Rate-induced tipping (R-tipping) describes the fact that, for multistable dynamic systems, an abrupt transition can take place not only because of the forcing magnitude, but also because of the forcing rate. In the present work, we demonstrate through the case study of a piecewise-linear oscillator (PLO), that increasing the rate of forcing can make the system tip in some cases but might also prevent it from tipping in others. This counterintuitive effect is further called non-monotonous R-tipping (NMRT) and has already been observed in recent studies. We show that, in the present case, the reason for NMRT is the peak synchronisation of oscillatory responses operating on different time scales. We further illustrate that NMRT can be observed even in the presence of additive white noise of intermediate amplitude. Finally, NMRT is also observed on a van-der-Pol oscillator with an unstable limit cycle, suggesting that this effect is not limited to systems with a discontinuous right-hand side such as the PLO. This insight might be highly valuable, as the current research on tipping elements is shifting from an equilibrium to a dynamic perspective while using models of increasing complexity, in which NMRT might be observed but hard to understand.
<p>Due to anthropogenic global warming since the pre-industrial era, sea level has been rising along with global temperature. This sea-level rise is due to thermal expansion of the ocean and melting of mountain glaciers and continental ice sheets, mainly Greenland (GrIS) and Antarctica (AIS). The latter are the potential largest contributors as they store a total amount of 63 meters of sea-level rise in the form of ice. Modelling studies agree that these ice sheets will melt more in the future, however results differ due to associated uncertainty in representing several physical processes, as well as in assessing warming projections. Past warm scenarios can help to elucidate this uncertainty as we can obtain information, such as the sea-level standings, the ice extension from continental ice sheets and infer global temperatures from proxy records. The mid-Pliocene warm period (3.3-3.0 million years ago) offers an ideal benchmark, as it is the most recent period with CO2 levels comparable to the present-day (PD; 350-450 ppmv), although showing global mean temperatures 2.5-4.0 degrees higher. The inferred sea-level reconstructions from that period estimate a sea level standing of 15-20 meters higher than PD. Whereas the modern GrIS was starting to form, the AIS was restricted to its eastern region due to warm oceanic temperatures. The Pliocene Model Intercomparison Project, Phase 2 (PlioMIP2) has brought together various climate outputs from different general circulation models to elucidate the pliocene climate conditions. Here we force a higher-order ice sheet model with these climatic outputs at a high spatial resolution. Our aim is to investigate how polar continental ice sheets respond to these different climatic fields and to infer tipping values that can lead these ice sheets to drastically change their topographic shape.</p>
<p>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., &#8220;noise&#8221;) 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.</p>
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