We first examine what low-frequency jet variability is skilfully reproduced by ASF20C. Figure  shows 10- and 30-year running means of the NAO, jet latitude, and jet speed for ERA20C and the ASF20C ensemble mean. One aspect of the signal-to-noise paradox is that the ASF20C ensemble mean standard deviation is considerably smaller than that of ERA20C; this can be seen here by comparing the magnitudes of the two y axes, which highlight that the standard deviation in ERA20C is around 4–5 times greater than that of the ensemble mean. It can be seen that ASF20C skilfully reproduces decadal NAO variability across the entire period 1900–2010, with a correlation coefficient of ∼0.4–0.7 depending on the choice of smoothing; using the raw seasonal data gives a correlation of 0.21. The correlations obtained using 10-year smoothing closely match those reported in and using genuine decadal forecasts, suggesting that the decadal forecast skill they reported might extend all the way back to 1900. Figure  also clearly shows that ASF20C cannot skilfully reproduce decadal jet latitude variability but can skilfully reproduce decadal jet speed variability. Furthermore, if we regress out the (decadally averaged) ensemble mean jet speed from the ensemble mean NAO and correlate the residual with the observed NAO, we obtain ≈0.1 using 10-year averages and ≈-0.1 using 30-year averages. Therefore, the majority of the skill that ASF20C has at reproducing decadal NAO variability is related to the jet speed. Figure S1 in the Supplement (SI) shows that, similarly, the coupled hindcast CSF20C has significant skill at predicting decadal variations in the speed but not the latitude.

Figure  shows that the same conclusion is true for the DPLE forecasts: there is no apparent predictability of decadal shifts in the jet latitude but high skill at predicting shifts in the jet speed. Note that taking 30-year means is much less sensible for DPLE, given its shorter coverage of 56 years, but these are included anyway for direct comparison with Fig. .

How significant are the jet speed correlations reported in Figs.  and ? The 1-year jet speed autocorrelation is ≈0.0 for all three datasets, and we are therefore justified in assuming a null hypothesis of the DJF jet speed as being white noise. The approximate Gaussianity of the jet speed distribution has been previously noted . By simulating 10 000 randomly generated DJF jet speed time series for each dataset, taking 10- or 30-year running means, and then computing correlations, we build up a distribution of correlations that can be obtained by chance. Note that taking running means will automatically introduce considerable autocorrelation to the resulting time series. Table  summarises the result of this significance testing. This shows that for ASF20C, whether considering 10- or 30-year smoothing, the decadal jet speed correlations are only significant to within p<0.1 and not p<0.05; the same is true for CSF20C (see Fig. S1). For DPLE, the conclusion is the same except that the correlations using 30-year smoothing appear to be significant also with p<0.05. However, as cautioned already, the small effective sample size here means that this level of confidence is probably not justified. The jet latitude correlations are never significant with respect to a similar null hypothesis, including the relatively large negative correlation emerging for 30-year jet latitude variability in DPLE (C=-0.35).

Our results here contrast somewhat with those of and , which both report statistically significant decadal NAO forecasts with p<0.05. However, their significance tests differ from ours, and the smoothing they use is also very close, but not identical, to the 10-year running means we use. Table  shows that the 10-year ASF20C and DPLE jet speed correlations sit neatly between the bounds of the 5 % and 10 % significance thresholds, and it is therefore plausible that these differences can explain why they report a p value less than 0.05 and we do not. For this article, we will assume that ASF20C and DPLE really do have significant skill at predicting decadal variations in the jet speed.

The similar behaviour of ASF20C and DPLE suggests that the extra information provided to ASF20C (the correct climate state every 1 November and the correct SSTs at all times) is not adding any extra jet speed skill beyond what is expected from an actual free-running, coupled decadal forecast. We interpret this as evidence for the assertion that the signals responsible for predictable decadal shifts in the jet speed are fully represented in ASF20C, and we will from now on assume that this is the case; we return to this point and alternative hypotheses later. Our assumption has two important consequences.

Firstly, since each of the 109 ASF20C winter forecasts only knows about the initial conditions and boundary forcings of the season in question, the sources of predictable decadal jet speed forcing must be present in their entirety within a single winter season. Put differently, since the atmospheric variability in ASF20C is generated by forecasts of a single season, any decadal variability ASF20C generates must arise due to atmospheric variability taking place within single seasons, even if this variability is ultimately forced by variables (e.g. SSTs) evolving on slower timescales. In particular, the predictable atmospheric signals, and the mechanisms involved, do not seem to inherently involve multiyear lags between the ocean and atmosphere or multiyear feedbacks within the atmosphere. Secondly, since the ASF20C forecasts are uncoupled, the forcing being exerted on the jet by the SSTs does not essentially depend upon atmosphere–ocean coupling in the sense that no within-season feedbacks are necessary. To the extent that there is any causal interaction between the SSTs and the atmosphere in AS2F20C, it must purely be from the former to the latter. In the sections that follow we will make use of these two points repeatedly to simplify the analysis and reasoning.

We emphasise straight away that while two-way surface coupling appears to not be required to reproduce the low-frequency jet speed variability, missing or deficient coupling may play a role in generating the signal-to-noise paradox, as suggested in . It is also likely that atmosphere–ocean coupling plays a role in generating the decadal-timescale SST variability.

In order to locate potential sources of skill in SSTs, we compute correlations of the winter jet speed against winter SSTs at every grid point. Because of our conclusion that these sources must be visible already on seasonal timescales (see Sect. ), we do this using both the raw DJF time series, as well as time series obtained by applying a 10-year running mean. Potential sources of skill are then assumed to correspond to regions of non-zero correlations that are common to ERA20C, ASF20C, CSF20C, and DPLE across both interannual and decadal timescales. While it is of course possible that the locations of signals differs somewhat across the datasets (e.g. due to biases in both the mean state and trends across the forecast models), the simplest – and more physically sound – possibility is that the signals are identical across the datasets, so we consider this possibility first.

Figure  shows grid point correlations for ERA20C, ASF20C, CSF20C, and DPLE at interannual timescales, while Fig.  shows grid point correlations of 10-year running means. Stippling indicates significance (p=5 %), where for interannual timescales the null hypothesis models the jet speed as white noise and models grid point SSTs using the Fourier phase shuffle method; on decadal timescales both the jet speed and SSTs are modelled using the phase shuffle method. At each grid point 1000 randomly generated samples from the null hypothesis are drawn in order to compute significance thresholds. Searching for commonalities across all the eight subplots by eye quickly highlights the SPNA. Already just comparing Fig. a and b makes this clear. A comparison with CSF20C and DPLE corroborates this and furthermore seems to rule out signals from both the tropical Pacific, tropical Atlantic, and Indian Ocean, since the correlations are opposite in sign between ASF20C–CSF20C and DPLE in these regions.

To justify this visual inspection more objectively, we have in Fig.  highlighted the grid points for which all the four datasets exhibit interannual- and decadal-timescale correlations with the same sign. This makes it clear that the SPNA is the only region where spatially coherent correlations of the same sign can be found. Figures  and  show that the correlations in the SPNA region are statistically significant in five out of eight subplots, including in ERA20C across both timescales. While Fig.  shows a narrow strip of shared negative correlations in the tropical Atlantic, these correlations are not significant in ASF20C on any timescale and are not significant in ERA20C on decadal timescales. The correlations in this region are also close to 0 in magnitude in ASF20C on interannual timescales and DPLE on decadal timescales (≈-0.05 on average in both cases). Only in the SPNA are correlations of appreciable magnitude (<-0.2) found in all datasets on all timescales. Furthermore, and crucially, the coupled DPLE forecasts have considerable skill at predicting decadal SST variability in the SPNA region but not in the tropical Atlantic .

The SPNA thus emerges as a common region of interannual-to-decadal correlations between SSTs and the jet speed across ERA20C, ASF20C, CSF20C, and DPLE, and it appears to be the only such common region. We interpret this as strong evidence for the importance of the SPNA in driving decadal jet predictability. We therefore define an SPNA time series as the DJF-averaged SSTs across the domain 49–57∘ N, 50–25∘ W. This box was chosen because it encloses almost precisely the negative correlations highlighted in Fig. c in the sub-polar region. The remainder of the analysis we carry out is not sensitive to even moderately large shifts in the definition of this box, as long as the box roughly belongs to the region highlighted in Fig. . Other differences between the datasets seen in Figs.  and , while interesting, do not seem relevant to the study at hand and so are not discussed.

It is worth mentioning the phenomenon of false discovery rates, namely the fact that if one looks for correlations across a sufficient number of predictors, then some are bound to be significant by chance. This effect would a priori be expected to be high when considering correlations across thousands of grid points with high spatial autocorrelation. However, based on the results and discussion of previous sections, we are now assuming that (a) there is decadal forecast skill which needs to be explained and (b) this skill comes from the SSTs. A rejection of any and all grid point correlations as “false discoveries” would be directly counter to this assumption and is therefore not done. The discovery of a region of correlations common across four datasets on the other hand can be seen as providing additional evidence towards our assumption.

Table  summarises the correlations between SPNA SSTs and jet speed for the different datasets across different timescales. Figure  visualises the 30-year running mean time series: the sign of the SST index has been flipped for visual convenience. To generate the 5 % significance threshold reported in the table, we assume a null hypothesis that the jet speed and SPNA are uncorrelated random variables. The interannual jet speed time series is modelled as a normal distribution with no memory across years, as before. To create synthetic SPNA time series, we apply the Fourier phase shuffle method to the interannual SPNA time series in order to generate random draws that preserve the considerable autocorrelation. By correlating 10 000 such synthetic time series, along with those obtained by applying a 10- or 30-year smoothing, we can then numerically estimate the 5 % significance threshold. Note that the confidence intervals for ERA20C, ASF20C, and CSF20C were found to be almost identical, so we only report a single confidence interval encompassing all three, obtained by taking the average across the three individual intervals.

The correlation between SPNA and the jet speed is highly significant in ERA20C for all timescales considered here, suggesting a robust physical link between these quantities. Both ASF20C and CSF20C have significant correlations on the interannual timescale and CSF20C also for 10-year timescales. The other correlations obtained do not pass the threshold. Of course, the lack of consistent statistical significance at 5 % does not mean the physical link in ERA20C is not simulated by the forecast models but only that these correlations would not be sufficient to establish such a link when viewed in isolation. As emphasised in , it is crucial to include physical reasoning and prior knowledge when drawing conclusions about significance. We return to this, and the question of causality, in the Discussion section.

When studying the impact of imposed temperature anomalies on the jet in a dry model, argued that much of the response could be understood simply in terms of changes to the meridional temperature gradient. This suggests a simple explanation for why the SPNA forces the jet in keeping with the analysis of : anomalously cold SSTs in the SPNA cool the atmosphere aloft, thereby strengthening the local meridional temperature gradient around the jet, causing an intensification of the eddies and thereby an increased jet speed. This is similar for warm anomalies but with the opposite sign. To strengthen the case for this pathway, Fig.  shows the vertical extent of the anomalies associated with SPNA SSTs in ERA20C by correlating November SPNA SSTs with zonally averaged (a) temperatures and (b) zonal winds at different pressure levels; the averaging is done over longitudes 60∘ W–20∘ E. Significance at 5 % (indicated by stippling) uses a null hypothesis which models the SPNA using the Fourier phase shuffle method and temperatures and winds as white noise. Figure c and d show the same but using DJF means. Figure a and c suggest that temperature anomalies do not remain confined to the surface but extend up to around 300 hPa, making the robust impact on the jet seen in Fig. b plausible. For completeness, the reverse link from the jet speed to temperatures and winds is shown in Fig. . Figure a shows that the temperature anomalies associated with the jet are maximal in the mid-troposphere. The temperature anomalies associated with the SPNA (Fig. a and c) project well onto the jet pattern but are maximal at the surface. Comparing Figs. d and b confirms that the association between the SPNA and the zonal winds projects onto the jet speed signature.

Detailed analysis of the tropospheric response to an SST anomaly in the North Atlantic, such as in , shows that the response generally proceeds in two stages. To begin with, the induced anomaly is baroclinic in nature and localised to the heat source. In the second stage the baroclinic anomalies are removed by eddy heat and momentum transport, leading to a relatively barotropic structure with a more hemispheric scope. Figure  shows that in DJF, the structures are relatively barotropic in nature, consistent with this tropospheric pathway having taken place. Note that this approximately barotropic structure is also visible when plotting regression coefficients instead of correlations (not shown).

To further test the importance of the tropospheric heating anomalies over the SPNA, we will compute a crude estimate of what ERA20C jet speed anomalies are expected purely from SPNA variability using geostrophic wind balance. Concretely, we will estimate the jet speed variability expected from the following assumptions:

First is that the local meridional temperature derivative at the jet core can be completely approximated using the difference in temperatures between the jet core and the SPNA region (which sits on the northern flank of the jet). In particular, we assume that the gradient between the southern flank and the jet core does not contribute to the local derivative.

To proceed, we define a region labelled “South” by 35–43∘ N, 75–40∘ W and a region labelled “North” using the same domain as the SPNA. The South region is chosen because it roughly encompasses the climatological core of the jet in ERA20C (not shown). We then assume a constant layer thickness between 1000 and 300 hPa, where 300 hPa is the upper limit of the heating associated with the SPNA, as seen in Fig. c. Let T^N and T^S denote the layer-averaged DJF air temperature between 1000 and 300 hPa in the North and South regions. By regressing our SPNA SST time series against T^N, we obtain the SPNA-driven component which we denote by T^N(SPNA). We let [T^S] denote the average of T^S across all years from 1900–2010. The time series of the difference T^N(SPNA)-[T^S] thereby roughly measures the layer-averaged meridional temperature gradient across the jet core purely associated with SPNA SST variability. Given our two assumptions, geostrophic balance with a constant layer thickness now relates this gradient to the zonal winds Ujet in the jet core according to 1Ujet=-Rf⋅log⁡(1000/300)⋅1dyT^N(SPNA)-T^S, where R=287.05 J kg-1 K-1 is the gas constant, f=1×10-4 rad s-1 is the approximate midlatitude Coriolis parameter, and dy=2.553×106 m. Here we have set 1∘ latitude to be roughly 111 km. The Ujet anomaly time series is compared to the jet speed time series for ERA20C in Fig.  using 30-year averages. Not only do they correlate extremely well (C=0.97), but the magnitudes of the anomalies are also almost identical. The raw means of the two time series were found to differ, with the jet speed mean being around 25 % larger. This is likely due to both the crude estimate of the local derivative we made use of and the fact that Ujet is an average across multiple layers, unlike JetSpeed, which is measured at the 850 hPa level only. Nevertheless, we conclude that the decadal jet speed variability in ERA20C can be accounted for purely by tropospheric temperature anomalies associated with the SPNA

We remark that we also found that around 60 % of the CMIP5/6 intermodel spread in climatological jet speeds could be accounted for by these tropospheric anomalies (not shown), further emphasising the importance of this region.

We emphasise that the specific nature of the fast-timescale processes responsible for bringing the jet into geostrophic balance, including the role of moist processes, is actively studied , and we do not shed any further light on these. The above analysis simply says that if the SPNA is heating the atmosphere aloft, then geostrophic balance effectively forces the jet speed to exhibit the decadal variability we observe.

In Sect. , we argued that the presence of skill in ASF20C implies that predictable jet speed variability is a result of forcing from the boundary conditions taking place already within a single season. Having now argued that this forcing is coming from SPNA SSTs, it remains to be tested whether the forcing exerted by the SPNA on the jet taking place on seasonal timescales suffices to explain the decadal-timescale correlations seen in Table . That is, we want to test the following hypothesis: that the jet's response to the SPNA is established within a single season and that the decadal signal seen in the jet speed arises purely from decadal power in the SSTs, without the need to invoke processes or feedbacks on slower, multiannual-to-decadal timescales.

To test this, we model the SPNA–JetSpeed system as follows. For a given dataset, we perform a linear regression of the interannual SPNA time series against the interannual JetSpeed time series to get 2JetSpeed=a⋅SPNA+b+ϵ for some constants, a and b, and a noise term ϵ, which is normally distributed with mean 0. We then generate a random, synthetic time series of DJF SPNA using the Fourier phase shuffle method, as in the previous subsection. A corresponding JetSpeed time series is then obtained using the linear relationship just derived; the synthetic jet speed thus relies only on the simultaneous synthetic SPNA in that season. We then take 10- and 30-year running means of these synthetic DJF time series and compute the correlations between them. By repeating this procedure 10 000 times we can assess what decadal-timescale correlations are expected from taking running means of the interannual SPNA–JetSpeed link.

The result of this for ASF20C is summarised in Fig. a–c. The synthetic seasonal-timescale correlations (Fig. a) capture the actual seasonal correlation by construction. After taking running means, the distribution of synthetic correlations becomes notably skewed. For both 10- and 30-year running means (Fig. b and c), the observed correlation is still comfortably within the 95 % confidence interval of the synthetic correlations. The same analysis for ERA20C is shown in Fig. d–f. The observed 10- and 30-year correlations are closer to the upper threshold here but still fall within it. This implies that the decadal-timescale correlations of ASF20C and ERA20C can be completely explained by the interannual SPNA–JetSpeed link, as hypothesised.

We emphasise that we are not suggesting the SPNA variability is purely interannual but rather that the connection between the SPNA and the atmosphere occurs within the span of a single season. The same conclusion can be seen to hold for CSF20C by comparing Table  with Fig. ; we also verified the analysis using the shorter DPLE (not shown). To further support this point, Fig.  shows lag correlations of the jet speed in ERA20C against the SPNA time series (black curve). The correlations peak at lag 0 and diminish towards 0 for increasingly negative lags, consistent with an instantaneous forcing from the (decadally varying) SPNA which slowly diminishes over time. The comparison with the AMV lag correlations (red curve in Fig. ) will be discussed in Sect. .

The question of how aerosols affect North Atlantic SSTs is still actively debated and could include the role of both direct radiative adjustments local to the region and more indirect impacts from upstream emissions . Here we will only consider the hypothesis put forth by due to its being based on a large multimodel ensemble, unlike most other studies. In their study, they argued that sulfate aerosol emissions over the eastern part of North America led to a cooling of surface temperatures there and that this cool air was then advected over the North Atlantic, thereby cooling the SSTs and ultimately modulating the AMOC. The possible direct impacts of emissions over the SPNA region itself will not be considered, since the emissions are generally very low in this region.

ERA20C, ASF20C, and CSF20C all share the same prescribed aerosol emissions, namely those used in CMIP5 . The climatological SO4 emissions are shown in Fig. a, showing a clear concentration of emissions over the eastern North American region. To study the impact of these emissions on the SPNA and jet speed, we define an SO4 time series by averaging the emissions over the box 30–45∘ N, 100–75∘ W. This box is visualised in Fig. a and approximately covers the eastern North American continent. This time series is compared to the 10-year-averaged SPNA SSTs and ERA20C jet speed in Fig. b. The SO4 time series matches both the SSTs and jet speed in the period 1940–2010, with a correlation of around 0.8. However, in the earlier period 1900–1940, the SO4 emissions are anticorrelated with the SSTs and jet speed, with a correlation of around -0.3. Note that the CMIP5 aerosol forcing data are constant across each 10-year period, explaining the step-like quality of the SO4 time series.

We conclude that while aerosol emissions over North America may have played a role in driving decadal SPNA variability, they are unlikely to explain the entire 20th century variability, especially in the early period when emissions are still very low. Similar conclusions were drawn in earlier work by . Note that the forecast models are able to capture the strong jet in this early period despite the low aerosol emissions (Fig. ). If the aerosols are driving some of the SPNA variability, then this would be expected to lead to predictable shifts in the jet speed, as discussed in the present paper. It should also be noted that an aerosol-induced cooling of North America would strengthen the land–sea contrast, which would also be expected to drive a stronger jet . It is unclear if such a change in land–sea contrast alone can generate decadal-timescale forecast skill.

To understand if the AMOC alone can drive SPNA-induced jet speed variability, we examine the two EC-Earth3 pre-industrial control simulations, which we refer to as piControl r1 and piControl r2. These simulations are particularly useful for assessing AMOC forcing, since they are known to exhibit large and striking centennial-timescale AMOC oscillations . The lack of any anthropogenic emissions means the associated variability in the SPNA will be entirely due to the AMOC.

Figure  shows 30-year DJF running means of SPNA SSTs vs. JetSpeed for the two ensemble members. The centennial AMOC oscillations are clearly visible in the SPNA time series. The correlations obtained between the SPNA and JetSpeed are -0.63 for the r1 member and -0.34 for the r2 member. A 5 % significance threshold using the same null hypothesis as before (modelling JetSpeed as white noise and SPNA with the Fourier phase shuffle method) is approximately ±0.5, implying that the r1 correlation is highly significant, while the r2 is not.

We cannot directly compare the correlations from these free-running coupled simulations to the ensemble mean correlations of ASF20C. However, we note that if we concatenate five back-to-back ASF20C ensemble members, we get a time series of length 5×109=545, approximately the same length as the piControl members. By randomly drawing five ASF20C members, concatenating them, and computing the correlations between the resulting SPNA and JetSpeed time series, we can compare ASF20C and piControl in a like-for-like manner. If we carry out 1000 such random draws, we find that the expected ASF20C correlation is around -0.2 with a 95 % confidence interval of approximately [-0.51, 0.18]. Almost identical results are obtained when using the CSF20C ensemble. This clearly suggests that the r2 correlation of -0.34 is perfectly consistent with the SPNA–JetSpeed link diagnosed in ASF20C–CSF20C. It also suggests that the r1 correlation of -0.63 is larger than expected, though not impossible, with a handful of concatenated ASF20C–CSF20C members producing correlations of around -0.6. Since the AMOC oscillations are particularly strong in the piControl runs, it is possible that this translates into SPNA–JetSpeed correlations which may be unrealistically large. The r1 member may also just be a random outlier.

Based on the above analysis we conclude that AMOC oscillations alone can in principle produce SPNA variations associated with an SPNA–JetSpeed link of the same strength as in the forecast models, even in the absence of any aerosol forcing. It is therefore natural to speculate that the AMOC is responsible for the coherent SPNA and jet speed variability seen in the early 20th century (Fig. ), and it likely contributes to the variability later on as well.

Our key argument for the importance of the SPNA can be understood as a conditional one: if one assumes that the skill comes from SSTs, then Figs. – suggest that the SPNA is the responsible region. How reasonable is this assumption? In other words, could the skill originate from somewhere other than the ocean?

It is possible in principle that the skill comes from the stratosphere , which has a decorrelation timescale of several months. However, the initial conditions of ASF20C (CSF20C) come from ERA20C (CERA20C), which only assimilates surface variables. Because these do not strongly constrain the stratosphere, the stratospheric variability in ERA20C is highly biased. Indeed, found that the amplitude of the quasi-biennial oscillation (QBO) is substantially weaker in ERA20C compared to reanalysis products that assimilate a broader range of atmospheric observations. They also reported a greatly reduced downward propagation in ERA20C. also considered the same ASF20C hindcasts and found that the seasonal-timescale association between the QBO and the NAO was essentially zero, unlike in forecasts assimilating the stratosphere. We interpret this as evidence that there is limited scope for skill from stratospheric initial conditions in ASF20C–CSF20C. Another argument towards the stratosphere not driving the predictability was given in , which showed using reanalysis that the magnitudes of stratospheric anomalies do not match those of the jet on decadal timescales. Note that while they only explicitly discussed March, their Fig. B1 suggest similar conclusions would likely be drawn for DJF.

Besides the stratosphere, the remaining obvious candidates are ice and anthropogenic emissions such as carbon dioxide and aerosols. However, the impact of ice on decadal jet variability has been found to be small compared to SSTs . Furthermore, observations of ice are sparse and unevenly distributed prior to 1979, with obvious implications for the potential quality of the ice data used in the ASF20C boundary forcing files. As for anthropogenic emissions, the analysis in showed that globally averaged emissions cannot explain the decadal variability in a closely related jet index. This leaves open the possible influence of local emissions. The most obvious way for such local emissions to alter the jet is indirectly by altering the radiative forcing and hence surface temperatures. Such indirect forcings on the jet would manifest themselves as an apparent forcing from surface temperatures. While this could potentially include forcing from temperatures over land, the decorrelation timescale over land is much faster than for SSTs, making a decadal-timescale forcing seem less likely. On the other hand, any indirect forcing via the SSTs would already be visible in Figs.  and , which highlight the SPNA.

It is hard to exclude the possibility of a more direct impact of aerosols on the jet, e.g. due to an altering of the local radiative fluxes in the troposphere (as opposed to at the surface). Figure a shows that sulfate aerosol concentrations are small on the north side of the jet core, making a direct contribution from there seem less likely. There are more emissions centred around the jet core, so these could be playing a role. However, as pointed out in Sect. , aerosol emissions drop considerably prior to 1940 and become anticorrelated with the jet speed time series in the period 1900–1940 even as forecast skill remains high (Fig. b). Such direct effects are therefore unlikely to explain all the observed skill.

While all these other potential sources of skill cannot be conclusively ruled out without targeted forecast experiments, we nevertheless conclude by process of elimination that there is strong evidence towards our assumption that the skill comes from the SSTs and hence from the SPNA in particular.

There is an obvious question concerning the causality of the SPNA–JetSpeed link we have proposed, especially since SSTs in the SPNA are known to be particularly sensitive to forcing from the jet . Are the correlations in Table  in fact just indicative of stochastic atmospheric forcing on the ocean? Here we discuss several lines of evidence which suggest that at least a considerable portion of the correlations is due to a genuine forcing from the ocean to the atmosphere.

The first key point is the apparent existence of skilful decadal forecasts. We have shown that the SPNA appears to be the only clear, common, SST-based signal between reanalysis and the forecasts we have analysed. If the SPNA–JetSpeed correlations are mostly or entirely reflecting a causal influence of the atmosphere on the ocean, then one seems forced to conclude that the decadal skill does not originate from the SSTs. This is problematic, given the discussion of Sect. .

Secondly, we remind the reader that ASF20C is uncoupled and uses prescribed boundary forcing, so correlations on interannual timescales in ASF20C cannot arise from a causal influence of the atmosphere on the SSTs in the model. While this is not true for CSF20C and DPLE, which are coupled, the fact that (i) the correlations they attain are entirely comparable to those of ASF20C and (ii) all these correlations are explainable from the interannual link alone (Sect. ) suggests that forcing from the SSTs to the atmosphere constitutes a pragmatic common explanation for the correlations found in all three forecast models. An alternative explanation for the correlations seen in the uncoupled ASF20C would be the existence of a different source of skill, not related to SSTs, which influences both the jet and the SSTs (possibly via the jet). Since the correct SSTs are prescribed to ASF20C, such a common driver could result in correlations of the sort seen in Table . However, as before, the hypothetical existence of such a non-SST-related driver is currently unfounded.

Figure  shows correlations between DJF SPNA and DJF temperatures and winds. If we rather correlate November SPNA anomalies against DJF temperatures and winds, we get a similar picture, albeit weaker in magnitude, especially for the winds (see Fig. S2). This suggests that the vertical heating is not purely coming from the adjustment of the jet itself but also from processes induced by the SST anomalies. The fact that the heating associated with the SPNA peaks at the surface (Fig. a and c) is also suggestive of SST driving. In general, replacing DJF SPNA SSTs with November averages leads to smaller but non-zero correlations of the same sign.

Another important reason for having a high prior for a causal influence from the SPNA is that several studies using idealised models and general circulation models (GCMs) have demonstrated that SST anomalies can causally affect the jet . Of particular relevance is the recent work of , who carried out pacemaker experiments which suggest that SSTs in the SPNA have a positive impact on decadal forecast skill. We also highlight , who used a dry model to show that imposed heating anomalies modulate the speed of the eddy-driven jet by altering the meridional gradient around the jet core, making the causal pathway we propose here a plausible explanation for the observed decadal forecast skill. An important caveat here is the increasingly recognised role played by moist processes in determining the jet variability, which are not represented in such a dry model . Note, however, that the results of are generally consistent with those in using a full moist GCM.

Finally, showed that the DPLE forecasts can skilfully predict decadal SPNA SST variability but fail to predict shorter-timescale North Atlantic winds of an appreciable magnitude, strongly suggesting that decadal SPNA variability is not purely driven by stochastic atmospheric forcing. This was further corroborated by , who found evidence that the SST skill has an abyssal origin. Consistent with this, quantitative estimates of the stochastic forcing in the coupled CSF20C hindcast, using methods such as the one described in , were found to be very small in the SPNA region on decadal timescales, roughly an order of magnitude smaller than the observed SPNA–JetSpeed correlations (not shown).

To conclude, we consider it likely that there is a sufficient causal influence of the SPNA on the jet to explain the observed decadal skill. Unambiguously confirming this would, however, require performing expensive forecast experiments, such as rerunning the full ASF20C hindcast using boundary forcing files from which the SPNA SST variability has been eliminated.

We have argued that the SPNA forces the NAO more or less instantaneously. How do our results relate to previous studies suggesting that the AMV forces the NAO, with the NAO response typically lagging the AMV by several years ? We suggest that this apparent discrepancy is a result of three factors.

Firstly, while the AMV pattern on interannual timescales is the famous horseshoe pattern, the pattern largely collapses to a signal confined to the SPNA after performing decadal-timescale smoothing . This suggests that as far as decadal atmospheric variability is concerned, the SPNA is more relevant than the horseshoe pattern. The importance of this region has been highlighted previously .

Secondly, anomalies in the SPNA (the northern part of the horseshoe) are observed to lead anomalies in the tropical Atlantic (the southern part of the horseshoe) by around 2 years . It is likely that this propagation of anomalies takes place both via subsurface ocean dynamics and coupling with the atmosphere . This means that performing analysis based on the standard AMV horseshoe pattern is mixing together different processes happening on different timescales. Since the SPNA anomalies arise first, restricting attention to these might be expected to give a clearer picture and better highlight causal pathways from the ocean to the atmosphere. This argument has also recently been made by . Note that this second point is presumably related to the first, since taking decadal averages would be expected to remove the shorter-timescale signals associated with the propagation of SST anomalies along the horseshoe and processes operating at much slower timescales, such as those associated with deep convection in the Labrador Sea. This argument was also made in .

Thirdly, the reverse impact of the NAO on the AMV has also been noted to operate on both fast and slow multiyear timescales , introducing additional lags to the coupled AMV–NAO system.

We therefore suggest that the apparent existence of an NAO response lagging the AMV by several years is, in fact, largely reflecting the existence of an essentially instantaneous atmospheric response to the SPNA, with the multiyear lag being an artefact of using an AMV index which averages across several different processes. This is further supported by Fig. . The AMV–JetSpeed lag correlations (red curve) show a peak at 7–15 years (depending on smoothing choices) when the AMV leads, reproducing what is found using the NAO index . When the SPNA index is used, this lag vanishes, with correlations now peaking at lag 0.

Several studies have argued that an AMV-driven NAO response involves a shift in both the strength and location of the storm track and/or baroclinic region . Such systematic latitudinal shifts in the storm track and/or baroclinicity, and hence the eddies, would be expected to manifest as predictable latitudinal shifts in the eddy-driven jet itself. However, as discussed in Sect. , there is no decadal predictability of the latitude of the jet in ASF20C, CSF20C, or DPLE. This suggests that on decadal timescales the eddies are randomly distributed around their mean position and that the mechanism driving predictable jet variability does not essentially depend on latitudinal shifts in the storm track. Rather, such predictable changes appear to be more clearly related to the direct constraint of thermal wind balance along with an intensification of the storm track. This is fully consistent with , who highlighted the contrasting nature of forced shifts to the latitude and speed of the jet.

Of course, it cannot be ruled out that SST anomalies in the SPNA, or indeed elsewhere, force shifts in the latitude of the jet in the real world that are simply not captured by the forecast models we considered. However, until predictability has been established it does not seem possible to reject the null hypothesis that decadal variability in the jet latitude is chaotic and unpredictable. Indeed, the inconsistent latitudinal response in multimodel studies such as lends concrete evidence for such inherent chaos. Further evidence for this is given in Fig. S3, which repeats the procedure of Sect.  to search for potential sources of jet latitude skill in ASF20C. This shows that there are no regions of significant SST–jet latitude correlations common to both ERA20C and ASF20C, consistent with the lack of jet latitude predictability.

It is also possible that biases in the climatological jet latitude (i.e. in the model mean state) of the forecast models are contributing to the apparent lack of jet latitude predictability. The sensitivity analysis of showed that the response of the jet latitude to thermal forcing changes sign abruptly around the jet core, while the response of the jet speed is more uniform across the jet. The accurate response of a model jet to a given SST anomaly may therefore differ dramatically based on its climatological position. This could go some way to explaining the inconsistent jet latitude response in multimodel studies such as .