Hysteresis of idealized, instability-prone outlet glaciers under variation of pinning-point buttressing

Abstract. Ice rises or ice rumples act as ice-shelf pinning points that can have 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 an Antarctic-type, instability-prone marine outlet glacier to a successive ungrounding of its ice shelf from a topographic high and a subsequent re-grounding. We show that the glacier retreat down the landward down-sloping (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 from but remains locked in its collapsed 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 stronger buttressed glaciers on more moderate retrograde slope, such as Pine Island Glacier. In particular, our results suggest that the wide and deep marine bed depression in the interior of Thwaites Glacier's drainage basin might promote potential future unstable retreat and also represent a strong limitation for a possible re-advance of the glacier in case it would collapse.