A single equation governs the fate of ice sheets. That equation—called a flow law—determines how quickly glaciers surge toward the sea, how rapidly shelves thin and collapse, how soon coastlines vanish beneath rising water. For decades, scientists have relied on formulas derived from narrow laboratory experiments. They've trusted these laws to forecast the speed at which Greenland and Antarctica will surrender their frozen mass to warming oceans.

They may have been wrong.

Researchers have now analyzed seventy years of ice deformation experiments, applying advanced statistical methods to hundreds of data points accumulated since the 1950s. Their findings reveal that the commonly used Glen flow law—the standard equation in most ice sheet models—fails to capture how ice actually behaves under the conditions found in nature.

The problem runs deeper than incorrect predictions. It touches the foundation of how we forecast sea level rise.

The Physics of Ice Under Pressure

Ice sheets move through two mechanisms: internal deformation within the ice itself and basal sliding along the bedrock beneath. Both respond to changes in driving forces that push inland ice toward the ocean. Floating ice shelves extending from these sheets provide buttressing—a restraining effect that holds back the ice behind them.

Ongoing ocean warming causes rapid thinning and calving at ice shelf edges, reducing buttressing forces and increasing stresses that drive inland ice movement, drastically accelerating ice mass loss. To assess how these changes will influence sea level, models must quantify the contributions of both internal deformation and basal sliding to overall ice flow velocity.

Here's where flow laws become critical. In practice, models represent internal deformation through flow laws that define relationships between driving force (stress) and deformation rate (strain rate). Basal sliding laws are then calibrated by comparing observed surface velocities with velocities calculated from the flow laws, with any excess attributed to sliding. The entire forecast of basal sliding's contribution to ice mass loss fundamentally depends on accurate flow laws for internal deformation.

Both the form of the flow law and the values of its parameters have a substantial impact on model outcomes. This makes robust flow laws critically important for accurate forecasts of future ice mass loss.

Seven Decades in the Laboratory

The team compiled a comprehensive database of 566 data points from published experiments spanning 1952 to the present, conducted across laboratories worldwide. They also performed four new experiments. The database included experiments across wide ranges of temperature, stress, and grain size.

Previous flow laws were typically derived from individual experimental datasets with narrow ranges of conditions. The Glen flow law, routinely used in ice sheet models, is an empirical power-law relationship that relates strain rate to stress and includes temperature dependence. However, it doesn't fit laboratory experiments particularly well and requires substantial modification to match field observations.

The researchers used Bayesian inference—a statistical method that combines experimental measurements with prior understanding—to test different mathematical forms and determine flow law parameters while accounting for their interdependencies and uncertainties. This approach enabled them to explore whether ice deformation operates through one mechanism or several acting simultaneously.

They analyzed two strain regimes. At low strains (1–2%), ice microstructure remains largely unchanged from the isotropic starting material, representing conditions relevant to peak stresses or minimum strain rates. At high strains (greater than or equal to 8%), ice has weakened due to microstructural changes including grain size reduction and development of anisotropy—a preferred orientation of ice crystals.

What the Ice Revealed

At low strains, commonly used flow laws failed to capture the full complexity of ice behavior. The analysis showed that a multicomponent flow law—one that sums strain rates from different deformation mechanisms—is needed to capture grain size and temperature sensitivities observed across all experiments.

The best fit came from a three-component law. One component represents dislocation creep, a grain-size insensitive mechanism involving movement of oxygen atoms within ice crystals. Two additional components represent dislocation-accommodated grain boundary sliding, a grain-size sensitive mechanism. The activation energies derived from the analysis matched theoretical predictions and experimental observations for these physical processes.

Why two grain boundary sliding components? The analysis suggests they represent a single mechanism with temperature-dependent activation energy. Near the melting point, increased premelting at grain boundaries changes how ice deforms. The three-component flow law fits experimental measurements better than simpler alternatives, predicting an increase in apparent activation energy from approximately 50 kilojoules per mole at minus thirty degrees Celsius to 110 kilojoules per mole at minus three degrees Celsius.

Only 4% of laboratory data exhibited stresses differing by more than a factor of 1.5 from the three-component flow law predictions, and fewer than 1% differed by more than a factor of 2. In contrast, 42% and 19% of data differed by factors greater than 1.5 and 2 respectively from Glen flow law predictions.

At high strains, the picture changes. Interactions among deformation mechanisms become complex due to development of crystallographic preferred orientation and changes in grain size. A one-component grain-size insensitive flow law fits the high-strain data reasonably well.

Extrapolating to Ice Sheets

Within experimental ranges of stress, temperature, and grain size, different flow laws yield similar predictions. But ice sheets operate under conditions far from laboratory experiments—lower stresses, slower strain rates, larger grain sizes.

When extrapolated to typical glaciological stresses (less than or equal to 0.1 megapascals), multicomponent flow laws predict strain rates an order of magnitude faster than one-component flow laws. This divergence increases as temperature and grain size deviate from experimental ranges.

The researchers applied their flow laws to the North Greenland Eemian Ice Drilling (NEEM) project data, using measured stress estimates, temperatures, and grain sizes as inputs. The Glen flow law predicted strain rates differing by factors of 0.1 to 1,000 compared with the three-component flow law. In the uppermost 2,300 meters, the Glen flow law predicted slower strain rates, indicating less internal deformation.

This matters because slower predicted internal deformation implies that more observed surface velocity must be attributed to basal sliding when models are calibrated against observations. If the flow law underestimates internal deformation, models will overestimate sliding contributions—and potentially miscalculate how ice sheets will respond to changing boundary conditions.

Choosing the Right Tool

The multicomponent flow laws provide the best fit to low-strain experimental data and may be applicable to natural scenarios where ice anisotropy is weak or where deformation kinematics differ from those that formed the crystallographic preferred orientation—situations including borehole closure, flexural deformation near grounding lines, ice transitioning onto shelves, and any scenario with sudden changes in flow direction.

However, the most appropriate flow law for most large-scale ice sheet models should ideally be derived from high-strain data, which reflect the microstructure established by ongoing deformation kinematics. Unfortunately, the experimental basis for high-strain flow laws remains far more limited. Existing datasets are sparse, typically lack detailed microstructural characterization, and cover narrow ranges of stress and strain rate—often several orders of magnitude faster than those in nature.

A promising resolution involves obtaining and testing naturally deformed ice that has reached near-steady-state conditions, allowing investigation of relationships between microstructure and mechanical response at realistic stress and strain rates.

For practical modeling purposes, the findings offer provisional guidance. Incorporating multicomponent flow laws into continental-scale simulations is hampered by scarcity of grain size data across vast ice sheet regions. Grain size varies markedly with depth, temperature, impurity content, and deformation history. Obtaining such data at necessary spatial resolution would require extensive field investigations, ice core analyses, and remote sensing techniques—many resource-intensive and practically constrained.

Encouragingly, the study shows that a one-component grain-size insensitive flow law provides reasonable fit to available high-strain experimental data, pointing to the possibility of a unified flow law that obviates the need for specifying grain size or crystallographic preferred orientation. For models where ice predominantly experiences high strain, the stress exponent should be 4 if very high temperature conditions (above minus five degrees Celsius) are excluded, but 3.5 if temperatures above minus five degrees Celsius are included.

The Forecast Ahead

The equations governing ice flow determine our coastal future. These new flow laws, derived from the most comprehensive analysis of ice deformation experiments ever conducted, reveal that previous formulations—while useful—captured only part of the story.

Robust extrapolation from experimental to natural conditions requires flow laws to have both the correct functional form and accurate values of parameters. This work provides both, offering multiple formulations suited to different modeling contexts and strain regimes.

The implications extend beyond academic refinement. Sea level projections inform infrastructure planning, coastal management, climate policy, and disaster preparedness for billions of people. Small differences in flow law parameters propagate through models into large differences in predicted ice mass loss rates and timelines.

Further high-strain experiments across broader stress, strain rate, and temperature ranges remain necessary. Natural ice samples from regions experiencing steady-state flow could bridge the gap between laboratory and field conditions. Remote sensing techniques and machine learning approaches may eventually provide the grain-size data needed for spatially resolved multicomponent modeling.

Until then, these new flow laws offer the most physically grounded, statistically rigorous description of how ice deforms—how it flows, how it thins, how it responds to the warming world around it. They represent seventy years of careful measurement, synthesis, and statistical analysis distilled into equations that will help determine which coastlines endure and which succumb to rising seas.

Credit & Disclaimer: This article is a popular science summary written to make peer-reviewed research accessible to a broad audience. All scientific facts, findings, and conclusions presented here are drawn directly and accurately from the original research paper. Readers are strongly encouraged to consult the full research article for complete data, methodologies, and scientific detail. The article can be accessed through https://doi.org/10.1038/s41561-025-01661-z