Flow Laws for Ice Sheet Modelling: what do Experiments tell us?

Abstract:

Field data highlight rapid changes occurring at the ice-ocean interface that potentially increase the driving force for sea-ward motion of ice sheets. Estimation of the timescales of ice sheet response, and resultant sea-level rise, depends critically on the use of realistic ice flow laws. Viscoplastic deformation is a significant component of ice movement, and laboratory experiments provide key data that can be extrapolated to natural strain rates.

In laboratory experiments, the viscosity of ice reaches a peak value at low strains (< 3%) before decaying to a steady-state value at intermediate to large strains (10–50%). This flow “enhancement” is accompanied by changes in the microstructure of the ice, primarily a reduction in grain size due to dynamic recrystallization and the development of a crystallographic fabric. At strains higher than 10–50%, a steady-state viscosity is obtained when the microstructure is in steady state.

As in all other minerals, the strain rate of ice (at a given stress and temperature) is the sum of the rates from to grain-size-sensitive (GSS) and grain-size-insensitive (GSI) creep mechanisms. Experiments on ice samples with different starting grain sizes reveal a grain-size sensitivity of the strain rate, and a power-law dependency of strain rate on stress, characterized by a stress exponent, n, with values between ~2 and ~4. Experiments at high stress and/or on samples with coarse grain size yield high n values (~4), whereas experiments at low stress and/or on fine-grained samples yield low values of n (~2). Intermediate values of n (3–3.5) are common, and a value of 3 is usually assigned, but such values have little relevance to the deformation of ice at high strains.

Experiments show that for large-enough strains to achieve a steady-state microstructure, the recrystallized grain size is inversely proportional to the differential stress. GSS mechanisms contribute significantly to deformation at these conditions, but, because the grain size is stress-dependent, the dependency of strain rate on grain size can be eliminated from a flow law and the apparent stress exponent at steady state will be equal to that of the GSI mechanism, n ~ 4. A simple flow law for high-strain natural scenarios, such as flow of basal and marginal glacier ice, and in ice stream margins, should use a stress exponent of n ~ 4.