The Atlantic Meridional Overturning Circulation (AMOC) is a large system of ocean currents involving differences in the temperature and salinity between the water in the tropics and the North Atlantic Ocean . The upper cell of the AMOC consists of warm and salty northward surface flow (the North Atlantic warm current, down to roughly 1200 m depth), along with colder and deep southward return flow (the North Atlantic Deep Water, 1500–4000 m depth). The lower cell of the AMOC is the northward flow of dense Antarctic Bottom Water (AABW) formed in the Southern Ocean . The AMOC acts as a heat pump at the high latitudes as the meridional transportation brings warm water to the colder sub-polar and polar regions then further modifies the climate in northern Europe and the east coast of North America . It is responsible for producing about half of the global ocean's deep waters, sourced from the northern North Atlantic .

Since the AMOC plays a vital role in air–sea interactions, along with its ability to transport and redistribute heat and its effect as a carbon sink in the Northern Hemisphere , studying the evolution of the AMOC strength in the past is of great importance for us. It helps us identify the mechanisms which lead to the AMOC changes and make projections for the future climate. Comparison of the AMOC changes between different geological eras can provide us with a better understanding of the roles of the external forcing in the AMOC strength variations. In addition, past AMOC variations suggest that the distribution of surface heat and freshwater flux can affect the location of deep water formation and result in transient changes in the AMOC .

Our study focuses on investigating the AMOC changes during the two interglacials: the Holocene (11.5 ka–1950 CE) and Last Interglacial (130–115 ka). Two time slice experiments, the midHolocene (representing 6 ka) and the lig127k (representing 127 ka), have been defined by the Palaeoclimate Modelling Intercomparison Project Phase 4 (PMIP4) ; 6 ka was chosen as the warmest point during the Holocene thermal maximum according to existing surface temperature reconstructions , although this is being re-evaluated at present . The midHolocene experiment is one of the entry cards for the PMIP4 component of the current phase of the Coupled Model Intercomparison Project (CMIP6); 127 ka is chosen as it represents the peak boreal warmth in the Last Interglacial , and it has been identified as a period of high interest, due to its higher average global temperature and sea level . In the context of PMIP4, the focus lies on changes in insolation arising from the differences in Earth's orbit, while the greenhouse gas (GHG) concentrations were similar to that in the piControl experiment, and the continental configuration (ice-sheet distribution and elevations, land–sea mask, continental topography, and oceanic bathymetry) was prescribed as the same as in piControl .

During the two interglacial periods, the orbital parameters are prescribed according to . Eccentricity, the deviation of the Earth's orbit from a perfect circle, was larger (more elliptic) than that during the preindustrial period, especially for lig127k. Meanwhile, perihelion, the closest point in the orbit to the sun, occurred much closer to the boreal summer solstice in lig127k. Obliquity, the tilt of the Earth's axis, was also higher during these two warm periods . This leads to a positive Northern Hemisphere summer insolation anomaly at both 127 and 6 ka, compared to preindustrial, while the difference in annual incoming insolation at the top of the atmosphere between the two periods is marginal see Fig. 3b offor the seasonal distribution of insolation. Due to the model differences in the internal model calendar and the impact of eccentricity and precession (the orientation of Earth's rotational axis) on the length of the seasons, the date of the vernal equinox must be fixed in all simulations to 21 March . More detail on the forcings and boundary conditions for the lig127k and midHolocene experiments can be found in and in for the piControl experiment. Based on the experimental set-up, midHolocene and lig127k, when the seasonal insolation is the strongest forcing, are two reasonable periods to study whether or not the changes in orbital forcing have altered the overall AMOC strength in the two past interglacials compared to the piControl experiment.

After introducing the methods used in this study (Sect. ), we first analyse the behaviour of AMOC during the Quaternary interglacials in individual PMIP4 models in Sect. , and then we explore the AMOC variations during the past two interglacials based on the model ensemble mean, which are shown in Sect. . In Sect. , as the seasonal changes in incoming solar radiation amplified in lig127k compared to midHolocene, we investigated further to see whether the simulated response shows similar amplification in these individual models or not. Meanwhile, we also devised a series of tests that must be passed for a forced response and also try to identify the causes for the changes in AMOC that we see in individual models. Furthermore, since we have identified that the AMOC changes could leave a fingerprint on the surface temperature and precipitation variation in midHolocene, as well as in piControl, regressions of surface conditions against AMOC have been computed for each simulation run for both midHolocene and piControl, and they are shown in Sect. . Based on the computed AMOC's fingerprint on the surface temperature and precipitation in individual models, we also show in this section that the percentage of simulated surface temperature changes that could be explained by AMOC changes is only minor. After investigating the changes in AMOC and the role of AMOC in the climate system in PMIP4 simulations, comparisons with proxy reconstructions for the Holocene and the Last Interglacial are discussed in Sect. .

To be included in this study, a model must have performed an experiment following the protocol for either midHolocene or lig127k as laid out by and then archived the output of this experiment with the Earth System Grid Federation. Twelve CMIP6 models have provided the necessary output of zonal-mean ocean meridional overturning mass streamfunction (called “msftmz” or “msftmyz” depending on the grid used) to undertake our analysis. Of these, eight models performed both interglacial experiments. Details of the individual models are shown in Table .

The AMOC intensity is computed using a modified version of the Climate Variability Diagnostic Package CVDP;. Rather than using principal component analysis to define the AMOC , the maximum overturning streamfunction at 30∘ N is used . Patterns of surface climate anomalies associated with AMOC variations are computed by the CVDP via linear regression (more details below), with the ability to determine precipitation patterns added by .

The maximum of the annual-mean meridional mass overturning streamfunction below 500 m at 30∘ N (and additionally at 50∘ N) is used to measure the AMOC strength. If the latitudes of, say, 35 or 55∘ N had been selected instead, the impacts on the results would be subtle and would be unlikely to alter our conclusions. Observational mooring arrays exist at 26∘ N (RAPID-MOCHA, since 2004) and at 53–60∘ N (OSNAP section, since 2014) .

All models are regridded onto a common 1∘ latitude grid with 61 depth levels ranging between 0–6000 m in the ocean to compute ensemble averages. All simulations are given equal weighting when calculating ensemble means.

A fingerprint of the AMOC on wider climate is computed separately for each simulation. The fingerprints are obtained by linearly regressing temperature and precipitation anomalies at each grid box over the globe onto AMOC strength at 30∘ N, using the equation: δT=αδΨ30N+c, where δ indicates a detrended anomaly within a simulation, T is the temperature (at the grid point), Ψ is the maximum overturning streamfunction at 30∘ N in the Atlantic, α is the fingerprint coefficient, and c is a constant. A 15-month low-pass Lanczos filter is applied to the AMOC time series prior to computing the regression. Precipitation fingerprints are computed using percentage variations, rather than absolute rainfall anomalies. The maximum contribution of local surface temperature changes that could be explained by AMOC changes is then estimated by comparing simulated changes to the AMOC change multiplied by the regression coefficient (averaged between the interglacial and preindustrial simulations) (ΔTΨ/ΔT).

The first-order determinant on the AMOC strength is the model used for the simulation (Table ). Figure a clearly shows that the piControl AMOC strength at 30∘ N is highest in FGOALS-g3, with it ranging between 12–25 sverdrups (Sv) in the rest of the models. The highest simulated AMOC strength is more than twice that of the lowest one, even excluding FGOALS-g3. The dashed green and pink horizontal lines in Fig. a show the average value from observational arrays. The observed AMOC strength at 26∘ N 17 Sv; is stronger than that at 53–60∘ N from the OSNAP section . The stronger sub-tropical strength feature is generally replicated by models, except for ACCESS-ESM1-5 and FGOALS-g3 (Fig. a).

The large spread in the simulated AMOC strength seen in the piControl experiment raises questions about whether the models can accurately simulate changes in AMOC . The spread is an unfortunate feature of both the wider CMIP6 and CMIP5 ensembles e.g.. Disappointingly the uncertainty in modern-day oceanographic observations is such that few of the simulations can be categorically ruled out . The piControl experiment represents an earlier time than that of the observations, and AMOC is known to have changed between them . However, the changes in AMOC seen during the historical simulations are relatively small compared to the differences between the models and observations, meaning that the consequences of the temporal offset are not important.

The extremely low value in the IPSL-CM6A-LR model is mainly caused by the inaccurate representation for the overflow waters or deep western boundary current (DWBC) and biases in the precipitation in the North Atlantic Ocean, which are challenging to resolve in climate models . In some models, the lack of overflow parameterisations which commonly occur in low-resolution models could be another reason for the slightly underestimated simulated AMOC strength. The AMOC strength in the FGOALS-g3 model in both sub-tropical and sub-polar regions is very high, even compared to its predecessor FGOALS-g2 . These can be attributed to the excessive deep convection in the Irminger Sea, Labrador Sea, and Nordic Seas, despite a mixed layer depth similar to observations .

The interannual variability in the AMOC is also model-dependent (Table ) and generally does not alter much between the various experiments. EC-Earth3-LR and the two models by FGOALS are the exceptions, but they do not provide a coherent message about the response to increasing orbital forcing. Therefore, we consider these to be different samples from the same underlying distribution .

The absolute AMOC changes in the midHolocene and lig127k experiments (with respect to piControl) are compared to the magnitude of the internal variability (1 standard deviation) of each model's piControl experiment (Fig. b). The magnitude of the simulated AMOC changes in midHolocene are within the range of the model's internal variability for all the models, except for HadGEM-GC31-LL and MRI-ESM2-0. The extent of AMOC changes in lig127k is generally larger, with three different models (ACCESS-ESM1-5, EC-Earth3-LR, and IPSL-CM6A-LR) showing changes that are larger than their internal variability.

Given the large spread in AMOC strength in piControl, it is also worth looking at the relative changes in AMOC seen in the midHolocene and lig127k experiments (Fig. c). Changes within the ±5 % range (dashed red horizontal lines) have previously been considered to represent no substantial AMOC changes . The majority of models do not demonstrate a substantial change in AMOC strength under the midHolocene experiment at 30 or at 50∘ N (Table , Fig. c). state that these findings are consistent with the palaeo-reconstructions for the mid-Holocene, something discussed further in Sect. . Similar results are seen for lig127k (Fig. c), although five models do have AMOC strength changes exceeding 5 % of the piControl strength. The extent of deviations in lig127k is generally larger than that seen in midHolocene.

We further investigate the role of AMOC in the interglacial climate system, particularly looking at the impact of AMOC on the simulated surface temperature and precipitation changes. First, we regress the temperature and precipitation at each grid box over the globe onto AMOC maximum at 30∘ N for each simulation to obtain the local response to a 1 Sv increase (see Sect. ). Larger regression coefficients indicate that the interdecadal variability in the AMOC has more impact on the surface temperature or precipitation changes at each grid box. There is a strong relationship between AMOC change and surface temperatures over the northern North Atlantic, and they are most obvious in the Nordic Seas, the area south of Greenland, the Labrador Sea, and along the track of the Gulf Stream (Fig. ). This reveals that the AMOC has a noticeable influence on modulating the surface temperature through heat transport in those regions . The regression coefficients are generally higher in the Nordic Seas than that in the area south of Greenland when referring to all the 11 PMIP4 models involved (not shown). The area of influence is generally confined to the northern North Atlantic (Fig. ), although the FGOALS-g3 L and GISS-E2-1-G models both have particularly low coefficient values (∼0.15) even there (not shown). Here we present regression coefficients from the midHolocene simulations, yet these are effectively unchanged in either the piControl or lig127k simulations (not shown).

The AMOC temperature fingerprints in the North Atlantic are accompanied by a dipole response in precipitation (Fig. ) with roughly a 5 % decrease in the mid-latitude (30–50∘ N) and a 5 % increase in the sub-polar and polar regions. The largest AMOC-induced precipitation changes occur in the tropics, with a reduction of about 10 %–15 % in the equatorial Pacific. FGOALS-f3 L (not shown) and NorESM2-LM show a larger decrease than other models (20 %–30 % and 30 %–40 %, respectively). The low-latitude (0–30∘ N) North Atlantic Ocean generally reveals an increases (up to 10 %) in rainfall as the AMOC changed by 1 Sv, and it is more obvious in IPSL-CM6A-LR and NorESM2-LM. The 25 %Sv-1 increase in precipitation in NorESM2-LM could be explained by the northward shifting of the Intertropical Convergence Zone (ITCZ) due to stronger AMOC in this region. NorESM2-LM shows the largest changes across the whole globe (Fig. ) and is somewhat of an outlier. The fingerprints are very similar if computed using either piControl or lig127k simulations (not shown), demonstrating that the influence of AMOC is a robust feature in the models with minimal state dependence. It should be noted that despite these fingerprints being computed from analysis of the internal variability within individual simulations, the spatial patterns are clearly reminiscent of those seen in hosing experiments e.g.. This demonstrates that it is valid to assume that the teleconnection patterns associated with internally generated changes in AMOC are the same as those from externally forced changes.

It is not uncommon to interpret terrestrial proxy records as being related to AMOC changes e.g. or to use compilations of proxy records to directly infer past AMOC changes e.g.. Since both the AMOC fingerprints and the changes in AMOC strength have been computed, we can determine the maximum percentage of the local midHolocene climate changes that could potentially be explained by the AMOC. Such analysis could help to identify the regions to target for further proxy-based studies that contain an AMOC signal during the mid-Holocene.

Figure  shows the percentage of the simulated surface air temperature changes that could potentially be explained by the AMOC changes in midHolocene. The AMOC is only one of many factors influencing the local temperature changes. For example, areas with a percentage smaller than 0 can occur when the AMOC fingerprint suggests changes of the opposite sign to the actual changes. This percentage of fingerprint-estimated changes can approach, or even exceed, 100 % when the midHolocene temperature change is very small, as simulated by the model when considering all factors. Both cases indicate that the AMOC changes cannot explain the midHolocene temperature response in those areas.

The four models with the largest changes in maximum AMOC strength at 30∘ N are shown in Fig. . In general, those places where AMOC could explain half or more of the temperature changes occur in regions where the midHolocene temperature signal itself is small. For HadGEM3-GC31-LL and EC-Earth3-LR, this means that only regions outside the northern North Atlantic are highlighted. Both IPSL-CM6A-LR and MRI-ESM2-0 show midHolocene temperature changes larger than 0.5 ∘C in the sub-polar gyre notable for the present-day “warming hole”;. Despite this, those regions demonstrate some of the weakest potential impact from midHolocene AMOC changes suggested across the North Atlantic and Nordic Seas for each model (Fig. ). AMOC-related changes cannot explain any of the temperature changes seen in the other models (not shown), as they see very small changes in the AMOC itself (Table ).

After analysing all the models, we conclude that the AMOC does not play a globally important role in explaining the temperature changes, and the role may be secondary to other factors even in the North Atlantic. This conclusion also applies to sea surface temperature and holds for lig127k as well (not shown). A similar analysis has also been performed to look at the AMOC-related precipitation changes (see Supplement). The vast majority of the globe has an estimated contribution of 10 % or less of the midHolocene and lig127k precipitation changes, questioning whether reconstructed precipitation changes can be used as inferring information about the AMOC.

Past changes in overall AMOC strength, especially its depth integral, are difficult to reconstruct. Many previous studies have instead focused on examining individual components of the AMOC or inferred changes in deep water mass geometry e.g.. However, one proxy technique is to use sedimentary Pa/Th e.g., although modern geochemical observations highlight the contribution of other factors controlling the Pa and Th distribution . For example, using a Pa/Th-enabled model revealed that the changes in biogenic particle fluxes can affect the Atlantic Pa/Th records, and the particle flux changes have been suggested to cause far-field Pa/Th variations as well.

High-resolution Holocene Pa/Th reconstructions from the North Atlantic show no observable changes, unlike the faint AMOC weakening in the Holocene shown by low-resolution Pa/Th data . As the high-resolution Pa/Th records are both single-site studies from the sub-tropical north-western Atlantic, it is unclear how well they represent the overall AMOC strength . Taken together, the Pa/Th records indicate relatively similar AMOC strength for the mid-Holocene and preindustrial. There are fewer sedimentary Pa/Th records for the Last Interglacial, although they also do not indicate substantial changes in AMOC strength

Reconstruction of changes in the density profile of the Florida Straits shows little change in the strength of the upper limb of the AMOC over the past 8000 years . Just under half the Florida Strait flow is associated with the AMOC, with the remainder relating to the wind-driven surface gyre circulation. Therefore the reported slight increase (4 Sv increase on a flow of 28–32 Sv) over the past 8000 years may be attributed instead to a strengthening of the wind-driven gyre circulation in the western Atlantic . To our knowledge, an equivalent reconstruction does not exist for the Last Interglacial. However, a recent benthic δ13C compilation shows no obvious changes in the spatial structure (latitudinal and depth extent) of the North Atlantic Deep Water (NADW) between the Last Interglacial and mid-Holocene, and suggests that the mean NADW transport was similar .

In summary, no palaeo-reconstructions demonstrate substantive changes in the depth-integrated AMOC strength between either of the two interglacial states and piControl. This, therefore, does not disagree with the PMIP4 ensemble demonstrating no consistent response in overall AMOC strength to the changes in orbital forcing (Sect. ). However, it is not yet possible to confidently assert that the PMIP4 ensemble is simulating the correct response. Two obstacles need to be overcome before that can happen: (i) a greater number of proxy records obtained throughout the basin, especially during the Last Interglacial, and (ii) a significant reduction in uncertainties in the proxy data and their interpretation. Greater application of proxy system models e.g. and proxy-enabled ocean general circulation models e.g., possibly combined with data assimilation approaches e.g., could potentially resolve the latter.

Further research into the various flow components of AMOC and their respective coupling to the climate system is required before one could conclude that there were no significant interglacial changes in AMOC. It is also worth noting that all the simulations and analysis here are looking at equilibrated time slice simulations, rather than transient simulations e.g.. Our conclusion of a minimal role for overall AMOC strength changes does not, therefore, apply to abrupt events where an AMOC response has long been identified .

The AMOC during interglacial conditions has been investigated in this study using the 12 PMIP4 models that performed the midHolocene and lig127k experiments, and the changes have been compared to the AMOC simulated for the piControl experiment. Obvious differences in the AMOC strength between individual models reveal that the climate models are still struggling to accurately simulate the strength of the AMOC, as well as to capture the depth profile of the AMOC . The overall AMOC strength between either lig127k or midHolocene and piControl has not markedly changed in individual simulations (Fig. ), nor has its spatial meridional structure changed in the ensemble mean (Fig. ). The two models that show the largest changes in the lig127k experiment change in the opposite direction. Many of the models show changes in amplitude that could be explained by internal variability, rather than a forced response . It therefore seems the changes in orbital forcing in both the lig127k and midHolocene experiments have very limited impact on the overall AMOC strength. This finding is not inconsistent with available proxy reconstructions.

The surface climate fingerprints arising from internal variability in the AMOC remain largely unchanged between midHolocene, lig127k, and piControl, although there are variations amongst the models in those patterns (Fig. ). We demonstrate that, unsurprisingly, the AMOC does not play a globally important role in explaining temperature changes in the midHolocene or lig127k experiments (Fig. ). Combined with the inconsistent simulated forced response of AMOC during the PMIP4 time slice simulations, the fingerprint analysis suggests that the overall AMOC strength changes should only be invoked to explain climate changes during abrupt events in interglacials.