Rate-induced tipping of ice sheets due to visco-elastic Earth response under idealized conditions

Abstract. The future evolution of the West Antarctic Ice Sheet may be characterized by self-reinforcing and irreversible retreat due to the unfolding of a marine ice sheet instability (MISI). How the stabilizing mechanism of glacial isostatic adjustment (GIA) does influence the timing and spatial extent of West Antarctica's present and potential future destabilization is highly uncertain and thus increasingly subject of numerical modeling studies that are based on observational data, striving for a most realistic representation of the Antarctic Ice Sheet. Here we employ an ensemble of idealized simulations in a synthetic model setup to systematically investigate how the interaction between ice-sheet dynamics and the visco-elastic response of the solid Earth affect the tipping dynamics of an inherently buttressed, Antarctic-type ice-sheet-shelf system that is perturbed by basal ice-shelf melting. Exploring a wide range of solid Earth structures we find that the threshold of bifurcation-induced tipping (B-tipping), i.e., the critical meltrate magnitude inferred for the ice sheet in quasi equilibrium, strongly depends on the timescale and the spatial extent of the solid-Earth response. Compared to the case of a fixed bed (no bed deformation), the B-tipping threshold increases for the strongest (East-Antarctic type) Earth structures by at least 80 % (from 0.8 to 1.5 m yr⁻¹) whereas for the weakest (West-Antarctic type) Earth structures the increase is more than one order of magnitude larger. 

Due to the different timescales involved in the interplay between the dynamics of the ice sheet and the solid Earth, we find that for half of the ensemble members rate-induced tipping (R-tipping) occurs. That is, a sufficiently fast ramp-up of the basal meltrates triggers a MISI even before the critical forcing threshold of B-tipping would be crossed. In fact, due to R-tipping the effective critical tipping threshold reduces by up to 80 % for high upper-mantle viscosities and thin lithospheres. In none of our simulations bed uplift can stop a MISI once it is triggered, due to the very fast timescale of self-reinforcing grounding-line retreat. Furthermore, we highlight the occurrence of grounding-line overshoots and demonstrate cases of self-sustaining oscillations between advanced and collapsed ice-sheet states. Once triggered, these oscillations continue perpetually just due to the internal, non-linear interaction between ice-flow and solid-Earth dynamics. Our findings highlight that the character of the solid-Earth structure underlying a MISI-prone ice sheet can strongly affect its tipping dynamics mediated by the strength and timescale of the GIA feedback that counteracts MISI. In the context of Antarctic ice-sheet stability under global warming, our results particularly underscore that besides the magnitude also the rate of future anthropogenic greenhouse gas emissions are likely to play a crucial role.