This study evaluates whether CMIP6 models reproduce the observed relationship between autumn North Atlantic SSTs and winter atmospheric circulation, and whether that relationship has an ocean driver. The analysis uses three steps to separate the simultaneous atmospheric forcing of SSTs and the ocean driven component. First, contemporaneous Maximum Covariance Analysis (MCA) of SST and MSLP within autumn and winter assesses atmospheric forcing of SST, which dominates on seasonal timescales. Comparison with univariate EOFs tests whether the coupled modes reflect the dominant variability of each field. Second, lagged MCA of autumn SST and winter MSLP tests whether models reproduce the observed autumn SST-winter MSLP relationship. Lagged covariance alone does not demonstrate a feedback, therefore third, we use circulation analogues to separate autumn THF into atmosphere-driven and ocean-driven components, and test which one is linked to the winter NAO.

MCA is used to identify the dominant modes of spatio-temporal covariance between North Atlantic mean sea level pressure (MSLP) and SST, applied separately within autumn (September–November) and winter (December–February) seasons, and across seasons. The approach is the same as that followed by .

Let S be the SST anomaly matrix and P the MSLP anomaly matrix (each with p spatial grid points × n temporal samples). The cross-covariance matrix between the two fields is: 1CSP=1nPST. Singular value decomposition (SVD) of the cross-covariance matrix yields: 2CSP=UDVT, where U and V are matrices containing the left and right singular vectors, representing spatial patterns in the SST and MSLP fields, respectively. D is a diagonal matrix with singular values dk ordered in decreasing magnitude. Each pair of singular vectors defines a coupled mode that maximises the covariance between the two fields and explains a portion of the total cross-covariance.

The associated expansion coefficients are obtained by projecting the anomaly fields onto their respective singular vectors. Homogeneous patterns are defined as the correlation between each field and its own expansion coefficients, while heterogeneous patterns are obtained by correlating each field with the expansion coefficients of the other field. These patterns highlight the spatial structures associated with coupled SST–MSLP variability.

The relative importance of each mode is quantified using the squared covariance fraction (SCF): 3SCFk=dk2∑i=1Kdi2, which represents the proportion of total squared covariance explained by mode k.

We use the circulation analogue method of to explore the relative roles of atmospheric and oceanic forcing of autumn THF anomalies. The method estimates the atmospheric circulation-driven component of THF anomalies using an atmospheric analogue technique that samples other years in the dataset with a similar MSLP field.

For each year in the dataset, i, the seasonal mean MSLP anomalies within the Euro-Atlantic domain (90° W–40° E, 20–85° N) are compared with all other years in the dataset using the area-weighted Euclidean distance. A subset of Na years with the smallest Euclidean distances from year i are identified as candidate analogue years. From this subset, Ns years are randomly selected and used to reconstruct the MSLP anomaly field for the target year as a weighted linear sum: 4MSLPi,j=∑kakMSLPk,j, where ak is the weight assigned to the kth analogue year, determined based on its proximity to the target year's anomalies.

The analogue years and their weights, ak, are then used to estimate the THF anomaly at each gridpoint, j, associated with the circulation state in the target year (THF_circ,i,j) independent of the SST state: 5THFcirc,i,j=∑kakTHFk,j.

This assumption relies on the distribution of weights, ak, being sufficiently broad such that THF_circ is not derived from only a small number of strongly weighted years which may not ensure independence of the SST state. The procedure is repeated Nr times using different random subsets of analogue years, and the resulting reconstructions are averaged to obtain the estimate of THF_circ,i. In this study, Na, Ns and Nr are 50, 30 and 100, respectively. demonstrated using a 500-year control simulation that the result is not strongly sensitive to the choice of these parameters and we have verified this for the shorter ERA5 dataset (not shown).

The residual between THF_i and THF_circ,i is inferred to be the THF component in year i primarily associated with the oceanic state (THF_res,i): 6THFi=THFcirc,i+THFres,i. THF_res,i encompasses concurrent ocean-driven variability, as well as the memory and persistence of preceding SSTs.

The characteristics of spatio-temporal variability in autumn THF, THF_circ and THF_res are assessed by computing the first two Empirical Orthogonal Functions (EOFs) and corresponding PC timeseries. The respective association of autumn THF with the winter NAO is assessed by linearly regressing the winter MSLP onto PC1 and PC2 of the THF component timeseries.

The NAO and EAP indices are defined as the first and second EOFs of seasonal mean MSLP anomalies. Indices are computed per ensemble member, then used separately. We multiply the EOF patterns by the standard deviation of their principal component (PC) timeseries to recover the patterns in units of hPa. EOF1 exhibits a largely consistent spatial structure across autumn and winter seasons (see Figs. S1 and S2 in the Supplement). In contrast, EOF2 shows notable seasonal variability. During winter, EOF2 corresponds to the recognised EAP and is consistent across ERA5 and the CMIP6 models (Fig. S2). However, in autumn ERA5 and most of the CMIP6 models show a south-eastward tilted pattern that resembles a Rossby wave train emanating from the tropical Atlantic (Fig. S1).

MCA and the circulation analogue methods were applied to each ensemble member and then averaged to make an ensemble mean for each model. Multi-model means were then computed from respective ensemble means and the model spread calculated as the standard deviation across the multi-model means.

Sampling uncertainty on the estimation of the spatio-temporal variability of THF, THF_circ and THF_res in ERA5 was assessed by bootstrapping the years used to calculate the EOFs without replacement, using a sample size of 40.

Figure  shows the first three MCA modes for autumn SST and MSLP in ERA5. The modes explain 39 %, 20 % and 17 % of the squared covariance, respectively, collectively accounting for 76 % of the covariance. For MCA1, SST anomalies exhibit a horseshoe pattern with warm anomalies in the central North Atlantic surrounded by cold anomalies extending from the Labrador Sea to the western UK, west of Portugal and across the subtropical Atlantic (Fig. a). The associated MSLP anomalies exhibit a positive NAO-like structure, but the anomalies across the basin are less zonal than the NAO with an additional centre of action in the North Sea and an intensified centre of action west of Portugal (Fig. d). The regression of autumn THF anomalies onto the MCA1 timeseries shows a pattern that is broadly anti-correlated with SST (Fig. g), indicative of atmospheric forcing of SST anomalies via anomalous THF.

Positive SST anomalies in MCA2 are exhibited across the subpolar north Atlantic, Labrador Sea and east of Canada accompanied by negative SST anomalies west of Europe (Fig. b). The associated MSLP anomalies (Fig. e) exhibit negative anomalies over the eastern North Atlantic, western Europe and North Africa and positive anomalies over Scandinavia, Greenland and a small region in the western part of the basin. Similar to MCA1, the THF regression pattern for MCA2 is anticorrelated with the SST anomalies (Fig. h).

In MCA3 there is a tripolar SST pattern with a band of warm anomalies extending from the Canadian coast to Portugal and cold anomalies to the east of the USA and surrounding Iceland and the UK (Fig. c). Positive MSLP anomalies are broadly collocated with positive SST anomalies with a slight northward phase shift of the wave train, and THF and SST anomalies are anticorrelated (Fig. f, i).

Figure shows the CMIP6 multi-model mean MCA modes 1–3 of autumn SST (Fig. a–c) and autumn MSLP (Fig. g–i). The inter-model standard deviation of the MCA modes are shown in Fig. d–f for SST and Fig. j–k for MSLP. The modes for the individual models are shown in Figs. S3–S16. Each ensemble member covers the same 1940–2014 period as ERA5 and MCA is applied to each member individually before averaging. The spread across ensemble members therefore represents the sampling distribution of MCA patterns obtained from a 75-year record. Hatching denotes where the ERA5 MCA amplitude exceeds the 97.5th percentile of the distribution of all model ensemble members, and equivalently falls below the 2.5th percentile for stippling. The spatial structure of MCA modes 1–3 of the autumn SST-MSLP relationships are, on average, well captured by the models. ERA5 lies within the ensemble spread at most gridpoints, which means individual members can produce autumn SST MCA patterns that are locally as strong as ERA5. The inter-model spread indicates strong agreement among the models on the structure of MCA1, with small regions where the spread exceeds the multi-model mean mostly in areas where the amplitudes are weak in both ERA5 and the models (Fig. d, j, p). The inter-model spread is relatively larger for MCA modes 2 and 3, mainly regarding the position of the nodes between centres of action but this spread is still proportionately small compared with the multi-model mean and the overall patterns are generally consistent across models (Figs. S3–S16).

MCA identifies patterns that maximise covariance between two variables, which may be distinct from the dominant modes of variability of the separate variables. Figure  shows the Pearson correlation coefficient between the MCA1 timeseries and PCs 1–3 of each variable, to quantify the similarity between the MCA1 patterns and the separate EOFs 1–3 of SST and MSLP. The autumn SST and MSLP EOFs 1–3 are shown in Figs. S17 and S1 for comparison. We focus on MCA1 because this explains the largest proportion of SST and MSLP covariance.

In ERA5, MCA1 SST primarily resembles EOF1 (r = 0.89, p = 1.3 × 10⁻²³), with a dominant warm anomaly in the central North Atlantic. The ERA5 correlation of SST MCA1 with EOF2 is weaker but significant (r = 0.40, p = 1 × 10⁻³) and insignificant for EOF3. In comparison with models, the ERA5 correlation between SST MCA1 and EOF1 lies in the extreme upper tail of the distribution of correlations across individual ensemble members for most models, generally above the 90th percentile (Fig. a). The correlation of SST MCA1 with PC2 lies well within the distributions of modelled correlations (Fig. b), while for PC3 the ERA5 correlation falls in the lower tail of the modelled distributions (Fig. c). This suggests that the modelled MCA1 SST anomalies do not resemble PC1 strongly enough and resemble PC3 more than in ERA5. However, in most cases, the ERA5 values lie within the spread of ensemble members meaning we cannot rule out that the reanalysis period was unusual. The exceptions are CMCC-CM2-SR5, CNRM-ESM2-1 and MIROC-ES2L where the MCA1 correlation with PC1 of SST is lower than in ERA5.

The autumn MSLP MCA1 in ERA5 is similarly correlated with MSLP PC1 (r = 0.66, p = 1.7 × 10⁻⁹) and PC2 (r = 0.62, p = 2.4 × 10⁻⁸). This means the autumn MCA1 resembles a mixture of EOF1 (Fig. S1a) and EOF2 (Fig. S1b), respectively. The ERA5 correlations of MSLP MCA1 with PC1 and PC2 lie within the spread of members for almost all CMIP6 models (Fig. d and e), indicating they are capable of capturing the resemblance of the MSLP MCA1 pattern to the separate MSLP EOFs. However, in all the models the resemblance of MCA1 to EOF3 is generally higher than in ERA5 and is comparable to that for the EOF2, indicating the MCA1 MSLP pattern is generally more of a mixture across different EOFs.

The analysis in this section has shown that the CMIP6 models simulate consistent covariability between SST, THF and MSLP in autumn to that found in ERA5, and that, after accounting for sampling uncertainty, the modelled MCA1 modes show consistent resemblance with the leading EOFs of each variable as in ERA5. Correlation analysis shows that MCA1 primarily corresponds to EOF1 of SST and EOF1 and 2 of MSLP, indicating that the coupled mode reflects large-scale variability patterns such as the NAO. Models capture these relationships, although they show a more variable representation of the relative similarity to each EOF compared to ERA5.

Lastly, we note that the analogous contemporaneous winter SST-MSLP MCA1 mode for ERA5 shows a tripolar SST structure (Fig. S18a) coupled with an NAO-like MSLP pattern (Fig. S18d). The winter THF anomalies associated with MCA1 are anticorrelated with SST (Fig. S18g), consistent with the autumn results. The CMIP6 models show similar contemporaneous winter MCA modes to ERA5 (Fig. S19), although some differences are evident. The band of positive SST anomalies extending from the Gulf Stream towards western Europe is weaker in the multi-model mean than in ERA5, with ERA5 anomalies lying beyond the 97.5th percentile of ensemble members (Fig. S19a) and the inter-model spread is larger in winter than in autumn.

This analysis provides a baseline for the remainder of the paper, as differences between model and ERA5 relationships in the lagged relationships are unlikely to arise from errors in atmospheric forcing of SST or in the dominant SST variability.

To investigate the potential effect of North Atlantic SST on the atmosphere, as discussed in Sect. , we next analyse the lagged MCA modes between autumn SST and winter MSLP. In ERA5, MCA1 explains 58 % of the squared covariance and is characterised by a positive SST anomaly in the central North Atlantic and negative anomaly in the tropical Atlantic and west of the UK and the Iberian peninsula (Fig. a), and a positive NAO-like MSLP pattern (Fig. d). The MCA1 SST pattern closely resembles that reported in for November SSTs, so this result supports their finding. MCA2 and MCA3 explain substantially less covariance in ERA5 compared with MCA1 (14 % and 8 %, respectively). Note that the colour bars are different from the contemporaneous autumn MCA modes in Figs.  and , highlighting that the lagged relationships are weaker.

The corresponding multi-model mean lagged MCA1 autumn SST and winter MSLP patterns are shown in Fig. , along with the inter-model spread. The modes for individual models are shown in Figs. S20–S33. The multi-model mean MCA1 MSLP pattern shows an NAO-like structure (Fig. d), similar to ERA5. The inter-model spread in MCA1 MSLP near the dominant centres of action is small compared with the mean amplitude, indicating broad agreement among models of this pattern. The modelled MCA2 and MCA3 MSLP patterns also show strong agreement with ERA5, with the main centres of action being well captured (Fig. h, i).

In contrast, the multi-model mean MCA1 SST pattern is markedly different from ERA5 both in amplitude and structure (Fig. a), and shows poor model agreement (Fig. d). This is similar for the SST patterns associated with MCA2 and MCA3, where the inter-model spread exceeds the multi-model mean amplitude (Fig. e–f). Despite the apparent differences between the modelled MCA SST patterns and ERA5, there are relatively few regions where ERA5 exceeds the 2.5th or 97.5th percentiles of the ensemble member spread (Fig. a–c), which is indicative that strong autumn SST MCA patterns can be found in individual members. The autumn-winter MCA SST patterns show more regions where ERA5 lies outside of the ensemble spread in individual models (Fig. S20–S33) for MCA1–3 where the main centres of action are either underestimated or have the opposite sign to ERA5.

The area averaged MCA1 autumn SST amplitude over the central North Atlantic region was computed for each ensemble member (Fig. S34). The ERA5 amplitude exceeds every member in 9 of 14 models. Across all models, only 5 ensemble members out of 371 have a lagged MCA1 autumn SST amplitude in the central North Atlantic equal to or greater than that in ERA5. The difference in the autumn SST precursor is therefore unlikely to be explained by sampling uncertainty alone.

To quantify the similarity between the autumn SST-winter MSLP MCA1 and the separate EOFs for each variable, Fig.  shows the Pearson correlation coefficient between the MCA1 timeseries and PCs 1–3. The corresponding EOFs of autumn SST and winter MSLP in ERA5 and the CMIP6 models are shown in Figs. S17 and S2. As previously discussed, MCA1 MSLP predominantly resembles the winter NAO (EOF1) for ERA5 and the CMIP6 models (Fig. d), with weak correlations with PC2 and PC3 of winter MSLP (Fig. e–f). In contrast, in ERA5 the autumn-winter MCA1 SST shows the strongest correlation with PC1 (r = 0.92, p = 6.8 × 10⁻²⁹), with a value above the range of ensemble members for most models and in the very edge of the distribution for only three models (Fig. a). Conversely, the models show a stronger relationship of MCA1 with PC2 and PC3 of autumn SST than is seen in ERA5, which lies at the lower end of the ensemble member distributions for both PCs.

These results show that the modelled covariance between autumn SST and winter MSLP appears to be different from ERA5. While ERA5 predominantly identifies PC1 of autumn SST as being related to the winter NAO, the models have a more mixed autumn SST signal which projects similarly onto EOFs 1–3 with no dominant preferred mode. This does not appear to be related to a systematic difference in the model representation of the EOFs of autumn SST or the relative variance explained by each mode (Fig. S17).

The lagged MCA cannot establish whether the ERA5 relationship reflects a feedback of the ocean onto the atmosphere. One possible explanation for the weaker lagged relationship in the models is that precursor autumn SST anomalies persist less strongly into winter than in ERA5. Figure  shows the regression of monthly SST anomalies for December, January and February onto the autumn SST-MSLP MCA1 expansion coefficients in the models and ERA5. We use the autumn MCA1 patterns because these are similar between the models and ERA5 (Figs. a and a), and they resemble the lagged autumn SST–winter MSLP MCA1 pattern in ERA5 (Fig. a), unlike the equivalent lagged MCA1 patterns in the models (Fig. a). The autumn SST pattern persists into winter in ERA5 and the models and the ERA5 regression lies within the 2.5–97.5th percentile range of all ensemble members over most of the North Atlantic. This result suggests that the weaker lagged autumn SST-winter MSLP relationship in the models cannot be attributed to weaker persistence of North Atlantic precursor SST anomalies.

Section 3.1 showed that autumn SST anomalies are largely generated by atmospheric forcing. A lagged covariance could therefore equally arise from persistence of an atmospheric anomaly into winter, or from a remote driver that forces both seasons. To distinguish between these possibilities, we separate the part of autumn air-sea heat exchange driven by the atmosphere from the part driven by the ocean.

The atmospheric circulation analogue method described in Sect.  was used to derive autumn THF anomalies associated with atmospheric forcing (THF_circ) and a residual, ocean-driven, component (THF_res). Following , the two leading EOFs of THF_circ and THF_res were calculated and the winter MSLP anomalies then regressed onto PC1 and PC2 of each THF component. While focused on PC1, we include PC1 and PC2 because the two modes explain similar amounts of variance in the THF components. The result gives the winter MSLP anomalies that co-vary with the autumn THF, THF_circ and THF_res.

Figure  displays the patterns for ERA5. For PC1 and PC2, the spatial structure of the autumn THF and THF_circ are very similar (Fig. a, b, g, h), which shows that the atmospheric forcing dominates the spatio-temporal variance of North Atlantic THF in autumn.

There is a strong resemblance between PC1 of THF and THF_circ in ERA5 (Fig. a, b) and the THF regressed onto MCA1 of autumn SST and MSLP (Fig. g), which is coincident with an autumn MSLP MCA1 pattern that projects similarly onto the NAO and EAP (Fig. d, e). However, the MSLP anomalies regressed onto PC1 of THF and THF_circ (Fig. d, e) are distinct from one another and do not resemble any single EOF, suggesting less coherent atmospheric spatio-temporal persistence from autumn into winter associated with PC1.

There is also resemblance between PC2 of THF and THF_circ in ERA5 (Fig. g, h) and THF regressed onto MCA3 for contemporaneous autumn SST and MSLP covariance in ERA5 (Fig. i). The corresponding autumn MSLP pattern associated with MCA3 resembles a Rossby wave train emanating from the tropical Atlantic which is similar to EOF2 of autumn MSLP, but with a phase shift of about half a wavelength (compare Fig. f and Fig. S1). In contrast, the regression of winter MSLP onto PC2 of autumn THF and THF_circ in ERA5 shows a positive NAO pattern (Fig. j, k). Together, these results suggest that in ERA5, the second leading mode of autumn THF variability is linked with atmospheric forcing connected to a tropically-forced Rossby wave train, and the same forcing may also contribute to winter NAO variability independent of autumn ocean-driven THF_res.

We now consider the signals associated with ocean-driven autumn THF variability. PC1 of autumn THF_res shows broad negative anomalies in the Gulf Stream region extending with a north-eastward tilt across the basin and positive THF_res anomalies at higher latitudes (Fig. c). The winter MSLP anomalies associated with PC1 of THF_res resemble any of EOF2 of winter MSLP (compare Fig. f and Fig. S2).

In PC2 of THF_res, there is a negative THF anomaly in the central North Atlantic and a positive anomaly in the Caribbean Sea and the southern flank of the Gulf Stream (Fig. i), which do not strongly resemble any of the THF anomaly patterns associated with autumn MCA1-3 (Fig. g–i). The winter MSLP regression onto PC2 of autumn THF_res is markedly different from THF and THF_circ and does not closely resemble the dominant EOFs of winter MSLP (compare Fig. f and Fig. S2).

The magnitude of winter MSLP anomalies associated with PC1 and PC2 of autumn THF_res is generally weaker than for THF and THF_circ. These results suggest that in ERA5 winter NAO variability is partly related to autumn atmosphere-driven THF anomalies, but is not related to ocean-driven autumn THF anomalies.

To examine sampling uncertainty, Fig.  shows the projection of the winter MSLP regression onto PC2 of autumn THF, THF_circ and THF_res onto the winter NAO for ERA5 and the CMIP6 models. R2 is the fraction of the variance in the MSLP regression pattern explained by the NAO, and c is the magnitude of the associated NAO index anomaly. These metrics quantify the extent to which autumn THF, THF_circ and THF_res variability correlates with the winter NAO. The individual ensemble member points provide information about the sampling uncertainty in the models. For ERA5, sampling uncertainty was assessed by bootstrapping without replacement the years used to compute the THF EOFs with a bootstrap sample size of N = 40.

For PC2 of THF and THF_circ, there is a robust projection onto the NAO in ERA5 and the CMIP6 models (Fig. a, b). We note that although the pattern correlations are similar between ERA5 and the models, the winter NAO index anomaly associated with autumn THF and THF_circ variability lies in the upper tail or outside of the ensemble spread in every model (Fig. d, e). Since this is the component of THF driven by autumn atmospheric forcing, this could imply there are issues with modelled atmospheric persistence or teleconnections that serve as a common forcing of the autumn and winter atmosphere. While the models show a stronger resemblance of the MSLP pattern associated with PC2 of THF_res than the near-zero anomaly in ERA5 (Fig. c), the magnitude of the associated NAO index anomaly is substantially smaller than for THF and THF_circ (Fig. f) suggesting this makes a small contribution to winter NAO variability.

The sampling uncertainty for all THF components is large, with the ensemble spread in R2 spanning a large range from near-zero to almost 1 in many models and the NAO index anomaly spanning positive and negative values. The sampling uncertainty in ERA5 is also substantial, but as expected less than the ensemble spread given the uncertainty is estimated using bootstrapping rather than different samples as in the ensemble members. This uncertainty highlights the challenge of estimating small signals in the winter atmospheric circulation which is influenced by myriad remote drivers and large internal atmospheric variability. Accounting for the sampling uncertainty in ERA5, the results reveal no systematic biases in the modelled relationships of winter MSLP with autumn THF_circ. An equivalent analysis based on PC1 of the THF components is shown in Fig. S36.

The circulation analogue decomposition has shown that autumn North Atlantic THF variability is primarily controlled by atmospheric forcing, with limited evidence for an influence of ocean-driven autumn THF anomalies on the winter NAO. The ocean driven component is associated with weak winter MSLP anomalies that do not project onto the NAO. The previously identified autumn–winter NAO relationship in ERA5 is therefore not explained by ocean-driven THF anomalies.

The models capture the pattern of the THF_circ–winter NAO relationship, but underestimate its magnitude. The winter NAO signal linked to THF_circ could reflect SST anomalies that are forced by the autumn atmosphere and then persist and feedback later. Alternatively, it could reflect a common remote driver acting on both seasons. The analogue method cannot separate these, as it attributes all circulation related THF to THF_circ.