How Glen’s Flow Law Exponent Affects Ice Sheet Mass Loss Projections

Study Reveals Critical Role of Glen’s Flow Law Exponent in Ice Sheet Projections

Glacier ice, a crystalline material flowing across Earth’s surface, is often near the pressure-melting point. Its deformation depends on multiple factors, including temperature, grain size, and ice purity. Numerical models of ice flow rely on Glen’s flow law (Glen’s Law), a relationship between stress and strain developed by John Glen and John Nye in the 1950s. This law calculates strain (ice deformation) using the applied stress raised to the power of the exponent n, multiplied by a temperature-dependent constant A.

While both linear and power-law forms of Glen’s Law have been proposed, a value of n = 3 is most commonly used. However, new research by Lilien et al. [2026] demonstrates that the choice of n can drastically alter projections of ice sheet mass loss.

Key Findings from the Study

The researchers used a flowline model to assess how different values of n and A—along with varying glacier sliding laws—affect ice sheet mass change projections. Their findings reveal a complex relationship between n and mass loss, which varies by glacier type:

• Dynamically controlled glaciers: Increasing n led to greater mass loss, as ice flowed more rapidly into ablation zones.
• Surface mass balance-controlled glaciers: Increasing n reduced mass loss, due to decreased ice flux at the equilibrium line.

The authors conclude that relying on a single value for n introduces significant uncertainties in ice sheet mass loss projections. They emphasize that future studies must account for spatial variations in the flow-law exponent to improve accuracy.

Citation and Publication Details

Lilien, D. A., Ranganathan, M., Shapero, D. R. (2026). Effect of the flow-law exponent on ice-stream sensitivity to melt. Journal of Geophysical Research: Earth Surface, 131, e2025JF008726. https://doi.org/10.1029/2025JF008726

— Ann Rowan, Editor-in-Chief, JGR: Earth Surface

Note: Text © 2026. The authors. CC BY-NC-ND 3.0. Images are subject to copyright unless otherwise noted. Any reuse without express permission from the copyright owner is prohibited.