Introduction

The possible connection between Arctic sea-ice loss, especially over the Barents-Kara Seas (BKS), and winter cold extremes over mid-latitude Eurasia remains contentious, with conflicting lines of evidence1,2,3,4. Despite observed significant correlation between the reduced BKS sea-ice and cold Eurasian winters, many modeling studies reveal contradictory results. While some model experiments suggest a significant winter Eurasian cooling2,5, many others lack a significant cooling signal, or even simulate significant warming6,7,8. Even those model experiments supporting a causal linkage between BKS sea-ice loss and Eurasian cooling suggest the cooling response is weak compared to internal variability and that the causal effect is weaker than implied from the observed statistical relationship9,10,11. Therefore, many studies argued that internal variability, instead of sea-ice decline, plays a major role in the recent frequent occurrence of cold outbreaks over Eurasia, while BKS sea-ice loss only makes a minimal contribution3,12. However, most of the above-mentioned modeling studies are based on atmosphere-only simulations, neglecting the potential contribution of ocean-atmosphere coupling that could enhance the response to sea-ice loss13,14.

The importance of ocean-atmosphere coupling for the atmospheric response to far-future pan-Arctic sea-ice loss has been examined, using different approaches to constrain sea-ice in a coupled model framework. Through adding an additional heat flux to melt sea ice towards a reference state (“ghost-flux forcing” method), Deser et al.13,14 and some other studies15,16 found that ocean-atmosphere coupling plays a critical role in extending the influence of Arctic sea-ice loss to the tropics and even into the Southern Hemisphere. However, Deser et al.14 found in their coupled simulations a weaker Eurasian cooling response to projected future sea-ice loss at the end of the twenty-first century, compared to that in uncoupled simulations. They hypothesized that a relatively greater enhancement of thermodynamical warming, stemming from the advection of air warmed by sea-ice loss, overwhelms dynamical cooling, arising from atmospheric circulation changes. Studies using other methods—specifically, through altering the surface albedo (“albedo forcing” method) and nudging sea-ice concentration (SIC) and volume (“direct nudging” method)—also suggest little influence of ocean-atmosphere coupling on the Eurasian cooling in response to projected sea-ice loss3,12,17,18,19,20.

The aforementioned studies examining the role of ocean-atmosphere coupling all considered the response to far-future pan-Arctic sea-ice loss under a high greenhouse gas emissions scenario. However, the nature of the response to sea-ice loss could change over time, dependent on the magnitude and spatial pattern of sea-ice loss. For example, there is evidence that the Eurasian cooling response is greater for near-future than for far-future sea-ice loss5, or is greater in response to moderate than large sea-ice loss21. Over Eurasia, the thermodynamic warming response might be relatively more important than the dynamical cooling response into the future or as the magnitude of sea-ice loss increases. Thus, the importance of ocean-atmosphere coupling to Eurasian cooling may also depend on the magnitude and spatial pattern of sea-ice loss. Here, we find that ocean-atmosphere coupling enhances the Eurasian cooling induced by historical sea-ice loss due to a stronger large-scale circulation response. However, ocean-atmosphere coupling has little influence on the Eurasian cooling response to projected end-of-the-twenty-first-century sea-ice loss, in which thermodynamical warming masks dynamically-induced cooling.

Results

Ocean-atmosphere coupling enhances Eurasian cooling response to historical sea-ice loss

To identify the role of ocean-atmosphere coupling in winter Eurasian cooling induced by BKS sea-ice loss, we performed two sets of CESM simulations. One set is atmosphere-only with prescribed historical BKS high- and low-SIC conditions (atm_hi and atm_lo), and the other is coupled to a full ocean model, with BKS sea-ice constrained towards the above-mentioned high and low states using a state-of-the-art sea-ice nudging method22 (cpl_hi and cpl_lo). For more details on the simulation scheme, please refer to the “Methods” section. Moreover, both our results (Supplementary Fig. 1) and some previous studies10,23 reveal a greater Eurasian cooling signal induced by BKS sea-ice loss in late winter (January–February) than in early winter (November–December). Therefore, in the following, we mainly focus on the late-winter Eurasian cooling.

Figure 1a clearly shows that there are strong late-winter cold anomalies observed over mid-latitude Eurasia, associated with historical early-winter BKS sea-ice loss. It should be noted, of course, that this does not necessarily indicate causality, which requires model simulations to elucidate. In our atmosphere-only simulations, there are no significant cold anomalies in response to BKS sea-ice reduction (Fig. 1b), consistent with many studies based on atmosphere-only experiments that found a minimal role of sea-ice loss7,8. On the contrary, in coupled simulations, strong and widespread Eurasian cooling appears, spanning from Eastern Europe to Eastern Siberia (Fig. 1c, d), albeit still notably weaker than the observed regression, especially over central Siberia. This suggests that ocean-atmosphere coupling enhances the Eurasian cooling response to historical BKS sea-ice loss, bringing it closer to the observed estimate. However, the estimate of the forced response in the coupled simulations remains less than observed, likely due to internal variability and confounding factors that lead to an overestimation of the forced response to sea-ice loss derived from observed statistical relationships11.

Fig. 1: Observed and simulated late-winter Eurasian cooling response to historical sea-ice loss.
figure 1

a Regression map of early-winter (November–December) BKS sea-ice concentration (SIC) against late-winter (January–February) T2m during 1979–2019, scaled by the early-winter BKS SIC difference between BKS low- and high-SIC years (K). b 200-year simulated differences of late-winter T2m between the atmosphere-only historical BKS low- and high-SIC simulations (atm_lo minus atm_hi). c The same as (b), but for the coupled historical BKS low- and high-SIC simulations (cpl_lo minus cpl_hi). d The differences between c and b (c minus b). Purple box in a denotes the BKS region (10°–120°E, 45°–60°N). Cross-hatching denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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To check whether the above-mentioned results are model-dependent, the multi-model atmosphere-only and long-coupled simulations (100-year simulation) provided by the Polar Amplification Model Intercomparison Project (PAMIP)24 are also analyzed (Fig. 2). Note that we used PAMIP simulations driven by pan-Arctic, rather than BKS, sea-ice loss, as the PAMIP project does not provide coupled simulations driven by the BKS sea-ice loss alone. However, in winter, the sea-ice changes in these experiments are largest over the BKS region24, which further justifies their use here. Although these PAMIP simulations compare present-day and near-future sea-ice states, the prescribed and constrained sea-ice loss is more similar to that in our historical experiments than in our far-future experiments (Supplementary Fig. 2b–d). The PAMIP multi-model ensemble (MME) reveals a similar result, with significant Eurasian cooling in the long-coupled simulations (Fig. 2h), but no cooling in the atmosphere-only simulations (Fig. 2d). The three individual models in the PAMIP ensemble also all show a similar dependence on ocean-atmosphere coupling (Fig. 2a–c, e–g). The PAMIP also provides ensembles of short (1 year)-coupled simulations. It is notable that these short-coupled simulations lack significant Eurasian cooling25, suggesting the necessity to include both fast sea-air interaction and slow ocean dynamics; timescale of the latter depends on ocean depth, that is, around 60–100 years for shallow ocean (above ~1000 m), while up to 1000 years or more for a deeper ocean25,26,27.

Fig. 2: Simulated Eurasian temperature responses to sea-ice loss in PAMIP simulations.
figure 2

Differences of late-winter (January–February) T2m between PAMIP pdSST-futArcSIC and pdSST-pdSIC runs, derived from a IPSL-CM6A-LR, b NorESM2-LM, c EC-Earth3, and d multi-model ensemble mean (MME). e–h are the same as (a–d), but for differences between pa-futArcSIC-ext and pa-pdSIC-ext runs. Cross-hatching denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Masked Eurasian cooling response to far-future sea-ice loss

Deser et al.13,14 found a weaker Eurasian cooling in the coupled simulations compared to atmosphere-only in response to far-future pan-Arctic sea-ice loss and hypothesized that ocean-atmosphere coupling enhanced thermodynamical warming relatively more than dynamical cooling. However, note that these studies arguing ocean-atmosphere coupling damps the sea-ice-induced Eurasian cooling focus on sea-ice loss of a much larger amplitude, compared with what we presented above. To reconcile our finding of a stronger cooling in the coupled experiments with the contradictory results from Deser et al.13,14, we performed additional experiments representing BKS sea-ice loss at the end of the twenty-first century under a high greenhouse gas emission scenario, more comparable to the experiments in Deser et al.13,14. In the case of far-future sea-ice loss, Eurasian cooling is weaker in the coupled than atmosphere-only experiments, consistent with Deser et al.13 (Fig. 3), and weaker than that in historical sea-ice coupled runs (Fig. 1c). The Eurasian temperature response to sea-ice loss can be understood as the balance between thermodynamical warming, stemming from the advection of air warmed by sea-ice loss, and dynamical cooling, arising from atmospheric circulation changes (like East Asian Trough28, Ural blocking29,30, Siberian High31, and so on). We further decompose the T2m response into the contribution of dynamical and thermodynamical processes, following a simple method of Zheng et al.32 (see “Methods”). In this method, the part of Eurasian cooling correlated with 500-hPa BKS geopotential height variability is regarded as contributed by large-scale circulation changes, i.e., “dynamical” process, with the residual attributed to “thermodynamical” process, including many other factors, like warm/cold air advection. However, this method is only approximate, since not all dynamical aspects are included in the “dynamical” term. It can be found in Fig. 4a, b that the Eurasian cooling induced by historical sea-ice loss is mainly contributed by the dynamical cooling, whereas the signal of thermodynamic process is relatively weak. In response to far-future sea-ice loss, which is of larger magnitude, both thermodynamical warming and dynamical cooling are enhanced (Fig. 4c, d), with the former largely canceling the latter and leading to a weaker Eurasian cooling in the coupled simulations (Fig. 3b). This could be due to that despite the strengthened atmospheric circulation adjustments (discussed in the following section) and the subsequent intensified Eurasian dynamical cooling (Fig. 4c), a much stronger and more widespread polar warming in response to far-future sea-ice loss (Supplementary Fig. 3) is also favorable for the warm air advection into the continent (Fig. 4d), which eventually cancels out the Eurasian cooling signal.

Fig. 3: Eurasian temperature responses to future sea-ice loss.
figure 3

a 200-year simulated differences of late-winter (January–February) T2m between the atmosphere-only BKS future and present-day SIC simulations (atm_fut minus atm_pd). b the same as (a), but for the coupled BKS future and present-day SIC simulations (cpl_fut minus cpl_pd). c The differences between b and a (b minus a). Cross-hatching denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Fig. 4: Decomposition of dynamical and thermodynamical contributions to Eurasian cooling.
figure 4

Contributions of a dynamical and b thermodynamical processes, respectively, to the 200-year simulated differences of late-winter (January–February) T2m (K) between the coupled BKS historical low- and high-SIC simulations (cpl_lo and cpl_hi). c, d are the same as (a, b), but for the differences between the coupled BKS future and present-day SIC simulations (cpl_fut and cpl_pd). Most of the results pass the 95%-level significance test, and therefore, the statistical significance tests are not shown for visual clarity.

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How ocean-atmosphere coupling amplifies Eurasian cooling response to historical sea-ice loss

We now return to the response to historical sea-ice loss and seek to explain why ocean-atmosphere coupling enhances the Eurasian cooling response. Figure 5 shows the differences of SIC, SST, and surface upward turbulent heat flux (THF) between low and high BKS SIC scenarios, derived from observations and model simulations. In the observed composite differences, there are negative SIC anomalies over the Chukchi Sea and Greenland Sea, in addition to the BKS (Fig. 5a). Moreover, there are warmer SSTs over the BKS, Bering-Chukchi Seas, the North Atlantic, and North Pacific (Fig. 5e), resulting in the enhanced surface upward THF over these regions (Fig. 5i). In the atmosphere-only simulations, SIC, SST (prescribed), and THF (simulated) anomalies are confined to the BKS (Fig. 5b, f, j). With ocean-atmosphere coupling included, there is a weak signal of sea-ice loss over the Chukchi Sea and around Greenland (Fig. 5c, d) and SST warming over the North Atlantic (Fig. 5g, h), which are also seen in the observed composite difference, suggesting BKS sea-ice loss is partly responsible for these SIC and SST anomalies. Sea-ice loss around Greenland and North Atlantic SST warming could enhance the poleward heat and moisture transport, favorable for the vertical extension of Arctic warming33,34,35, while Chukchi Sea sea-ice loss could also lead to Eurasian winter cooling36,37.

Fig. 5: Atmospheric lower boundary response to historical sea-ice loss.
figure 5

a Regression map of early-winter (November–December) BKS SIC against early-winter SIC during 1979–2019, scaled by the early-winter BKS SIC difference between BKS low- and high-SIC years (1). b Differences of the prescribed early-winter SIC between the atmosphere-only BKS historical low- and high-SIC simulations (atm_lo and atm_hi). c 200-year simulated differences of early-winter SIC between the coupled BKS historical low- and high-SIC simulations (cpl_lo and cpl_hi). d Differences between c and b. e–h are the same as (a–d), but for early-winter SST (°C). i Regression map of early-winter BKS SIC against early-winter surface upward THF during 1979–2019, scaled by the early-winter BKS SIC difference between BKS low- and high-SIC years (W/m2). j 200-year simulated differences of early-winter surface upward THF between the atmosphere-only BKS historical low- and high-SIC simulations (atm_lo minus atm_hi). k The same as (j), but for the coupled BKS historical low- and high-SIC simulations (cpl_lo minus cpl_hi). l The differences between k and j (k minus j). Cross-hatching denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Figure 6a–d shows the vertical extent of warming induced by BKS sea-ice loss in observations and simulations. Observed warming is clear throughout the polar troposphere, with two maxima: near the surface and in the upper troposphere (Fig. 6a). In the atmosphere-only simulations, Arctic warming is more confined to the lower troposphere, and the upper tropospheric maximum is absent. Consistent with some previous studies17,38, deeper and stronger Arctic warming is simulated in the coupled experiments, more alike the observations. Blackport and Kushner39 suggest that the extratropical ocean warming induced by Arctic sea-ice loss could play a critical role in the vertical extension of polar warming. We also found in our coupled simulations that BKS sea-ice loss could lead to the North Atlantic SST warming (Fig. 5g, h), which is favorable for the northward heat transport and the formation of this deep warming structure25,26,27,28,29,30,31,32,33,40. However, it should be noted that coupled simulations still lack the upper tropospheric maximum. This implies that the observed polar upper tropospheric warming maximum is related to factors other than BKS sea-ice loss or, given its dependence on stratosphere-troposphere coupling41, it might suggest too weak stratosphere-troposphere coupling in the model simulations. Previous literature highlighted the importance of stratosphere-troposphere coupling in the Arctic-mid-latitude teleconnection. Specifically, Arctic sea-ice loss could amplify the sea-ice-loss-induced Eurasian winter cooling through modulating the SPV’s intensity9,10, position42 or shape43,44,45. Figure 7 shows the responses of planetary-scale wave activity and zonal-mean wind to historical BKS sea-ice loss. Although observation implies this well-documented stratospheric pathway (Fig. 7a, d), there is no evidence that historical BKS sea-ice loss enhances the upward propagating waves and weakens the stratospheric polar vortex in either the atmosphere-only or coupled simulations (Fig. 7b, c, e, f). The insignificant response of the stratospheric polar vortex in model simulations could be due to insufficient ensemble size20,46 or other aspects of this model and/or experimental design. Also note that despite the same model and similar experimental design, the atmosphere-only simulations in this study fail to reproduce the results reported in our previous studies10,41,47. This could be partly due to the different simulation mean states between this and previous studies, like the SST climatology applied. Therefore, in this study, the stratospheric pathway could play a minimal role in the Eurasian cooling due to historical BKS sea-ice loss. In addition, it is worth noting that both atmosphere-only and coupled simulations driven by far-future sea-ice loss capture the signal of SPV weakening, with the latter stronger than the former (Fig. 8). This suggests the SPV response to BKS sea-ice loss could depend on the magnitude of sea-ice loss, consistent with Zhang et al.21. Previous works suggest that a deeper Arctic warming is more likely to stimulate a southeastward-propagating wave train, which subsequently modulates the mid-latitude large-scale circulation, like westerly jet, Ural blocking, and so on41,48,49,50,51,52,53,54. Thus, we could expect a stronger response of large-scale atmospheric circulation in the coupled than atmosphere-only simulations.

Fig. 6: Large-scale circulation responses to historical sea-ice loss.
figure 6

a Regression map of early-winter (November–December) BKS SIC against late-winter (January–February) 0°–150°E-mean zonal-mean air temperature (shading; K) and zonal wind (purple contours, with solid/dashed lines denoting positive/negative values; m s−1) during 1979–2019, scaled by the early-winter BKS SIC difference between BKS low- and high-SIC years. b 200-year simulated differences of late-winter 0°-150°E-mean zonal-mean air temperature (shading) and zonal wind (purple contours) between the atmosphere-only historical BKS low- and high-SIC simulations (atm_lo minus atm_hi). c The same as (b), but for the coupled historical BKS low- and high-SIC simulations (cpl_lo minus cpl_hi). d The differences between c and b (c minus b). e–h, i–l are the same as (a–d), but for SLP (Pa; shading), 250-hPa Rossby wave flux (m2 s−2; purple vector) and 500-hPa geopotential (gpm; with zonal mean removed), respectively. Purple contours in (i–l) denote the climatology of i ERA-5 1979–2019 reanalysis, j atm_hi and k, l cpl_hi, respectively (with zonal mean removed; solid/dashed line denotes positive/negative values). Black stippling denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Fig. 7: Stratospheric polar vortex response to historical sea-ice loss.
figure 7

a Wintertime (December–January–February) EP fluxes (purple arrows; scaled by air pressure; the vertical component is scaled by 104 and the meridional component is scaled by 106; m s−2) of zonal wave 1–2 and their divergence (shading; scaled by air pressure; s−2) regressed against early-winter BKS SIC, scaled by the early-winter BKS SIC difference between BKS low- and high-SIC years. b 200-year simulated differences of wintertime (December–January–February) EP fluxes (purple arrows; scaled by air pressure; the vertical component is scaled by 104 and the meridional component is scaled by 106; m s−2) of zonal wave 1–2 and their divergence (shading; scaled by air pressure; s−2) between the atmosphere-only historical BKS low- and high-SIC simulations (atm_lo minus atm_hi). c the same as (b), but for the coupled historical BKS low- and high-SIC simulations (cpl_lo minus cpl_hi). d–f are the same as (a–c), but for wintertime zonal-mean zonal wind (m/s). Purple contours denote the climatological mid-winter zonal-mean zonal wind derived from d ERA-5 reanalysis during 1979–2019, e atm_hi and f cpl_hi simulations, with solid/dashed lines denoting positive/negative values. Black stippling denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Fig. 8: Stratospheric polar vortex response to future sea-ice loss.
figure 8

a 200-year simulated differences of wintertime (December–January–February) EP fluxes (purple arrows; scaled by air pressure; the vertical component is scaled by 104 and the meridional component is scaled by 106; m s−2) of zonal wave 1–2 and their divergence (shading; scaled by air pressure; s−2) between the atmosphere-only BKS future and present-day SIC simulations (atm_fut minus atm_pd). b The same as (a), but for the coupled BKS future and present-day SIC simulations (cpl_fut minus cpl_pd). c The differences between b and a (b minus a). d–f are the same as (a–c), but for wintertime zonal-mean zonal wind (m/s). Purple contours in (d–f) denote the climatological wintertime zonal-mean zonal wind derived from d atm_pd and e, f cpl_pd simulations, with solid/dashed lines denoting positive/negative values. Black stippling denotes the statistical significance at the 95% confidence level according to bootstrap resampling.

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Notably, both observation (Fig. 6a) and our coupled simulations (Fig. 6c) capture the signal of westerly jet deceleration over the Eurasian sector (0°–150°E) by historical BKS sea-ice loss, with the latter weaker than the former. Instead, there is no significant signal of westerly deceleration in the atmosphere-only simulations (Fig. 6b, d), confirming Arctic deep warming is more likely to decelerate the westerly jet stream than a shallow warming. This creates a favorable environment for the southeastward propagation of Rossby waves55 from the BKS region to north Eurasia (Fig. 6e, g), strengthening the high-pressure anomalies over northern Eurasia, implying a strengthening of the Siberian High. The Siberian High modulates Eurasian winter weather and climate, with a stronger Siberian High favorable for anomalous cooling56,57. In addition, there are also southward propagating Rossby waves over the North Pacific in the coupled simulations, leading to a deepening of the Aleutian Low (Fig. 6g), which could also induce Eurasian cooling58. However, a deeper Aleutian Low is not found in observation (Fig. 6e), possibly masked by other signals. As there is only a shallow warming, the above-mentioned signals of southeastward-propagating Rossby wave, strengthened Siberian High, and deepened Aleutian Low are not found in the atmosphere-only simulations (Fig. 6j, l), consistent with the absence of Eurasian cooling in these experiments. At 500-hPa, the coupled simulations show negative geopotential height anomalies over East Asia (Fig. 6k), implying a deepening of the East Asian Trough, which is favorable for Eurasian cold anomalies47,59. A similar feature but lacking significance is presented in the observations, but is absent in the atmosphere-only simulations (Fig. 6i, j). Although Ural blocking is a key part in the Arctic-mid-latitude tele-connection29,30, no significant increase of its frequency is found in our model simulations driven by historical BKS sea-ice loss (Supplementary Fig. 4), implying its relatively minor role in this case. It should be noted that the above-mentioned mechanism could work in both directions: a stronger Siberian High may also favor deeper Arctic warming60. However, additional simulations beyond the scope of this study would be required to separate these influences. While we argue that deeper Arctic warming is a potential cause for stronger Eurasian cooling, supported by observed and modeled evidence48,49, further investigation is warranted.

Discussion

Previous studies have suggested that ocean-atmosphere coupling damps, or has little effect on, the Eurasian cooling response to sea-ice loss. Whilst we were able to replicate their results for the response to far-future sea-ice loss, we reached an opposite conclusion in the context of historical sea-ice loss. We find that ocean-atmosphere coupling enhances the late-winter Eurasian cooling response to historical BKS sea-ice loss. The simulated cooling in the coupled runs is still weaker than observed, likely due to internal variability and confounding factors that contaminate estimates of the forced response to sea-ice loss derived from observations11. In the coupled simulations, the resultant Arctic warming is deeper and stronger than without coupling, and this deeper warming stimulates southeastward-propagating Rossby waves, further strengthening the Siberian High and East Asian Trough, both of which are favorable for Eurasian cooling. Moreover, our results also imply there could be a point in time when Arctic sea-ice loss ceases to have a cooling effect over Eurasia, which warrants further detailed study.

Although the inclusion of ocean coupling increases the modeled estimate of the forced response to BKS sea-ice loss, bringing it closer to observations, we need to be mindful that it could be the wrong mechanisms. Concerns have been raised that nudging methods artificially add heat to the climate system and may overestimate the response to sea-ice loss61,62,63. Although the hybrid sea-ice nudging method used here is arguably less prone to this problem than the original “ghost-flux” method, it still introduces artificial heat into the model and therefore could induce spurious signals62,63. It is possible that the stronger responses in the coupled simulations, compared to uncoupled, are, at least partly, a spurious effect of the nudging technique, rather than a genuine effect of ocean-atmosphere coupling; although we note that the separation of “spurious” and “genuine” effects is open to interpretation (e.g., whether sea-ice loss is a sufficient or necessary causal driver). Therefore, further study is required in the future to reduce the “spurious” effect of this hybrid sea-ice nudging method as much as possible.

Methods

Reanalysis

Daily- and monthly-mean atmospheric fields during 1979-2020 are derived from the ECMWF ERA-5 reanalysis dataset, with a horizontal resolution of 1° × 1°64. Monthly SST, SIC, and thickness (SIT) are derived from the Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS), which assimilates satellite SIC and SST observations65. PIOMAS has a horizontal resolution of 276 × 360 (latitude×longitude).

Definition of BKS high- and low-SIC years

The geographical extent of the BKS region is 20°–90°E, 65°–85°N (purple box in Fig. 1a). Winter is defined as December–January–February mean, with early- and late-winter defined as November–December and January–February mean, respectively. The BKS high- and low-SIC years are selected based on the de-trended time series of PIOMAS 1979–2019 early-winter BKS SIC, using ±1 standard deviation as the criterion. 1988, 1998, 2002, 2003, 2014, and 2019 are selected as the BKS high-SIC years, while 1979, 1984, 2009, 2012, and 2016 for the low-SIC years (Supplementary Fig. 2a). The observational analysis and SST/SIC/SIT boundary conditions for the model simulations are based on these selected years. In this study the sea-ice related signals from observations are estimated according to the following steps41: firstly, regress the atmospheric fields (near-surface temperature, sea-level pressure and so on) upon the early-winter BKS SIC time series; then, multiply the obtained regression maps by the composited difference of early-winter BKS SIC between its low and high years (−0.20 in this case; Supplementary Fig. 2b). Compared with directly compositing differences between BKS low- and high-SIC years, this method takes into consideration the whole sea-ice time series and its co-variability with atmospheric circulation. However, it should be noted that both methods include signals from other external forcings.

Decomposition of dynamical cooling and thermodynamical warming

The method proposed by Zheng et al.32 is applied to estimate the contributions of dynamical and thermodynamical processes in the Eurasian temperature response to sea-ice loss. Firstly, the 200-year simulated T2m response to sea-ice loss (T2mBKS) is randomly resampled 10,000 times, with a subset size of 100 years. Then, the response of 500-hPa geopotential height over the BKS (Z500BKS) is also resampled in the same way. Zheng et al.32 found that Z500BKS could well represent the tropospheric circulation response to BKS sea-ice loss and is highly correlated with the sea-ice-loss-induced Eurasian T2m anomalies. Lastly, the T2m responses are regressed upon the Z500BKS responses based on these 10,000 100-year subsamples (Eq. 1). In Eq. 1, a and b denote the regression coefficient and residual term, respectively. The two terms on the right-hand side of Eq. (1) approximate the dynamical and thermodynamical contributions.

$${{\rm{T}}2{\rm{m}}}_{\mathrm{BKS}}=a* {{\rm{Z}}500}_{\mathrm{BKS}}+b$$
(1)

E-P flux calculation

Eliassen-Palm flux (EP flux) is calculated using the following equations66:

$${F}_{\phi }={\rho }_{0}a\cos \phi (\bar{{u}_{z}}\bar{{v}^{{\prime} }{\theta }^{{\prime} }}/\bar{{\theta }_{z}}-\bar{{v}^{{\prime} }{u}^{{\prime} }})$$
(2)
$${F}_{z}={\rho }_{0}a\cos \phi \{[f-{(a\cos \phi )}^{-1}{(\bar{u}\cos \phi )}_{\phi }\bar{{v}^{{\prime} }{\theta }^{{\prime} }}/\bar{{\theta }_{z}}-\bar{{w}^{{\prime} }{u}^{{\prime} }}]\}$$
(3)
$${D}_{F}=\frac{\nabla \cdot \vec{F}}{{\rho }_{0}a\cos \phi }=\frac{{(a\cos \phi )}^{-1}\frac{\partial }{\partial \phi }\left({F}_{\phi }\cos \phi \right)+\frac{\partial {F}_{z}}{\partial z}}{{\rho }_{0}a\cos \phi }$$
(4)

where \({F}_{\phi }\), \({F}_{z}\) and \({D}_{F}\) denote the meridional and vertical components of EP flux and its divergence, \(u\), \(v\), \(w\), \(\phi\), \(\theta\), \(a\), \(f\), \(z\) and \({\rho }_{0}\) denote zonal, meridional and vertical wind components, latitude, potential temperature, Earth’s radius, Coriolis parameter, log pressure and air density. Overbars and primes represent zonal-mean and departure from zonal mean.

Takaya & Nakamura Rossby wave flux

According to Takaya & Nakamura55, horizontal Rossby wave fluxes \(\vec{W}\) are calculated using the following equation:

$$\vec{W}=\frac{p\cos \varphi }{2\left|\vec{U}\right|}\left(\frac{\displaystyle \frac{U}{{a}^{2}{\cos }^{2}\varphi }\left[{\left(\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\right)}^{2}-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial {\lambda }^{2}}\right]+\frac{V}{{a}^{2}\cos \varphi }\left[\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial \lambda \partial \varphi }\right]}{\frac{U}{{a}^{2}{\cos }^{2}\varphi }\left[\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial \lambda \partial \varphi }\right]+\frac{V}{{a}^{2}}\left[{\left(\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }\right)}^{2}-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial {\varphi }^{2}}\right]}\right)$$
(5)

where \(p\), \(\varphi\), \(\lambda\), \(\psi\), \(\vec{U}\), \(U\), \(V\) and \(a\) denote pressure/1000 hPa, latitude, longitude, stream function, horizontal wind velocity and its zonal and meridional component, and Earth’s radius. Prime and | | denote perturbation and norm of a vector.

Model description and simulation scheme

CESM1.2.0 model is used to perform the simulations. The atmosphere, sea-ice, and ocean components used in this study are the Whole Atmosphere Community Climate Model 4 with Specified Chemistry67, Community Ice CodE 468, and Parallel Ocean Program 269.

Two pairs of experiments are performed, with each pair including a simulation with high BKS SIC and a simulation with low BKS SIC, using the atmosphere-only (atm_hi and atm_lo) and coupled (cpl_hi and cpl_lo) frameworks. In the atmosphere-only simulations, the SST/SIC conditions are prescribed using the above-mentioned composited BKS high- and low-SIC conditions, while the SST/SIC conditions in the remaining regions are fixed at year 2000 conditions. SIT is constant in the atmosphere-only simulations. In the coupled simulations, a new hybrid nudging method developed by Audette and Kushner22 is applied to nudge the SIC/SIT state towards the target values. In this method, SIC and SIT are nudged towards the target values using direct sea-ice nudging17 and ghost-flux nudging18, respectively, to better capture the partitioning between SIC and SIT. Moreover, additional freshwater flux and equivalent water mass from the sea-ice melting are added to the model to conserve the total water content. Audette and Kushner22 provide evidence that this method has advantages over the traditional ghost-flux method, by allowing for better control over the SIC/SIT partitioning while conserving total water conservation. In our study, sea-ice nudging is confined only in the BKS region, and the nudging time-scales for SIC and SIT are 3 h and 5 days, respectively, which is determined after testing and validation to minimize the differences between the simulated and reference sea ice states. It can be found from Supplementary Fig. 2b that coupled simulations well reproduce the seasonal cycle of historical BKS SIC loss.

In addition, another 2 pairs of CESM experiments are performed with BKS sea-ice loss of a larger magnitude. These simulations are driven by the BKS SIC/SIT conditions during the years 1980–1999 under a historical scenario and years 2080–2099 under the Shared Socioeconomic Pathway 5-8.5 (SSP585) scenario, derived from MME of 23 CMIP6 models. The full list of the used models is shown in Supplementary Table 1, and the composite seasonal cycle of BKS SIC differences between the two scenarios is shown in Supplementary Fig. 2d. Except for the BKS sea ice, all the remaining forcings are identical to the simulations driven by historical BKS sea-ice loss. The simulation time for atmosphere-only and coupled simulations is 203 and 260 years, respectively, and only the last 200 years are analyzed. Note that long-coupled simulations, rather than short-coupled runs in some relevant studies20,32, are deliberately performed in this study to include both the signals of fast sea-air feedback and slow ocean dynamic processes. Supplementary Table 2 shows the simulation scheme of the above-mentioned experiments.

PAMIP multi-model ensemble

MME simulations from the PAMIP24 are used to check whether our results are model-dependent and robust in a larger ensemble with better sampling of internal variability. The models used in PAMIP and their corresponding ensemble sizes are included in Supplementary Table 3. Note that in these PAMIP simulations, sea ice is perturbed across the whole Arctic, not just in the BKS. The PAMIP project also provides simulations driven by the BKS sea-ice loss alone, but no coupled simulations are performed with nudged BKS sea-ice. Therefore, we only used pan-Arctic sea-ice simulations from the PAMIP project. Four PAMIP experiments are used: pdSST-pdSIC, pdSST-futArcSIC, pa-pdSIC-ext, and pa-futArcSIC-ext. As atmosphere-only simulations, pdSST-pdSIC and pdSST-futArcSIC are prescribed with the climatological SIC and SST during 1979-2008 derived from the HadISST1 dataset70, with Arctic SIC/SST in pdSST-futArcSIC prescribed to that projected at 2 °C global warming above preindustrial levels. Each member in pdSST-pdSIC and pdSST-futArcSIC starts from April 2000 and ends in May 2001, with the first 2 months discarded as model spin-up. To keep in accordance with our coupled simulations, the extended coupled simulations of pa-pdSIC-ext and pa-futArcSIC-ext are used. In these simulations, Arctic SIC and SIT are nudged towards the present-day and 2-degree-global-warming states, respectively, through direct nudging. We use output from three models: EC-Earth3, NorESM2-LM, and IPSL-CM6A-LR. Although a fourth model (CNRM-CM6-1) also participated in these experiments, it applied an albedo reduction, instead of direct nudging, that resulted in more sea-ice loss than that prescribed in the atmosphere-only simulations (Supplementary Fig. 2c).

Statistical significance testing

Bootstrap resampling is applied to validate whether the composite analysis is statistically significant at the 95% level71. The two samples are resampled 1000 times with replacement, with a subset size of 10% of the total sample size.