lichtenburg structures) depends on the voltage field, water injection depends on a pressure field.

Left, a branching colony of Paenibacillus sp bacteria on an agar plate. Photo credit, Tomislav Vološen, (thanks @EvolvedBiofilm). Right, a satellite image of the branching network of the Wax Lake Delta, in coastal Louisiana. Bottom, snapshot of the model of the growing channel network (white), light blue lines are flow lines, blue colors are water surface.

Are branching river deltas another member of this family of branching processes? This was the motivating question of a group of researchers at the University of Arkansas. They hypothesized that the water surface elevation outside the channel network (a kind of pressure field) would serve as the key variable in the evolving network, and would be sufficient to produce a reasonable branching structure observed on river deltas in nature. This justification was based on previous work that revealed that the unchannelized water surface elevation field could be important in determining branching angle of a pair of channels.

They tested this hypothesis by building a model of channel network growth that depended only on the water surface elevation field outside the network. As with the previously studied models of bacterial growth or fluid injection, the model spontaneously produced a series of channels that branched and extended (see figure). Channels generally extended the most rapidly where they were had the most concave tip and were the furthest from the network source. The function that related water surface slope to channel extension, which was based on the complex equations for how sediment is eroded, exerted remarkable control on the eventual shape of the network. For erosion functions that mimicked muddy sediments, the model produced fewer, narrower channels. For functions that mimicked sand, the model produced fatter channels with more branches. The shape of this structure, including the shape of the channels and the angle at which they branched corresponded well to a prototype delta from coastal Louisiana.

The authors were able to conclude that distributary channel networks are indeed a member of the broad family of branching processes. This is an exciting advance for two reasons. First, the fundamental processes that influence a river delta’s channel structure have become clearer. For example, the growth of channels at concave areas could mean that a dominant channel in a growing sediment diversion could be initiated with very little work early on in the development of a costly sediment diversion. Second, it opens the door for growth models used in other fields of physics to be applied to river deltas. In other parts of physics, the growth history, conditions for individual branches, and trajectories of future channels are being estimated. Perhaps these properties could be deduced for river deltas in the future

The research paper, “Distributary Channel Networks as Moving Boundaries: Causes and Morphodynamic Effects” was published in the Journal of Geophysical Research: Earth Surface. Readers without a journal subscription may download an unformatted version of the manuscript from EarthArxiv, a free preprint server.

The study was written by Wun-Tao Ke (@kewuntao), John Shaw(@johnburnhamshaw), Robert Mahon (@robertcmahon) and Chris Cathcart. Dr. Shaw’s research program investigates modern and ancient river deltas, with emphasis on the deltas surrounding the Gulf of Mexico. This project was funded by a Department of Energy Grant to understand the growth of channel networks on river deltas.