Omar Wani

Rivers are rarely the calm, orderly streams we imagine on maps. Over time, their winding paths — called meanders — shift, bend, and occasionally snap off in sudden “cutoff” events that shorten loops and reshape the landscape. While scientists have long suspected that such cutoffs inject a dose of unpredictability into river evolution, a new study published in Communications Earth & Environment demonstrates that these abrupt events are, by themselves, enough to produce chaos in river channels.

Harvard Ph.D. candidate Brayden Noh and NYU Tandon Assistant Professor Omar Wani used a widely-used computational model to explore how meandering rivers evolve over time. This model isolates the essential dynamics: bends migrate laterally in proportion to curvature, and loops are occasionally severed through cutoffs. Other real-world complexities — like sediment transport, bank composition, and vegetation — are treated as secondary, allowing the researchers to focus squarely on the geometry-driven behavior of rivers.

To test the role of cutoffs, the team simulated rivers starting from nearly identical initial shapes, then introduced infinitesimally small perturbations to each of the multiple copies. They tracked how the channels diverged over time by mapping their evolving shapes onto a fixed grid and measuring differences cell by cell. In a striking counterfactual experiment, when cutoffs were disabled, the two channels stayed nearly identical over large time horizons. When cutoffs were allowed, even tiny initial differences grew exponentially, a hallmark of deterministic chaos.

The researchers quantified this sensitivity using the finite-time Lyapunov exponent, a metric from dynamical systems theory that measures how fast nearby trajectories diverge. They found that the rate of divergence depended primarily on the speed at which bends migrated, not on the specific cutoff threshold. In other words, faster meander migration amplifies chaos, while the geometric criteria for triggering a cutoff mostly determine how frequently the river “resets” its local shape.

Importantly, this chaotic behavior was robust across a wide range of initial river geometries. Whether the model started with gentle or pronounced bends, the presence of cutoffs consistently created sensitive dependence on initial conditions. The team also showed that the predictability of a river’s course is bounded: beyond a certain horizon, roughly the number of cutoffs expected in one Lyapunov time, deterministic forecasts of channel position become unreliable.

The study highlights a subtle but powerful insight: continuous meander migration creates gradual stretching of the river planform, while cutoffs act as abrupt topological resets. Together, these processes produce a hybrid system that is both structured and inherently unpredictable. The finding resonates with broader observations of natural rivers, where cutoffs cluster or cascade, triggering sequences of rearrangements along the channel.

While the model is simplified — it does not include full fluid dynamics, sediment heterogeneity, or flood variability — it provides a clear counterfactual experiment: no real river can evolve without cutoffs, but simulations can, revealing the mechanism behind chaotic divergence. This approach connects geomorphology with fundamental concepts from chaos theory, offering a concrete way to quantify a river’s predictability horizon.

Ultimately, the research suggests that some limits to forecasting river evolution are intrinsic. Even in the absence of storms, landslides, or human intervention, the combination of smooth bend migration and occasional cutoffs ensures that lowland rivers retain a degree of inherent unpredictability. For engineers, ecologists, and planners, this work underscores the importance of probabilistic frameworks over deterministic predictions when assessing river migration and floodplain evolution.

Researchers are calling for a more reliable approach to understanding water-related hazards by explicitly accounting for uncertainty in their predictions, arguing this could improve how communities prepare for the risk of floods, droughts, and river-related erosion.

Omar Wani, a hydrologist at NYU Tandon School of Engineering, and co-authors argue in a recent opinion piece published in PLOS Water that many current hydroclimatic hazard assessments have a major flaw: they only give one answer. These models might predict, for example, that a river will flood to 15 feet, but they don't say how confident scientists are in that prediction or what other outcomes are possible.

Wani, who joined NYU Tandon as an Assistant Professor in the Civil and Urban Engineering Department in 2023, leads the Hydrologic Systems Group, which combines statistical and computational methods to study water dynamics in built and natural environments. His group focuses on understanding hydroclimatic risk and enabling more reliable decision-making under uncertainty.

This uncertainty-focused approach is central to Wani and his PLOS co-authors' argument for models that work more like weather forecasts, giving a range of possibilities with probabilities attached. Rather than saying "the water level in the river will reach 15 feet," these models might say "there's an 80% chance of the water level exceeding 15 feet, a 30% chance of it exceeding 18 feet, and a 10% chance of it breaching the 20 feet mark."

The approach has real-world urgency. Approximately 75% of flood-related fatalities occur when people drive into or walk through floodwaters, while climate change is expected to cause additional capacity deficits in stormwater infrastructure, leading to enormous financial losses. Overwhelmed and damaged drainage structures under roads can cost millions to replace.

In research published in Earth Surface Dynamics, Wani and collaborators demonstrated practical applications of this approach, showing how probabilistic models can generate "geomorphic risk maps" that display the probability of riverbank erosion at different locations over time.

Using satellite data from the rapidly-migrating Ucayali River in Peru's Amazon basin, the researchers showed their novel probabilistic approach consistently outperformed traditional predictions. The method combines mathematical models based on river shape and curves with computer simulations that run thousands of different scenarios to explore possible future outcomes.

Apart from the scientific value of this research in improving our understanding of the river systems, such "risk maps are relatively more informative in avoiding false negatives, which can be both detrimental and costly, in the context of assessing erosional hazards," said Wani. Their results showed that probabilistic forecasts assign appropriate probabilities to regions that might erode, avoiding the overconfident binary classifications of traditional approaches.

The implications extend beyond academic research. Behavioral science research shows that people can exhibit loss aversion and risk aversion when making decisions under uncertainty. However, these psychological preferences can only be utilized when the requisite uncertainty information is available.

"To allow for individuals to use these preferences and risk attitudes during hydroclimatic warning or design decisions, people would need to be aware of the uncertainties in quantitative analysis and forecasts," Wani explained.

His group's current work spans from improving the reliability of flood early warning systems for distributed stormwater infrastructure to testing advanced probabilistic algorithms for satellite-based flood damage classification.

The framework represents a shift from seeking the single "most likely" outcome to embracing the full range of possibilities.

The research has immediate practical applications for infrastructure planning, emergency management, and community resilience. As climate change introduces additional uncertainties into the behavior of streams and rivers globally, the researchers argue that probabilistic approaches become increasingly important. The work reflects growing recognition that uncertainty is not a limitation to overcome, but rather crucial information that enables better decision-making.

In addition to Wani, the PLOS opinion piece's authors are Mason Majszak, who is currently working on a Swiss National Science Foundation project as a Postdoctoral Fellow at NYU Tandon and in the NYU Department of Philosophy, Victor Hertel from the German Aerospace Center, and Christian Geiß from the German Aerospace Center and University of Bonn. Funding for the work was provided by the Swiss National Science Foundation.

The Earth Surface Dynamics paper's authors are, in addition to Wani, Brayden Noh from Caltech, Kieran B. J. Dunne from Caltech and Delft University of Technology, and Michael P. Lamb from Caltech. Funding for the research was provided by the Swiss National Science Foundation and the Resnick Sustainability Institute at Caltech under National Science Foundation awards.