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

The future evolution of the West Antarctic Ice Sheet will likely be subject to 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) influences the timing and spatial extent of the present and potential future destabilization of the West Antarctic Ice Sheet is highly uncertain. It is thus increasingly subject of numerical modeling studies that are based on observational data, striving for a more 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 a very slow change in sub-shelf melting (meltrate change of 1 m yr ⁻¹ every 100 000 years, aiming for quasi-equilibrium conditions). Using a “Lingle-Clark” bed deformation model we explore a wide range of solid-Earth structures, finding 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 spatial extent of the solid-Earth response and its characteristic viscous response timescale (spanning several orders of magnitude from ∼10 to ∼100 000 years). Compared to the case of a fixed bed (no bed deformation), the bifurcation point increases for the strongest (East-Antarctic type) Earth structures by at least 60 % (from 0.8 to 1.3 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 rate-induced tipping (R-tipping) occurs for half of the ensemble members. 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 tipping threshold reduces by up to 40  % with respect to the B-tipping threshold (for representative combinations of the upper-mantle viscosity and the lithosphere thickness). In none of our simulations bed uplift can stop a MISI once it is triggered, due to the very fast rate of self-reinforcing grounding-line retreat down the retrograde bed slope and the associated rapid drop in GL bed elevation. 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 lithosphere thickness and the upper-mantle viscosity 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.