Quantifying Feedbacks Between Ice Flow, Grain Size, and Basal Meltwater on Annual and Decadal Time-Scales Using a 2-D Ice Sheet Model

Because there are few direct observations of the ice-bed interface, numerical modeling is a useful tool to quantify subglacial processes. For decades, the Glen flow law has been the most widely-accepted constitutive relation for modeling ice flow. Though the Glen law captures the temperature-dependent, nonlinear viscosity of ice, it does not explicitly incorporate ice grain size, which has been shown in laboratory experiments to play a significant role in ice rheology. To compensate for the lack of an explicit grain size term, ice models often utilize an enhancement factor, which modifies the flow law to better match observations, but does not provide insight into the physical processes that could be at play. Using a grain size sensitive rheology that incorporates grain size evolution due to dynamic recrystallization and grain growth, we model the effects of seasonal variations in subglacial hydrology in a 2-D vertical cross-section of ice flow on both short (annual) and long (decadal) timescales. As subglacial water reduces the frictional coupling between the ice and the bed, we simulate the presence of water beneath the ice during the melt season as patches of free-slip. We explore a range of patch sizes and geometries and investigate their role on ice surface velocities and grain size within the ice. We extract summer and winter surface velocities and compare them to observations taken on the western margin of the Greenland Ice Sheet. We find that realistic winter ice surface velocities are achievable by using a grain-size sensitive flow law without the introduction of an enhancement factor. Further, using this methodology we make first-order estimates of the extent and configuration of the subglacial hydrologic system that are required to match observed summer velocities. We also explore the transient effect of grain size evolution and its impact on changes in ice velocity in response to changes in frictional coupling at the bed.