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Research over the past decade has shown that multiple elements of the climate system, such as the Arctic Winter sea ice or the Amazon rainforest, could undergo abrupt shifts, but there are large uncertainties regarding their timing and spatial extent. In this study we investigated when and where abrupt shifts occur in the latest generation of climate models (CMIP6) under a scenario of a 1% annual increase in CO$_2$. We considered 82 ocean, atmosphere, and land variables across 57 models. We used a Canny edge detection method -- adapted for spatiotemporal dimensions -- to detect abrupt shifts occurring on time scales from years to decades. Then, we performed a connected component analysis to quantify the spatial extent of these shifts. The systems analyzed include the North Atlantic subpolar gyre, Tibetan Plateau, land permafrost, Amazon rainforest, Antarctic sea ice, monsoon systems, Arctic summer sea ice, Arctic winter sea ice, and Barents sea ice. With the exception of the monsoons systems, we found abrupt shifts in multiple models per system. We observed a considerable variation across the different CMIP6 models in terms of timing and spatial extent. Higher levels of global warming increased the risk of abrupt shifts in CMIP6 models. Even at a global warming level of 1.5 $^\circ \text{C}$, six out of ten studied climate subsystems showed abrupt shifts that cover a substantial area in multiple models.

The subpolar gyre is at risk of crossing a tipping point which would result in the collapse of convection in the Labrador Sea. It is important to understand the mechanisms at play and how they are represented in climate models. In this study we use causal inference to verify whether the proposed mechanism for bistability of the subpolar gyre is represented in CMIP6 models. In many models an increase of sea surface salinity leads to a deepening of the mixed layer resulting in a cooling of the water at intermediate depth, in line with theory. The feedback from the subsurface temperature through density to the strength of the gyre circulation is more ambiguous, with fewer models indicating a significant link. Those that do show a significant link do not agree on its sign. One model (CESM2) contains all interactions, with both a negative and delayed positive feedback loop., Comment: Submitted to Geophysical Research Letters

The standard approach when studying atmospheric circulation regimes and their dynamics is to use a hard regime assignment, where each atmospheric state is assigned to the regime it is closest to in distance. However, this may not always be the most appropriate approach as the regime assignment may be affected by small deviations in the distance to the regimes due to noise. To mitigate this we develop a sequential probabilistic regime assignment using Bayes Theorem, which can be applied to previously defined regimes and implemented in real time as new data become available. Bayes Theorem tells us that the probability of being in a regime given the data can be determined by combining climatological likelihood with prior information. The regime probabilities at time $t$ can be used to inform the prior probabilities at time $t+1$, which are then used to sequentially update the regime probabilities. We apply this approach to both reanalysis data and a seasonal hindcast ensemble incorporating knowledge of the transition probabilities between regimes. Furthermore, making use of the signal present within the ensemble to better inform the prior probabilities allows for identifying more pronounced interannual variability. The signal within the interannual variability of wintertime North Atlantic circulation regimes is assessed using both a categorical and regression approach, with the strongest signals found during very strong El Ni\~no years., Comment: Accepted for publication in Journal of Climate

A new technique to derive delay models from systems of partial differential equations, based on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the Atlantic Multidecadal Oscillation. The Mori-Zwanzig formalism gives a rewriting of the original system of equations which contains a memory term. This memory term can be related to a delay term in a resulting delay equation. Here the technique is applied to an idealized, but spatially extended, model of the Atlantic Multidecadal Oscillation. The resulting delay difference model is of a different type than the delay differential model which has been used to describe the El Ni\~no- Southern Oscillation. In addition to this model, which can also be obtained by integration along characteristics, error terms for a smoothing approximation of the model have been derived from the Mori-Zwanzig formalism. Our new method of deriving delay models from spatially extended models has a large potential to use delay models to study a range of climate variability phenomena., Comment: Submitted to Proceedings of the Royal Society A - revised version

Atmospheric circulation is often clustered in so-called circulation regimes, which are persistent and recurrent patterns. For the Euro-Atlantic sector in winter, most studies identify four regimes: the Atlantic Ridge, the Scandinavian Blocking and the two phases of the North Atlantic Oscillation. These results are obtained by applying k-means clustering to the first several empirical orthogonal functions (EOFs) of geopotential height data. Studying the observed circulation in reanalysis data, it is found that when the full field data is used for the k-means cluster analysis instead of the EOFs, the optimal number of clusters is no longer four but six. The two extra regimes that are found are the opposites of the Atlantic Ridge and Scandinavian Blocking, meaning they have a low-pressure area roughly where the original regimes have a high-pressure area. This introduces an appealing symmetry in the clustering result. Incorporating a weak persistence constraint in the clustering procedure is found to lead to a longer duration of regimes, extending beyond the synoptic timescale, without changing their occurrence rates. This is in contrast to the commonly-used application of a time-filter to the data before the clustering is executed, which, while increasing the persistence, changes the occurrence rates of the regimes. We conclude that applying a persistence constraint within the clustering procedure is a superior way of stabilizing the clustering results than low-pass filtering the data., Comment: Submitted to Quarterly Journal of the Royal Meteorological Society (accepted)

Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Nino Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposed ad-hoc conceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations., Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figures