Our results reveal generic early warning signals for a collapse of the AMOC in a fully coupled atmosphere-ocean general circulation model: the most realistic simulation of the climate system in which this type of signal has been tested. The hosing experiment carried out in FAMOUS involved a relatively slow, linear forcing. Nevertheless, comparison of the transient simulation with the equilibrium runs (Fig. 3) shows that the AMOC was forced fast enough to shift it away from equilibrium, such that it lagged the forcing (that is, collapse is delayed in the transient simulation). The theory of CSD is derived for systems close to equilibrium, yet it still seems to work in this case where the timescales of the forcing and the internal dynamics of the AMOC are comparable. In reality, anthropogenic forcing of the AMOC may be faster and more non-linear than simulated here. It is believed that recent freshwater forcing, over approximately the last 50 years, has increased by 0.026 Sv (ref. 28), which is comparable to the 0.05 Sv per century increase used to force FAMOUS here. However, anthropogenic forcing may increase faster in the future. It needs to be examined whether a more realistic forcing scenario can still produce early warning signals, or whether it eliminates them, as it does for another climate tipping element29. If anthropogenic forcing is faster than the intrinsic timescale of the ocean, then the early warning signals should not work as well as the system will not be near to equilibrium.

Our calculation of the length of time it takes for the early warning signals to become significant uses time series at annual resolution. In reality, palaeoclimate reconstruction of the AMOC would be required to gain enough data to begin to determine, if early warning signals are significant with enough time before collapse to be useful. Although existing palaeo reconstructions of the AMOC are at coarser temporal resolution than annual, our results also show that significant signals can be observed at a decadal resolution and thus potentially could also appear in these reconstructions27. Also the AMOC will not have been subjected to anthropogenic forcing for most of the paleo reconstruction era, which could be beneficial for observing a signal once the forcing begins. It has also been shown that the warm phase of the Atlantic multidecadel oscillation (AMO) coincides with a strengthening of AMOC and the cool phase, a weakening30 and multidecadal sea surface temperature (SST) variations are closely related to the AMOC in GCMs. The AMO has been reconstructed using SST records (including in-filling) since 1856 at a monthly resolution31 and using tree-ring palaeo data, it has been reconstructed at an annual resolution from 1567 (ref. 32). These reconstructions could act as a proxy for AMOC to test these early warning signals on, although caution should be used when comparing mean data at annual resolution from the model and annual SST reconstructions.

Dynamical systems theory suggests that CSD occurs due to the weakening of a restoring (negative) feedback as a tipping point is approached, causing an increase in the time taken for the system to recover from perturbations. In the case of the AMOC collapse in FAMOUS, the existence of CSD signals suggests that the gradual freshwater forcing is causing a negative feedback to weaken. An important stabilizing feedback on the AMOC involves changes in meridional heat transport33. A weakening of the AMOC leads to a reduction in northward ocean heat transport, causing a cooling of the high latitude North Atlantic and associated increase in density, which promotes a recovery of the circulation through increased deep water formation. However, as the freshwater forcing is applied in the transient experiments analysed here, the AMOC undergoes a gradual weakening (as can be seen in Fig. 3) before the collapse. In contrast to salinity anomalies, surface ocean temperature anomalies are strongly damped by atmosphere-ocean heat fluxes. This means that when the AMOC is weaker, with slower northward advection of surface water masses, the increased transit time allows increased damping of the temperature anomalies, weakening the negative feedback from the AMOC itself. This theoretical explanation for the CSD has perhaps the broadest applicability, but many previous studies have provided evidence for other, more detailed, restoring feedback mechanisms that are responsible for controlling the time scale of decadal-centennial variability in coupled AOGCMs. These include an ocean-only mode excited by atmospheric variability, in which heat and salinity transport both play a role and the overturning and gyre circulations interact34,35; a coupled ocean-atmosphere mode, in which AMOC variations trigger dynamical feedbacks in the atmosphere that act to oppose the AMOC anomaly36; feedbacks that involve shifts in the inter-tropical convergence zone, leading to salinity anomalies in the tropical Atlantic, which feed back onto the AMOC strength as they are advected northwards37; and feedbacks that involve links with the Arctic38,39. To properly understand the precise dynamical reason for CSD in FAMOUS, further work will be required to identify the dominant negative feedback that controls the time scale of AMOC variability in this model, and identify how it is influenced by freshwater forcing. As there is still debate about the key feedbacks that stabilize the AMOC in different AOGCMs, generalization of these results to other models and the real world remains an important challenge.

The early warning signals in the annual resolution data are most reliable in the high northern latitudes and towards the southern boundary of the Atlantic. Current monitoring of the AMOC occurs at 26.5°N, where in this model, early warning signals are somewhat less reliable. However, there are already plans to monitor the AMOC in the sub-polar North Atlantic with the OSNAP (Overturning in the Subpolar North Atlantic Program) monitoring array (~55–60°N, red in Fig. 6). There are also proposals for a SAMOC (South Atlantic Meridional Overturning Circulation) array located in southern boundary of the basin (~34.5°S, blue in Fig. 6). Our results based on annual resolution data suggest that these could be the best locations to try to diagnose trends in the dynamical stability of the AMOC. However, the latitudinal results are rather different with decadal averaged data (Fig. 7) and may well vary from model to model. Thus, at this stage we can only conclude that early warning signals are likely to be latitude dependent and therefore monitoring at more than one location may increase the likelihood of observing a robust early warning signal.

Latitudinal variation in the reliability of early warning indicators might potentially be understood in terms of the latitudinal characteristics of natural AMOC variability. There are several dynamical components to the AMOC40,41, whose relative contributions differ with latitude and have been diagnosed in a (100-year) control simulation of HadCM3 (ref. 42) (from which the FAMOUS model we use is derived). To leading order, the meridional velocity across a zonal section can be dynamically split into Ekman and geostrophic components. By definition, the Ekman component is surface-intensified and directly driven by the zonal mean wind stress. The geostrophic component can be further decomposed into baroclinic (vertical shear) and barotropic (depth-independent) contributions. The barotropic component arises due to an interaction between sloping topography and the component of the flow that is constant with depth. In an idealized basin with vertical sidewalls, the barotropic component of the overturning circulation would be zero. In reality, variations in ocean depth across the zonal section cause vertically constant flow to project onto the meridional overturning circulation. For example, a northward depth-independent flow in a shallow part of the section (for example, near the boundaries) and a southward depth-independent flow at longitudes where the ocean is deeper, when zonally and vertically integrated, would produce a net positive contribution to the meridional overturning transport. The remaining, baroclinic, component arises through thermal wind balance associated with zonal density gradients across the basin. There are several physical mechanisms that control basin-wide density gradients, including coastal wind-driven upwelling and downwelling43, local buoyancy forcing44 and changes in the formation rate and transport of remote water masses. The latter is of particular relevance to the present study, as a change in the density and transport of North Atlantic Deep Water (NADW) as it spreads southwards along the western part of the basin will be reflected in a change in the zonal density gradient and therefore the vertical shear and the baroclinic component of the AMOC45,46,47,48.

CSD occurs because a restoring feedback is weakening as a bifurcation-type tipping point is approached. This negative feedback involves the component of the AMOC that is thermohaline-driven and acting on multi-decadal to centennial time scales. It is likely that this will be reflected in the baroclinic (vertical shear) component associated with zonal density gradients, as this is the component in which changes in the density and extent of NADW are likely to be most strongly visible. Within the South Atlantic and at some latitudes in the northern North Atlantic, this baroclinic component dominates the AMOC42, and we speculate that this could be consistent with the enhanced significance of the early warning signal based on annual data from these locations. In the low-latitude North Atlantic, in contrast, there is a large influence from other components of AMOC variability, particularly that associated with strong, depth independent flow over sloping topography42, which may help to explain the reduced significance of the early warning signal there. However, a clear distinction between the dynamical drivers of the AMOC components remains elusive, and several studies suggest that the baroclinic and barotropic components can be closely linked. For example, the barotropic component can also be influenced by zonal density gradients, and it is clear that wind forcing plays a crucial role in sustaining the AMOC49.

In addition, it remains to be established whether the latitudinal variation in relative dominance of the dynamical components in HadCM3 (ref. 42) holds on longer (centennial) time scales, and in other models. Further work will be required to establish whether the latitudinal variation in early warning signal reliability exists in other models and to fully understand the dynamical reasons behind this.

While preparing this manuscript, another study was published that explores a different method for detecting early warning of AMOC collapse in the same model50. In that study, the indicators of CSD theory appear to fail to provide early warning of AMOC collapse. However, their analysis was unusual in looking for temporal spikes in the indicators and averaging the data over latitudes.