Calving multiplier effect controlled by melt undercut geometry

Quantifying the impact of submarine melting on calving is central to understanding the response of marine-terminating glaciers to ocean forcing. Modeling and observational studies suggest the potential for submarine melting to amplify calving (the calving multiplier effect), but there is little consensus as to under what conditions this occurs. Here, by viewing a marine-terminating glacier as an elastic beam, we propose an analytical basis for understanding the presence or absence of the calving multiplier effect. We show that as a terminus becomes undercut it becomes more susceptible to both serac failure (calving only of ice that is undercut, driven by vertical imbalance) and rotational failure (full thickness calving of ice behind the grounding line, driven by rotational imbalance). By deriving analytical stress thresholds for these two forms of calving, we suggest that the dominant of the two calving styles is determined principally by the shape of melt undercutting. Uniform undercutting extending from the bed to the waterline promotes serac failure and no multiplier effect, while glaciers experiencing linear undercutting that is greatest at the bed and zero at the waterline are more likely to experience rotational failure and a multiplier effect. Our study offers a quantitative framework for understanding where and when the calving multiplier effect occurs, and, therefore, a route to parameterising the effect in ice sheet-scale models.