Accurate representation of the viscous flow of ice is fundamental to understanding glacier dynamics and projecting sea-level rise. Ice viscosity is often described by a simple but largely untested and uncalibrated constitutive relation, Glen’s Flow Law, wherein the rate of deformation is proportional to stress raised to the power n. The value n = 3 is commonly prescribed in ice-flow models, though observations and experiments support a range of values across stresses and temperatures found on Earth. Here, we leverage recent remotely-sensed observations of Antarctic ice shelves to show that Glen’s Flow Law approximates the viscous flow of ice with n = 4.1 ± 0.4 in fast-flowing areas. The viscosity and flow rate of ice are therefore more sensitive to changes in stress than most ice-flow models allow. By calibrating the governing equation of ice deformation, our result is a pathway towards improving projections of future glacier change.

Accurate representation of the viscous flow of ice is fundamental to understanding glacier dynamics and projecting sea-level rise. Ice viscosity is often described by a simple but largely untested and uncalibrated constitutive relation, Glen’s Flow Law, wherein the rate of deformation is proportional to stress raised to the power n. The value n = 3 is commonly prescribed in ice-flow models, though observations and experiments support a range of values across stresses and temperatures found on Earth. Here, we leverage recent remotely-sensed observations of Antarctic ice shelves to show that Glen’s Flow Law approximates the viscous flow of ice with n = 4.1 ± 0.4 in fast-flowing areas. The viscosity and flow rate of ice are therefore more sensitive to changes in stress than most ice-flow models allow.

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<p>Ice is a non-Newtonian fluid whose rheology is typically described using Glen's flow law, a power-law relationship between stress and strain rate with a stress exponent, n, generally taken to be 3. Recent observation-based work suggests that a more accurate choice for the Glen’s law exponent in high-strain regions like ice shelves may be n=4, implying that ice viscosity is more sensitive to changes in stress than is generally assumed. The implications of a higher stress exponent for ice sheet models and their projections of ice sheet response to climate forcing are unclear and likely to be complex. Rheological parameters, such as ice viscosity, are fundamental to ice sheet dynamics and influence the evolution of marine ice sheets. </p> <p> </p> <p>Here, we present work that explores the rheological parameter space within the idealized MSIMIP+ marine ice sheet configuration using the BISICLES model. We explore the impacts of increasing  the stress exponent from 3 to 4, highlighting the considerable changes to the ice sheet system caused by increasing the stress exponent. Beyond dynamic changes in the ice behavior, changes become necessary to the other flow law parameters generally computed during initialization. For example, it may be that viscosity modifiers typically interpreted as “damage” may instead be indications of mismatches in rheology.  This study underscores the dynamic sensitivity of glacial ice to changes in the rheological parameters and calls attention to the key variables influencing ice sheet evolution. </p> <p> </p>

<p>Glaciers and ice sheets flow as a consequence of ice rheology. At the temperatures and pressures found on Earth, several creep mechanisms allow glacier ice to flow as a non-Newtonian (shear-thinning) viscous fluid. The semi-empirical constitutive relation known as Glen’s Flow Law is often used to describe ice flow and to provide a simple expression for an effective viscosity that decreases with increasing stress and deformation rate. Glen’s Flow Law is a power-law relation between effective strain rate and deviatoric stress, with two parameters defining the rheology of ice: a rate factor, A, and stress exponent, n. The rate factor depends on features such as temperature and grain size, while the stress exponent is primarily representative of the creep mechanism. Neither A nor n are well constrained in natural ice, and the stress exponent is typically assumed to be n = 3 everywhere. Here, we take advantage of recent improvements in remotely sensed observations of surface velocity and ice shelf thickness to infer the values of A and n in Antarctic ice shelves. We focus on areas of ice shelves that flow in a purely extensional regime, where extensional stresses are proportional to observed ice thickness, drag at the base of the ice is negligible, and extensional strain-rates are calculated from the gradients of observed surface velocity fields. In this manner, we use independent observational data to derive spatially dependent constraints on the rate factor A and stress exponent n in Glen's Flow Law. The robust spatial variability provides insights into the creep mechanisms of ice, thereby capturing rheological properties from satellite observations. Our analysis indicates that n ≈ 4 in most fast-flowing areas in an extensional regime, contrary to the prototypical value of n = 3. This finding implies higher non-linearity in ice flow than typically prescribed, influencing calculations of mass flux and the response of ice sheets to perturbations. Additionally, This result suggests that dislocation creep is the dominant creep mechanism in extensional regimes of Antarctic ice shelves, indicative of tertiary creep. This analysis unites theoretical work and synoptic-scale observations of ice flow, providing insights into the rheology and stress-states of ice shelves in Antarctica.</p>