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Accurately modeling the deformation of temperate glacier ice, which is at its pressure-melting temperature and contains liquid water at grain boundaries, is essential for predicting ice sheet discharge to the ocean and associated sea-level rise. Central to such modeling is Glen’s flow law, in which strain rate depends on stress raised to a power ofn= 3 to 4. In sharp contrast to this nonlinearity, we found by conducting large-scale, shear-deformation experiments that temperate ice is linear-viscous (n ≈1.0) over common ranges of liquid water content and stress expected near glacier beds and in ice-stream margins. This linearity is likely caused by diffusive pressure melting and refreezing at grain boundaries and could help to stabilize modeled responses of ice sheets to shrinkage-induced stress increases. 

Abstract Results of ice-stream models that treat temperate ice deformation as a two-phase flow are sensitive to the ice permeability. We have constructed and begun using a custom, falling-head permeameter for measuring the permeability of temperate, polycrystalline ice. Chilled water is passed through an ice disk that is kept at the pressure-melting temperature while the rate of head decrease indicates the permeability. Fluorescein dye in the water allows water-vein geometry to be studied using fluorescence microscopy. Water flow over durations of seconds to hours is Darcian, and for grain diameter d increasing from 1.7 to 8.9 mm, average permeability decreases from 2 × 10 −12 to 4 × 10−15 m 2. In tests with dye on fine ( d= 2 mm) and coarse (d = 7 mm) ice, average area-weighted vein radii are nearly equal, 41 and 34 μm, respectively. These average radii, if included in a theory slightly modified from Nye and Frank (1973), yield permeability values within a factor of 2.0 of best-fit values based on regression of the data. Permeability values depend on d −3.4, rather than d−2 as predicted by models if vein radii are considered independent of d. In future experiments, the dependence of permeability on liquid water content will be measured. 

Ice at depth in ice-stream shear margins is thought to commonly be temperate, with interstitial meltwater that softens ice. Models that include this softening extrapolate results of a single experimental study in which ice effective viscosity decreased by a factor of ∼3 over water contents of ∼0.01–0.8%. Modeling indicates this softening by water localizes strain in shear margins and through shear heating increases meltwater at the bed, enhancing basal slip. To extend data to higher water contents, we shear lab-made ice in confined compression with a large ring-shear device. Ice rings with initial mean grain sizes of 2–4 mm are kept at the pressure-melting temperature and sheared at controlled rates with peak stresses of ∼0.06–0.20 MPa, spanning most of the estimated shear-stress range in West Antarctic shear margins. Final mean grain sizes are 8–13 mm. Water content is measured by inducing a freezing front at the ice-ring edges, tracking its movement inward with thermistors, and fitting the data with solutions of the relevant Stefan problem. Results indicate two creep regimes, below and above a water content of ∼0.6%. Comparison of effective viscosity values in secondary creep with those of tertiary creep from the earlier experimental study indicate that for water contents of 0.2–0.6%, viscosity in secondary creep is about twice as sensitive to water content than for ice sheared to tertiary creep. Above water contents of 0.6%, viscosity values in secondary creep are within 25% of those of tertiary creep, suggesting a stress-limiting mechanism at water contents greater than 0.6% that is insensitive to ice fabric development in tertiary creep. At water contents of ∼0.6–1.7%, effective viscosity is independent of water content, and ice is nearly linear-viscous. Minimization of intercrystalline stress heterogeneity by grain-scale melting and refreezing at rates that approach an upper bound as grain-boundary water films thicken might account for the two regimes.