Interdecadal variations of the AMOC components at 26.5°N. Figure 1a shows the decadally averaged time series of the AMOC anomalies at 26.5°N from the decade centered in 1960 (i.e., 1955-64) to the decade centered in 2050 (i.e., 2045-54), derived from CESM2 (green), OMIP2 (blue) and RAPID (magenta). To allow a better visual comparison of the three interdecadal AMOC time series, the time-averaged RAPID AMOC transport value of 16.7 Sv is removed from each time series (Methods). Hereafter, the decade centered in a particular year is simply denoted as the centered year (e.g., the period of 1985-94 is denoted as 1990). The AMOC values derived from OMIP2 and RAPID are referred to as the total component, and those from the ensemble mean of CESM2 as the externally forced component. The differences between the two (i.e., total - externally forced) are referred to as the residual component (orange bars in Fig. 1a), which would represent natural variability provided OMIP2 and CESM2 yield realistic levels of the total and externally forced AMOC components, respectively. It should be noted that the relative strengths of the three AMOC components are sensitive to the AMOC adjustments (i.e., bias corrections) in OMIP2 and CESM2 (Methods); thus, our analysis is for the most part based on the rate of interdecadal change in the AMOC (Fig. 1b) since it is not affected by the adjustments in OMIP2 and CESM2.
As shown in Fig. 1a, the total and externally forced AMOC components show a similar interdecadal swing with an increase from 1960 to 1990 and a decrease from 2000 to 2020. This suggests that the interdecadal variation in the AMOC from 1960 to 2020 represents a response to the external forcing. However, the total AMOC peaks in 2000, whereas the externally forced AMOC component peaks in 1980-90. Additionally, the internal variability in the CESM2 ensembles (i.e., error bars in Fig. 1a, Methods) is much larger than the externally forced signals; thus, the interdecadal AMOC swing from 1960 to 2020 could also be of natural origin45–47. Indeed, the total increase from 1960 to 1990 is much greater than the externally forced increase during that period, whereas the total decrease from 2000 to 2020 is much weaker than the externally forced decrease during that period (Figs. 1a and 1b). Thus, the residual component is strongly negative prior to 1990 and positive afterward (Fig. 1a).
More specifically, the residual component contributes + 1.1 Sv to the total increase between 1960 and 1990. Thus, the total increase in the AMOC from 1960 to 1990 (+ 2.2 Sv) can be partitioned into a + 1.1 Sv increase (50%) in the externally forced component and a + 1.1 Sv increase (50%) in the residual component (Fig. 1b). It appears that the external forcing plays a major role in increasing the AMOC from 1960 to 1980 (Fig. 1b). However, a steep increase in the residual component from 1980 to 1990 (+ 1.6 Sv) is almost completely responsible for the AMOC increase during that period (Fig. 1b). After reaching its peak in 1980-90, the externally forced component starts decreasing. From 1990 to 2000, it decreases by -0.6 Sv. However, the total AMOC continues to increase moderately by + 0.4 Sv due to a large increase in the residual component (+ 1.0 Sv). Thus, the external forcing is not the primary driver of the AMOC increase from 1980 to 2000 in agreement with previous studies48,49.
As indicated in Figs. 1a and 1b, the decrease in the externally forced AMOC component from 2000 to 2020 (i.e., due to increased CO2 and reduced aerosol loading) is -2.6 Sv. This is mitigated by a + 1.0 Sv increase in the residual component, yielding a -1.6 Sv decrease in the total. Although this is somewhat small (i.e., a 10% of the total), it is important to note that the external forcing is the sole driver of the AMOC slowdown from 2000 to 2020. This result is in disagreement with the conventional argument that the reduction of the AMOC after its peak in 2000 is largely due to the concurrent weakening of the NAO24–29. In contrast to that argument, the residual component remains positive and continues to increase overall after 1990, despite a small decrease from 2000 to 2010, and thus largely mitigates the externally forced weakening of the AMOC after 1990 (Figs. 1a and 1b). The mitigating effect of the residual component becomes quite strong during the recent period from 2010 to 2020 (+ 1.1 Sv); thus, the externally forced weakening of the AMOC (-1.3 Sv) is nearly compensated for during that period (Fig. 1b).
The interdecadal variation of the externally forced AMOC component derived from CESM2 is largely consistent with that derived from CMIP6 and SPEAR (Fig. 2). However, several differences are noteworthy. For instance, the rate of weakening in the externally forced component (after 1990) is generally smaller in CMIP6 compared to that of CESM2 and SPEAR although the inter-model spread is very large among the 20 CMIP6 models used in this study (i.e., error bars in Fig. 2a, Methods). In particular, the rate of interdecadal weakening in the externally forced component from 2000 to 2010 is smallest in CMIP6 (-0.8 Sv), slightly larger in SPEAR (-0.9 Sv) and largest in CESM2 (-1.3 Sv). Accordingly, the residual AMOC component decreases from 2000 to 2010 by -0.6 Sv if CMIP6 is used to represent the externally forced component, -0.5 Sv if SPEAR is used, and only − 0.1 Sv if CESM2 is used. Thus, the residual component plays an active role in the weakening of the AMOC from 2000 to 2010 (-1.4 Sv) if either CMIP6 or SPEAR is used to represent the externally forced component.
In summary, our analysis suggests that the increase in the AMOC at 26.5°N from 1980 to 2000 is mainly driven by an increase in the residual component while the external forcing suppresses the increase in the AMOC from 1990 to 2000. In contrast, the slowdown of the AMOC at 26.5°N from 2000 to 2010 is primarily driven by the external forcing and possibly augmented by the residual component. From 2010 to 2020, however, a large increase in the residual component nearly compensates for the externally forced weakening of the AMOC. In the next section, we examine if the interdecadal variation of the residual AMOC component can be ratified as a physically consistent response to its main driver - interdecadal NAO variability37–44.
Interdecadal variation of the residual AMOC. The residual component represents not only natural variability of the AMOC, but also deficiencies in the climate and surface-forced ocean models used involving, for instance, the lack of land-ice melting, and the insufficient model resolution for boundary currents, deep water formation, and mesoscale eddies50. Therefore, in this section, we investigate if the residual component reasonably represents natural variability despite potential contaminations arising from deficiencies in the climate and surface-forced ocean models used. If we assume that the residual component reflects natural variability to a reasonable degree, Figs. 1a and 1b suggest that natural variability keeps the AMOC in a relatively weakened state from 1960 to 1980 and then produces a steep increase from 1980 to 1990 in tandem with the external forcing during 1960-80. Then, it works against the external forcing to mitigate the slowdown of the AMOC from 1990 to 2020. As such, the residual AMOC component at 26.5°N increases greatly from 1980 to 2020 (+ 3.6 Sv). Figure 1b further shows that the increase occurs mainly during three interdecadal periods from 1980 to 1990 (+ 1.6 Sv), from 1990 to 2000 (+ 1.0 Sv), and from 2010 to 2020 (+ 1.1 Sv). As shown in Fig. 2, if either CMIP6 or SPEAR is used to represent the externally forced component, the corresponding residual AMOC transports show similar interdecadal variations.
Given the well-known physical relationship between the NAO-induced surface buoyancy flux, deep convection in the subpolar North Atlantic, and the AMOC37–44, we examine if the interdecadal increases in the residual AMOC at 26.5°N during the 1980s, 1990s and 2010s (Figs. 1b, 2b and 2d) can be explained as a physically consistent response to interdecadal NAO variability. As indicated in Fig. 3 (top panel), a strong negative December-May NAO prevailed from 1960 to 1970 (Methods). After a pause (i.e., a neutral NAO) in 1980, it switched to a strong positive NAO in 1990, and then weakened to a neutral NAO in 2000 and 2010. This was followed by the development of another strong positive NAO in 2020.
The development of a strong positive NAO in 1990 from a neutral NAO in 1980 aligns well with the large increase in the residual AMOC from 1980 to 1990. Similarly, the development of another strong positive NAO in 2020 from a neutral NAO in 2010 matches well with the large increase in the residual AMOC from 2010 to 2020. However, no such direct relationship between the NAO and residual AMOC is found in other interdecadal periods. For instance, the strong negative NAO in 1960 and 1970 turned into a neutral NAO in 1980, but the residual AMOC remains strongly negative in 1980. Additionally, the strong positive NAO in 1990 turned into a neutral NAO phase in 2000. However, the residual AMOC persists and even increases from 1990 to 2000.
Thus, it appears that when a strong NAO develops and continues for a decade, it provides sufficient momentum and duration for the AMOC to spin up during that decade. Furthermore, if the strong NAO recedes into a neutral NAO in the next decade, the NAO-driven residual AMOC state tends to persist and even intensify throughout the neutral phase that follows. These results are by and large consistent with the NAO leading the AMOC at 26.5°N by 3–15 years in the majority of climate and surface-forced ocean models40,42,43. Thus, at interdecadal time scales, the residual AMOC at 26.5°N may be roughly regarded as a time-integrated response to the NAO39,40,51 as shown in Fig. 3 (top panel). More specifically, the NAO-driven surface buoyancy flux is integrated into ocean density changes in the subpolar North Atlantic producing a meridional ocean density gradient anomaly between the subpolar and subtropical North Atlantic Ocean. The NAO-driven surface buoyancy flux continues to drive the anomalous density gradient until the NAO turns into a neutral phase. Thus, the anomalous ocean density gradient increases until a strong NAO turns into a neutral phase, and then remains at that amplitude while the neutral NAO condition continues. The anomalous meridional density gradient in turn should drive the residual AMOC via dynamic ocean adjustment processes with a time delay. Thus, the residual AMOC at 26.5°N can be described as a delayed ocean dynamic adjustment to the time-integrated NAO (hereafter, a time-integrated & delayed response to the NAO). However, if the neutral NAO continues for an extended period, the anomalous density gradient should be eventually dissipated by the residual AMOC-driven meridional heat and salt transports; thus, the residual AMOC should also be dissipated, but it may take much longer than a decade for that to happen.
To validate the above rationale, we use the December-May NAO and the residual AMOC derived from the 80-member CESM2 ensembles to carry out a composite analysis. First, the NAO index time series is computed and averaged for each decade from 1850 to 2020 for the entire 80 ensembles to derive a total of 1,360 decadal NAO index samples (Methods). These samples are then sorted to identify positive NAO (upper-terciles), neutral NAO (mid-terciles) and negative NAO cases (lower-terciles). The first composite is under a negative NAO during the first decade followed by a neutral NAO during the subsequent decade (case-1). The second composite is under a neutral NAO during the first decade followed by a positive NAO in the subsequent decade (case-2). The third composite is under a positive NAO phase during the first decade followed by a neutral NAO during the subsequent decade (case-3).
As shown in Fig. 3 (middle and bottom panels), if a negative NAO develops and persists for a decade, the residual AMOC decreases during that decade (case-1). Similarly, if a positive NAO develops and continues for a decade, the residual AMOC increases during that decade (case-3). If the negative or positive NAO recedes into a neutral NAO during the subsequent decade, the NAO-driven residual AMOC state largely persists in the subtropical North Atlantic throughout the neutral phase that follows, and even intensifies in some latitudes (cases-1 and − 3). Additionally, if a neutral NAO persists for a decade followed by a positive NAO for the subsequent decade, the residual AMOC increases during the latter decade (case-2). Thus, the composite analysis supports the relationship between the NAO and the residual AMOC at 26.5°N shown in Fig. 3 (top panel) and thus the rationale that at interdecadal time scale the residual AMOC at 26.5°N can be regarded as a time-integrated & delayed response to the NAO.
It is worthwhile to note that the residual AMOC component at 26.5°N decreases from 2000 to 2010 (Figs. 1b, 2b & 2d) although the extent of the decrease depends on the climate model used to represent the externally forced component. This decrease appears to be a dissipation of the elevated residual AMOC in response to the prolonged near-neutral NAO condition during 2000 and 2010 (Fig. 3, upper panel).
An important point to note from the case-1 and case-3 is that while the residual AMOC remains strong in the subtropical region during the neutral NAO period in the latter decade, it tends to dissipate in the subpolar region during that period. This result is in agreement with previous modeling studies39,42, and suggests that the residual AMOC in the subpolar region responds much more quickly and directly to the NAO-driven deep convection anomalies compared to the residual AMOC in the subtropical region. See Supplementary Fig. 4 for the residual AMOC responses to the nine different possible cases of interdecadal NAO variability.
To summarize, we show in Fig. 4 the sea level pressure anomalies in December-May for each decade from 1960 to 2020 derived from the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis-5 (ERA5)52 and the implied interdecadal changes (i.e., the difference between the first and subsequent decades) in the residual AMOC derived from the composite analysis. The development of a strong positive NAO in 1990 from a neutral NAO in 1980 increases the residual AMOC from 1980 to 1990, and the development of another strong positive NAO in 2020 from a neutral NAO in 2010 increases the residual AMOC from 2010 to 2020, consistent with case-2. The strong negative NAO in 1960 and 1970 turned into a neutral NAO in 1980, but the residual AMOC remains negative and slightly decreases further in 1980 in the subtropical North Atlantic, consistent with case-1. Lastly, the strong positive NAO in 1990 turned into a neutral NAO in 2000, but the residual AMOC remains positive and increases in the subtropical North Atlantic between 1990 and 2000, consistent with case-3.
Potential decadal predictability of the residual AMOC. The externally forced AMOC weakening is projected to continue in the next decade and beyond throughout the rest of the 21st century (Supplementary Figs. 1c, 2c & 3c). Between 2020 and 2030, for instance, the AMOC at 26.5°N is expected to weaken by -0.8 Sv according to CESM2 (Figs. 1a and 1b). Therefore, in reference to the observed value of the AMOC during 2015-21 (i.e., 16.6 Sv), the expected mean value of the AMOC at 26.5°N in 2030 is 15.8 Sv assuming that the residual AMOC in 2020 remains the same in the next decade. A similar value of 15.9 Sv is projected from both CMIP6 and SPEAR. However, based on the composite analysis and previous studies39,40,42,43, the residual AMOC at 26.5°N may stay elevated and further increase during the next decade as a time-integrated & delayed response to the strong positive NAO in 2020. Thus, we further explore in this section the potential decadal predictability of the residual AMOC at 26.5°N.
We first explore the lead-lag correlations between the December-May NAO index and the residual AMOC at 26.5°N derived from all 80-member CESM2 ensembles. As shown in Fig. 5a, the correlations tend to be maximized when the NAO leads the residual AMOC by 0 ~ 15 years. For some ensemble members, the maximum correlations are quite high exceeding the 95% confidence level. However, the ensemble spread is very high; thus, when all 80 ensemble members are merged together (green line), the maximum correlation drops below the 95% confidence level, in agreement with an earlier study based on the Coupled Model Intercomparison Project Phase 5 (CMIP5) models43. Therefore, despite the positive correlation between the NAO and residual AMOC, the history of NAO is not a reliable predictor of the residual AMOC at 26.5°N for the future. A consistent result is found when either 22 CMIP6 models under the preindustrial scenario (Supplementary Table 2) or 30 ensemble members of SPEAR are used to compute the lead-lag correlations between the December-May NAO index and the residual AMOC at 26.5°N (Figs. 5b and 5c).
We next explore if the history of the residual AMOC serves as a potential predictor for the future evolution of the residual AMOC. Figure 5d shows the autocorrelations of the residual AMOC derived from the CESM2 ensembles. When all 80 ensemble members are merged together (green line), the autocorrelations are statistically significant above the 95% confidence level at the time lead-lag of 13-year and shorter. Additionally, for the majority of the ensemble members (i.e., 71 out of 80), the autocorrelation values are above the 95% confidence level at the time lead-lag of 10-year, suggesting that the history of the residual AMOC is a potential source for predicting the future residual AMOC. This result is not very surprising since the history of the NAO forcing is implicitly integrated into the residual AMOC of the past. Additionally, the initialization of the AMOC has been shown to be a useful source of decadal predictability of, if there is any, potential internal oscillations53. A similar result is found from the 22 CMIP6 preindustrial runs (Fig. 5e). However, the autocorrelation values from the 30-ensemble SPEAR are significant only for the subsequent 1–6 years (Fig. 5f).
Based on the above result, the residual AMOC values at 26.5°N averaged for each decade from 1850 to 2020 are plotted against the residual AMOC values for the corresponding subsequent 1–5 years (Fig. 5g). For instance, the residual AMOC averaged for 2005-14 is plotted against the residual AMOC averaged for 2015-19. As expected, the residual AMOC during a past decade appears to be useful for predicting the residual AMOC in the subsequent 1–5 years. The mean slope is about 0.8. This means that if the residual AMOC value of + 2.2 Sv for 2015-21 is used (Fig. 1a), the expected value of the residual AMOC during 2022-26 is about + 1.7 Sv. According to CMIP6 and SPEAR, this value is reduced to + 1.0 Sv in both cases (Figs. 5h and 5i). Therefore, we can conclude based on the above analysis that the highly elevated state of the residual AMOC at 26.5°N in 2020 is unlikely to dissipate away during the next several years. Obviously, the autocorrelation-based estimates should not be used as an actual decadal prediction tool because there are skillful decadal dynamic forecast systems with realistic initializations of the ocean54–56. Nevertheless, the global annual-to-decadal climate synthesis report for 2023–27 issued by the World Meteorological Organization57 predicted that the total AMOC around 30°N is likely to be near or slightly below the recently observed values, largely in agreement with our conclusion.