Transition indicators on a flowline ice sheet model

Marine ice-sheet behaviour and grounding line stability have been fundamental objects of study in the last two decades. In particular, the ice sheet-shelf transition deserves special attention as it determines the outflow of ice from the grounded region and, together with accumulation, governs the global mass balance. Yet, the dynamics of ice flow are strongly coupled to the climate system via surface mass balance, frontal ablation and atmospheric temperature among others. The interplay of such variables combined with the bed geometry determine the equilibrium position of a glacier terminus, which can display bistability due to the marine ice-sheet instability. These variables further define the boundary conditions of an ice-sheet model and are given by the particular climate scenario. However, a realistic representation of the climate must be described as a stochastic process (short-term variability i.e., “noise”) interacting with long-term deterministic dynamics. The response of a multi-stable system to noisy forcing can be used to predict abrupt transitions by means of so-called transition indicators. That is, a direct application of classical slowdown theory to capture the essence of shifts at tipping points. In the present work, we apply some of these indicators to a 1-D flowline model to study whether a glacier collapse can be predicted by critical slowdown theory. A key challenge with transition indicators is to determine when the system can be expected to tip given that a critical slowdown begins to occur. We explore this issue through a large ensemble of simulations.