The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law

Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.