As densely populated coastal communities struggle to keep up with rising sea levels, new research reveals a way to predict how river deltas build land and protect coastal regions from encroaching oceans. This insight will help engineers and policymakers estimate how much new land can be created or maintained when human intervention is used to redirect river channels, making these efforts more effective for coastal restoration and flood protection.
The new study, inspired by a 1950s-era finding called Hack’s law — which states that the length of the longest tributary near the start of a river system is proportional to the size of its drainage basin — finds that coastal river deltas appear to follow a similar predictable pattern when it comes to sediment deposition.
“Hack’s law is a simple way of describing how the leading ends of rivers and their tributaries spread out across the landscape,” said University of Illinois Urbana-Champaign civil and environmental engineering professor Hongbo Ma. “For a long time, researchers have observed similar patterns at the other end of rivers, known as deltas, but efforts to define these observations into distinct models for practical use have lagged.”
Rivers form when smaller gravity-driven streams, called tributaries, coalesce to form a larger main river channel, moving sediment from their drainage basins downstream. River deltas, in contrast, accumulate sediment when the main channel branches into smaller distributaries, depositing sediment from the drainage basin and forming new land.
The study, led by Ma, examined satellite images of deltas over time at 29 locations worldwide, including the Wax Lake Delta in Louisiana and the Po River Delta in Italy, to find two distinct river delta growth patterns: uniform and composite. The findings are published in the journal Science.
“Our study found that some deltas show uniform growth where their networks follow Hack’s law consistently,” Ma said. “Others show composite growth, meaning they spread quickly at first, filling space like ink in water, then slow down and grow mainly along a few main channels.”
The findings are significant for engineering and restoration projects and could provide a rule of thumb for estimating land build-up based on channel length, Ma said.
For people living in low-lying coastal areas, the way a delta grows can be the difference between losing ground to the sea and gaining new land. This research turns a traceable natural process into clear guidance that can help communities and agencies decide where to invest in channel-building and restoration projects. By showing which parts of a delta are likely to build land quickly and which are nearing their limits, the work helps direct limited resources to the places where they can do the most to protect homes, infrastructure and livelihoods from rising seas and worsening floods.
This study includes contributions from researchers from the University of Texas Rio Grande Valley; the University of California, Irvine; the Universidad de Zaragoza, Spain; and the University of Texas at Austin. The National Science Foundation, the National Aeronautics and Space Administration and the Agencia Española de Investigación supported this research.
Editor’s note:
To reach Hongbo Ma, email hongboma@illinois.edu. The paper “Apparent Hack’s law in river deltas“ is available online. DOI: 10.1126/science.ady6805. Civil and environmental engineering is part of The Grainger College of Engineering.
