*3.3. Relevance to the Present and Future*

AMOC instability is highly relevant to the future climate state and abrupt changes [94], which remain highly uncertain [95]. AMOC instability can be state dependent such that the AMOC stability differs in different times, glacial periods, Holocene, the present and future. What is then needed is the understanding of how the AMOC stability changes with climate state. In spite of the uncertainty, the stability indicator can serve as a useful starting point. The indicator implies an unstable AMOC in observations at the present time. This unstable AMOC, however, seems to contradict the lack of abrupt events in the Holocene (except for the modest 8.2 ka event, [96]), if the Holocene is taken as an analogue of the present. Alternatively, this lack of large abrupt changes in the Holocene could be caused by the lack of a strong trigger in the Holocene.

If we take the evidence of a likely unstable AMOC in the glacial cycle and assume the indicator is correct for the present period, most current CGCMs would be too stable, implying an underestimation of the possibility of abrupt climate changes in the future [79]. This over-stable AMOC is consistent for most recent CGCMs without flux adjustment, in which the AMOC responded gradually to the future rise of CO2 [49]. There are, nevertheless, three exceptions for CGCMs without flux adjustment that show abrupt collapse in hundreds of years, as presented in ref. [57,93,97]. The evolution of the AMOC in the future will be affected further by the melting of ice sheets in Greenland and Antarctica in the long run. It therefore remains highly uncertain how the AMOC will change in the future. It should be kept in mind that abrupt changes in models with flux adjustment should be treated with great caution [37], because of the potential distortion of the AMOC stability by flux adjustment, as analyzed in simple models [98]. Equally, however, it should be realized that there is no reason to trust the projections more from those current models without flux adjustment, as long as these models still suffer from severe salinity bias and, in turn, the AMOC freshwater transport, even if the stability indicator may not be perfectly correct.

#### **4. Discussion**

Recent progress in paleoceanographic proxies seem to favor the oceanic origin of AMOC instability as the cause of the abrupt climate changes during the glacial–interglacial period. Most CGCMs, however, seem to be over-stable, judging from the limited sensitivity experiments available, as well as the stability indicator Δ*Mov*, although it remains uncertain how correct this indicator is across CGCMs and in the real world.

Further paleo proxy records, especially those with high-temporal resolution, are needed to distinguish the AMOC instability from the ice-sheet instability as the origin for abrupt climate changes. These records may further include those outside the North Atlantic, say, in the North Pacific [99], because of their potential links to the abrupt changes in the AMOC.

Even more challenging is the assessment of the AMOC instability in the real world for the present and future. For the present, it has remained difficult to detect the AMOC response to the global warming of rising CO2. This is because the direct instrument measurement of AMOC transport has only been available for two decades. This short record can be significantly distorted by multidecadal variability and therefore is too short to detect the trend response to CO2 rise. Observational evidence of deep warming in the Atlantic and Southern Ocean [100–104] is not good evidence of the AMOC response either. Besides also being too short, the deep warming could be caused simply by the advection of the mean circulation, notably, the deep western boundary current [105], instead of a change in the AMOC circulation. Nevertheless, a recent study of two AMOC fingerprints in the North Atlantic surface temperature [106,107] and South Atlantic surface salinity [108,109] seemed to provide the clearest evidence so far of the AMOC slowdown response to global warming. This slowdown response, if true, could be simply the forced response of the AMOC, even without instability.

Finally, it is certainly worrisome, to say the least, that the state-of-the-art CGCMs still show the opposite AMOC freshwater transport, which is potentially related to the salinity feedback and in turn, AMOC instability. A diagnostic indicator, even if imperfect, provides the only way that the AMOC stability can be assessed for the present day real world, which then can be compared with models. Given all the odds of potential feedback beyond a simple conceptual model, it is already surprising that the indicator Δ*Mov* even works in many EMICs and some CGCMs. In EMICs, this indicator has been shown to represent the physical process of basin-wide salinity feedback associated with perturbation flow on mean salinity, while the gyre-induced freshwater transport is not sensitive to AMOC changes [32,33]. These feedback processes may be altered in CGCMs, especially in high-resolution models, leading to inconsistency between the indicator and AMOC stability [37,73,110]. Is it then possible to derive an improved stability indicator? For example, should the AMOC freshwater transport be calculated at a latitude other than 30◦ S, such as the intergyre boundary where the gyre transport change seems to be weak [73,90]?

#### **5. Conclusions**

Ultimately, AMOC instability, including any potential instability indicator, should be studied in the most realistic models without flux adjustment: high-resolution models with little bias in model climatology. This poses several challenges. First, the high-computational cost for the eddy resolving high-resolution models makes it difficult to perform extensive and long simulations that are needed to test any stability indicator. Second, if the indicator is related to a certain model bias, such as the tropical bias, these biases need to be significantly reduced in these CGCMs for a credible test of the indicator. The reduction of this bias, however, will be challenging because some biases are stubborn, notably the tropical bias which has been one of the most stubborn biases in CGCMs. Finally, AMOC instability may involve different feedback on different time scales, which may also be related to various transient behaviors of the AMOC responses, the latter being more relevant in the near future of climate change [93,97,110–112]. The different transient behaviors may be related to the basin-wide salinity feedback [35], as well as other feedback, such as the local convective feedback in the subpolar North Atlantic [113], feedback with atmosphere and sea ice [114], and the salinity feedback between the tropical and North Atlantic [89].

**Funding:** LSKJ202203303: NOAA20AR4310403, DOE ImPaCT.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** I would like to thank W. Liu, J. Lynch-Steiglitz, P. Clark, J. Mecking and J. Mc-Manus for our discussions. I would also like to thank three anonymous reviewers for their comments.

**Conflicts of Interest:** The authors declare no conflict of interest.
