Introduction

The Atlantic Meridional Overturning Circulation (AMOC) is one of the key drivers of global climate variability and change, owing to its significant role in global heat redistribution. Studies have shown that a strengthening of the AMOC leads to warming and cooling in the northern and southern hemispheres, respectively1,2,3,4,5,6, with such changes further shaping various aspects of the surface climate, such as the European summer temperatures7, Atlantic hurricane activity8,9, mid-latitude jet intensity10,11, latitude of the Intertropical Convergence Zone12,13,14,15, and African/Asian/Indian monsoons16,17,18,19. Due to its wide-ranging climatic influence, the AMOC also has significant socioeconomic impacts, affecting harvest and fisheries20,21,22,23. Therefore, an accurate prediction of future AMOC change is required to minimize climate risk for the sake of socioeconomics.

Generating accurate and reliable future predictions and projections of the AMOC requires a full understanding of its: (i) response to various external forcing (e.g., orbital configurations, meltwater flux from ice sheets, and greenhouse gas concentration) and (ii) internal dynamics. The former has been intensively studied in the context of increasing greenhouse gas concentrations, leading to the current consensus that the mean AMOC intensity will weaken in response to greenhouse gas-induced warming24,25,26,27,28,29,30. This is because greenhouse warming is likely to enhance the stratification of the ocean in the North Atlantic, through increases in surface heat31,32 and freshwater33,34 fluxes (i.e., precipitation–evaporation and runoff). However, the internal dynamics of the AMOC are not yet fully understood35, despite being considered a crucial factor for decadal-scale climate predictions as a slow-varying component of the climate system36,37.

Because direct observations of the AMOC are limited, researchers have used climate models as a tool to improve knowledge of the variability of the AMOC; using model-based approaches, various mechanisms explaining the AMOC variability have been proposed. Some studies suggested that oceanic processes such as freshwater supply from the Arctic38 and the interaction between sea surface temperature (SST) variability and density-driven circulation anomalies39,40,41,42 are key processes underlying its variability. Other studies have stressed the role of the atmosphere by considering AMOC variability as an atmospheric noise-driven linear oscillator43 or an air–sea coupled mode at the interdecadal timescale44,45,46.

The North Atlantic Oscillation (NAO) is a widely known atmospheric factor that contributes to changes seen in the AMOC36,45,47,48,49,50,51,52,53,54,55. Although the NAO has been better recognized for its sub-seasonal variability, which is much shorter compared to the timescale at which ocean circulation varies56, observations show that it also exhibits annual and longer timescale variabilities36,57,58. These variabilities could physically influence the decadal and longer variability of the AMOC. For example, the NAO can modulate the AMOC intensity through changes in surface buoyancy fluxes in the deep water formation regions59,60,61,62,63,64; that is, the Labrador65,66,67,68 and Irminger Seas, Iceland basin69,70 (we shall refer the above regions as the subpolar North Atlantic [SPNA]), and Nordic Seas68,71. In ocean-only models, in which atmospheric NAO forcing is prescribed, the AMOC changes driven by the NAO are consistently simulated where it is often portrayed as positive peaks when the NAO precedes48,53,55 in lagged correlations between smoothed NAO and AMOC indices. However, ocean–atmosphere coupled global climate models (CGCMs) show a wide range in the magnitude of the correlation and the time lag in which maximum correlation appears, with many models underestimating the correlation compared to ocean-only models36,55,72. Such large uncertainty in the NAO–AMOC relationship in CGCMs could be attributed to various factors. For example, previous studies pointed out that the variability of the NAO is often underestimated in coupled climate models36,72,73 and the heat flux forcing from the NAO to the sea surface may not be well-represented over the deep water formation region55. Also, the influence of the NAO on the AMOC via the Nordic Sea deep water formation can depend on the model’s ability to represent the Nordic Sea–Atlantic Ocean exchange (e.g., through the Greenland–Scotland ridge overflow)64,74. Yet, the source of the intermodel diversity in the NAO–AMOC relationship has not yet been fully understood. In particular, the roles of oceanic processes and mean states have not been examined.

To understand why the decadal variability of the AMOC associated with the NAO differs widely in the coupled models, we analyzed preindustrial runs made with state-of-the-art CGCMs that participated in Coupled Model Intercomparison Project phase 6 (CMIP6; Table 1). Specifically, we thoroughly examined possible physical factors that could be responsible for different NAO–AMOC relationships between models, such as differences in NAO forcing or AMOC responsiveness. We show that the diverse NAO–AMOC relationships in the CGCMs are primarily shaped by oceanic mean states, which determine the sensitivity of the AMOC response to the surface buoyancy forcing induced by the NAO.

Table 1 CMIP6 model configurations and classification based on the temporal relationship between the NAO and AMOC.
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Results

Large intermodel diversity of the NAO–AMOC relationship in CMIP6

The influence of the NAO on ocean circulation manifests itself through surface fluxes. During the positive phase of the NAO, anomalous westerly winds recurring in the SPNA provide a negative surface heat and freshwater fluxes to the ocean surface; these winds yield increases in seawater density and the strengthening of deep water formation in the SPNA, which is known to be closely related to the AMOC intensity75,76,77,78. Thus, a positive NAO tends to be followed by a strong AMOC. This relationship is evaluated using lagged regression coefficients between smoothed NAO and AMOC indices (βτ where τ indicates lag). The observed NAO index can be measured as the difference between zonally averaged sea level pressure (SLP) at two latitudes during winter, with the SLP normalized at each latitude before subtracting36 (Methods). In Fig. 1a (inset), its temporal relationship with various AMOC indicators, which are derived from the SST, salinity, and subsurface temperature28,79,80,81,82 (for details, see Methods and Supplementary Fig. 1), is assessed. Although these indirect indicators do not directly represent the AMOC intensity and bear some uncertainties, being influenced by other local/remote factors83,84,85,86,87, the consistency among them suggests a significant lead of the NAO over the AMOC. Previous study88 has also reported a similar relationship in the observation where a positive NAO leads warm North Atlantic SST at the decadal timescale, which is thought to be made via heat transport of the AMOC. With the AMOC index for climate models defined as the maximum streamfunction at 40°N (Methods), most models except for 13 out of 42 reproduced a similar temporal relationship between the smoothed NAO and AMOC indices with a positive peak occurring at negative lags (‘+NAO leading +AMOC’ in Table 1; see Supplementary Fig. 2). The time lag is generally shorter in models compared to what is inferred from AMOC proxies. This could partly be attributed to the underestimation of the characteristic timescale of the NAO, indicated by significant peaks of power spectrums of the observed and simulated NAO indices (not shown). Another notable feature in the proxy-based relationship (Fig. 1a, inset) is significant negative peaks that tend to occur at positive lags, which is not simulated in CMIP6 models (discussed later). While the qualitative feature of a positive relationship where the NAO leads are largely consistent, the sensitivity of the AMOC to the NAO, which is assessed by the peak magnitude of βτ (hereafter, β, the value assessed within lag −10 to 0 years), differs greatly between the models (Fig. 1a). This shows that in CMIP6, significant intermodel diversity exists. Such diverse patterns have also been found in the coupled models of the CMIP phase 5 (CMIP5) generation55. However, for ocean-only models with the prescribed atmospheric forcing, the NAO’s influence on the AMOC was robustly simulated across models55.

Fig. 1: Simulated/Estimated NAO–AMOC relationships and their mean state dependency.
figure 1

a The maximum regression coefficients (β; unit: Sv; 1 Sv = 106 m3 s−1) when the NAO leads the AMOC by less than 10 years for each model (both 5-year filtered; see Methods and Supplementary Fig. 2). The inset shows lagged regression coefficients (βτ; unitless) of various AMOC indicators on the observed NAO index where τ indicates a lag (Methods). b A scatterplot of FMA-season climatological mean SPNA MLD (unit: m) and β. Color code for individual models follows that of (a). Regression slope for all available models is shown in black, and red is for Group 2 (closed circles) only. Open circles and crosses are for Group 1 and 3. The equations at the top left correspond to each regression line that has the same color. In the parenthesis, the goodness of fit (R2; in %) and the Pearson correlation coefficient (r) are shown. The range of observed/observation-constrained MLD (Methods) is shown by vertical solid line with a 95% confidence interval (shaded). Based on the established relationship from CMIP6 (black line and equation), β is estimated for the observed MLD (dashed line and hatched area); gray for EN4 and pink for ECCO datasets. The bold dots in the inset of (a) and the asterisk symbol ‘**’ in (b) indicate statistically significant values at the 95% confidence level, which was evaluated using a two-tailed Student’s t test. In the inset, the effective sample size was considered (Methods).

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Strong mean state-dependency of β

Figure 1b shows that the sensitivity of the AMOC to NAO (β) strongly depends on the mean characteristics of the SPNA (65°W–0°, 45°–63°N; hatched area in Fig. 2b), especially on the mixed layer depth (MLD) averaged over the strong-convection (FMA) season. Here, although both SPNA and Nordic Seas are known to be major deep water formation regions, in this study, we focus on the SPNA only because the NAO’s influence on each region is known to be different64 and the detailed physical processes in the Nordic Seas may be significantly model-dependent under the influence of overflows64,74. Among the 42 CMIP6 models, 39 (except INM-CM4–8, INM-CM5-0, and MIROC-ES2L) provided the MLD as an output variable, and it was found that the larger AMOC response tended to be induced by the NAO when the SPNA MLD was deeper on average. The correlation between the two is remarkably high (r = 0.76, black line), indicating that the mean SPNA MLD explains 58% of the variability of β. Although this high correlation value is to some extent attributable to the two models with the deepest mean MLD (GISS family), the correlation when excluding these two models (r = 0.51) still remains statistically significant at the 95% confidence level, indicating a robust relationship between the mean MLD and β. In other words, the diverse NAO–AMOC relationships in the CMIP6 models are closely related to diversity in the mean state of the SPNA. Note that no such relationship was found when the same analyze was conducted for the Nordic Seas (20°W–10°E, 65°–80°N, Supplementary Fig. 3).

Fig. 2: FMA-mean characteristics in the SPNA and the North Atlantic.
figure 2

a Sea ice concentration (SIC; unit: %) averaged over the SPNA region (hatched area in b) for each model where color code for individual models follows that of Fig. 1a. Models are arranged by descending order of the SPNA-averaged SIC. Gray vertical line divides each group. For three models in Group 3, the SIC variable was not available (N/A). b, c Ensemble mean of FMA-mean mixed layer depth (shaded; unit: m) and SIE outline (dark blue line) for each group. The number of models used for each group is shown as N. Here, SIE was defined as the boundary of the region where the sea ice concentration is maintained larger than 15%. Individual model results are shown in Supplementary Fig. 4.

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Physical relationship between MLD and β

To understand the physical factors underlying the strong MLD dependency in the NAO–AMOC relationship in CMIP6, we first examined wintertime sea ice concentration (SIC) over the SPNA. In Fig. 2a, the mean SICs for each model are shown in descending order. Here, we divided the CMIP6 models into three groups based on this result (i.e., Groups 1, 2 and 3 in Fig. 2a). The criterion for dividing Group 1 and 2 is 15%, which is the value conventionally used when defining the sea ice extent (SIE). Group 3 was defined due to data availability, not for a physical reason, so we do not conduct separate analysis on Group 3. For Group 1, the sea ice during winter extends so far southeast that it covers a wide area in the SPNA (Fig. 2b). As this sea ice cap prevents surface flux anomalies from being delivered to the ocean, the mean MLD remains shallow, and the sensitivity of the AMOC to the NAO also decreases. Therefore, the Group 1 models are in the regime of shallow mean MLD and low β in Fig. 1b (open circles). Note that the eleven models in Group 1 do not necessarily share the same ocean component (ICON-O for ICON-ESM-LR, NEMO3.4.1 for the CanESM family, MPAS-Ocean for the E3SM family, and NEMO3.6 for the EC-Earth3 family and IPSL-CM6A-LR; Table 1). Although the mean SIE is rather large in Group 1 models, we cannot conclude that this is unrealistic, since the simulated mean field in this study represent the preindustrial condition whose atmospheric greenhouse gas concentration was lower. In fact, some of Group 1 models (E3SM-1-0, EC-Earth3-Veg, and CanESM5) have a relatively high climate sensitivity compared to others89, which could have contributed to the colder mean state in the North Atlantic in the preindustrial simulation.

The second group consisted of the models that simulated smaller sea ice extent. While the cause of the low β in Group 1 can be easily understood through the sea ice cover effect, it is not straightforward why β is proportional to the mean MLD within Group 2 (r = 0.80, red line in Fig. 1b). The low sea ice concentrations and open sea surface in SPNA during winter in Group 2 (Fig. 2c and Supplementary Fig. 4) are a prerequisite for high β, but not a direct cause. The mean SIC is significantly correlated with the magnitude of β in Group 2 (r = −0.47). However, this relationship becomes insignificant when excluding one outlier of GISS-E2-1-G (r = −0.31). Thus, the strong proportionality between the MLD and β within Group 2 indicates that factors other than the sea-ice cap affect the NAO–AMOC relationship. Considering that Group 3 models (Fig. 1b, cross marks) lie well within the range where Group 2 models are located and tend to have larger β as the mean MLD is deeper, it is also likely that the same underlying physical mechanism may be applicable for Group 3.

Given that the MLD is defined based on the vertical density gradient, the ocean stratification is a possible candidate for why the MLD and β are closely related. A relatively shallow average MLD in a model indicates strong stratification. The high vertical stability in the strongly stratified models inhibits the cross-isopycnal exchange of seawater, making the lower layer insensitive to surface processes. In contrast, models with a deeper average MLD, by definition, tend to be weakly stratified. Presumably, the weak vertical stability in these models easily permits deep sinking when surface water is densified, producing a deeper water mass. In other words, under the same buoyancy loss at the surface, deep water formation is induced more effectively by convection as the ocean column is more weakly stratified65,90. Thus, when negative buoyancy forcing is applied over the SPNA surface in association with a positive NAO, AMOC strengthening can be more effectively induced in weakly stratified models.

In Fig. 3a, b, we evaluate the relationship between the mean stratification and the sensitivity of the deep water formation to the surface flux in CMIP6. In particular, given that deep convection by buoyancy loss of the surface water is a key process in maintaining the AMOC, we focus on the role of the surface buoyancy flux (i.e., heat and freshwater fluxes; Methods). The sensitivity of the deep water formation rate to the buoyancy flux (γ) was quantified for wintertime as the regression slope of anomalous MLD on the surface buoyancy flux, namely, on the effect of heat flux (γH) and freshwater flux (γF), separately. Here, among the components that constitute freshwater flux into the SPNA, that from runoff tends to be one order smaller in its magnitude compared to the net precipitation (precipitation minus evaporation [P−E]; not shown), so we do not consider the runoff effect. For the same reason and the sake of simplicity, we do not take sea ice effect into account, although its close location to the deep water formation region may have some role. Figure 3a, b show that in Group 2 (red slopes), when the model has a deeper climatological mean MLD, the magnitude of γ tends to become larger for both types of surface buoyancy forcing, indicating that the effect of the NAO can be better transmitted to the AMOC (i.e., a higher β for larger negative γ; Fig. 3c, d and schematically shown in Fig. 5). At first glance, both the mean MLD and β seem more strongly linked to γH than to γF, judging by their correlation coefficients (for example, the correlation of the MLD with γH is r = −0.75 for Group 2, which is larger in its magnitude than r = −0.61 of that with γF). However, we find no statistically significant difference, making it difficult to conclude the relative importance of heat and freshwater fluxes in shaping the intermodel diversity.

Fig. 3: Effect of mean stratification on γ and β.
figure 3

a, b Scatterplots of FMA climatological mean SPNA MLD (unit: m) and γ (a measure of the sensitivity of the deep water formation rate to each surface flux) with color code for individual models following that of Fig. 1a; (a) for buoyancy flux by heat (γH; unit: kg m−2 s−1), and (b) for buoyancy flux by freshwater (γF; unit: kg m−2 s−1). (c) and (d) show γH and γF against β. Without an outlier (GISS-E2-1-G) in (c), the correlation is −0.35, which is significant at the 95% confidence level. The notation of lines and equations follows that of Fig. 1b. Among 42 CMIP6 models, 36 models provided all variables required for (a) and (c) (MLD, heat flux, SLP, and oceanic streamfunction) except CMCC-ESM2, CMCC-CM2-SR5, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, and MIROC-ES2L. For (b) and (d) where freshwater flux is required, 32 models were used except CNRM-CM6-1, E3SM-1-1-ECA, FGOALS-g3, and MIROC6 in addition to the above. Asterisk symbols ‘*’ and ‘**’ indicate statistically significant values at the 90% and 95% confidence level, respectively.

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The role of NAO forcing

Now, we examine the possible contributions of NAO forcing to the wide intermodel spread of β. In previous studies, it has been considered that the inherent characteristics of the NAO in each model, such as the magnitude of its amplitude36,72 or how the associated surface flux pattern is simulated55 are related to the different NAO–AMOC relationships in CGCMs. If the NAO amplitude is a critical factor in shaping the NAO–AMOC relationship in climate models, the larger the amplitude of the NAO forcing, the stronger its influence on the AMOC (i.e., higher β). To examine whether such relationship exists for CMIP6 models, we measure the NAO amplitude as the contrast of between maximum and minimum pressure anomalies that is induced by the NAO in the North Atlantic (see Methods). However, Fig. 4a shows that there was no significant relationship between β and NAO amplitude at the decadal timescale. Similar analysis was repeated with unsmoothed NAO index (Supplementary Fig. 5) and again, no significant contribution of the NAO amplitude to β was found. We also investigated a different definition of the NAO amplitude: the standard deviation of the zonal mean SLP differences at each latitude (without normalizing). In this case as well, the interannual or low-frequency variability of the NAO was not a good predictor for β (r = −0.21 and −0.25, respectively, both not statistically significant). Thus, we conclude that the NAO amplitude is unlikely to be a major factor in shaping different NAO–AMOC relationships between CMIP6 models. It is also worth discussing that in Fig. 4a, 20 out of 42 models simulated the decadal variability of the NAO close to the observed value (8.415, the bias being less than 5%), which is located exactly at median (i.e., 21 models simulate smaller values than the observation, and 21 models simulate larger values). This differs from previous studies that reported underestimation of low-frequency variability of the NAO in climate models36,72,73, which may be attributed to differences in a generation of models (i.e., CMIP5 and CMIP6) and/or a definition of the NAO amplitude.

Fig. 4: Role of the NAO forcing in β diversity.
figure 4

a Scatterplot of the amplitude (unit: hPa; see Methods for the definition) of decadal NAO forcing and β (unit: Sv) with color code for individual models following that of Fig. 1a. b, c: as in (a), but for αH (unit: W m−2) and αF (unit: mm day−1) on the x-axis. αH and αF are used as a measure of the NAO efficiency to induce surface heat and freshwater flux at decadal timescale, respectively. The notation of lines and equations follows that of Fig. 1b. The qualitative results are insensitive to the window length. Among 42 CMIP6 models, 36 models provided all variables required for (a) and (b) (heat flux, SLP, and oceanic streamfunction) except CMCC-ESM2, CMCC-CM2-SR5, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, and MIROC-ES2L. For (c) where freshwater flux is required, 32 models were used except CNRM-CM6-1, E3SM-1-1-ECA, FGOALS-g3, and MIROC6, and MIROC-ES2L. Asterisk symbols ‘*’ and ‘**’ indicate statistically significant values at the 90% and 95% confidence levels, respectively.

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Another possible contributor to diverse NAO–AMOC relationships is the spatial pattern of the surface flux forcing induced by the NAO. Although CMIP6 models generally well-reproduce the dipole structure of the NAO (Supplementary Fig. 6), the detailed spatial feature somewhat differs between models, being consistent with a previous study that used the CMIP5 models91. It further leads to different surface flux forcing patterns to the SPNA surface (Supplementary Figs. 7, 8). Xu et al.55 showed that in a coupled model in which the NAO does not induce significant heat flux anomalies in the deep water formation region, the NAO–AMOC relationship is not well-simulated. We also found that in Group 1, the region where the NAO induced significant heat and freshwater flux anomalies tended to be inconsistent with the climatological deep-convection site (Supplementary Figs. 7, 8). Thus, the spatial pattern of NAO forcing, in addition to the insulation created by the sea ice, contributed to the weak influence of the NAO on the AMOC in Group 1. Similarly, in the three models in Group 2 (ACCESS-CM2, ACCESS-ESM-1-5, and CNRM-ESM2-1) that simulate low β, the NAO forcing region does not match the deep water formation region well. However, in most of the Group 2 models (22 out of 25), the regions of significant NAO forcing and that of deep water formation are generally co-localized. Therefore, how well the surface flux pattern is overlapped with the deep water formation region can explain the diverse NAO–AMOC relationships only in a limited manner, particularly for models with low β.

Furthermore, we quantitatively examined the effect of the NAO’s efficiency in inducing the buoyancy flux anomaly in the SPNA, as the regression slope (α) of the SPNA-averaged buoyancy flux anomalies onto the NAO index. Again, both heat and freshwater fluxes were considered by αH and αF. The relationships between α and β (Fig. 4b, c) suggest that the stronger the surface buoyancy flux induced by the NAO (large negative α), the greater the sensitivity of the AMOC to the NAO (high β) when all models are considered (black lines). This relationship partly depends on the small α and low β of Group 1 (open circles), which arise from the sea ice cover effect. The relationship between α and β within Group 2 is rather weak (red lines) and substantially affected by a single extreme case (GISS-E2-1-G). Without GISS-E2-1-G, neither αH nor αF significantly contributes to the β diversity (r = −0.15 and r = −0.24, respectively). Therefore, we conclude that the β diversity is to some extent physically related to the synchronicity between the NAO forcing and deep water formation regions and the surface forcing efficiency of the NAO, but they are not likely to be a direct factor to determine β, particularly in Group 2.

Discussion

Through the analyses above, it has been shown that the spread of β in CMIP6 is strongly linked to how the mean climate states are simulated; if the sea ice extends too far to cover the SPNA or the upper-level ocean stratification in the SPNA is strong, the surface forcing caused by the NAO does not effectively lead to AMOC change. On the other hand, if the SPNA surface remains open during winter and the oceanic stratification is relatively weak, the NAO forcing easily perturbs the deep water formation rate of the AMOC, yielding a positive relationship where the NAO leads the AMOC. This implies that if the average oceanic state is similar between the models, the influence of the NAO on the AMOC variability is also expected to be similar. Indeed, for ocean-only models whose mean states are less diverse (e.g., comparing Fig. 13 of Danabasoglu et al.92 and Supplementary Fig. 4), the relationship where the NAO leads the AMOC is consistent among these models55. The small diversity in ocean models further suggests that differences in model configurations (e.g., parameterization schemes for vertical mixing) have a relatively minor effect on the intermodel spread when they are not coupled to atmospheric models. That is, the atmosphere–ocean feedback processes in CGCMs are likely the key factor that enables small biases to grow and constitute the different oceanic mean states in the SPNA across models, and hence, the NAO–AMOC relationship. In ocean-only models, as the prescribed atmospheric field lowers the degree of freedom, prohibiting the two-way interaction between the atmosphere and ocean, oceanic states appear less diverse.

So far, the influence of the NAO on the AMOC has been investigated for a decadal and longer timescale, from which a further question may be raised: where does atmospheric low-frequency (annual and longer) variability come from? Previous studies have proposed evidence of oceanic influence on the Atlantic atmospheric variability based on climate models. For example, Wen et al.54 and Gastineau and Frankignoul93 suggested that changes in the NAO could be driven by the internal variability of ocean circulation. Msadek and Frankignoul94 and Sun et al.45 suggested a coupled atmosphere–ocean variability, where the atmosphere-induced AMOC change feeds back the atmosphere through meridional heat transport and sea surface warming using IPSL-CM4 and CCSM3 climate models, respectively. For the estimated result for the observation (Fig. 1, inset), the negative peaks of the NAO–AMOC relationship, when the AMOC proxies lead the NAO, imply the possibility for such a coupled mode to operate in situ. In CMIP6, on the other hand, the AMOC influence on the NAO (i.e., correlations when the AMOC leads) is somewhat unclear and depends on the model (Supplementary Fig. 2), suggesting that the feedback from the AMOC to the NAO is weak or absent in most models. Since fast response of the atmosphere to the ocean forcing may be more notable at the interannual timescale (i.e., without applying a low-pass filter), we also investigated the influence of the AMOC on the NAO using raw annual time series. However, no clear evidence of coupled mode was found (not shown). Therefore, further investigation at an individual model level is required to identify how NAO variability is affected by oceanic processes in the CMIP6 models.

Summary and implications

It is thought that to improve climatic predictions in the Northern Hemisphere, climate models should be capable of simulating the NAO–AMOC relationship36. This is because the AMOC fluctuation, which significantly modulates the North Atlantic surface temperature, can be driven by changes in the NAO. The NAO–AMOC relationship was robustly simulated in ocean-only models when NAO-type atmospheric forcing was prescribed; however, this was not the case in fully coupled models where the models were allowed to resolve two-way air–sea feedback. This study thus attempted to determine what causes inconsistent, different NAO–AMOC relationships in coupled models based on a quantitative comparison, and to provide hints for a better simulation of AMOC variability. As a result, we found that models with a deep SPNA MLD tend to simulate the high sensitivity of the AMOC to the NAO. This relationship is related to two important factors: (i) the sea-ice cover effect in shallow-MLD models and (ii) the high sensitivity of deep convection to surface buoyancy forcing in deep-MLD models. Judging from the difference between ocean-only models and coupled models, the diverse mean MLDs in the SPNA can further be attributed to the two-way interaction between the atmospheric and oceanic fields. The above processes are schematically illustrated in Fig. 5.

Fig. 5: Schematic representation of NAO influence on the AMOC for each group.
figure 5

This schematic illustrates why coupled climate models simulate different sensitivities of the AMOC to the NAO (β). Colored box indicates a group of models that share the similar background states; pink for Group 1 and blue for Group 2. ‘SIE’ means sea ice extent and ‘DWF’ represents deep water formation. See Text for more detailed illustration.

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These results provide valuable insights into decadal climate predictions. First, they emphasized that the key to improving the NAO-related AMOC variability in climate models (ultimately, to help improving the predictability of the northern hemisphere surface climate) might lie in the intermediate process by which the NAO signal is delivered to the AMOC, and it may eventually be achieved by reducing biases in the mean state. This result is different from ones brought forth by previous studies that focused more on the role of NAO forcing. Nevertheless, our results do not completely rule out this established viewpoint, as the NAO forcing pattern and efficiency also contribute to the β diversity to some extent. Second, the strong mean-state dependency of β provides some potential for using the observed NAO index to estimate AMOC strength for the next decade. Here, while β itself does not provide detailed information of time lag (which instead, can be inferred from the relationship between the observed NAO and AMOC proxies in Fig. 1a, inset), it can be used to estimate the magnitude of the AMOC change. The CMIP6-based regressive relationship implies an AMOC sensitivity of 0.53 (0.47) Sv per unit NAO change for the observed MLD of 450.30 (402.44) m in the EN4 (ECCO) dataset (Fig. 1b and Methods). It is also noteworthy that CMIP6 models tend to underestimate the NAO influence on AMOC variability, given that the majority of the models (37 out of 42 models) underestimated the mean MLD. Finally, according to climate models, anthropogenic greenhouse gas warming is expected to strengthen oceanic stratification through surface heat and/or freshwater fluxes, shoaling the MLD32,95,96,97. Overall, this study suggests that the future AMOC is likely to be less sensitive to NAO change, providing important insights for decadal prediction under climate change. Indeed, Ma et al.98 has reported a diminished relationship between the NAO and the AMOC in a greenhouse gas-forced simulation compared to the preindustrial, although a positive NAO induced negative AMOC in their study due presumably to the model-specific deep water formation site. It should also be noted that climate change modulates characteristics of the NAO and AMOC as well, such as their amplitude, frequency, and mean intensity26,98,99,100,101, which will affect future NAO–AMOC interactions.

Methods

Observational dataset

We used the Hadley Centre’s monthly historical mean SLP dataset102 (HadSLP2) for the NAO index and the monthly Extended Reconstructed Sea Surface Temperature version 4103 (ERSST v4) for the SST-based AMOC indices for the period 1854–2015. For one of the salinity-based AMOC indices, the Hadley Centre EN4 dataset104 (EN4) for the period 1950–2019. The other salinity-based index was obtained from a combination of two datasets, ISHII105 and Scripps106,107 (1945–2019) where the ISHII data was used for the period before 2012, and the Scripps data for the subsequent period.

The MLD was retrieved from two datasets. One was derived using the oceanic temperature and salinity obtained from EN4. Because the vertical grid spacing becomes relatively coarse below 100 m, linear interpolation was first applied to the temperature and salinity at a 5-m interval. The potential density was then calculated, and the MLD was defined as the depth at which the potential density differed from the surface value by 0.125 kg m−3. The other is the ECCO Version 4, Release 4 (v4r4)108, which is a general circulation model (MITgcm) result constrained by satellite and in situ observations for the period 1992–2017. In this dataset, the MLD is defined using a different criterion; the depth at which the temperature differed from the surface value by 0.8 °C. Since no significant trend over time was found in the MLD derived from EN4 (which has a longer data length), we assume that the regression model obtained from CMIP6 preindustrial runs (Fig. 1b) can be employed for the more recent observation.

All observational data were linearly detrended at the beginning of any calculation to eliminate the effect of anthropogenic forcing and to focus on the natural variability.

Index definition

For the CMIP6 models, the AMOC index was defined as the maximum streamfunction at 40°N and below 500 m in the Atlantic basin80. A latitude of 40°N was chosen to focus on the specific process associated with the AMOC: sinking at high latitudes by deep water formation. It is also known that the AMOC definitions at lower latitudes tend to vary coherently with that at 40°N with time lag109,110,111.

To estimate the observed AMOC intensity, five indirect AMOC indices were used because the data obtained via direct observation is insufficient (Supplementary Fig. 1 and inset of Fig. 1). The SST-based index of Ramhstorf et al.28 (AMOC_SST_R2015) is defined as the difference of SST between the subpolar gyre region and the Northern Hemisphere by subtracting the latter from the former. By this, the temperature in the subpolar area, where changes in the ocean circulation leave their characteristic footprint on the sea surface79, is isolated from the anthropogenically-induced large-scale temperature changes (represented by the Northern Hemisphere mean temperature). The subpolar gyre region was selected as the area whose linear trend of the SST is negative during the period 1880–2015112. The AMOC_SST_C2018 index is a modified version of AMOC_SST_R2015, developed by Caesar et al.79 It is defined as the subpolar North Atlantic SST minus global mean SST during wintertime (November to May). The third and fourth indirect indices are derived from the salinity, using the same definition but different datasets. Based on the fact that the AMOC transports salty water from the subtropics to the subpolar region, they are defined as the integrated salinity in 0–1500 m and 45–65° N in the Atlantic81. The EN4 dataset (1950–2019) and ISHII and Scripps dataset (1945–2019) were used for AMOC_salt_EN4 and AMOC_salt_I + S, respectively. Finally, the fingerprint index of Zhang80 (AMOC_Tsub_Z2008) is obtained from the first principal component of the leading mode of the annual mean subsurface (400 m) temperature using the EN4 temperature. This index reflects the realignment of the oceanic current system that involves northern recirculation gyre and western boundary currents with changes in the AMOC strength. All proxies are normalized to indicate whether the AMOC is in an anomalously strong or weak state (i.e. qualitative feature of temporal evolution of the AMOC) and to be compared with each other (Supplementary Fig. 1). Although these indirect AMOC indices were developed upon physical basis, it should be borne in mind that the SST and salinity as well as the subsurface temperature in the North Atlantic can also be modulated by other sources than the AMOC, such as external forcings83,84,113,114,115,116 or forcings from other areas85,86,87.

The observed/modeled NAO index was defined as follows. First, correlations of zonally averaged sea level pressure (SLP; where X indicates the zonal mean of X) in the Atlantic basin (80°W–30°E) between any two latitudes were calculated; then, the two latitudes with the largest negative correlations were identified in each model or observation. The difference in the normalized SLP between those two latitudes was defined as the NAO index36. It represents the SLP contrast between the Subtropical (Azores) High and the Subpolar Low, and it is similar to the conventional station-based definition which is more widely used, except that the former is defined as the difference between two latitudes and the latter as the difference between the two points (Lisbon, Portugal and Stykkisholmur/Reykjavik, Iceland)117. The major difference in physical meaning is that the NAO definition used here considers the spatial structure of the NAO, which could depend on the individual model, instead of using fixed station points.

As NAO variability is known to be most pronounced during boreal winter, DJF-mean values are taken for all variables when conducting the regression analysis related to the NAO forcing.

NAO amplitude

The amplitude of a climate variability is often measured as the standard deviation of its index time series. However, since the above definition of the NAO index requires normalization at each latitude as a preprocess, the standard deviation of the final index does not appropriately represent the magnitude of variability of the NAO. Thus, as an alternative, we normalize the NAO index and regress the SLP anomalies at each grid point to it so that the regression slope represents the SLP anomaly (in hPa) induced by a unit NAO index change. Then, the difference between maximum and minimum SLPs in the North Atlantic, which are detected at the cores of high and low pressures systems, is defined as the NAO amplitude.

Quantitative evaluation of α, β, and γ

All variables were linearly detrended before the following analysis to avoid being affected by any model drift. The AMOC sensitivity to NAO (β) was measured based on linear regression analysis using

$${{{\mathrm{AMOC}}}}\left( t \right) = b_\tau + \beta _\tau \cdot {{{\mathrm{NAO}}}}\left( {t + \tau } \right)$$
(1)

where τ represents the time lag (years), and bτ and βτ indicate the y-intercept and slope corresponding to lag τ, respectively. To reflect the intrinsic timescale of the AMOC associated with its large inertia, the NAO and AMOC indices were smoothed using a 5-year low-pass Lanczos filter before calculating βτ. The qualitative result (i.e., strong dependency of the NAO–AMOC relationship on the mean MLD; see Text) is not sensitive to the choice of window length or cutoff period. The results of βτ for each model are shown in Supplementary Fig. 2 for a lag τ between −20 and 20 years (a negative value indicates that the NAO leads).

In general, there is qualitative agreement in CMIP6 models that a positive peak appears when the NAO leads or co-occurs with the AMOC, namely, between lag −10 and 0 (Supplementary Fig. 2). Considering that the AMOC index represents a basin-wide large-scale circulation rather than a local process, the exact locations of the peaks may depend on the model. Therefore, for a quantitative comparison between models, AMOC sensitivity to NAO (β) was defined as the maximum βτ between lag −10 and 0. The results in Fig. 1a reveal a difference between the smallest (−0.029 Sv for EC-Earth3-CC) and the largest (1.273 Sv for GISS-E2-1-G) cases by two orders of magnitude.

Similarly, α and γ are measured as the regression slope as follows:

$${{{\mathrm{Flux}}}}\left( t \right) = a + \alpha \cdot {{{\mathrm{NAO}}}}\left( t \right)$$
(2)

and

$${{{\mathrm{MLD}}}}\left( t \right) = c + \gamma \cdot {{{\mathrm{Flux}}}}\left( t \right)$$
(3)

Here, Flux is the surface heat or freshwater flux from the atmosphere to the ocean, and a and c are the y-intercepts. The time lag is not considered when measuring α and γ, because interactions between the NAO and the surface fluxes and between the surface fluxes and the MLD are most efficient at lag 0.

Effective sample size of auto-correlated data

For the temporal correlated data such as low-pass filtered NAO/AMOC index in this study, its ‘effective’ sample size is less than the number of individual sample measurements (i.e., the number of time steps in time series). When evaluating the statistical significance of the correlation/regression coefficients between such auto-correlated two datasets with a raw sample size of N, the effective sample size (Neff) can be taken into account by using the following formula36,50,118:

$$\frac{1}{{N_{{{{\mathrm{eff}}}}}}} \approx \frac{1}{N} + \frac{2}{N}\mathop {\sum}\limits_{j = 1}^N {\frac{{N - j}}{N}\rho _{xx}\left( j \right)\rho _{yy}\left( j \right)}$$
(4)

where ρxx(j) and ρyy(j) are the autocorrelations at lag j for each data x and y. With this effective sample size, we evaluated the statistical significance of regression slopes (α, β, and γ) using the two-tailed Student’s t-test.

Buoyancy flux by heat and freshwater

To facilitate direct comparison of heat and freshwater effects on MLD deepening, we derived surface buoyancy flux by heat (Bh) and by freshwater (Bw) using bulk formula119 so that Bh and Bw have the same unit (kg m−2 s−1). Bh and Bw are then substituted into Flux(t) when calculating γ. Bh is obtained from

$$B_{{{\mathrm{h}}}} = \frac{{\alpha _{{{\mathrm{h}}}}Q_{{{{\mathrm{net}}}}}}}{{C_{{{\mathrm{p}}}}}}$$
(5)

where αh and Cp are the thermal expansion coefficient (10−4 K−1) and specific heat of the seawater (4000 J K−1 kg−1)120, assumed to be constants for the sake of simplicity. Qnet is the net surface heat flux.

The buoyancy flux by freshwater flux (Bw) is given by

$$B_{{{\mathrm{w}}}} = \beta _{{{\mathrm{w}}}}\rho S\left( {P - E} \right)$$
(6)

Similarly, the haline contraction coefficient (βw = 8.0 × 10−4 psu−1), water density (ρ = 1022.4 kg m−3), and the sea surface salinity (S = 35 psu)120 are regarded as constants. P and E represent precipitation and evaporation, respectively.