Impacts of Temperature- and Stress-Dependent Rheology on Ice-Shelf Front Bending

Classical treatments of ice-shelf bending suggest that shelf fronts should bend downwards, due to the distribution of hydrostatic water pressure at the front. However, there are several observed instances in lidar data of upward-bending ice-shelf fronts. While this phenomenon has often been attributed to a buoyant force created by a submerged ice bench, recent work suggests that vertical variations in viscosity within the ice shelf, caused by a temperature gradient, can induce an internal bending moment that causes the shelf front to bend upwards, even in the absence of a bench.

To investigate this novel bending mechanism, we present the first two-dimensional, viscoelastic models of ice-shelf-front bending assuming a standard dependence of ice rheology on temperature and depth. Our results confirm the thin-plate analytic prediction that an ice-shelf front can bend upwards with a sufficiently cold surface temperature and a sufficiently high ratio of activation energy to flow-law exponent. The results also demonstrate that the temporal evolution of the flexural wavelength and the relationship between the edge deflection amplitude and the flexural wavelength are consistent with thin-plate analytic predictions, though modeled uplift starts to gradually outpace analytic predictions over time. These deviations are attributed to two distinct forms of two-dimensional flow effects that we term “bulge” and “flare”.

Model results also demonstrate that the internal moment mechanism produces uplift with a shorter flexural wavelength than the submerged bench mechanism. This difference can be leveraged to discern between causal mechanisms of the upward bending seen in lidar data, which we illustrate with an example from the Ross Ice Shelf front. We also illustrate how comparing model results with data offers a way to constrain the parameters describing ice rheology.