1-D Grain Size Evolution Model for Ice

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. The Matlab code provided here is based on the model of Behn et al. (2021), which couples grain-size evolution with a composite viscous flow law that incorporates both grain-boundary sliding and dislocation creep to provide a self-consistent description of deformation and grain size evolution in ice. Grain size evolution is modeled using the “wattmeter” (Austin & Evans, 2007; 2009). 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 this code, grain size evolution can be calculated in a 1-D column as a function of depth within an ice sheet. This modeling study was conducted at Boston College between 2018–2021. Austin, N. J. and Evans, B.: Paleowattmeters: A scaling relation for dynamically recrystallized grain size, Geol., 35(4), 343, doi:10.1130/G23244A.1, 2007. Austin, N. and Evans, B.: The kinetics of microstructural evolution during deformation of calcite, J. Geophys. Res., 114(B9), B09402, doi:10.1029/2008JB006138, 2009. Behn, M.D., Goldsby, D.L., and Hirth, G.: The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law, The Cryosphere, v. 15, 4589-4605, https://doi.org/10.5194/tc-15-4589-2021, 2021.