Introduction

The Earth’s global mean near-surface temperature continues to rise, with 2024 being the first year to temporarily exceed 1.5 °C above pre-industrial levels1. As expected, however, regional temperatures often show significantly larger variability due to changes in atmospheric circulation patterns, which can either mask or exaggerate underlying anthropogenic warming trends. These can either result from internally generated atmospheric variability and/or external drivers of the climate system. It is essential, therefore, to study and understand the drivers and predictability of recent regional climate variability so that we can make more confident and skilful future regional climate predictions to inform mitigation and adaptation planning.

The observed decadal Eurasian winter cooling that straddled the end of the 20th and the start of the 21st centuries (Fig. 1a) is a key example of regional climate variability opposing the general global warming trend2, with the Siberian region in particular cooling by −1.1 °C/decade over 1990–2014 (Fig. 1b). This was associated with a strengthening of the Siberian High3 and an amplification of the East Asian winter monsoon4. Over approximately the same period, a strong regional warming occurred in the Arctic and was particularly pronounced over the Barents-Kara Sea region (Fig. 1a) where there was also a strong decrease in autumn-winter sea-ice extent. The coincidence of these events, often referred to as the “warm Arctic-cold Eurasia” (WACE) pattern5, led to speculation at the time that this behaviour could be an emerging climate change signal6,7, with amplified Arctic warming driving mid-latitude Eurasian cooling8. Many observational and modelling studies have investigated the WACE pattern, but there is little consensus about the cause of the cooling9,10,11. On the one hand, observational studies12 and some modelling studies undertaking idealised perturbation experiments13,14 find evidence in support of a causal link with reduced Arctic sea-ice driving a cooling over Eurasia. Other studies, however, find limited evidence15 or point to different causal relationships whereby low-frequency variability in atmospheric dynamics is driving both Eurasian cooling and amplifying Arctic sea-ice loss10,16,17,18. Furthermore, coordinated multi-model studies on the impact of Arctic sea-ice decline from the Polar Amplification Model Intercomparison Project (PAMIP19) have found only weak dynamical responses of the North Atlantic extratropical jet and little consistent Eurasian cooling response20,21. Indeed, perturbation experiments with large Arctic sea-ice loss can produce a thermodynamic warming signal that overwhelms the associated dynamical cooling signal22,23.

Fig. 1: Observed and simulated decadal temperature trends over Eurasia.
Fig. 1: Observed and simulated decadal temperature trends over Eurasia.
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a observed ERA5 near-surface air temperature difference and Siberian temperature timeseries (b) with the trend plotted calculated over the 25 year period 1990–2014 as used in previous studies (e.g., Wang and Chen41). c distribution of the 462 CMIP6 historical simulations (see Methods) of Siberian temperature trends with the vertical dashed line showing the ERA5 reanalysis trend. d DePreSys3 (‘model’) ensemble mean initialised on 1st November predicting winter (forecast months 2–4, December–February), near-surface air temperature difference and Siberian temperature timeseries (e) with the distribution of 1000 possible permutations (Methods) of model ensemble member Siberia temperature trends (f) with the black dashed vertical line showing the observed trend. g–i as panels d-f but now for the ‘adjusted’ ensemble that accounts for spuriously weak model circulation signals (see “Methods”, text and Fig. 3).

The most complete simulations of historical climate with realistic external forcings from the sixth Coupled Model Intercomparison Projects (CMIP624), which we revisit below, show negligible evidence for an externally forced cooling signal over central Eurasia25. We also now know that the strong Eurasian cooling signal has disappeared (Fig. 1b) over the decade since 2015 and central Eurasia has been warming at a rate similar to the Northern Hemisphere average26, despite continued Arctic warming and sea-ice loss. These findings therefore led to the suggestion that the observed cooling was in fact largely a result of internal variability generating synchronous changes over Eurasia and the Arctic27,28,29,30.

Another possibility, however, is that current climate models may underestimate the strength of forced atmospheric circulation signals over Eurasia and that they might be predictable. Indeed, several studies using retrospective seasonal climate predictions (hereafter hindcasts) have shown evidence for predictable but spuriously weak winter circulation signals in the North Atlantic Oscillation (NAO), upstream of Eurasia31,32,33,34. Here we use seasonal predictions to explore their simulation of the Eurasian strong cooling period and assess whether atmospheric circulation signals are underestimated.

Results

Observed and modelled trends

We consider winter (December–February) seasonal predictions, from hindcasts starting on 1st November each year from 1981 to 2022 using the Met Office DePreSys3 (hereafter the ‘model’) near-term prediction system33 (see “Methods”) with 40 ensemble members. As seasonal predictions are initialised from our best estimate of the current conditions in the atmosphere, ocean, and cryosphere, they have knowledge of the current state of the slowly evolving components of the climate system. However, with a lead-time of 1 month the ensemble loses deterministic atmospheric predictability of the synoptic evolution of mid-latitude climate. Seasonal predictions therefore give us the opportunity to study the impact of slowly evolving signals in the climate system on atmospheric variability impacting Eurasia. We first explore whether these hindcasts improve the prediction of Eurasian surface temperature relative to uninitialized CMIP6 historical simulations, which are forced only by changing external forcings alone.

Analysis of 38 free-running CMIP6 historical models (Fig. 1c, see Methods) shows an average warming trend for 1990–2014 over Siberia of +0.64 C/dec (cf -1.1 C/dec observed). Of the 462 individual uninitialised CMIP6 ensemble members, only one member (0.2%) simulates a cooling as strong as that observed. However, it is important to note that because we have pre-selected the strong cooling period in the observations, with no a-priori information on its location or timing, that we should not treat this as a probability of occurrence35. That said, the fact that only 13% of CMIP6 members simulate a Siberian cooling trend at all suggests that any strength of Siberian cooling is not a robust response to external forcings in these coupled ocean-atmosphere climate models.

Examining trends from the model (DePreSys3 near-term prediction system) ensemble, we find on average zero (0.0 C/dec) Siberian warming trend (Fig. 1d and e). Exploring individual model ensemble members to generate a distribution of possible model trends, using resampling of the members (see “Methods”), we find that approximately half (48%) of members exhibit a cooling trend but only 0.8% of model sample trends are as large as the observed trend (Fig. 1f). Hence the initialised model does not simulate an overall warming trend and thus improves upon the uninitialized CMIP6 historical simulations (which we consider no further in this paper), but the ensemble mean does not capture the observed cooling. In summary, our analysis suggests that the observed Siberian cooling could be an example of relatively rare internal variability and/or errors in the model’s response to forcing (e.g., either from external forcings and/or from slowly evolving components of the climate system that we initialise in the model hindcasts) over this period. We keep both these possibilities in mind as we now explore the large-scale circulation associated with the Eurasian cooling. Note that we will return later in this paper to discuss the results shown in Fig. 1g–i, once we have explored the dynamical circulation drivers and their model simulation.

Large-scale dynamical circulation changes

Decadal changes in the observed large-scale atmospheric circulation, coincident with the Eurasian cooling, are explored for the upper-troposphere zonal and meridional winds (Fig. 2a and b). In 250 hPa zonal winds, we find a strong dipole over Eurasia, with weakening in the westerly flow over high latitudes and a strengthening over mid-latitudes. Dynamically this corresponds to weakening (reduction in the eastward extent) of the extratropical jet and a northward shift of the sub-tropical jet. The longitudes of the strongest centres of this dipole pattern are located over Europe (Scandinavian and the Mediterranean) and eastern Asia (Siberia and China), with this longitudinal structure implying a strong meridional circulation component. We see this when we examine the 250 hPa meridional wind differences, where we find a striking Rossby wave structure across Eurasia, with alternating centres crossing the North Atlantic to Eurasia. This is similar to the wave-train previously identified36 and corresponds to positive geopotential height anomalies located over the Ural Mountains during the later period37. This expands and amplifies the climatological Siberian High, with more persistent atmospheric blocking, and favours northerly advection of colder Arctic air into Siberia.

Fig. 2: Dynamical circulation changes in observations and model members.
Fig. 2: Dynamical circulation changes in observations and model members.
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Observed differences 2000–2014 minus 1985–1999 in observed ERA5 upper troposphere 250 hPa zonal a and meridional (b) winds. c, d The second Empirical Orthogonal Function (EOF) from a joint EOF analysis of 250 hPa zonal and meridional winds, calculated over the domain shown and years 1980–2022. e, f The mean of ensemble member resamples that produce the strongest model Siberian temperature trends (those 19 members from 1000 resamples that have <−1.0 K/dec as shown by dashed vertical line in g), with stippling showing locations where this signal is significantly different from the mean of all (unconditioned) ensemble member resamples according to a one-sided Student’s t test at the 95% confidence level. g Siberian temperature trends (1990–2014) are plotted against the EZJD index (highlighted by the green boxes on a, c, e) for each of 1000 model member resamples along with the ERA5 reanalysis value. Contours in a, c, e show the climatological ERA5 250 hPa zonal winds to highlight locations of the mid-latitude jets.

To address whether these observed upper-level circulation signals correspond to a commonly occurring pattern of interannual variability we perform a joint (multivariate) Empirical Orthogonal Function (EOF) analysis using the zonal and meridional winds over 1980–2022 and the domain shown in Fig. 2. We find that the second joint-EOF (Fig. 2c and d), explaining 16% of the interannual variance, matches very closely the patterns we have already described (in Fig. 2a and b). We note that the signals over the western North Atlantic, seen in Fig. 2a are removed in this second joint-EOF, as they correspond to meridional shifts in the extratropical jet associated with the higher-frequency interannual behaviour in the North Atlantic Oscillation (NAO) which is represented by the first joint-EOF (not shown). Instead, the second joint-EOF very well picks up the circulation changes across Eurasia which, as we will see, are more closely related to the lower-frequency changes in the strength of the jet38,39.

To further investigate whether these observed large-scale circulation changes also drive those model ensemble member combinations that have the strongest Siberian cooling trends, we repeat our analysis using the 2% of model members that simulate a strong <−1.0 °C/dec cooling trend (close to the observed −1.1 °C/dec). Interestingly, we find very similar large-scale circulation differences, with changes in both zonal (Fig. 2e) and meridional (Fig. 2f) winds similar to that observed (Fig. 2a and b). As expected, they are somewhat weaker, especially for the meridional winds which also appear to be shifted approximately 10–15 degrees east compared to that observed.

We further investigate the relationship between Eurasian temperature and circulation changes by defining a European zonal jet dipole index (EZJD, green boxes in Fig. 2a, c and e) and relate this to the Siberian temperature trend across all model samples (Fig. 2g). We find a robust relationship (r = 0.58, p < 0.001) highlighting a strong link between upstream dynamical changes in the east North Atlantic extratropical jet and downstream Eurasian temperatures. We again find that the observations are located right on the edge of the cloud of model points—having both a strong EZJD dynamical signal and Siberian cooling.

Predictable but spuriously weak model dynamics

Earlier we showed that the model ensemble mean simulates zero trend for Siberian temperature over the observed Siberia cooling period. However, the fact that it also does not simulate a significant warming, as the uninitialized CMIP6 models do, suggests that the model may be capturing a predictable dynamical signal that is acting to oppose the greenhouse gas induced warming signal. Examining the ensemble mean circulation anomalies, we do indeed find very similar dynamical patterns in upper-troposphere winds (Fig. 3a and b) as that observed (Fig. 2a and b), and also to that found in the strongest members (Fig. 2e and f), with both a weakening of zonal winds over high latitude Eurasia and a wave-like structure in meridional winds. However, we note that this forced signal is much weaker and highlight that the colorbar scale is only a half (±2 m/s cf ±4 m/s) of that shown in Fig. 2, revealing that the forced predictable dynamical signal is very much weaker than that observed.

Fig. 3: A predictable dynamical signal which is spuriously weak.
Fig. 3: A predictable dynamical signal which is spuriously weak.
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a, b zonal and meridional 250 hPa wind differences (as in Fig. 2e and f) but now for the ensemble mean of all model members and plotted with half of the colour bar range, to highlight the similar spatial pattern but weak amplitude of the forced circulation signal. correlation skill at gridpoints of the model ensemble mean predicting the observed ERA5 interannual variability in zonal (c) and meridional winds (d). e, f the corresponding skill of the model predicting itself (see Methods). g, h the ratio of predictable components (RPC, see Methods) where values RPC > 1 suggest the presence of spuriously weak models circulation signals. i standardised timeseries of the observed and predicted European zonal jet dipole (EZJD) index. j absolute EZJD values (m/s) are plotted for the ensemble mean (red), ERA5 reanalysis (black) along with individual ensemble members (pink circles) and the adjusted ensemble using the matching method (see text and Methods) is shown in green.

To better understand the strength and predictability of these key circulation anomalies, we examine the interannual correlation skill over 1981–2022 (Fig. 3c and d). We find significant skill in the model ensemble mean predicting the observed variability (model-obs skill), in the same key locations of the dynamical anomalies we have identified, in both zonal and meridional winds associated with Siberian cooling. For meridional winds, we also find some weaker regions of negative skill, which is a consequence of the earlier identified model wave phase shift relative to that observed. A key question is whether these predicted Eurasian dynamical signals are of the correct amplitude relative to that observed, as there is reason to believe from studies of the winter NAO that extratropical circulation signals may be spuriously weak in current climate models32,33,34. We explore this by calculating the skill of the model in predicting itself, a single withheld ensemble member predicted by the remaining 39 members, a robust estimate of which can be obtained via bootstrap resampling. The resulting model-model skill maps (Fig. 3e and f) are largely devoid of skill over Eurasia, in sharp contrast to model-obs maps (Fig. 3c and d), with almost no locations with correlation coefficient of r > 0.2 in either zonal or meridional winds. The ratio of the model-obs to model-model skill gives us the ratio of predictable components32 (RPC) and is plotted in Fig. 3g and h. Regions where RPC»1 are indicative of underconfidence, whereby the model has higher skill at predicting the observed circulation than its own and hence suggesting that the model may have spuriously weak dynamical signals. We find that the same regions of zonal and meridional winds associated with the Siberian cooling period are highlighted by this analysis with RPC > 1. For comparison, we note that this in contrast to some other low latitude regions, e.g., south-east North America, where the model skilfully predicts both the observed variability and itself (and hence RPC ~ 1).

To explore further we use the previously defined EZJD index upstream of Siberia, with the resulting timeseries plotted in standardised form in Fig. 3i. We find that the model has significant skill (r = 0.43, p = 0.004) in predicting the interannual EZJD variability. However, we also note that the EZJD exhibits low-frequency decadal variability, including a negative trend over 1990–2014, which is also well simulated by the model ensemble mean, with a 5-year running mean smoothed timeseries (not shown) being even more highly correlated (r = 0.75). Despite the significant correlation with the observed EZJD temporal variability, when we plot this in absolute units of m/s (Fig. 3j) we find that the model ensemble mean signal is very weak in amplitude (red line), consistent with the RPC map in Fig. 3g. Put another way, the distribution of individual member EZJD each year (pink circles in Fig. 3j) are very evenly split between positive and negative anomalies and hence the model-model skill of the EZJD is only r = 0.13 (cf r = 0.43 in model-obs). This results in the EZJD having a RPC = 3.3 (see Methods) which is consistent with, and perhaps stronger than, that found for the NAO in the same model (RPC = 2.3)33, and again highlights the spuriously weak model dynamical signals.

Adjusting the dynamics and re-examining Eurasian cooling trends

We can adjust the model dynamical signal, by inflating it to account for the spuriously weak dynamical signal and then use a ‘member matching’ methodology40 to re-examine the Siberian temperature trends. First, we inflate the model EZJD signal by the ratio of predictable signals (see Methods) resulting in the green line (‘Model_Adj’, Fig. 3j) with higher amplitude. We can then use the inflated EZJD, along with a bootstrap resampling from the estimated internal variability (see Methods), to pick individual ensemble members (pink circles in Fig. 3j) each year that happen, by chance, to be the closest match. This gives us a distribution of ‘adjusted’ model members that accounts for the spuriously weak model dynamics, which we can then use to probe the downstream impacts on temperatures over Siberia.

Using our adjusted ensemble, we recalculate the map of Eurasia temperature change (Fig. 1g) to reveal a much stronger cooling difference between the early and late period, especially over Siberia. We also find stronger warming over much of the Arctic, especially the Barents-Kara seas region, in better agreement with that observed. The 1990–2014 Siberian temperature trend (Fig. 1h) now reveals a robust cooling of −0.60 K/dec (cf zero trend originally) which is approximately half the strength of the observed cooling. Furthermore, the distribution of trends in the new adjusted ensemble distribution (Fig. 1i) shows that 90% of samples now produce a cooling trend (cf 48% originally). Importantly, the probability of a cooling trend as strong as that observed has increased by over an order of magnitude in the adjusted model, from 0.8 to 12.7%, making it now a much more plausible sample from internal variability. Additionally, we also find that the interannual Siberian temperature skill increases to r = 0.52 (from r = 0.36) and the low-frequency 5-year smoothed component of temperature variability is now simulated with a correlation of r = 0.70 (from r = 0.41). This highlights that when the spuriously weak dynamical variability in the jet dynamics upstream over Europe is accounted for, we can simulate much stronger predictable downstream changes in Siberian surface temperature.

Discussion

We have highlighted a distinct pattern of zonal and meridional atmospheric circulation anomalies associated with Eurasian temperature variability in both observations and in near-term prediction ensemble members with the strongest Siberian cooling trends. Importantly we also find a very similar, but much weaker, predictable signal in the model ensemble mean. Analysis of seasonal predictions reveals significant skill in predicting observed dynamical interannual variations, but that the skill within the model itself (so-called ‘perfect predictability’) is much lower. This suggests that the model atmosphere is responding too weakly to slowly evolving boundary conditions. Furthermore, it implies that studies examining inter-member spread of large ensembles of historical climate projections41 likely overestimate the role of internal atmospheric variability.

Some studies11 present two clearly divergent views regarding the cause of the early 21st century Eurasian cooling, that either internal variability or sea-ice decline are primarily responsible. However, recent studies18 and reviews28 have attempted to reconcile these apparently opposing narratives, suggesting that they could co-exist. For example, ref. 28. used the analogy of a roll of a dice to represent internal variability and that slowly varying boundary conditions, such as Arctic sea-ice, had ‘loaded’ the dice in favour of Eurasian cooling. Our results are in broad agreement with this framework and, extending their analogy, we have demonstrated that the dice in the real-world may well be considerably more ‘loaded’ than current dynamical climate models simulate, i.e., that the real-atmosphere exhibits a stronger forced dynamical response.

Having identified a forced predictable atmospheric circulation signal, it should in principal be possible to probe which part of the boundary conditions provided to the model has driven this (i.e., the atmosphere, ocean, cryosphere, land surface and external forcings). For example, model perturbation experiments could be undertaken, but these are beyond the scope of the current analysis. Instead, we briefly examine the lagged correlation between the observed principal component timeseries (Fig. 4a), associated with the winter second joint-EOF (Fig. 2a), and fields of meridional 250 hPa winds, sea surface temperature and sea-ice concentration from the preceding October–November. We do this by separately examining the low-frequency (5-year smoothed) and high-frequency (interannual residual) variability (see methods). On the interannual (‘high-frequency’) timescale (Fig. 4b–d), we find evidence of a Eurasian wave starting in the tropical east Pacific (Fig. 4b) associated with interannual ENSO variability (Fig. 4c) but with no significant connection to Arctic sea-ice anomalies (Fig. 4d). However, on the key low-frequency (5-year mean) timescale, we find that the Eurasian wave is shifted slightly further north and has less obvious connection to the equatorial Pacific (Fig. 4f). Instead, we find relatively strong positive correlations with sea surface temperatures in both the North Atlantic and North Pacific (Fig. 4f), with the typical ‘horseshoe pattern’ of the positive phase of Atlantic Multidecadal Variability (AMV) and the negative phase of Pacific Decadal Variability (PDV). We also find strong negative correlations with Arctic sea-ice concentrations, particularly over the Barents-Kara Seas region (Fig. 4g). It is not possible to come to any casual conclusions from this analysis of observed behaviour, however these findings are consistent with many previous studies linking low-frequency changes in extratropical SSTs36,42,43,44, and/or Arctic sea-ice extent13,45, with North Atlantic jet behaviour38, East Atlantic pattern, Eurasian atmospheric circulation37 and Eurasian surface temperature variability. It remains an open question as to the extent to which Arctic sea-ice variability is a response to atmospheric circulation anomalies, a driver of them, or part of a coupled feedback.

Fig. 4: Searching for possible drivers of the observed wave.
Fig. 4: Searching for possible drivers of the observed wave.
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a the timeseries of the joint-EOF PC2 (as shown in Fig. 2a and b) with a 5-year running mean (thick line) used here as the low-frequency timeseries of the Eurasian wave and the residual (not shown) giving the high-frequency timeseries. Maps of the lagged correlation between this high-frequency timeseries of the winter Eurasian wave and the ERA5 fields of meridional 250 hPa winds (b) and also the preceding October–November observed HadISST SST (c) and sea-ice extent (d). e–g, as b–d but now using the low frequency Eurasian wave timeseries shown in (a).

In summary, we have used a large ensemble of near-term predictions to show that Eurasian winter decadal temperature variability is intimately linked with large-scale changes in atmospheric circulation, from the North Atlantic across Eurasia. Our key finding is that the model has skill in predicting this atmospheric circulation, at least on seasonal timescales, but that the predictable dynamical signal in individual model members is spuriously weak and hence results in weak downstream surface Eurasian temperature changes. When we correct for this then we can reproduce stronger Eurasian temperature changes with higher skill. This is promising for the future development of skilful real-time forecasts of Eurasian winter temperatures using improved and/or calibrated climate prediction systems. It also implies that the observed strong Eurasian cooling was not the result of purely unpredictable atmospheric internal variability but was partly a predictable response to slowly evolving boundary conditions. We note that some of these slowly evolving boundary conditions are increasing being linked to changes in external forcings such as emissions of anthropogenic aerosols and greenhouse gases (e.g., in the AMV46 and PDV47). Hence further examination of the forced atmospheric dynamics in large ensembles of uninitialized simulations should be undertaken, where model differences/errors can be exploited to gain further understanding and develop observational constraints48.

Methods

Initialised prediction system

The near-term climate prediction system used is the Met Office DePreSys3 system33 referred to here as the ‘model’). It is based on the HadGEM3-GC2 coupled climate model49. The atmosphere has a horizontal resolution of approximately 60 km (and 85 vertical levels) and an ocean resolution of 0.25° (75 vertical levels). A full-field data assimilating simulation is performed where the climate model is nudged in the ocean, atmosphere and sea-ice components towards observations. In the ocean, temperature and salinity are nudged towards a monthly analysis created using global covariances50 with a 10 day relaxation timescale. In the atmosphere, temperature and zonal and meridional winds are nudged towards the ERA-Interim51/ERA552 reanalysis with a six hourly relaxation timescale. Sea ice concentration is nudged towards monthly values from HadISST53 with a one day relaxation timescale. Hindcasts are started from the 1st November initial conditions of this assimilation simulation and a 40 member ensemble is created using randomly generated seeds to a stochastic physics scheme. The assimilation run, and hindcasts, have full knowledge of external forcing data sets (for example, greenhouse gases, aerosols, ozone, solar and volcanic forcings) as per the CMIP5 protocol54, and follow the representative concentration pathway (RCP4.5) after 2005.

Uninitialised historical simulations

Uninitialised historical simulations come from the sixth Coupled Model Intercomparison Project (CMIP624). 38 free-running CMIP6 historical models are used with varying ensemble sizes, as recorded in Table 1. In total 462 individual ensemble members are used.

Table 1 The names and ensemble size of the individual CMIP6 model uninitialized historical experiments used in this study
Full size table

Model member resampling

Individual ensemble members in DePreSys3 are created using random seeds to a stochastic physics scheme and so there is no connection between the same ensemble member number from different start dates (i.e., member #12 in the 1st November 1991 start date ensemble is not linked to member #12 in the 1st November 1992 start date ensemble). We can therefore create a distribution of possible model Siberian temperature trends, whereby for each sample we randomly pick a different ensemble member for each of the DePreSys3 hindcast start dates and concatenate these to make a single timeseries of the same length as the observations. Doing this 1000 times creates a smooth distribution of possible model Siberian temperature trends (Fig. 1f).

Signal-to-noise calculation

The signal-to-noise paradox is characterised by the ratio of predictable components (RPC) and is calculated as follows32,34:

$$RPC=\frac{P{C}_{{o}{b}{s}}}{P{C}_{{m}{o}{d}}}\ge \frac{{r}_{{m}{o}}}{{r}_{{m}{m}}}\,$$

where the predictable component (PC) of the real world (PCobs) can be conservatively estimated by the correlation between the model ensemble mean and the observations (rmo), and the predictable component of the model can be estimated by the correlation between the model ensemble mean and one of its own members (rmm). A robust estimate of rmm is obtained by bootstrap resampling over 1000 times with each trial picking a single ensemble member for each November start date (we note that in the 40 member DePreSys3 ensemble no properties are transferred across start dates, i.e., ensemble #1 of November 1990 has no relation to ensemble #1 starting in November 1991) and that each member chosen each start date is then excluded from the ensemble mean of that start date which is made with the remaining 39 members.

Adjusted model

We use a ‘model matching’ methodology, inspired by ref. 40, to correct for the spuriously weak predictable circulation signals (RPC»1) we find in the model (Fig. 3j, red line). We inflate the ensemble mean prediction of the EZJD index by the ratio of predictable signals (RPS). This is essentially the regression between forecast ensemble mean and observed EZJD timeseries, and has a value RPS = 3.8. This results in the inflated ensemble mean signal (green line in Fig. 3j). We then account for the unpredictable internal variability. We estimate this by subtracting the predictable signal, which is diagnosed from the inflated ensemble mean EZJD variance, from the total observed EZJD variance. We create a probability distribution function by taking random samples from a normal distribution with this width, centred on the predictable (inflated) EZJD value each start date (green line in Fig. 3j). We then find the closest original ensemble member (pink circle in Fig. 3j). In this way we construct individual bootstrap trials that are consistent with the predictable (inflated) EZJD signal that corrects for the spuriously weak model dynamical signal, but still samples unpredictable internal variability. We then use this ‘adjusted ensemble’ to examine the downstream impact on the Siberian temperature trends, producing new distribution of Siberian temperature trends as shown in Fig. 1i.

High and low frequency analysis

We create a ‘low frequency’ version of the observed principal component timeseries (Fig. 4a), associated with the winter second joint-EOF (Fig. 2a), using a 5-year running mean window, reflecting the start and end of the timeseries. We then subtract this low-frequency version from the original timeseries to obtain a ‘high frequency’ version. These are then used in the analysis in Fig. 4.