Central elements of the climate system are at risk for crossing critical thresholds (so-called tipping points) due to future greenhouse gas emissions, leading to an abrupt transition to a qualitatively different climate with potentially catastrophic consequences. Tipping points are often associated with bifurcations, where a previously stable system state loses stability when a system parameter is increased above a well-defined critical value. However, in some cases such transitions can occur even before a parameter threshold is crossed, given that the parameter change is fast enough. It is not known whether this is the case in high-dimensional, complex systems like a state-of-the-art climate model or the real climate system. Using a global ocean model subject to freshwater forcing, we show that a collapse of the Atlantic Meridional Overturning Circulation can indeed be induced even by small-amplitude changes in the forcing, if the rate of change is fast enough. Identifying the location of critical thresholds in climate subsystems by slowly changing system parameters has been a core focus in assessing risks of abrupt climate change. This study suggests that such thresholds might not be relevant in practice, if parameter changes are not slow. Furthermore, we show that due to the chaotic dynamics of complex systems there is no well-defined critical rate of parameter change, which severely limits the predictability of the qualitative long-term behavior. The results show that the safe operating space of elements of the Earth system with respect to future emissions might be smaller than previously thought.

Over the last decade, our understanding of climate sensitivity has improved considerably. The climate system shows variability on many timescales, is subject to non-stationary forcing and it is most likely out of equilibrium with the changes in the radiative forcing. Slow and fast feedbacks complicate the interpretation of geological records as feedback strengths vary over time. In the geological past, the forcing timescales were different than at present, suggesting that the response may have behaved differently. Do these insights constrain the climate sensitivity relevant for the present day? In this paper, we review the progress made in theoretical understanding of climate sensitivity and on the estimation of climate sensitivity from proxy records. Particular focus lies on the background state dependence of feedback processes and on the impact of tipping points on the climate system. We suggest how to further use palaeo data to advance our understanding of the currently ongoing climate change

Abstract. The strongest mode of centennial to millennial climate variability in the paleoclimatic record is represented by Dansgaard–Oeschger (DO) cycles. Despite decades of research, their dynamics and physical mechanisms remain poorly understood. Valuable insights can be obtained by studying high-resolution Greenland ice core proxies, such as the NGRIP δ18O record. However, conventional statistical analysis is complicated by the high noise level, the cause of which is partly due to glaciological effects unrelated to climate and which is furthermore changing over time. We remove the high-frequency noise and extract the most robust features of the DO cycles, such as rapid warming and interstadial cooling rates, by fitting a consistent piecewise linear model to Greenland ice core records. With statistical hypothesis tests we aim to obtain an empirical understanding of what controls the amplitudes and durations of the DO cycles. To this end, we investigate distributions and correlations between different features, as well as modulations in time by external climate factors, such as CO2 and insolation. Our analysis suggests different mechanisms underlying warming and cooling transitions due to contrasting distributions and external influences of the stadial and interstadial durations, as well as the fact that the interstadial durations can be predicted to some degree by linear cooling rates already shortly after interstadial onset.

Abstract. Large volcanic eruptions occurring in the last glacial period can be detected by their accompanying sulfuric acid deposition in continuous ice cores. Here we employ continuous sulfate and sulfur records from three Greenland and three Antarctic ice cores to estimate the emission strength, the frequency and the climatic forcing of large volcanic eruptions that occurred during the second half of the last glacial period and the early Holocene, 60–9 kyr before 2000 CE (b2k). Over most of the investigated interval the ice cores are synchronized, making it possible to distinguish large eruptions with a global sulfate distribution from eruptions detectable in one hemisphere only. Due to limited data resolution and large variability in the sulfate background signal, particularly in the Greenland glacial climate, we only list Greenland sulfate depositions larger than 20 kg km−2 and Antarctic sulfate depositions larger than 10 kg km−2. With those restrictions, we identify 1113 volcanic eruptions in Greenland and 737 eruptions in Antarctica within the 51 kyr period – for which the sulfate deposition of 85 eruptions is found at both poles (bipolar eruptions). Based on the ratio of Greenland and Antarctic sulfate deposition, we estimate the latitudinal band of the bipolar eruptions and assess their approximate climatic forcing based on established methods. A total of 25 of the identified bipolar eruptions are larger than any volcanic eruption occurring in the last 2500 years, and 69 eruptions are estimated to have larger sulfur emission strengths than the Tambora, Indonesia, eruption (1815 CE). Throughout the investigated period, the frequency of volcanic eruptions is rather constant and comparable to that of recent times. During the deglacial period (16–9 ka b2k), however, there is a notable increase in the frequency of volcanic events recorded in Greenland and an obvious increase in the fraction of very large eruptions. For Antarctica, the deglacial period cannot be distinguished from other periods. This confirms the suggestion that the isostatic unloading of the Northern Hemisphere (NH) ice sheets may be related to the enhanced NH volcanic activity. Our ice-core-based volcanic sulfate records provide the atmospheric sulfate burden and estimates of climate forcing for further research on climate impact and understanding the mechanism of the Earth system.

Abstract. We propose a conceptual model comprising a cascade of tipping points as a mechanism for past abrupt climate changes. In the model, changes in a control parameter, which could for instance be related to changes in the atmospheric circulation, induce sequential tipping of sea ice cover and the ocean's meridional overturning circulation. The ocean component, represented by the well-known Stommel box model, is shown to display so-called rate-induced tipping. Here, an abrupt resurgence of the overturning circulation is induced before a bifurcation point is reached due to the fast rate of change of the sea ice. Because of the multi-scale nature of the climate system, this type of tipping cascade may also be a risk concerning future global warming. The relatively short timescales involved make it challenging to detect these tipping points from observations. However, with our conceptual model we find that there can be a significant delay in the tipping because the system is attracted by the stable manifold of a saddle during the rate-induced transition before escaping towards the undesired state. This opens up the possibility for an early warning of the impending abrupt transition via detection of the changing linear stability in the vicinity of the saddle. To do so, we propose estimating the Jacobian from the noisy time series. This is shown to be a useful generic precursor to detect rate-induced tipping.