Introduction

The Northern Hemisphere eddy-driven jet (EDJ) is the central component of the boreal extratropical circulation and the leading regulator of weather and climate in the mid-latitudes. Due to its close relation to many tropospheric and surface processes, such as the storm track1, regional surface weather conditions2 and extreme events3, the study of future EDJ changes remains a priority. The EDJ response to an atmospheric increase of greenhouse gas (GHG) concentrations has been a topic of interest since the first phases of the Coupled Models Intercomparison Project (CMIP). A robust consensus has been found across general circulation models (GCMs) and generations on the poleward shift of the EDJ when considering annual and zonal averages4,5,6,7,8. However, the picture changes for the winter season and the North Atlantic sector (NATL). The NATL EDJ response to climate change presents a seasonal cycle characterised by a poleward shift from spring to autumn, peaking in summer but without a clear latitudinal displacement in winter9,10. Climate change projections of the EDJ latitude in winter display a large inter-model spread, spanning from poleward to equatorward responses. This behaviour has sometimes been interpreted from the multimodel mean perspective as an increasing presence of the EDJ on its central latitude in the future7,11,12.

In addition to the latitudinal position, future projections indicate a strengthening of the EDJ core region with a reduction of the zonal wind on the poleward and equatorward flanks6,10,12, sometimes interpreted as a squeezing7. However, there is no consensus either on this reinforcement of the EDJ, as some studies find it insignificant or do not detect it4,9,11. Apart from the responses in the typically studied EDJ features (latitude and intensity), changes in other aspects have also been detected. An eastward elongation over Europe12,13,14 and increased zonalization11,15 have been reported since early CMIP phases. However, these changes have often been inferred from the analysis of EDJ-related variables such as the zonal wind12 or European blocking frequency9,16. Finally, although some of the aforementioned studies12,13,16 have analysed the EDJ from a multimodel perspective, little attention has been paid to the inter-model spread, particularly for attributes other than latitude and intensity.

The uncertainties of the EDJ response to climate change are determined by multiple factors, such as changes in large-scale phenomena, and different drivers can induce different responses in the EDJ. A well-known example is the ‘tug-of-war’ between the strong upper tropospheric tropical warming (or Tropical Amplification, TA) and the rapid near-surface warming in the Arctic (i.e. the Arctic Amplification, AA). Both phenomena imply changes in the air temperature distribution, leading to a strengthening of the upper tropospheric meridional temperature gradient and a weakening of the lower one, respectively. Consequently, the TA (AA) can potentially shift the EDJ poleward (equatorward)17,18,19,20,21. There is high confidence that both regions warm at faster rates than the global mean under GHG increases6,22,23. As TA and AA act simultaneously, the combined effect can result in poleward or equatorward EDJ migrations, depending on which one dominates. In turn, these EDJ migrations can lead to further changes in the meridional gradients24.

Something similar happens for the projected changes in sea surface temperature (SST). There is a large agreement across GCM projections about a global heterogeneous warming of the oceans, particularly more pronounced in the tropics and Northern Hemisphere25. However, this generalised warming exhibits a striking anomaly in the NATL ocean. Projections of the NATL subpolar gyre region indicate a lack of warming or even a cooling, a feature known as the NATL Warming Hole (WH)26. The NATL WH modifies the baroclinicity over the western basin, which can affect the storm tracks and the EDJ latitude and intensity through thermal wind responses26,27. An EDJ eastward extension has also been linked to the baroclinicity strengthening13,28,29. Although the NATL WH is a robust aspect of climate change, the magnitude of the change presents a large spread across GCMs, which propagates to the EDJ response29.

The uncertainties of the EDJ projections further increase when not only the magnitude but also the sign of the driver’s response to climate change is uncertain. For instance, the stratospheric polar vortex (SPV), whose intensity also modulates the EDJ latitude and intensity30,31, is projected to reinforce or weaken under increasing GHG concentrations depending on the GCM32,33. Changes in the longitudinal SST gradients of the tropical Pacific can also affect the mid-latitude NATL circulation through Rossby waves and teleconnections34,35. The sign of SST gradients determines the location of the wave source along the tropical Pacific, potentially affecting the position and structure of the EDJ35.

Non-stationary signals in the drivers or the background flow through the winter would further increase the uncertainty of EDJ projections by inducing seasonally varying responses. For the tropical Pacific SST, it is well established that the teleconnections linking the Pacific and Atlantic basins are different in early and late winter, yielding intraseasonal influences on the EDJ36,37,38,39. Little attention has been given to studying intraseasonal responses of the NATL circulation40. Finally, the presence of biases in GCMs is an additional source of uncertainty. For example, GCMs often present systematic biases in the representation of the EDJ latitudinal position, which tends to be equatorward shifted compared to observations4,41. This may potentially contribute to the spread in the projections of the NATL circulation10.

In this paper, we describe the climate change projections of the winter NATL EDJ in the last generation of climate models (CMIP6). The uncertainties of the EDJ projections are related to those of well-known drivers. To do so, we use a novel approach presented by Barriopedro et al., (2023)42, which describes the EDJ from a multiparametric perspective. For each day, the method provides (i) a suite of ten parameters, each of them quantifying a specific aspect of the EDJ structure; (ii) a 2D detection of the EDJ (i.e., grid points comprising the zonal wind maxima over the NATL). The latter provides an explicit spatial representation of the EDJ and enables the computation of maps with the spatial frequency of EDJ occurrence over a given time interval. A detailed description of the EDJ parameters, the 2D EDJ frequency field and their computation based on the NATL lower tropospheric zonal wind are provided in the Methods section (see Jet parameters subsection and Table 1 for a summary). We find that the EDJ latitudes do not show consistent changes across the whole winter in a multimodel ensemble of future projections, but opposite intraseasonal meridional shifts. The mixture of contrasting signals in early and late winter reflects different influences from thermodynamical (meridional temperature gradient at 200hPa) and dynamical (SPV) responses to climate change. Moreover, equatorward GCM biases also contribute to the intraseasonal differences in latitudinal shifting by enhancing the poleward migration during the whole season.

Table 1 EDJ parameters
Full size table

Results

Seasonal analysis of projections

Figure 1 shows the multimodel mean future change in the frequency of occurrence of EDJ during the extended winter (November-to-February, NDJF). The spatial pattern features a tripolar structure, which resembles a squeezing of the climatological EDJ, depicted by an intensification of its central part and a weakening of the northern and southern flanks (Fig. 1a). A similar pattern is found for the 850 hPa zonal wind but with noisier characteristics (Fig. S1). The tripolar pattern in Fig. 1a does not necessarily imply a change in the latitudinal position (Lat) or intensity (Int) of the EDJ in the future, as shown by the distributions of the changes in the corresponding parameters (see the grey whiskers for Lat and Int in Fig. 1b), which are centred around the zero-line. The similarity of the Lat distributions in both future and historical periods (Fig. S2a) confirms the lack of changes in the latitudinal position of the EDJ (Fig. 1a).

Fig. 1: Winter projections of the EDJ.
figure 1

a Multimodel mean climate change signal in the winter (NDJF) 2D EDJ frequency (shading, [%]). The 1979–2009 NDJF climatology is shown with green contours (starting at 20% and drawn every 20%). Crosses indicate the grid-points with non-significant differences at the 95% confidence level (after a 1000-trial Monte Carlo test). b Boxplots with the future changes in the EDJ parameters (Int, Sh [m/s]; Lat, Latn, Lats [°N]; Lon, Lone, Lonw [°E]; Til, Dep [°N/60°]) for NDJF (grey), ND (blue) and (JF) red. The distance between the box limits denotes the interquartile range and the horizontal line corresponds to the median. Whiskers indicate the extremes of the distribution without considering outliers. Outliers, defined as values >1.5 times the interquartile range, are represented with crosses. The climate change signal is defined as the difference between future (2069–99; SSP5–8.5) and present-day (1979–2009; historical) means.

Full size image

The tripolar pattern influences the EDJ zonality, herein represented by the Departure (Dep) parameter, which measures the deviation of the EDJ from a structure with a single wind maximum. Large values of this parameter indicate a split-like pattern with two or more wind maxima. GCMs project a robust increase in zonality and a tendency towards EDJs with a single flow configuration since the distribution of the Dep changes is displaced toward negative values. This is consistent with the increased frequency of winter days with EDJ over western Europe (Fig. 1a). An eastward displacement of the EDJ is also captured by the projected changes in the longitudinal parameters (Lon, Lone and Lonw; Fig. 1b), although the associated spread is large, spanning from negative (westward) to positive (eastward) values.

Despite the general consistency of the future changes in the EDJ parameters and 2D EDJ frequency, the apparent squeezing shown by the latter (Fig. 1a) and several works6,7,11,15 is not detected in the analysis of the EDJ parameters (Fig. 1b). This emphasises the complementary information provided by these two EDJ perspectives and calls for caution when interpreting changes in zonal wind and/or 2D EDJ frequency. In particular, the tripolar pattern of Fig. 1a allows various interpretations, since changes in different EDJ features can lead to the same pattern. The combined analysis of the 2D EDJ frequency and the EDJ parameters provides a more complete view of the EDJ, making it possible to deepen into its complex structure. In this sense, the parameter Sh measures the sharpness of the EDJ and can be taken as an indicator of the squeezing, with a narrowing and widening of the EDJ translating to positive and negative changes in Sh, respectively. The median of the multimodel changes of Sh indicates a slight narrowing, in agreement with all the above-mentioned previous works. However, our parametric approach also reveals a large uncertainty (non-significant narrowing): the distribution of the changes is centred around the zero line, ranging from positive to negative values. Alternatively, the apparent squeezing pattern of Fig. 1a might be understood as sole changes in the latitudinal frequency, involving more frequent central EDJs and less poleward and equatorward excursions, but without changes in the EDJ width. However, as previously mentioned, Lat and Int parameters do not show clear changes in the future either (Figs. 1b and S2). Thus, none of the interpretations of the spatial pattern depicted by the 2D EDJ frequency is supported by the future changes in EDJ parameters.

Considering the mentioned consensus on the projected squeezing of the EDJ6,7,11,15 and the strong impacts of the EDJ on European regional climates and extreme events42,43, the mismatch between the projected changes retrieved from the two EDJ perspectives (2D EDJ frequency pattern and EDJ parameters) needs to be reconciled. One possible explanation for the apparent inconsistency is that the squeezing is the result of including in the same analysis elements that are responding differently to climate change. One of these elements might be the consideration of the NDJF as a whole, given that the signals of certain EDJ drivers, such as the SPV or the equatorial Pacific SSTs, are not stationary during the winter. The next section presents the EDJ projections for the early (ND) and late (JF) winter separately, in order to address the aforementioned inconsistency and further dissect the spread in the EDJ projections.

Subseasonal analysis of projections

The projected changes in the pattern of 2D EDJ frequency (Fig. 2a, c) and distribution of EDJ parameters (coloured whiskers in Fig. 1b) show large intraseasonal variations and notable differences between ND and JF winter. Considering the EDJ width (Sh parameter), the corresponding distributions for ND and JF (Fig. 1b) do not show appreciable changes, similarly to NDJF. However, this is now consistent with the two subseasonal EDJ frequency maps, neither of which show a squeezing-like pattern (Fig. 2a, c). Note that in both subseasons, the change in the 2D EDJ frequency is dominated by a dipole pattern, indicating meridional shifts rather than changes in the EDJ width over the NATL sector.

Fig. 2: Projections of the EDJ for early and late winter.
figure 2

a and c As Fig. 1a but for early (ND; a) and late (JF; c) winter. b and d Multimodel mean of the future (2069–99) minus present-day (1979–2009) difference in the zonal wind averaged over the NATL. Crosses indicate the grid-points with non-significant differences at the 95% confidence level (after a 1000-trial Monte Carlo test).

Full size image

More interestingly, the early winter EDJ shows a statistically significant displacement to the pole, to the east and toward positive tilts (a higher SW-NE orientation of the EDJ) (Fig. 2a and blue whiskers in Fig. 1b; note that the interquartile range for the associated EDJ parameters of Lat, Lon and Til does not include zero). The poleward shift can also be clearly seen in the two meridional flanks of the EDJ (Latn, Lats), confirming the absence of changes in the EDJ width, as well as in the NATL zonal wind cross section (Fig. 2b, poleward peak in Fig. S2b). Differently, the late winter EDJ does not show such changes but, if any, a tendency to be southward displaced (equatorward peaks in Fig. S2c), although this equatorward shift is not very well captured in the cross-section of Fig. 2d. The reason is that the EDJ is tilted in the NATL, therefore presenting positive and negative frequency changes at the same latitude (Fig. 2c). As a consequence, the signal weakens when the longitudinal average is computed over the NATL (Fig. 2d). Like in early winter, the distributions of longitudinal parameters continue to display an eastward EDJ shift in late winter. However, there are marked differences in uncertainty: during ND, there is a high model agreement on the EDJ elongation over Europe, whereas the distribution of the JF changes presents a large spread and, hence, an uncertain projection.

Out of the ten EDJ parameters, only the latitudinal ones (Lat, Latn and Lats) present significant changes in early and late winter, but of opposite sign. The latitudinal parameters are the most salient features of the NATL EDJ and they explain most of its variability. Indeed, the EDJ latitudinal shift is the primary mode of variability of the NATL zonal wind44. Besides, the changes in the latitudinal parameters are consistent with those found for the 2D EDJ frequency. Therefore, from now on, we will focus on the projections of the EDJ latitude (Lat) and the cause of its opposite responses to climate change in early and late winter.

Projections of the subseasonal temperature and zonal wind mean state

To understand the intraseasonal change in EDJ latitudes, we assess the future changes in the mean state of NATL zonal mean temperature (T), zonal mean zonal wind (U) and SSTs (Fig. 3). The climate change pattern of T is characterised by a stratospheric cooling and a tropospheric warming, the latter being dominated by the TA and AA throughout the entire winter (Fig. 3a, d). The main intraseasonal difference is that the change in T at upper levels and polar latitudes is not statistically significant in late winter (Fig. 3d), suggesting that the intensification of the negative meridional temperature gradient at 200 hPa is stronger in early than in late winter. On the other hand, the SST changes display very similar characteristics in both subseasons (Fig. 3b, e): besides the NATL WH, longitudinal asymmetric warming is present in the equatorial Pacific, leading to a weakening of the longitudinal SST gradient between the western and eastern edges of the basin.

Fig. 3: Climate change projections of temperature, SST and zonal wind.
figure 3

Multimodel mean future changes (shading) and 1979–2009 climatology (contour) of the zonal mean T over the NATL [K] (a, d), SST [K] (b, e) and hemispheric zonal mean U [m/s] (c, f). The future (2069–2099; SSP5–8.5) minus present-day (1979–2009) differences are computed for early (upper row) and late (bottom row) winter separately. Crosses indicate the grid-points with non-significant differences at the 95% confidence level (after a 1000-trial Monte Carlo test).

Full size image

Moving to the zonal mean zonal wind changes, a reinforced subtropical jet is observed in both subseasons (Fig. 3c, f). Moreover, the maximum wind speeds are located at higher levels than in the historical period, which is consistent with the expansion of the troposphere and the subsequent rise of the tropopause23,45. Note that in Fig. 3c and f, the latitudinal shifts of the NATL EDJ are masked by the zonal mean (the zonal wind is averaged globally). Interestingly, the stratospheric zonal wind response to climate change in extratropical latitudes differs between subseasons. Early winter displays an intensification of the zonal wind at polar latitudes and stratospheric levels, which expands from the subtropical jet (Fig. 3c). The reinforcement of the zonal wind in the polar stratosphere does not extend to tropospheric levels, though suggesting that the changes in the two atmospheric layers are not coupled in this case. Late winter shows a very different picture (Fig. 3f). Contrary to the early winter case, the SPV weakens in late winter, and the stratospheric and tropospheric changes are coupled since the zonal wind weakening is vertically continuous along the atmospheric column. Late winter is also the typical timing of the strongest stratosphere-troposphere coupling46. Therefore, our results suggest a potential influence of the stratospheric future changes on the troposphere (and the EDJ) in late winter only.

In the following section we explore the linkages between the projected changes in the EDJ and its drivers (atmospheric and oceanic mean states) in order to explain the intraseasonal differences in the latitudinal shift of the EDJ. To simplify the analysis, we consider some of the aforementioned drivers of the EDJ reported in the literature, including the meridional temperature gradient at 200 hPa (Grad200) and 850 hPa (Grad850), the NATL WH, the SPV and the zonal asymmetries in the equatorial Pacific SST (see the “Methods” section). The chosen phenomena are well-established drivers of the EDJ and capture the most relevant signatures of the atmospheric and oceanic changes identified in Fig. 3.

Drivers of the intraseasonal future changes in EDJ latitude

Early winter

Starting with early winter, we use the regression framework described in Eqs. (1) and (2) of the Methods section to model the dependence of the latitudinal EDJ parameters and the NATL atmospheric circulation on the response of the remote drivers to climate change. The multiple linear regression (MLR) identifies Grad200 and WH as the main large-scale drivers of the future changes in the early winter EDJ latitude (ΔLat). GCM biases of the EDJ latitude also have an influence. The three mentioned drivers explain together 72% of the ΔLat variance simulated by the multimodel ensemble (Grad200 explains 18%, WH 33% and the GCM biases 21% of the ΔLat variance). Similar explained variances are obtained for Latn and Lats as they are correlated with Lat. The influence of the drivers’ responses on the projected changes in EDJ frequency is shown in Fig. 4. For all drivers, their climate change fingerprints induce a meridional dipole in the EDJ extending along the NATL. Grad200 is expected to decrease further, which implies a strengthening of the (negative) meridional temperature gradient. A deeper Grad200 is expected to move the EDJ poleward (Fig. 4a). The WH directly affects the location of the strongest baroclinicity in the NATL26. As the WH deepens, the region of no warming also has a larger extension. In that case, the southern edge of the deep WHs reaches lower latitudes, shifting the baroclinicity region and the EDJ equatorward (Fig. 4b). Contrary, shallow WH would indicate a small warming in that area, but still weaker than in the rest of the NATL. This would confine the WH at very high latitudes, which in turn would push the baroclinicity and EDJ poleward.

Fig. 4: Contributions of future changes in EDJ Lat drivers to the early winter (ND) EDJ response to climate change.
figure 4

a EDJ frequency response (scaled by global warming) [%/K] to a + 1 sigma future change in Grad200. Green contours show the multimodel mean climatology of the 1979–2009 period (starting at 20% and drawn every 30%). Stippling indicates significance at the 95% confidence level (i.e. local regression coefficients of the corresponding driver that are significantly different from zero). b Same as (a) but for the NATL WH. c Same as (a) but for the Lat EDJ Bias. d Same as Fig. 1b but for Neutral-GCMs (see the “Methods” section).

Full size image

Finally, the historical biases in the EDJ latitude influence its response to climate change, especially in the southern flank of the EDJ (Fig. 4c). The dipole pattern of Fig. 4c indicates that equatorward biased GCMs (i.e. with a negative Lat EDJ bias) display more poleward shifted EDJs in the future than the unbiased (Neutral-GCMs) ones. There are 11 GCMs with a significant bias in EDJ Lat (Biased-GCMs), out of the 21 GCMs of the multimodel ensemble (see Methods), and all of them present a southward shifted EDJ in the historical period (Fig. S3a and c). Therefore, the contribution of GCM biases to the multimodel EDJ response to climate change consists of a poleward shift of the EDJ. In fact, if we analyse the projected changes in the latitudinal parameters for the Neutral-GCMs sample, the poleward displacement of the EDJ is no longer present in early winter (blue boxplots in Fig. 4d), and there is no meridional shift in the EDJ projections. These results show that at least part of the detected poleward migration of the EDJ under climate change scenarios can be a consequence of the GCM biases. For Neutral-GCMs, the biases in EDJ latitude are small and the other drivers (Grad200 and WH) explain most (~90%) of the spread in ΔLat, with ~27% of the variance corresponding to Grad200 and ~63% to WH. As the climate change responses in Grad200 and WH involve opposite changes in the EDJ latitude, Neutral-GCM projections reflect the competing effects of these two drivers. This explains the lack of agreement in the sign of the early winter latitudinal EDJ parameters in Fig. 4d.

Late winter

The picture changes when assessing the drivers of the changes in EDJ latitude for late winter. In this case, our regression approach indicates that the multimodel spread in ΔLat is largely explained by only one large-scale driver, the SPV. A weakening of the SPV is associated with an equatorward shift of the EDJ (Fig. 5a), as expected from the stratosphere-troposphere coupling46. The projections of SPV and EDJ in late winter show a consistent picture: in the future, the SPV weakens (Fig. 3f) and the EDJ shifts equatorward (see also the red boxplot in Fig. 1b). For this subseason, the bias in EDJ latitude is again found to influence ΔLat. The spatial pattern is similar to the ND one, but with the meridional dipole more defined and displaced to the east (Fig. 5b). Like in early winter, all Biased-GCMs are shifted equatorward, contributing to a poleward shift of the EDJ that opposes the equatorward shift induced by the weakening of the SPV. The SPV, together with the Lat EDJ Bias, explains half of the total variance in ΔLat. For the Neutral-GCMs subsample, the SPV is the only driver influencing the EDJ latitudinal response to climate change (~50% of the explained variance). In addition, the consensus on the equatorward shift detected in the multimodel ensemble is stronger in the Neutral-GCMs sample (compare Fig. 1b vs. Fig. 4d). Therefore, the results for late winter reinforce the fact that the projected poleward migration of the EDJ can be substantially driven by GCM biases. Note that future changes in the other drivers (equatorial Pacific SST and Grad850) have negligible influences on EDJ latitude for both early and late winter.

Fig. 5: Contributions of future changes in EDJ Lat drivers to the late winter (JF) EDJ response to climate change.
figure 5

Same as Fig. 4a but for the drivers of EDJ latitude in late winter (JF).

Full size image

Discussion

In this paper, we have described the future winter changes of the North Atlantic (NATL) eddy-driven jet (EDJ) in the last generation of general circulation models (GCMs) by exploiting a novel daily description of the EDJ, which relies on two complementary approaches: an explicit 2D diagnosis and a multiparametric description of the complex EDJ structure.

Although there is consensus on the future poleward shift of the EDJ at hemispheric scales, several studies did not find clear latitudinal migrations in the NATL. Instead, a large spread in the projections of EDJ latitude has been detected across GCMs, ranging from poleward to equatorward displacements6,9. Other studies report that the lack of a robust EDJ response to climate change is due to opposing effects of two drivers of the NATL EDJ, the Tropical (TA) and Artic (AA) amplifications, which result in small net changes in latitude, but a pronounced squeezing of the EDJ6,9. However, our results indicate that the future squeezing pattern of the winter EDJ could be an artefact from mixing different intraseasonal EDJ responses to climate change that involve opposite meridional shifts of the EDJ. By splitting the winter (November-to-February, NDJF) into two subperiods, we find a high model agreement on a poleward EDJ shift in early winter (ND), followed by a slight equatorward shift in late winter (JF). In fact, when we diagnose changes in the EDJ width explicitly, we do not find significant changes towards narrower or wider EDJs in the future, not even in early and late winter. Indeed, the apparent winter squeezing evidenced in the zonal wind and 2D EDJ frequency maps is no longer present when the EDJ changes are computed for early and late winter separately. Therefore, the effect of combining the two winter subseasons is two-fold: it yields a disproportionate increase in the uncertainty of the projections of the EDJ parameters, and a misleading response of the EDJ due to averaging opposite signals that occur at different times of the winter.

The intraseasonal latitudinal responses of the EDJ to climate change are shown to be promoted by different drivers: the upper tropospheric temperature meridional gradient (Grad200) and the NATL sea surface temperature (SST) warming hole (WH) in early winter, and the stratospheric polar vortex (SPV) in late winter. This means that the processes that drive the future changes in the EDJ latitude change throughout the winter from thermodynamic to dynamic processes. In particular, the strong influence of the SPV on the EDJ latitudes in late winter outweighs the effect of other active drivers of this subseason32, such as Grad200 and NATL WH. According to our regression model, SPV, and not the AA, represented herein as the low tropospheric temperature gradient (Grad850), would be the main responsible for the projected equatorward shifts of the EDJ, albeit limited to late winter. Therefore, the drivers of the ‘tug-of-war’ could be different (or at least should be expanded) from those previously thought. The stratosphere-troposphere coupling is typically stronger in late than in early winter, which could explain why the SPV plays an active role in the JF period but not in ND. Although some authors have linked AA to an equatorward shift of the EDJ9,17,18,47, more recent studies, such as Zappa and Shepherd (2017)33 have not found a significant impact of the AA on the zonal wind across the NATL region.

GCM biases in the EDJ latitude also influence its projections. GCMs simulating an equatorward-shifted EDJ in the historical period project a larger poleward shift of the EDJ in the future than unbiased GCMs. Indeed, when analysing the sample formed by the GCMs without biases in the EDJ latitude, the projections present no clear shift of the EDJ in early winter and a strong displacement towards the equator in late winter. This suggests that part of the projected poleward shift of the EDJ under climate change could be exacerbated by the GCM biases. One may speculate about the underlying mechanism for this influence. The answer could be found in the relative location of the EDJ to the tropical warming. Experiments carried out with idealised GCMs have shown that tropical warming forces a poleward shift of the EDJ through eddy heat and momentum fluxes18. More recently, Baker et al. (2017, 2018)48,49 have designed a set of experiments to study the sensitivity of the EDJ to different warming locations and intensities. They found that the poleward displacement of the EDJ was driven by warming sources situated at its equatorial flank, with larger tropical warmings inducing larger poleward shifts. Accordingly, Biased-GCMs, which are equatorward shifted in present-day conditions, would exhibit larger poleward shifts in the future than Neutral-GCMs, since their EDJs are closer to the equator and experience greater warming on their equatorial flank.

In summary, the multiparametric perspective of the EDJ has provided a better understanding of the winter EDJ responses to climate change, allowing us to question some established changes like the EDJ squeezing, disentangle the ambiguous latitudinal EDJ responses and identify the key role of GCM biases. Furthermore, the use of the EDJ parameters together with the multiple linear regression (MLR) framework has enabled the identification of the major drivers of the future changes in the EDJ latitude, and the quantification of their relative roles and spatial fingerprints, facilitating the interpretation of the mechanisms behind the intraseasonal latitudinal shifts. Although useful, our approach also presents some drawbacks. For instance, the EDJ detection method does not account for multiple EDJs and their associated latitudes. This restriction might affect the latitudinal projections, although the effects should be small because multiple EDJs are relatively uncommon. The MLR framework also presents some limitations because it only captures the linear relations between the drivers’ responses and future EDJ changes, but not more complex behaviours such as asymmetric or non-linear responses to the drivers’ changes or eventual interactions among the drivers. Unravelling the potential dependencies among the drivers and their non-linear effects on the EDJ could further improve the assessment of the uncertainties in regional climate change projections.

The multiparametric EDJ perspective could also shed some light on other interesting, albeit less controversial, topics that remain for future work, such as the eastward displacement of the EDJ over Europe and the tendency towards EDJs with a single flow configuration. The occurrence of more zonal and eastward displaced EDJs in the future is consistent with projected decreases in European blocking9,50, although feedbacks between the eddies and the mean flow prevent separating cause and effect. Finally, our approach could, in principle, be extended to analyse future projections of the EDJ in other seasons, including the summer EDJ, which has been linked to recent changes in the NATL atmospheric circulation and an unprecedented increase in the frequency of extreme events51.

Methods

In this study, we use the output of historical and SSP5–8.5 simulations from the 6th phase of the Coupled Model Intercomparison Project (CMIP652). Our multimodel ensemble is formed by one member of 21 global climate models (GCMs), listed in Table S1. The climate change signal is defined as the difference of the climatological means computed over two 30-year periods with different levels of anthropogenic forcings: 1979–2009 of the historical and 2069–2099 of the SSP5–8.5 runs. For each year of these periods, we compute time averages over the winter (November-to-February, NDJF) season and its two halves, i.e. early (ND) and late (JF) winter. The considered variables include daily zonal wind at 850 hPa (u850), monthly means of zonal wind (U) and air temperature (T) at different pressure levels, and sea surface temperature (SST). For model evaluation, we use the ERA5 reanalysis53. Model data and ERA5 have been linearly interpolated to the same regular 2.5° × 2.5° grid before performing additional computations.

Jet parameters

The new method presented by Barriopedro et al. (2023)42 is used to characterise the eddy-driven jet (EDJ) on a daily scale. The EDJ is described by ten daily parameters computed from the 10-day low-pass filtered u850. The set is formed by two categories of parameters. The basic ones are derived from the meridional profile of the zonal wind averaged over the NATL sector ([60°W, 0°]), Uc:

  • The latitudinal position (Lat) and intensity (Int) are similar to those introduced by Woollings et al. (2010)44 (see Table 1).

  • Sharpness (Sh) measures how steep the zonal wind peak is.

  • Poleward (Latn) and equatorward (Lats) flanks, located at either side of Lat, identify the meridional boundaries of the EDJ.

The remaining parameters employ additional meridional profiles (Uλ), which are computed as running means of the zonal wind over longitudinal windows of 60° width centred at each longitude λ of the [90°W, 30°E] sector. These parameters refer to specific attributes of the 2D zonal wind structure detected by Lat. This structure is defined by the pairs (Lat*λ, Intλ), which are obtained by zonally tracking the latitudinal peak Lat (detected in Uc ≡ U30W) over the contiguous Uλ profiles of the NATL sector. The search of Lat*λ is constrained so that Lat*λ values at contiguous longitudes do not fall apart by more than 5°. Note that the so-tracked latitudes Lat*λ do not necessarily coincide with Latλ, which are the latitudes of maximum Uλ within the [15°N, 75°N] band.

  • Tilt (Til) quantifies the slope of the zonal wind maxima along the NATL. Positive (negative) values indicate SW–NE (NW–SE) tilts.

  • Longitudinal position (Lon) indicates whether the zonal wind maxima are larger over the eastern or western NATL.

  • Westward (Lonw) and eastward (Lone) extensions inform on zonal elongations of the EDJ by detecting its outermost regions of influence (i.e. the longitudes where the zonal gradient of zonal wind is the largest).

  • Departure (Dep) measures the spread of the latitudinal positions of the zonal wind maxima detected across the NATL, therefore quantifying the extent to which the EDJ presents multiple branches (split-like pattern) or a single continuous structure. High values indicate large spread and hence the presence of multiple zonal wind maxima.

In order to facilitate the interpretation of the EDJ parameters, Table 1 describes the equations employed in their computation, along with a brief explanation. The method also provides a daily 2D detection of the EDJ, which relies on the identification of Latn and Lats for each longitudinal sector Uλ of the [120°W, 60°E] domain (hereafter Latnλ and Latsλ). The EDJ is defined as the grid points lying between Latnλ and Latsλ (the latitudinal flanks of Latλ). Labelling them with ones and the rest with zeros, we generate a binary field describing the 2D structure of the EDJ. The daily binary fields of a given time interval can be employed to obtain 2D maps with the local frequency of EDJ occurrence. To do so, we simply count the number of days of the considered period when the EDJ was detected at each grid point. These 2D EDJ frequency maps describe the local recurrence and preferred spatial configuration of the EDJ over the considered period and are expressed in percentage of time. The methodology has already been applied to examine the relationship between the EDJ and winter temperature extremes over Europe43.

Definition of drivers of the future changes in EDJ

The metrics used in this study as drivers of the future changes in EDJ are collected from previous studies7,10,33, which allow us to gather a set of remote factors that impact the NATL circulation. The climate change response of each driver is defined as the difference between the climatological mean metrics of the end of the 21st century (2069–2099) and the historical period (1979–2009). The drivers and associated metrics are defined as follows:

  • Meridional temperature gradient at 200 hPa (Grad200): the difference between the polar ([70°N, 90°N]) and tropical ([0°, 20°N]) averages of the zonal mean temperature computed over the [120°W, 60°E] domain at 200 hPa.

  • Meridional temperature gradient at 850 hPa (Grad850): same as Grad200 but at 850 hPa.

  • Stratospheric polar vortex (SPV): zonal mean zonal wind averaged between [60°N, 75°N] at 10 hPa.

  • Warming Hole (WH): SST averaged over [35°N, 60°N; 40°W, 10°W].

  • Zonal asymmetries in the equatorial Pacific SST: SST difference between the NIÑO4 [5°S, 5°N; 160°E, 150°W] and the NIÑO3 [5°S, 5°N; 150°W, 90°W] region.

The consideration of these phenomena as large-scale drivers of the EDJ latitude is supported by the literature. The direction of the relationship is clear for all of them, with the driver acting on the EDJ variability rather than the other way around. The thermodynamical drivers, namely, Grad200, Grad850 and WH affect the EDJ by modifying the NATL baroclinicity, which is the main source of variability of the NATL zonal wind. Grad200 is linked to (and largely modulated by) the TA, which induces EDJ shifts7,10,18,47. Similarly, Grad850 is associated with the AA, which modifies the EDJ latitude17,18,20,21. There are multiple causes behind AA (e.g. albedo and cloud feedbacks, changes in oceanic and atmospheric heat transport, modification of the surface type, etc.)22. The NATL WH is associated with the slow-down of the Atlantic Meridional Overturning Circulation (AMOC), which leads to reduced heating over the subpolar gyre region54, changes in the meridional SST pattern, baroclinicity and ultimately, the EDJ latitude26,27. The slow-down of the AMOC has been attributed to different factors, including the Greenland ice-sheet melting55 and sea-ice loss in the polar regions56. The NATL WH also influences the zonal gradient of near-surface air temperature across the NATL sector. Moving to the dynamical drivers (SPV), there exists mounting evidence about the effects of the SPV on the NATL EDJ46, although the exact mechanism explaining the downward influence of the stratosphere on the troposphere is still not clear. Several studies have shown the potential impacts of future changes in SPV on the NATL tropospheric circulation30,32,33. Finally, the zonal asymmetries of the equatorial Pacific SST are expected to increase their influence on the NATL circulation through the reinforcement of the atmospheric teleconnections10,34. Additional drivers, such as the location of the NATL subtropical jet, the global near-surface temperature or the zonal 850 hPa temperature gradient in the NATL, were also analysed. However, they are not included in the presented analysis as they were not found independent from other drivers.

In addition to the large-scale drivers, we analyse whether future projections of the EDJ latitude are influenced by GCM biases (i.e., the ability of the GCM to capture present-day conditions). In particular, we focus on GCM biases in the EDJ latitude (Lat) regardless of the source leading to these biases. For each GCM, this bias is defined as the difference between the climatological means (1979–2009) of the Lat parameter obtained for the historical run and ERA5. EDJ Lat biases are computed for the two winter subseasons separately because they can exhibit intraseasonal variations (Fig. S3).

Multiple linear regression framework

The future change in the frequency pattern and parameters of the EDJ can be described as a linear combination of the drivers’ responses to climate change. To find the leading drivers of the projected changes of the EDJ in the multimodel ensemble, we perform a multiple linear regression (MLR) similar to Zappa and Shepherd (2017)33. The predicted variables are the future changes in the EDJ parameters (Eq. (1)) and in the 2D EDJ frequency field (Eq. (2)). In both cases, the predictors correspond to a vector constructed from the simulated climate change responses of that driver across the multimodel ensemble (each element of the vector represents the driver’s response in one GCM). For instance, for the sample considering all GCMs, the changes in the EDJ latitude and the changes in the drivers’ vectors have 21 elements, the number of GCMs that form the sample. Before building the regression models, the predictors and predicted variables were scaled by the global warming of each GCM, dividing them by the simulated change in the global surface temperature. This allows us to account for the different climate sensitivities across the multimodel ensemble:

$$\frac{\varDelta {{{\rm {Param}}}}_{m}}{\varDelta {{{\rm {GW}}}}_{\!m}}=a+\mathop{\sum }\limits_{i=1}^{6}{b}_{i}{\left(\frac{\varDelta {{\rm {Driver}}}}{\varDelta {{\rm {GW}}}}\right)}_{\!m,i}+{{\rm {res}}}\,$$
(1)
$$\frac{\varDelta {{{\rm {Freq}}}}_{x,m}}{\varDelta {{{\rm {GW}}}}_{\!m}}={a}_{x}+\mathop{\sum }\limits_{i=1}^{6}{b}_{x,i}{\left(\frac{\varDelta {{\rm {Driver}}}}{\varDelta {{\rm {GW}}}}\right)}_{\!m,i}+{{{\rm {res}}}}_{x}\,$$
(2)

where the variables \(\varDelta {{\rm {Param}}}\), \(\varDelta {{\rm {Freq}}}\), \(\varDelta {{\rm {GW}}}\) and \(\varDelta {{\rm {Driver}}}\) are the changes between the future (2069–2099, SSP5–8.5) and present-day (1979–2009, historical) averages of the EDJ parameters, the 2D EDJ frequency field, the global mean surface temperature and the drivers, respectively. The coefficient \(a\) provides the response of the EDJ in the absence of drivers’ changes, \({b}_{i}\) gives the EDJ response to anomalies in the remote driver \({\varDelta {{\rm {Driver}}}}_{i}\), and \({{\rm {res}}}\) represents residual variations not captured by the MLR. The suffixes m and x represent the GCM and the location in the longitude-latitude field. The MLR framework is applied to winter averages of the EDJ, as well as to the early and late winter subseasons, separately. The sign of EDJ frequency maps in Figs. 4 and 5 corresponds to that associated with the southward EDJ Lat Bias and the projections of the drivers detected in Fig. 3, i.e., a reinforcement of the negative Grad200, the intensification of the WH and a weakening of SPV.

The predictor selection is based on the computation of the p-value, which assesses the effect of the predictor candidate on the MLR model, following a stepwise procedure with forward selection and backward elimination. Starting with an empty MLR model, the predictors are added and removed sequentially, retaining those with significant (p < 0.05) non-zero coefficients and the smallest p-value. The process is repeated until adding and removing predictors do not improve the MLR model. This type of MLR model deals with the potential collinearity among predictors, because it includes only predictors that explain a significant additional fraction of the variance (provide independent information).

Model populations and statistics

We study the projected changes in the EDJ for different populations of GCMs. The first one is the full multimodel ensemble, which considers the 21 GCMs of Table S1. A second group only includes those GCMs that represent the climatological EDJ latitude sufficiently well for the 1979–2009 period. The purpose is to investigate if the projected changes depend or not on the ability of the GCMs to capture the mean EDJ features. The GCM bias is defined as the difference of the historical (1979–2009) monthly EDJ latitude climatology of each GCM minus that corresponding to the ERA5 reanalysis. The significance of the difference is assessed with a 1000-trial Monte Carlo at the 95% confidence level applied to the monthly series of EDJ latitudes (defined for early or late winter). Monthly series are computed from the daily values of EDJ latitude. The quantification of biases allows us to construct an ensemble of Neutral-GCMs, which comprise those with non-significant differences in the EDJ latitude with respect to ERA5 (Fig. S3b and d). The remaining GCMs, those that present a significantly biased EDJ Lat (Fig. S3a and c) are characterised by southward displaced EDJs with respect to ERA5.

For all of the diagnosed variables, the significance of the climate change signal, defined as the 30-yr mean state difference between the historical and SSP5–8.5 simulations, is tested using a Monte-Carlo test of 1000 realisations at the 95% confidence level. To do so, the projected change is tested against a 1000-sample distribution of differences between two randomly generated subsets. These subsets have the same number of cases as the historical and SSP5–8.5 but are generated by selecting random simulations from the total number of available experiments, namely, the 21 historical and SSP5–8.5 simulations.