Look outside after a heavy rain and you may find a miniature Grand Canyon in your backyard, complete with a complex network of tributaries. The precise conditions that cause rivers of all sizes to form branches have long been a mystery; now, a new study pinpoints two opposing physical forces that work together to produce the intricate patterns. The discovery could help scientists better understand rivers at all scales and even on other worlds; for example, the icebound methane rivers on Titan, one of Saturn's moons.
When rain hits a tilted surface, like the side of a mountain or a hill, it tends to flow toward existing depressions. The flow of water erodes the rock or soil, widening and deepening the depressions. Called incision, the process is competitive and even somewhat cannibalistic. As individual rills grow from incision, they capture smaller neighbors, forming tributaries. One would expect incision to spread indefinitely if unchecked, but a process called soil creep smoothes over the land, filling up the cracks with a slow, yet steady, drift of soil.
Scientists have known for more than 100 years that these processes shape rivers, but they hadn't been able to quantify their relative importance, or figure out how they work together to create river basins that are finely branched in some landscapes but not others, says Taylor Perron, a geomorphologist at the Massachusetts Institute of Technology in Cambridge and lead author of the new study. "We saw the form, but didn't understand the mechanism that leads to the development of this branching shape."
Perron and colleagues guessed that a certain ratio between rates of incision and soil creep acts as a "tipping point" for the creation of river branches. Below that unknown value, they expected that no tributaries would form, and that above that value, rivers would begin to capture smaller rivers and form a network of tributaries. To test their hypothesis, they compared California's Salinas Valley with the Allegheny Plateau in southwest Pennsylvania. While each 25 km2 region contains thousands of river basins, the rivers in California are four times as finely branched as those in Pennsylvania. Neither region is strongly influenced by the faults and folds of a tectonic boundary, Perron says, allowing the team to compare incision and soil creep without too much interference from other variables.
After mapping the river networks in each region, the team created a mathematical model that included equations for soil creep and incision in river channels surrounded by raised mountain ridges. They manipulated the model to see if it could produce the same branching patterns, and it soon identified a specific ratio between the forces of incision and soil creep that acted like a tipping point or switch. Beyond the tipping point—a dimensionless value between 250 and 300—incision overrides soil creep, Perron says. Watching the modeled rivers go beyond that tipping point in accelerated geologic time is like watching petals on a flower that's opening, he says: "You watch these valleys bloom as they cannibalize their neighbors." Below that critical value, a river will shrink back to the size of its neighbors and ultimately lose its tributaries.
The new mathematical principle, reported today in Nature, will allow scientists to better evaluate the underlying forces at work in a river system  even if they can't take on-the-ground measurements, Perron says. The intricate networks of tributaries in California's Salinas Valley, for example, indicate that incision is winning out over soil creep, he says—a sign of the softer rock and higher levels of runoff in the region, compared with Pennsylvania's older, harder rocks and higher infiltration of water into the soil. That kind of analysis could be applied to much more distant rivers, he says: even the rivers of methane on Titan, Saturn's moon. It also raises interesting questions: In a landscape made of ice, he asks, "What's the analog to soil creep?"
Many aspects of real landscapes, such as seasonal variations in rainfall, rock fractures, and differences in rock type and strength are intentionally left out of the model, Perron notes. This simplicity is both a strength and a limitation of the study, says Joel Johnson, a geomorphologist at the University of Texas, Austin. He suggests that the new findings, which he describes as "elegant," could provide a baseline to which more complex landscapes could be compared. "Future work should look at deviations from the idealized landscapes explored here."