Hysteresis of idealized, instability-prone outlet glaciers in response to pinning-point buttressing variation

Ice rises or ice rumples act as ice-shelf pinning points that can play an important role in regulating the ice discharge of marine outlet glaciers. As an example, the observed recent gradual ungrounding of the ice shelf of West Antarctica's Thwaites Glacier from its last pinning points likely diminished the buttressing effect of the ice shelf and thus contributed to the destabilization of the outlet. Here we use an idealized experimental setting to simulate the response of a marine outlet glacier resting on a landward down-sloping (retrograde) bed to a stepwise ungrounding of its ice shelf from a topographic high and a subsequent re-grounding. We show that the glacier retreat down the retrograde bed, induced by the loss in pinning-point buttressing, can be unstable and irreversible given a relatively deep subglacial bed depression. In this case, glacier retreat and re-advance show a hysteretic behavior, and if the bed depression is sufficiently deep, the glacier does not recover but remains locked in its retreated state. Conversely, reversibility requires a sufficiently shallow bed depression. Based on a simple flux balance analysis, we argue that the combination of a deep bed depression and limited ice-shelf buttressing hampers grounding-line re-advance due to the dominant and highly non-linear influence of the bed depth on the ice discharge across the grounding line. We conclude that outlets that rest on a deep bed depression and are weakly buttressed, such as Thwaites Glacier, are more susceptible to abrupt and irreversible retreat than more strongly buttressed glaciers on more moderate retrograde slopes, such as Pine Island Glacier. Our findings further suggest that the (ir)reversibility of large-scale grounding-line retreat may be strongly affected by calving-front migration and associated changes in ice-shelf buttressing.