At what angle do river channels split? New research shows that when one channel splits into two, the average angle is 72 degrees. This matches the angle of two channels joining together in wet environments. This remarkable symmetry is a useful tool for understanding river delta channel networks.

Branching river channel networks are a classic example of pattern formation in nature. Whether two tributary channels flow together into one at a confluence or one channel splits into two, as on river deltas, the resulting structure sets the primary pathways by which water and sediment are transported across Earth’s surface. The study of channel networks is hot science, with recent studies shedding light on how networks organize in mountain valleys as well as river deltas (see here and here). However, the various types of networks are rarely compared to one another, so breakthroughs studying one type of network (for instance, channels that come together) are rarely applied in the study of other types of networks. In our recent study, we applied theory from networks of confluences to distributary networks on river deltas and found surprising similarities.

The left picture shows a digital elevation model of the channel network at Apalachicola Bluffs and Ravines Preserve, near Bristol, Florida. Here, the network branches where two channels flow into one at a confluence. The colors refer to an elevation above sea level. This figure is published here. The right picture shows the Wax Lake Delta near Berwick, Louisiana. Here, the colors show elevations relative to low tide. This is a distributary network, where most of the branches form where one channel splits into two. This figure is published here.

We took advantage of a study of tributary confluences (where two channels flow into one), which showed that the angle that forms can be predicted in certain cases. Where channel tips are fed by flowing groundwater rather than over-land flow from rain, the branching angle at a confluence is theoretically predicted to be 72˚. This value has been validated on channel networks in Florida (see left image above), where the average angle happens to be 71.98˚. It is important to note that in other cases (notably deserts), the confluence angle is clearly less than 72˚. However, in wet, groundwater fed areas, theory and measurements agree on an emergent critical angle.

When reading this work, we noticed that the assumptions leading to the 72˚ prediction also apply to the branching networks of river deltas. The groundwater flowing into channel tips in Florida appears analogous to water flowing over the submerged banks of river delta channels. This encouraged us to see if the conditions would hold in the branching channel networks of river deltas.

We set out to measure the angles of branches on river deltas. We selected 10 deltas from around the world that exhibited strongly branching structures as well as a laboratory experiment. In the end, we accumulated 197 natural and 25 experimental bifurcation measurements. If you are curious, all of the bifurcation angles measured are available in the supplementary information. The average of these river delta branching angles was 70.4˚ and the average of the experimental delta branches was 68.3˚, remarkably similar to the theoretical prediction of 72˚.

The average branching angle of channel networks approaches 72˚ in many cases. The red circles, blue triangles, and green squares show a histogram of measured angles. The colored lines show normal distributions (bell curves) fit to each dataset. In each case, the average angle is close to the theoretical prediction of 72˚.

Just like the Florida seepage network case, the average bifurcation was remarkably close to the theoretical prediction, providing strong evidence that the theoretical model of flow over river deltas is accurate. This also demonstrates the similarities between splitting river delta channels and river confluences. However, there were also differences. First, we checked how the angle changed as a function of the measurement length. Branching delta channels tended to bend toward one another with distance from a split, so the angle tended to get smaller than 72˚ as the measurement distance grew to be longer than channel feeding the branch. Tributary confluences, on the other hand, tended to have the same angle no matter what the measurement length.

As the histogram of measured angles shows, tributary confluences and distributary branches each exhibited quite a large variance around the average angle. This means that an individual branch may have an angle significantly narrower or wider than the theoretical prediction. It is only when many angles are measured that the average angle approaches the theoretical prediction. We also showed that on average, branching angles remained the same over time although individual branches widened and narrowed as a result of erosion and deposition.

What does this mean for the study of channel networks on river deltas? First, it provides a new framework for assessing why and where river deltas will branch. The conditions of flow from channels into bays has been established for certain well-studied deltas, but has not been regarded as universal. However, our work over 10 deltas around the world suggests that it might well be. Many of the world’s river deltas are at risk of submerging due to rising sea levels, subsidence, and human alteration, and large land building sediment diversions are being designed to engineer sustainable land-forms. This work may help with such planning. Finally, much of the world’s sedimentary rocks were deposited by ancient deltas. New insights may emerge if geologists can use the 72˚ angle as a rule-of-thumb when interpreting these rocks.

This study is published in Geophysical Research Letters as Congruent Bifurcation Angles in River Delta and Tributary Channel Networks by Thomas Coffey and Dr. John Shaw. It presents Coffey’s Masters Thesis at the University of Arkansas. Dr. Shaw’s (@johnburnhamshaw) research program investigates modern and ancient river deltas, with emphasis on the deltas surrounding the Gulf of Mexico. He is an assistant professor in the Department of Geosciences.