Introduction

Some severe European weather events in summer, such as heatwaves, droughts, and floods, have been linked to extreme states of the North Atlantic Oscillation (NAO)1,2,3,4,5,6, the leading mode of atmospheric variability over the North Atlantic sector7,8. The NAO represents a large-scale seesaw pattern in the atmospheric pressure anomaly. Its positive phase reflects an enhanced south-north pressure gradient associated with stronger zonal jet stream winds, and its negative phase reflects a reduced pressure gradient associated with weaker zonal jet stream winds. The probability of severe summer weather in Europe has increased disproportionately compared to the rest of Northern Hemisphere midlatitudes over the past 40 years9,10. This amplified probability raises the concern that global warming could influence the summer NAO extremes, enhancing the likelihood of heat extremes over Europe. However, previous studies addressing changes in the summer NAO have focused on changes in the mean—particularly the long-term trends under global warming11,12. To date, no study has examined changes in the variability, particularly the extreme states of the summer NAO, in response to global warming. To fill this gap is the purpose of this paper.

Long-term trends in the NAO index reveal the response of the mean state of the NAO to global warming and have been extensively studied, mostly for winter. In winter, the state-of-the-art climate models in the frame of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) show a large spread in the trends of the NAO13,14, with most models agreeing on a positive trend til late 21st century (2080–2099) under the representative concentration pathway (RCP) 8.5 scenario14. This positive NAO trend in winter is intimately linked to adjustments of the jet stream: the models predict a strengthening and a poleward shift of the zonal jet in response to global warming15,16,17,18,19. Although an accelerating jet stream is also emerging in observations20, a robust long-term trend in the winter NAO remains virtually undetectable21,22,23. In summer, climate models tend to simulate a positive trend in the NAO in the historical period, which is also subject to a large model dispersion and deviation from observations11,24,25. The large uncertainty in the trend of the NAO arises from the fact that different models respond differently to the same radiative forcing26, trends predicted by models are biased from observations over the North Atlantic sector19,20,27, and the NAO exhibits strong internal variability.

As a consequence of the positive trend, a previous study has reported more positive extreme states of the NAO in winter under simulated global warming28. This is expected as the fast upper-level zonal jet stream winds increase more than the average zonal jet stream winds under climate change15. While an upward trend in the mean state of the NAO would increase the likelihood of positive NAO extremes, an enhancement in the variability of the NAO would increase the likelihood of both positive and negative NAO extremes. A potential change in the NAO variability is suggested by recent advances in seasonal forecasting. The predictive skill of the NAO variability is beyond the deterministic timescales of weather forecasts29,30. This skillful prediction suggests that some fraction of the NAO variability are driven by predictive boundary conditions, such as sea surface temperature that changes with external forcing19. Indeed, a major source of the predictive skill for the NAO variability in the late 20th century is external forcing31. In addition, a study has shown that global warming will expand the spatial footprint of some internal atmospheric variability modes in winter32. Both the prediction and the climate impact studies suggest that the variability of the NAO may be altered by global warming, and the probability of both—the positive NAO extremes corresponding to enhanced zonal winds and the negative NAO extremes corresponding to enhanced blocking33,34,35—would increase.

The increasing likelihood of NAO extremes would raise a particular concern in summer, given their close association with the occurrence of temperature and precipitation extremes. For summer, studies have reported changes in both zonal and blocked atmospheric flows in response to global warming. For instance, the zonal component of the jet stream over North Atlantic sector exhibits a poleward shift and acceleration, especially over higher altitudes15,16,36. Meanwhile, Greenland blocking appears to be enhanced in the last 40 years23,36,37,38,39. Overall, changes in atmospheric flows represent a closely balanced tug-of-war between tropical warming over the upper-tropospheric16 and polar warming close to the surface23,36,36,37, but which effect will dominate remains inconclusive19. It is plausible that both the zonal flow and blocked flow will change in summer under global warming. Given that the NAO variability is associated with transitions between the zonal and the blocked flows33, changes in both, due to global warming, would suggest changes in summer NAO variability. However, examining such changes in the NAO variability is difficult because a small number of realizations of climate change simulations, e.g, from Coupled Model Intercomparison Project (CMIP), do not allow the internal variability to be properly diagnosed40,41,42 and multi-model ensembles suffer from the additional structural uncertainty between models26,43.

Instead, a large ensemble of simulations with a single model allows the changing internal variability in a transient climate to be determined. The ensemble spread of such “initial-condition large ensembles (LEs)" is an expression of the internal variability at each individual time step44,45. Temporal changes in the ensemble spread of the transient LEs under historical and future radiative forcing scenarios thus reveal changes in the internal variability—beyond the change in the mean state—against global warming32,45. Using a collection of such LEs from various Earth system models further ensures the robustness of the results by accounting for the bias of each model43. It is also possible, albeit with large uncertainties, to isolate the internal variability in reanalysis data. In this case, temporal variability over a relatively short time window is usually taken as the internal variability (e.g., ref. 12). In this study, we use five LEs under historical condition and the representative concentration pathway (RCP) 8.5 future scenarios43, one LEs under 1% CO2 scenario, one LEs under RCP 4.5 scenario46, and the 20CR data47 (Supplementary Table 1). We examine changes in the summer NAO between the first 10 years and the last 10 years of the LEs, which respectively represent the preindustrial climate and a simulated  ~4K warmer climate. In particular, we investigate the occurrence of summer NAO extremes every non-overlapping 10 years in LEs. The findings from LEs are compared with the 20CR in historical periods.

Results

Increased summer NAO variability and extreme states under global warming

We begin by investigating the summer NAO response to global warming at 500 hPa in LEs. The summer NAO is decomposed from 500 hPa geopotential height (Z500) data by applying the empirical orthogonal function (EOF) analysis along the ensemble dimension (Methods). The LEs largely reproduce the spatial pattern of the summer NAO as a seesaw pattern for both the preindustrial climate and the simulated  ~4K warmer climate (Fig. 1a for Max Planck Institute for Meteorology Grand Ensemble (MPI_GE), and Supplementary Fig. 1 for other LEs). In contrast to the apparent northward shift of the jet stream (contours, Supplementary Fig. 3c), the spatial pattern of the summer NAO changes only slightly under global warming (Supplementary Fig. 3i). We show that the resilience of the summer NAO pattern to global warming is consistent with a local enhancement, rather than a spatial shift, of the variability of the jet stream and Z500 (Supplementary Fig. 3f). This enhancement largely overlaps with the southern center of actions of the summer NAO, leading to the increase in the explained variance of the summer NAO from 18 to 24% (Fig. 1a). Since the NAO dominates the weather over much of Europe, a more relevant question would be how global warming affects the strength of the NAO, i.e., the NAO index.

Fig. 1: The occurrence of summer NAO extremes at 500 hPa increases under global warming.
Fig. 1: The occurrence of summer NAO extremes at 500 hPa increases under global warming.The alternative text for this image may have been generated using AI.
Full size image

a Spatial patterns of the summer NAO in the first 10 years (1850–1859, shading) and the last 10 years (2090–2099, contour) of the Max Planck Institute Grand Ensemble (MPI_GE) historical and RCP8.5 runs. The percentages in the top parentheses indicate changes in the explained variance. b The distribution of the NAO index widens under the simulated global warming in the MPI_GE. Numbers in the top parentheses indicate changes in the standard deviation, with an asterisk indicating significance at the 5% confidence level based on bootstrapping. c Evolution of the occurrence of the positive NAO extremes every non-overlapping 10 years in the MPI_GE and MPI_GE_onepct. MPI_GE_onepct runs for 100 years with the initial condition of 1850, and forced by 1% CO2 increase per-year. Shading represents the 5–95% confidence interval based on bootstrapping. Numbers in the legend show the ensemble size. d Same as (c) but for negative NAO extremes. e Spatial pattern of the NAO in the NOAA-CIRES-DOE 20th century reanalysis (20CR) data during (1850–2015). The percentage in the top parentheses indicates the explained variance. f Distribution of the NAO index in the 20CR. The first 40 years represent (1850–1889) and the last 40 years represent (1976–2015). Numbers in the top parentheses indicate changes in the standard deviation, with an asterisk indicating significance at the 5% confidence level. g The occurrence of positive NAO extremes in the 20CR. 20CR_ens represents the 20CR with all the ensemble members. Error bars represent the 5–95% confidence interval based on bootstrapping. h Same as (g), but for negative NAO extremes.

Changes in the NAO index due to global warming can be partioned into two parts: (1) changes in the mean state of the NAO that is reflected by the shift in the mean of the NAO index distribution and (2) changes in the variability of the NAO that is reflected by changes in the shape of the NAO index distribution. The changes in the mean state is evident when the NAO index is generated using the Z500 without removing the ensemble mean (Supplementary Fig. 4a)—all LEs used in this study agree on a positive long-term trend in the summer NAO index til the end of the 21st century (Supplementary Fig. 5). Given the evidence described in the introduction, we also examine changes in the variability of the NAO after removing the mean-state change (Methods). Our analysis provides strong evidence for a secondary summer NAO response to anthropogenic forcing: we find significant widening in the distributions of the summer NAO index in MPI_GE (Fig. 1b). Such an enhanced summer NAO variability is also seen in the NAO index generated by the classical method—difference between Iceland and the Azores (Supplementary Fig. 6a). The response of the summer NAO variability to global warming, superimposed on the mean state change, is projected by all Earth system models used in this study (Supplementary Fig. 2).

The enhanced variability would manifest itself in higher probabilities of both positive and negative NAO extremes. In this study, we define the summer NAO index above 1.5 standard deviation as positive NAO extremes, and those below −1.5 standard deviation as negative NAO extremes. We extract such NAO extremes every non-overlapping 10 years throughout the time span of the LEs (Methods). The MPI_GE, forced by historical and RCP8.5 future scenarios, shows continuous increases in the occurrence of both positive and negative summer NAO extremes at the 500 hPa pressure level, either the NAO index is generated via EOF (Fig. 1c, d) or box difference-based methods (Supplementary Fig. 6b, c). The MPI_GE_onepct, same as MPI_GE but driven by a stronger anthropogenic forcing—the CO2 concentration increases by 1% per year—shows more pronounced increases in the occurrences of positive and negative extremes (red lines, Fig. 1c, d). The MPI_GE forced by a more moderate warming scenario, RCP 4.5, shows weaker but still statistically significant increases (Supplementary Fig. 7).

The increase in the occurrence of the summer NAO extremes at 500 hPa is fairly consistent across different LEs (Fig. 2), indicating that such an increase is not due to model biases. Community Earth System Model (CESM1_CAM5) (blue lines, Fig. 2) and Commonwealth Scientific and Industrial Research Organization MK3.6 model (MK3.6) (green lines, Fig. 2) show increases in the occurrence of both positive and negative extremes. Two other models, geophysical fluid dynamics laboratory’s coupled model (GFDL_CM3) and Canadian Earth System Model (CanESM2) behave differently from MPI_GE in terms of positive NAO extremes, either with varying NAO patterns (yellow and purple lines, Fig. 2) or a fixed NAO pattern (yellow and purple lines, Supplementary Fig. 10) (Methods). The different behavior of the GFDL_CM3 seems to be due to its five times smaller ensemble size compared to MPI_GE, so that the prediction is overwhelmed by the decadal variability. Indeed, if 20 ensemble members are randomly selected from 100 ensemble members of MPI_GE, the increase in the positive NAO extremes does not significantly emerge (compare filled yellow bar with unfilled orange bar, Fig. 2c). The different behavior of CanESM2 in terms of positive NAO extremes will be explained in section “Changes in the summer NAO extremes are associated with changes in the atmospheric flow regimes” with respect to the representation of flow regimes.

Fig. 2: Upward trend in the occurrence of summer NAO extremes at 500 hPa across different Earth system models.
Fig. 2: Upward trend in the occurrence of summer NAO extremes at 500 hPa across different Earth system models.The alternative text for this image may have been generated using AI.
Full size image

a Evolution of the occurrence of positive NAO extremes per decade. Shadings represent a 5–95% confidence interval based on bootstrapping. b Same as (a), but for negative extremes. c The rate of increase in the occurrence of positive summer NAO extremes per decade during 1950–2100, shown as a solid line for each model. Filled bars represent the 5–95% confidence interval by student's t-test. Unfilled bars represent the 5–95% confidence interval by student's t-test of resampled historical and RCP8.5 runs of Max Planck Institute Grand Ensemble (MPI_GE). d Same as (c) but for the negative summer NAO extremes. Numbers in the brackets of the legend indicate ensemble size.

Hints of the increasing probability of NAO extremes in summer are emerging in the historical periods. We extract the internal variability of the summer NAO in the historical periods from the 20CR (Methods). The 20CR data are used because, compared with other reanalysis data, it assimilates only sea-level pressure and sea surface temperature fields rather than utilizing all available observations in the troposphere, making it less sensitive to temporal inhomogeneities in the observations48 and less constrained so that it includes some of the variability due to internal atmospheric processes47. The distribution of the summer NAO index in the last 40 years (1976–2015) is wider than in the first 40 years (1850–1889) of the record (Fig. 1f). For comparison, the widening is also evident when all the ensemble members of the 20CR (20CR_ens) are used to isolate the internal variability (Methods). Based on a threshold of 1.5 standard deviation of the first 40 years, the occurrence of the NAO extremes increases in the last 40 years (Fig. 1g, h). Assessing the significance of the increase appears to be difficult in the reanalysis data. Bootstrapping-based methods show that the increase in 20CR is insignificant and that in 20CR_ens is significant (error bar, Fig. 1g, h). This uncertainty is partly due to the fact that bootstrapping requires a large sample size, and underlies the difficulty of extracting internal variability from reanalysis data (Methods). Nevertheless, the uncontroversial results between the 20CR and the LEs enhance our confidence that the increasing probability of both positive and negative summer NAO extremes is likely to emerge in the historical periods.

The increasing occurrence of the summer NAO extremes is shown not only at 500 hPa, but throughout most of the troposphere. Except for the near-surface altitudes, the rise in the occurrence of NAO extremes due to global warming appears to be significant up to 200 hPa, either under the 1% CO2 scenario (Fig. 3a, b), or the Historical and RCP8.5 scenarios (Supplementary Fig. 11a, b) in MPI_GE. The vertically consistent changes are also evident in the 20CR (Fig. 3c, d) and 20CR_ens (Supplementary Fig. 11c, d). Note that the 20CR doesn’t show obvious changes in the occurrence of summer NAO extremes at the upper troposphere (200 hPa). This is consistent with a recent study showing that the upper atmospheric response to global warming would not emerge until 205015. Bootstrap-based methods show that the increase in the 20CR is insignificant, and that in 20CR_ens is significant. Again, sample size may contribute to this uncertainty.

Fig. 3: The occurrence of summer NAO extremes increases throughout most of the troposphere.
Fig. 3: The occurrence of summer NAO extremes increases throughout most of the troposphere.The alternative text for this image may have been generated using AI.
Full size image

a Profile of the occurrence of the positive summer NAO extremes in Max Planck Institute Grand Ensemble 1% CO2 run (MPI_GE_onepct). b Same as (a), but for negative summer NAO extremes. c Profile of the occurrence of the positive summer NAO extremes in the first 40 years (1850–1889) and the last 40 years (1976–2015) in the NOAA-CIRES-DOE 20th century reanalysis (20CR). d Same as (c), but for negative NAO extremes. Shading represents 5–95% confidence intervals based on bootstrapping.

Increased climate impacts of summer NAO extremes over northwestern Europe

The large sample size of the extremes in LEs allows us to investigate changes in the climate impacts of the summer NAO extremes under global warming. To do so, we first remove long-term trend by removing the ensemble mean from each ensemble member, and then calculate the composite mean of surface temperature and precipitation during these summer NAO extremes (Methods). A positive extreme summer NAO event has a warming effect over northwestern Europe and central North America, and a cooling effect over Greenland and the Mediterranean, a pattern that is consistent across different models and reanalysis data under preindustrial climate (Fig. 4a–f). However, under the simulated  ~4K warmer climate, the warming effect over Northwest Europe is increased and expanded (Fig. 4g–k). Such an amplification is statistically significant and consistent across different models (Fig. 4m–q). The opposite change—increased cooling over northwestern Europe—occurs during negative summer NAO extremes (Fig. 5).

Fig. 4: The impact of positive summer NAO extremes on (near) surface temperature amplifies over northwestern Europe in a warmer climate.
Fig. 4: The impact of positive summer NAO extremes on (near) surface temperature amplifies over northwestern Europe in a warmer climate.The alternative text for this image may have been generated using AI.
Full size image

a–e The impact of positive NAO extremes on surface temperature (shading) and sea-level pressure (contours) in the first 10 years of simulations from different Earth system models. Contours are drawn at intervals of 1 hPa, ranging from −5 to 5 hPa, excluding the 0 hPa contour. g–k Same as (a–e), but for the last 10 years of the simulations. m–q The difference between the last 10 years and the first 10 years. Crossed patches represent areas where the difference is significant at a 5% confidence level based on bootstrapping. f The impact of positive NAO extremes on the near-surface temperature in the first 40 years (1850–1889) of 20CR_ens. l Same as (f) but for the last 40 years (1976–2015). r The difference between the last 40 years and the first 40 years in the 20CR_ens. Changes in the 20CR_ens appear to be significant everywhere. This is due to the high similarity between ensemble members of the 20CR, is therefore not statistically meaningful and not shown here.

Fig. 5: The impact of negative summer NAO extremes on (near) surface temperature amplifies over the northwestern Europe in a warmer climate.
Fig. 5: The impact of negative summer NAO extremes on (near) surface temperature amplifies over the northwestern Europe in a warmer climate.The alternative text for this image may have been generated using AI.
Full size image

a–e The impact of negative NAO extremes on surface temperature (shading) and sea level pressure (contours) in the first 10 years of simulations from different Earth System Models. Contours are drawn at intervals of 1 hPa, ranging from -5 hPa to 5 hPa, excluding the 0 hPa contour. g–k Same as (a–e), but for the last 10 years of the simulations. m–q The difference between the last 10 years and the first 10 years. Crossed patches represent areas where the difference is significant at 5% confidence level based on bootstrapping. f The impact of negative NAO extremes on the near surface temperature in first 40 years (1850-1889) of 20CR_ens. l Same as (f) but for the last 40 years (1976-2015). r The difference between the last 40 years and the first 40 years in the 20CR_ens.

The amplified impact of summer NAO extremes on the surface temperature is also evident in the 20CR_ens (Figs. 4, 5). The magnitude of the changes is smaller in the reanalysis data than in the LEs (Fig. 4r), because the background climate warmed by less than 1.5K in historical periods, compared to  ~ 4K at the end of the RCP8.5 runs of the LEs. The 20CR_ens additionally shows an apparent amplification of the warming effect over the Mediterranean basin during the negative NAO extremes under a warmer background climate (Fig. 5l). Such an amplification is also seen in the MPI_GE (Fig. 5m), CESM1_CAM5 (Fig. 5i), and GFDL_CM3 (Fig. 5k), but it is mostly insignificant, whereas changes of the opposite sign are shown in the CanESM2 and MK3.6. This highlights the challenge for climate models to project the regional climate change—uncertainty from both the strong internal variability and model difference49,50.

The temperature dipole pattern in Figs. 4,5 may be induced by other factors, such as variability of the soil moisture. However, an analysis based on singular value decomposition (SVD) (Methods) shows that a dipole pattern of soil moisture over Europe can not induce a temperature pattern as strong as the summer NAO at the same time scale (Supplementary Figs. 14, 17). To further ensure that the temperature dipole patterns shown in Figs. 4, 5 are effects of the summer NAO extremes and not vice versa, we perform SVD analysis with time lead/lag. When the NAO is leading the surface temperature by one month, the surface temperature resembles the dipole pattern shown in Fig. 4 (Supplementary Fig. 15), whereas when the NAO is lagging the surface temperature, the temperature pattern is distinct (Supplementary Fig. 16). This difference confirms that the summer NAO extremes induce the temperature dipole pattern, rather than the temperature dipole pattern induces the summer NAO extremes.

In addition to surface temperature, we also examined changes in the effect of summer NAO extremes on precipitation (Supplementary Figs. 12, 13). Similar to surface temperature, all models show consistency in the impact of the summer NAO extremes on precipitation. Under global warming, this pattern is amplified for both positive and negative summer NAO extremes. However, none of the models show that this amplification is statistically significant based on bootstrapping (Methods).

Changes in the summer NAO extremes are associated with changes in the atmospheric flow regimes

Atmospheric circulation exhibits multiple flow regimes51, and transitions between them over the North Atlantic sector are associated with the summer NAO variability33,34. Therefore, investigating changes in the flow regimes would provide a different perspective on changes in the summer NAO extremes, and enhance the robustness of the finding. In this study, because we use monthly data, the eddy-driven jet stream location52 is used as a proxy for the strength of the zonal flow regime, and the Greenland blocking index53 is used as a proxy for the frequency of the blocked flow regime (Methods).

Changes in the two flow regimes over time are shown in Fig. 6a, b. We observe both an obvious poleward shift of the eddy-driven jet (black line, Fig. 6a) and an enhancement of the Greenland blocking (black line, Fig. 6b) under climate change. The northward shift of the mean-state of the eddy-driven jet stream would suggest more extreme episodes of eddy-driven jet being located further north; and the increased time-mean state of the Greenland blocking index would suggest more extreme episodes of the eddy-driven jet stream being located south and merged with the subtropical jet34. Indeed, if we focus on the frequency of extreme states of the two regimes, the increases are more prominent (red lines, Fig. 6a, b).

Fig. 6: Changes in the frequency of flow regimes coincide with changes in the summer NAO extremes.
Fig. 6: Changes in the frequency of flow regimes coincide with changes in the summer NAO extremes.The alternative text for this image may have been generated using AI.
Full size image

a Temporal evolution of the eddy-driven jet stream location per non-overlapping decade. Shading shows 1 standard deviation along time and ensemble dimension for each decade. b Same as (a) but for the Greenland blocking index. c Density plot of occurrence of summer NAO extremes as a function of eddy-driven jet stream location and Greenland blocking index. Contours represent the negative summer NAO extremes, and shadings represent the positive summer NAO extremes. Blue colors represent the extreme events in the first 10 years, and orange colors the last 10 years. Dashed lines represent the climatology of the eddy-driven jet location (vertical dashed lines) and the Greenland blocking index (horizontal dashed lines), respectively, for the first 10 (blue dashed lines) and the last 10 years (orange dashed lines). d Scatter plot of occurrence of summer NAO extremes as a function of counts of eddy-driven jet stream location more north than 1.5 standard deviation of the first 10 years and counts of Greenland blocking index higher than 1.5 standard deviation of the first 10 years. Counts correspond to per decade per member. All plots are shown for historical and RCP8.5 runs of the MPI_GE. Definitions of eddy-driven jet and Greenland blocking can be found in the Methods.

Changes in both flow regimes are associated not only with the positive trend of the summer NAO (Supplementary Fig. 4c, d), but also with the increase in the summer NAO extremes (Fig. 6c). Under the preindustrial climate, the negative and positive phases of the summer NAO extremes lie correspondingly in the second and fourth quadrant of the coordinate plane defined by the eddy-driven jet stream location and the Greenland blocking index (blue lines, Fig. 6c), confirming the close link between two flow regimes and the occurrence of positive and negative summer NAO extremes. Under the simulated  ~4K warmer climate, the zonal flow shifts northward, and the Greenland blocking enhances (from blue dashed lines to orange dashed lines, Fig. 6c). Meanwhile, the occurrence of summer NAO extremes increases (compare orange contours with blue contours, Fig. 6c). We further show that increasing negative summer NAO extremes are linked with increasing number of extreme episodes of Greenland blocking, while increasing positive summer NAO extremes are linked with increasing extreme episodes of both northward diverting eddy-driven jet and Greenland blocking (Fig. 6d).

Finally, other models that show similar changes in the summer NAO extremes as MPI_GE show similar changes in the zonal and blocked flow regimes (Supplementary Fig. 22). The different behavior of CanESM2 with respect to the positive NAO extremes (Fig. 2c) compared to the other LEs is also evident in the flow regimes: the link between northward shifts of the eddy-driven jet stream location and the increase in the positive NAO extremes is weak (Supplementary Fig. 22g). This is probably because the location of the climatological eddy-driven jet stream in this model is more northerly than in the other models (dashed lines, Supplementary Fig. 22b).

Conclusion

It is well established that the mean state of the summer NAO changes in response to global warming. The mechanisms for such a change include changes in the zonal jet stream winds16,17,18. All LEs used in this study support a positive trend in the mean state of the summer NAO under global warming.

Here, we argue for a secondary response of the summer NAO to global warming—an increase in its variability. This increase is consistent with the implications of a simple conceptual Lorenz model54. The enhanced variability causes the extreme states of the summer NAO—for both positive and negative phases—to become more frequent and their impact over Northwestern Europe to increase. The increased occurrence of the summer NAO extremes is vertically consistent throughout most of the troposphere. The enhanced impact of these extremes over northwestern Europe is consistent with the slight strengthening of the NAO pattern over this region (Supplementary Fig. 3i). Such an enhanced impact of the NAO extremes in summer under global warming is consistent with its winter counterpart32. The increased occurrence and impacts of the summer NAO extremes are supported by most of the state-of-the-art LEs under consideration. Notwithstanding the differences in the production of ensemble members between simulations and reanalysis data, the 20CR reanalysis data suggest that the increasing probability of the summer NAO extremes is emerging in the historical period.

The increasing occurrence and impact of the summer NAO extremes is robust to various configurations of the approach we used. For instance, the NAO index from both EOF and box difference methods supports the increasing occurrence; the analysis based on both composite mean and SVD supports the enhanced impact. Overall, the increase in the NAO extremes is more robust for the negative phase than the positive phase. A stronger increase in the negative summer NAO extremes is consistent with the enhancement of the jet variability particularly over the southern flank of the mean jet (Supplementary Fig. 3f). Nevertheless, as the mean state of the summer NAO becomes more positive under global warming, a small increase in the positive summer NAO extremes would still have a considerable effect.

The changes in both phases of summer NAO extremes are consistent with enhanced likelihood of poleward diverts of the eddy-driven jet stream and of intensified Greenland blocking episodes by global warming. While the increasing negative NAO extremes is dominated by enhanced Greenland blocking, the increasing positive NAO is linked to variations in both flow regimes. Our results thus suggest that both the ‘fast gets faster’ response15 (corresponding to enhanced positive NAO extremes) and the ‘wave gets wavier’ response37,55,56 (corresponding to enhanced negative NAO extremes) in jet stream winds are likely to occur in a transient warming climate, rather than one being dominant.

Methods

Data

Historical and RCP8.5 runs of five single model initial-condition large ensemble simulations (SMILEs) from the “multi-model large ensemble archive” (MMLEA)43, one SMILEs forced by RCP 4.5 scenario, and an experiment of 1% CO2 run with Max Planck Institute Grand Ensemble (MPI_GE_onepct)46 are used (Supplementary Table 1). The results from climate simulations are compared with those of the 20CR data47. The 20CR has 80 ensemble members. These ensemble members are generated using the Ensemble Kalman Filter57, and are designed to reflect observational uncertainty. From the Monte Carlo aspect of the Ensemble Kalman Filter theory, each member is equally likely. By only assimilating the surface pressure and sea surface temperature, and using the coupled atmosphere-land model, the ensemble spread includes some of the uncertainty from the internal dynamics of the atmospheric circulation57. Therefore, the analysis of 20CR is also tested with all the ensemble members of the 20CR (20CR_ens). All the data are monthly and confined to the boreal summer (June-July-August).

Generating summer NAO index

The NAO is decomposed from geopotential height data at all available levels in the troposphere over the domain [20–80°N and 90°W–40°E] using empirical orthogonal function (EOF) analysis. For each level, the geopotential height data are first weighted by the cosine of the latitude. The NAO index is identified as the first principle coefficients (PCs) of the EOF analysis, and is standardized by dividing the index with the spatial standard deviation of the eigenvector instead of the usual way of being multiplied by the temporal standard deviation of itself. Since the EOF is applied independently for each 10-year interval (see section “Extracting internal variability of the NAO in SMILEs”), this way of standardization ensures that the index generated from different eigenvectors are comparable, and the multiplication of the index and the corresponding eigenvector still gives an estimate of the geopotential height field. We have also tried with a fixed spatial pattern for all different warming stages, the results are included in the Supplementary and do not change the main conclusion. The spatial pattern of the NAO is then obtained by projecting the geopotential field onto the standardized index, showing the change in the geopotential height field corresponding to the change in the NAO index of one standard deviation.

For comparison, the NAO index using the difference between two boxes (25°W–5°E, 45°N–55°N) and (52– 22°W, 60°N–70°N)6 is also investigated for MPI_GE.

Extracting internal variability of the NAO in SMILEs

In SMILEs, the ensemble members differ only slightly in their initial conditions. The considerable ensemble spread during the simulation is then mainly due to internal variability of the climate system. The internal variability of the NAO is then extracted by applying the EOF analysis along the ensemble dimension of the SMILEs, after removing the ensemble mean from each of the ensemble members as previous studies32,45. Note that the ability for the ensemble spread to estimate internal variability differs across different Earth System Models. MPI-GE provides the best representation of internal variability according to ref. 58, partly due to its large ensemble size. Therefore, the ensemble size of all the SMILEs is expanded by concatenating all the ensemble members and all the summer months (June, July and August) within a 10-year interval. We refer to this combined dimension as “pseudo ensemble”.

To examine the temporal evolution of summer NAO variability in SMILEs, the EOF along the pseudo ensemble dimension is conducted separately over each non-overlapping decade. This allows the spatial patterns of the NAO to vary across different warming periods. This is expected, as variations in the spatial structure of the NAO can lead to different impacts59, and contribute to its response to global warming6,33. As a reference, the decomposition using a fixed pattern (Supplementary Fig. 8) instead of the temporally varying patterns is also applied (Supplementary Figs. 9,  10). In this case, the magnitude of the increase was reduced for both positive and negative NAO extremes compared to that with the varying pattern. So that the increase in the occurrence of positive NAO extremes in CESM1_CAM5 does not significantly emerge.

The full NAO response, that includes changes in the variability and the mean state of the NAO for MPI_GE is given in Supplementary Fig. 4. The index for full NAO response are generated by projecting the Z500, without removing ensemble mean, to the NAO pattern of the first 10 years of the simulation.

Extracting internal variability of the NAO in 20CR

The internal variability in the 20CR are extracted with two different methods, (1) with the ensemble mean only and (2) with all the ensemble members. The first method follows the typical use of the 20CR data. In this case, a quadratic fit of the single realization is taken as a representation of the externally forced signal. After removing the quadratic fit from the time series at each pixel, the residuals are taken as a representation of the internal variability. The second method uses all the ensemble members of the 20CR. Different from SMILEs, the spread of the 20CR is not designed to measure the internal variability, and the ensemble mean includes both the externally forced signal and the internal variability. Therefore, same as the first method, the quadratic fit of the ensemble mean is used to represent the externally forced signal, and is removed from all the ensemble members at each pixel.

Both methods have shortcomings in extracting the internal variability in the 20CR. For the first method, a single realization would underestimate the internal variability, and the small sample size would limit the use of bootstrapping. For the second method, although up to 80 ensemble members are available, the ensemble spread is much narrower than that of the MPI_GE, and shows clear decadal variability (Supplementary Fig. 20), indicating that the ensemble spread of the 20CR strongly underestimates the internal variability if it is treated the same as SMILEs. To minimize the effects of the above limitations, the NAO from 20CR data are decomposed differently from the SMILEs. First, the full length of the data is used to decompose the NAO spatial pattern. This is because the leading mode decomposed from 40 years of data do not fully resemble the typical summer NAO pattern (Supplementary Fig. 1f). Second, 40 years instead of 10 years are used as a window to compare changes in the internally generated NAO extremes.

The occurrence of the summer NAO extremes

1.5 standard deviation of the NAO index in the first period (first 10 years in SMILEs and first 40 years in 20CR) is used as a threshold to extract the NAO extremes for positive phase (above the threshold) and negative phase (below-1 times threshold). Although the standard deviation based threshold assumes Gaussian distributions, the results should be very similar if percentile based threshold is used. The advantage of the percentile based threshold is that it allows possible asymmetry of the NAO index. However, in MPI_GE, 1.5 standard deviation roughly corresponds to 93% percentile of the index, and −1.5 standard deviation to 7% of the index in LEs (Supplementary Fig. 21a). If 90th and 10th percentiles are used as the thresholds, the corresponding value in standard deviation are roughly 1.3 and −1.3. Therefore, the NAO index in the first 10 years of the MPI_GE is actually symmetric. Other LEs show similar results as MPI_GE (Supplementary Fig. 21). As a reference, such positive NAO extremes occur 1.6 times per decade, and such negative NAO extremes occur 0.9 times per decade in 20CR based on Extreme Value Theory.

In the SMILEs and 20CR_ens, the summer NAO extremes in each period are counted from all the ensemble members and all the months within each period, and then divided by the ensemble size. The linear trend of the occurrence in SMILEs is calculated between 1950 and 2099, where all the models have an output. The rate of increase per decade is then represented by dividing the linear slope by the occurrence in the first 10 years and expressed as a percentage. For the ensemble mean of the 20CR, the summer NAO extremes are counted from all the months within each 40-year period, and the rate of increase per decade is estimated simply by (Olast40 − Ofirst40)/(2015–1889) × 10, and represented as percentage by dividing this value with the occurrence in the first 40 years.

Climate impacts of the summer NAO extremes

The impacts of summer NAO extremes on the surface temperature, the sea-level pressure, and precipitation are examined using the composite analysis. The impact on the surface temperature in MPI_GE is verified with singular vector decomposition (SVD). In both methods, the background changes are removed by removing the ensemble mean in all SMILEs, and the quadratic fit in the 20CR_ens.

For composite analysis, the pre-processed data in the months and ensemble members where the NAO indexes are identified as positive (or negative) extremes are averaged. As the occurrence of the NAO extremes differs between different warming stages, the same number of the most extreme cases as in the preindustrial climate are included. The composite analysis using all the extreme cases in the first interval and the last interval (rather than the same number of extreme cases) gives very similar results (plots not shown).

For SVD analysis, the variables are first normalized by their mean and standard deviation across all ensemble members and each decade. Then the pre-processed surface temperature and the Z500 are fed into the SVD. For comparison, the same analysis is performed for the surface temperature and the soil moisture. To examine the causal relationship, the SVD with time lead/lag of one month is performed.

Eddy-driven jet stream location and Greenland blocking index

Because we use monthly data, the eddy-driven jet stream location and Greenland blocking can not be measured directly. Instead, we use two proxies on monthly data, which represent the statistical frequency of the occurrence of each regime in transient atmospheric flow. Following ref. 34, the eddy-driven jet stream are identified as zonal wind averaged between levels of 925 and 700 hPa. The location of the eddy-driven jet is defined as the latitude where the zonally averaged jet stream winds over a longitudinal sector (0–60°W for the North Atlantic) is in its maximum. Following ref. 53, the Greenland blocking is simply estimated as the mean 500 hPa geopotential height for the [60–80°N and 20°–80°W] region.

Statistical significance test

Bootstrap-based methods are used to test the statistical significance of the widening of the NAO index distribution at the 5% level, and determine the 5–95% confidence interval of the occurrence of NAO extremes under different warming stages. Specifically, for testing the significance of the widening of the NAO index distribution, the NAO index of the first interval and the last interval are randomly resampled separately with replacement, and the difference between the standard deviations of the two generated samples are calculated. Such resampling and calculation are repeated 1000 times. If 0 is outside of the 5–95% percentile of these differences, changes in the shape of the distribution is considered as significant. For the 5–95% confidence interval of the occurrence of NAO extremes, at each 10-year (40-year for the 20CR) intervals, the NAO index is randomly resampled 1000 times with replacement. The occurrences of the extreme cases in these generated samples are counted in the same way as the original index. The 2.5–97.5% quantile of these occurrences is identified as the 5–95% confidence interval for the occurrence of NAO extremes.

Bootstrap method is also used to check whether the difference in the impact of the extreme NAO between the first interval and the last interval is statistically significant at the 5% confidence level. Specifically, 1000 samples of the NAO index are generated by resampling with replacement. For each of the generated NAO time series, extract the extreme cases, and examine their impacts on surface temperature using composite analysis as the original NAO index, separately for the first internal and the last interval. And then calculate the difference between the impacts of these two intervals. Such calculations are repeated for all the generated NAO time series. After getting the whole 1000 temperature differences, the 2.5–97.5% quantile of these differences is calculated. If 0 is not in the range, the difference of the composite mean temperature field between the last interval and the first interval is considered significant.

The 5–95% confidence interval of the linear trend of the evolution of extreme NAO occurrence is obtained using student’s t-test.