Introduction

Arctic sea ice cover has been declining over recent decades across all seasons1,2,3. The most significant sea ice loss in winter is found in the Barents and Kara Seas (Fig. 1A, red box). The area-averaged Barents–Kara sea ice concentration has decreased from 74% to 63% from 1980 to 2022 (black line, Fig. 1B). However, the downward trend is not steady: Barents–Kara sea ice loss accelerated around 1997 and the acceleration has slowed down since 2017 (i.e., the strongest 20-year sea ice trend was found over 1997–2017 with a magnitude of −11%/decade). While anthropogenic warming is presumed to play a dominant role in sea ice decline in all seasons4,5,6, internal variability occasionally accelerates or decelerates the sea ice decline over shorter periods7,8,9,10,11,12,13. Although the role of the two processes has been well recognised, their relative contribution to recent sea ice loss still remains uncertain, especially in the cold season. Climate model simulations have been used as a tool to facilitate the partitioning of the two processes8,10,11,14.

Fig. 1: Barents–Kara sea ice experienced accelerated loss in recent winters.
figure 1

A Linear trends of December-to-February (DJF) Arctic sea ice concentration (shading, %/decade) from 1980/81 to 2021/22 and climatological sea ice extent (black contours showing 15% concentration) from NSIDC satellite observations (CDR algorithm). The red box indicates the Barents–Kara Sea region (70–82°N, 15–100°E) for computing the Barents–Kara sea ice time series. B Time series of weighted area-averaged DJF Barents–Kara sea ice concentration (%) from NSIDC satellite observations (CDR algorithm, black) and CMIP6 forced simulations (blue) from 1980/81 to 2021/22. The thin blue lines indicate individual ensemble members (12 models and each has 10 members) and the thick blue line indicates the ensemble average.

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Climate model simulations forced by historical anthropogenic forcing (i.e., transient changes in greenhouse gases, aerosols and land use) are run with different initial conditions to produce many possible realisations of the real-world observations arising from internal variability. Thin blue lines in Fig. 1B represent possible trajectories of Barents–Kara sea ice changes arising from internal variability and model differences. Their average (thick blue line) closely isolates the anthropogenically forced response and removes bias arising from a single model, showing a steady downward trend of the area-averaged Barents–Kara sea ice concentration (−5%/decade) from 1980 to 2022. The observed sea ice variability (black line) appears to be well within the spread of the model trajectories, but deviates from the simulated anthropogenic sea ice trend over the period with accelerated sea ice loss in observations (1997–2017). The difference between the observed and simulated anthropogenic sea ice trends is often used as an estimate of the contribution of internal variability11,15,16,17. However, this residual estimation is based on an assumption that the simulated anthropogenic sea ice trend is realistic, which cannot be proved or disproved.

One approach to directly estimate the contribution of internal variability is to replay observed winds in climate models (known as nudging) and examine the resulting sea ice loss. This assumes that the dominant source of internal climate variability at mid to high latitudes might be reflected in large-scale atmospheric circulation18,19. In this case, the sum of sea ice loss responding to the observed winds and anthropogenic forcing is able to explain Arctic sea ice loss in summer9,20, but not in winter20,21,22. This might result from specific model biases21 and/or how observed winds are nudged in the models20. An alternative but novel approach is to use pattern recognition tools to identify statistical relationships between atmospheric circulation patterns and sea ice changes from a large ensemble of freely evolving simulations (i.e., in the absence of anthropogenic forcing and observed wind changes), and then infer how much the observed winds contribute to sea ice changes. Similar pattern recognition techniques have been used to detect and attribute observed climate signals to internal climate variability and anthropogenic warming23,24,25,26,27,28,29.

In this study, we use large ensemble simulations (at least 10 ensemble members) from Coupled Model Intercomparison Project Phase 6 (CMIP6) and a pattern recognition tool (carried out by Ridge Regression) to quantify how much anthropogenic forcing and observed winds contribute to wintertime (December to February) Barents–Kara sea ice loss over the satellite-era (1980–2022). We further identify the spatial patterns of atmospheric circulation trends responsible for significant Barents–Kara sea ice loss, and determine whether the circulation trends arise from internal atmospheric variability, sea surface temperature variability and/or Arctic sea ice loss.

Results

Attributing observed sea ice loss to anthropogenic and internal variability components

To highlight the accelerated Barents–Kara sea ice loss in recent decades, we break down the satellite period (1980–2022) into 20-year moving windows for which linear trends of Barents–Kara sea ice are calculated. The observed sea ice trends (black shading in Fig. 2) are negative in all 20-year periods but exhibit large variability: the negative trends minimise in the early period (1982–2002) but maximise in a recent period (1997–2017), consistent with the accelerated sea ice loss shown in Fig. 1B. We aim to decompose the observed sea ice trend in each period into anthropogenic and circulation-driven components. To estimate the anthropogenic component (red bars in Fig. 2), we calculate multi-model ensemble averages (12 models with each having exactly 10 ensemble members) using historical and future-scenario forced simulations from CMIP6. To estimate the circulation-driven component (blue bars), we first use Ridge Regression to learn relationships between atmospheric circulation trends in all seasons in the Euro-Atlantic sector (individual grid points of the spatial patterns as input) and winter Barents–Kara sea ice trends (a weighted area-averaged index as output) from the same set of forced simulations but with ensemble-averaged, or anthropogenic, signals removed. Afterwards, we apply the learned relationships to infer how much observed circulation trends from atmospheric reanalysis (Fig. 2 for MERRA2 and Fig. S1 for ERA5 and JRA55) contribute to Barents–Kara sea ice trends. The red and blue shadings indicate sensitivity ranges of the anthropogenic and circulation-driven components respectively. Readers are referred to the Methods section for details. Since the high-latitude Euro-Atlantic atmospheric circulation trends (represented by sea level pressure) are largely unforced (shown in the last subsection in Results) and coupled with the oceanic surface variability30,31,32, the estimated circulation-driven sea ice trends could reflect the sea ice changes arising from internal variability. Nevertheless, the internal variability related to the deep ocean that is not coupled with the surface variability might not be fully reflected here.

Fig. 2: Internal variability significantly contributes to the accelerated Barents–Kara sea ice loss up to 2017.
figure 2

The black shading indicates linear trends of winter (DJF) Barents–Kara sea ice concentration (%/decade) from NSIDC satellite observations (the range considers three detection algorithms: CDR, NASA Team and NASA Bootstrap) in all possible 20-year periods from 1980/81 to 2021/22 (first to second last columns) and their average (last column). 80-00 refers to the period of DJF 1980/81 to 1999/2000, and so on. Bars show the estimated anthropogenic (red) and internal variability (blue) components for the observed Barents–Kara sea ice trends. The anthropogenic components are estimated by the multi-model ensemble averages from 12 CMIP6 forced simulations. The internal variability components are estimated by the machine-learning regression approach. The red shading shows half of the standard deviation of the model spread (after taking the ensemble average for individual models). The blue shading shows half of the standard deviation of errors between actual and estimated sea ice trends for the validating models under a “take-one-model-out” approach. The numbers inside the parentheses in the legend indicate the standard deviation (std, %/decade) of the two components over all 20-year periods.

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The 20-year moving window observed Barents–Kara sea ice trends (black shading in Fig. 2) are largely reproduced by the sum of the estimated internal variability (blue bars) and anthropogenic (red bars) components, though the sum slightly overestimates and underestimates the observed sea ice loss in the early and later satellite periods, respectively (using ERA5 and JRA55 yields similar results; see Fig. S1). This method is not only reproducing the observed sea ice trends well, but also successfully reproduces the sea ice trends in many individual ensemble members of the model simulations (Fig. S2 illustrates a few examples). Previous studies attempted to quantify the contribution of internal variability to sea ice loss using dynamical nudging experiments (i.e., replaying observed winds in coupled models20,33). However, the nudging experiments performed by two versions of the National Center for Atmospheric Research Community Earth System Model (NCAR-CESM) 1 and 2 and their estimated anthropogenic trends largely underestimate the winter Barents–Kara sea ice loss in recent decades (Fig. S3), due to specific model biases21. The machine-learning model trained on only CESM2 also shows similar underestimation (Fig. S4). This could result from a lack of training data using CESM2 only, or the fact that CESM2 exhibits biases in reproducing observed sea ice variability. Here we use multiple models that can remove specific model biases arising from a single model3,24, and provide a large amount of model data to train the circulation-ice relationships. Both factors contribute to an improved estimate of the anthropogenic and internal variability components that help better reproduce the real-world sea ice loss (Fig. 2), although the uncertainties of both components are large due to the model spread and machine-learning estimation (red and blue shadings respectively).

Our findings highlight that the accelerated Barents–Kara sea ice loss up to 2017 winter mostly results from enhanced internal variability rather than accelerating anthropogenic warming (Fig. 2). The contribution by internal variability is negligible in the early 20-year windows, but gradually increases with time. The contribution reaches its maximum over the 20-year windows of 1996–2016 and 1997–2017, explaining more than 50% of the Barents–Kara sea ice loss. Since 2017, the contribution by internal variability gradually weakens, and even turns positive in the latest 20-year period (e.g., 2002–2022). While the contribution of internal variability varies significantly from the early to late satellite era, the contribution of anthropogenic forcing is more steady across the entire period. The anthropogenic contribution to Barents–Kara sea ice loss has steadily increased from −3.1 to −4.6%/decade from the first (1980–2000) to the last (2002–2022) 20-year window. The variability of the 20-year observed sea ice trends (the average of the black shading) appears to be dominated by the internal variability components (blue bars), supported by their strong correlation (ρ = 0.92, with time series detrended), compared to a weaker correlation (ρ = 0.79) between observed sea ice trends and the anthropogenic components (red bars). The contrasting temporal variability of the two components can be further quantified by standard deviations of the blue and red bars across all 20-year windows (2.34 versus 0.8%/decade respectively). The steady increase in anthropogenic sea ice loss is likely driven by greenhouse gas forcing which also experiences a steady increase over historical periods7. In contrast, internal variability can induce either sea ice loss or growth at any specific period.

Although our findings highlight the importance of internal variability in modulating the 20-year observed Barents–Kara sea ice trends, the role of anthropogenic warming is substantial in all periods. Considering the whole satellite period by averaging all 20-year periods (last column), anthropogenic forcing explains about 70%, while internal variability explains about 30%, of Barents–Kara sea ice loss in winter. Even during the periods when internal variability contributes the most (1996–2016 or 1997–2017), anthropogenic warming still accounts for about 50% of the total.

The results to this point indicate that internal variability plays a significant role to augment or oppose the Barents–Kara sea ice loss signal due to the anthropogenic forcing over shorter decadal periods. For example, the accelerated Barents–Kara sea ice loss in recent decades (from 1996 to 2017) arises from significant enhancement by internal variability, rather than a rapid increase in anthropogenic warming.

The responsible atmospheric circulation patterns and physical mechanisms

We next address the question what atmospheric circulation trend pattern could be responsible for significant Barents–Kara sea ice loss on decadal time scales, with a particular focus on the 20-year periods of 1996–2016 and 1997–2017 that show the strongest contribution by circulation (or internal variability, blue bars in Fig. 2). The observed circulation trends in winter (DJF) during these two periods both show a high pressure centre over the Urals and a low pressure centre near Iceland (Fig. 3A, B, contours) associated with significant Barents–Kara sea ice loss (shading). Although 1996–2016 (Fig. 3A) shows a stronger magnitude of dipole trend pattern compared to 1997–2017 (Fig. 3B), the circulation-driven sea ice trends over these two periods are similar. This is possibly related to a persistent dipole pattern in the preceding autumn that preconditions a stronger Barents–Kara sea ice loss for the 1997–2017 winter (see Fig. S5). Although circulation trends in all preceding seasons (autumn, summer and spring) could help modulate the winter Barents–Kara sea ice trends, winter circulation trends are always the most important for winter sea ice loss, which is evident in a permutation feature importance test in the machine-learning regression framework (Fig. S6).

Fig. 3: Circulation patterns featured by southerly winds over the Barents–Kara Sea favour sea ice loss.
figure 3

Linear trends of sea level pressure (black contours at 100 intervals starting at |100| Pa/decade; dashed contours indicate negative values; thick contours indicate significant values at 10% level using a two-tailed t-test), and 10-m zonal and meridional winds (green vectors, m/s/decade; see scales at the bottom right corners) from MERRA2 reanalysis for (A) DJF 1996/97–2015/16 and (B) DJF 1997/98–2016/17. Shading shows the corresponding linear trends of sea ice concentration (shading, %/decade) from NSIDC satellite observations (CDR algorithm). The red boxes enclose the regions of Urals (50-70°N, 25-90°E) and Iceland (52–70°N, 37–1°W) for calculating the circulation index.

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Although this study intends to quantify the relative role of anthropogenic forcing versus internal variability in driving winter Barents–Kara sea ice loss, it is still worthwhile to discuss the underlying physical processes (e.g., atmospheric versus oceanic heat transport). The low pressure centre over southern Greenland/Iceland and high pressure centre over Urals/Scandinavian are recognized to drive Barents and Kara sea ice loss in the cold season via thermodynamic and dynamic pathways from synoptic34,35,36 and seasonal36,37 to decadal timescales22,38,39. Thermodynamic pathways refer to westerly and southerly winds (vectors in Fig. 3A, B) that bring heat and moisture from lower latitudes to the Barents–Kara Sea and melt the underlying sea ice via turbulent heat fluxes and downward longwave radiation. Dynamic pathways refer to the same northward winds that drift sea ice away from the Barents–Kara Sea via advection. Thermodynamic pathways are usually reported as the dominant mechanism in driving Arctic sea ice changes on longer timescales20,22,36. Such atmospheric circulation patterns and associated surface winds are coupled with the oceanic surface circulation, and hence enhance the oceanic heat transport towards the Barents Sea via the Barents Sea Opening, melting the sea ice from the bottom or laterally12,16,37,40,41,42. The atmospheric and oceanic processes leading to Barents–Kara sea ice melting are nevertheless strongly coupled30,32,43,44 so that fully separating their roles remains challenging.

The extreme and unforced high-latitude atmospheric circulation trends

What dynamic drivers trigger the high-latitude circulation trend pattern in the cold season remain largely uncertain. Previous studies suggest that remote sea surface temperatures45,46 and anthropogenic warming including Arctic sea ice loss47,48 acting as boundary forcings are able to produce similar circulation patterns over the high-latitude Euro-Atlantic sector. However, how much these processes have explained the observed circulation trends is questionable given that atmospheric internal variability can dominate trends evaluated over short observational records49,50,51,52. Here we use modelling and statistical tools to examine what roles anthropogenic forcing, sea surface temperature, sea ice loss and internal atmospheric variability play in modulating the 1996–2016 and 1997–2017 winter atmospheric circulation trends in the Euro-Atlantic sector.

We find that the winter circulation trends over 1996–2016 (see Fig. S7 for 1997–2017) in the high-latitude Euro-Atlantic sector are a rare event over the past two centuries. To visualise this, we create a circulation index as the difference of sea level pressures between the Urals and Icelandic regions (red boxes in Fig. 3) to represent the dipole pattern of interest. We calculate the linear trends of such an index over 1996–2016 (diamond shows MERRA2; square shows ERA5; cross shows JRA55; Fig. 4) and all possible 20-year slicing windows from 1836 to 2015 (20th-century reanalysis; black boxplot). The circulation trends from the long observations show a large spread encompassing negative and positive values with a median close to zero. The circulation trend from 1996 to 2016 is unprecedented compared to any 20-year period over the long observational records. Although the circulation trends are particularly strong in recent decades, they exhibit apparent fluctuations between negative and positive values from 1836 to 2022 in observations, rather than a monotonic change one might expect as a typical response to increasing anthropogenic forcing (Fig. S8). This highlights the role of internal variability in modulating the circulation trends in any 20-year period. Next we will show that unforced and forced climate simulations also support this conclusion.

Fig. 4: Trends of Euro-Atlantic circulation dipole exhibit large spread in long observations, forced and unforced simulations.
figure 4

Distribution of linear trends of circulation indices (Pa/decade) in observations (left), CMIP coupled models (middle) and atmosphere-only models (right). The black boxplot (left) shows the observed trends of circulation indices for all possible 20-year periods from DJF 1836/37 to 2014/15 in 20th-century reanalysis V3. Black diamond, cross and square show the observed trends for DJF 1996/97 to 2015/16 in MERRA2, JRA55 and ERA5 reanalysis respectively. Grey boxplots show the simulated trends for all possible 20-year periods in unforced, control simulations from coupled (800 years long, middle) and atmosphere-only (999 years long, right) models. Orange boxplots show the simulated trends for DJF 1996/97 to 2015/16 in forced, transient large-ensemble simulations from coupled (middle) and atmosphere-only (right) models. The boxes indicate the 25th and 75th percentiles, whiskers indicate the 5th and 95th percentiles, and dots indicate outliers. Numbers on the top of the boxplots show the likelihood of reproducing the MERRA2 1996/97 to 2015/16 circulation trend or anything stronger. The circulation index is defined as the difference in sea level pressures between the regions of Urals and Iceland shown in the red boxes in Fig. 3.

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Unforced coupled simulations (preindustrial control experiments from CMIP6) are run with anthropogenic forcing fixed at the preindustrial era and are long enough to sample a large range of circulation variability internally generated within the climate system. These simulations show a large range of circulation trends centred at zero with considerable spread (grey boxplot in the middle in Fig. 4). The simulations are able to reproduce the observed circulation trends over 1996–2016 and even stronger ones, but with a very low probability (0.7%). The same models forced by 1996–2016 anthropogenic forcing (historical and future-scenario experiments from CMIP6) with many ensemble members do not enhance the occurrence of such circulation trends (orange boxplot in the middle, 0%). Similar to the long observations, the 20-year trends from these forced simulations also show fluctuations between negative and positive signs from the preindustrial era to the end of this century (Fig. S8), again highlighting the strong modulation by internal variability in any 20-year period.

Finally, we compare unforced and forced atmosphere-only models to further test the combined role of anthropogenic forcing, sea surface temperature and Arctic sea ice loss in shaping the 1996–2016 circulation trend pattern. The unforced atmosphere-only models are run with greenhouse gases, sea surface temperature and sea ice conditions fixed in the preindustrial era (grey boxplot in the right of Fig. 4). The forced simulations are run with transient forcings and boundary conditions (i.e., greenhouse gases, sea surface temperature and sea ice) taken from observations in the period of 1996–2016 (orange boxplot). We are specifically interested in exploring whether the forcings in 1996–2016 increase the likelihood of reproducing the strong circulation trends. However, we only identify a very weak increase in the probability of reproducing the 1996–2016 circulation trend from unforced to forced simulations (0.4% versus 1.3% respectively). A statistical regression model applied to long observations also shows that none of the sea surface temperature modes (Pacific Decadal Oscillation, El Niño-Southern Oscillation or Atlantic multi-decadal Oscillation) can explain the strong circulation trend pattern in this period (see Fig. S9). Overall, observational and modelling evidence both support the idea that the Euro-Atlantic circulation trends in winter over 1996–2016 arise from internal atmospheric variability rather than other physical processes (see Fig. S7 that shows similar results for the period of 1997–2017).

Discussion

Our study uses a novel machine-learning and multi-model approach to successfully reproduce the observed Barents–Kara sea ice trends by summing the estimated anthropogenic warming and internal variability components. Across all 20-year slicing windows over the entire satellite period (1980–2022), anthropogenic warming and internal variability respectively account for about 70% and 30% of Barents–Kara sea ice loss on average. Over shorter periods (~20 years), while the impact of anthropogenic warming on wintertime Barents–Kara sea ice loss has been steadily increasing over the past four decades, internal variability plays the dominant role in explaining the recent accelerated winter Barents–Kara sea ice loss. The largest Barents–Kara sea ice loss over recent decades (1996–2017) is significantly strengthened by internal variability (>50%) acting on top of anthropogenic warming. We further use long observations, unforced and forced simulations to show that the significant sea ice loss due to internal variability in this period is consistent with an extreme, unforced high-latitude atmospheric circulation dipole trend in the Euro-Atlantic sector (a high-pressure centre over the Urals and a low-pressure centre over southern Iceland in winter). This is consistent with recent literature showing that atmospheric variability drives recent observed Arctic sea ice changes rather than the other way around52,53,54,55. Future studies should further investigate the underlying physical processes (i.e., atmosphere versus ocean heat transport, and wind-driven sea ice drifts) responsible for the anthropogenic and internal-driven sea ice loss, comparing observations and models, to further ascertain the fidelity of the decomposition of the two processes derived from climate models.

Although model uncertainties in projecting Arctic climate can have numerous sources56,57,58,59,60, our study and others61,62 suggest that internal variability will act as a main source of uncertainty in future sea ice projection considering its significant role in shaping sea ice from decadal to bi-decadal timescales. On multi-decadal or even longer timescales, it is expected that the role of internal variability will be less apparent and anthropogenic warming will dominate the sea ice loss signal, but this is still subject to the future emission levels of anthropogenic greenhouse gases. Our findings, and the use of machine learning pattern recognition to attribute sea ice loss, will have important implications to guide future studies to better understand projections of the Arctic climate and the broader climate, which are more susceptible to Arctic changes in the future decades.

Methods

Observations and models

The main observational basis for this study is the sea ice concentration data from the National Oceanic and Atmospheric Administration/National Snow and Ice Data Centre (NOAA/NSIDC) Climate Data Record of Passive Microwave Sea Ice Concentration Version 4 (CDR, NASA Team and NASA Bootstrap algorithms)63 and atmospheric circulation data (sea level pressure, 10-m zonal and meridional winds) from the National Aeronautics and Space Administration Modern-Era Retrospective analysis for Research and Applications Version 2 reanalysis (NASA MERRA2)64 covering the period of 1980–2022. To further support the results, we also use sea level pressure data from the European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ECMWF ERA5)65, Japanese 55-year Reanalysis (JRA55)66 covering the period 1980–2022 and the National Oceanic and Atmospheric Administration–University of Colorado Boulder’s Cooperative Institute for Research in Environmental Sciences–U.S. Department of Energy 20th Century Reanalysis version 3 (NOAA-CIRES-DOE 20CRV3)67 covering the period 1836–2015.

For main climate modelling results, we use the sea ice concentration and sea level pressure data from the Coupled Model Intercomparison Project Phase 6 (CMIP6) model simulations68. To estimate anthropogenic and circulation-driven Barents–Kara sea ice trends for observations, we select models with forced simulations (forced by time-varying greenhouse gases, land use, aerosols, and insolation) having at least 10 ensemble members that cover the period of 1960–2040. Periods before 2015 are taken from historical experiments, while the following years are taken from future-scenario emission experiments (either Shared Socioeconomic Pathways SSP2-4.5, SSP3-7.0 or SSP5-8.5; SSP3-7.0 is used if more than one are available). This results in 12 models (see Table 1). Our result is generally not sensitive to which future-scenario emission experiment is used because the difference of Barents–Kara sea ice loss across future-scenario experiments in a single model is small over the analysed periods of this study (Fig. S10). To test the dynamic drivers of high-latitude circulation trends, we compare these coupled, forced simulations with the coupled, unforced simulations (i.e., preindustrial control, forced by greenhouse gases, aerosols, etc. fixed in the preindustrial era). Similarly, we select and compare a few forced (forced by time-varying anthropogenic forcing, observed sea surface temperature and sea ice) and unforced (forced by climatological sea surface temperature, Arctic sea ice and radiative forcing fixed at preindustrial era) atmosphere-only models that follow the CMIP5 or 6 protocol. Readers are referred to Table 1 for details.

Table 1 Model simulations used in this study
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Methods to estimate anthropogenic and circulation-driven Barents–Kara sea ice trends

We calculate the linear trends of observed Barents–Kara sea ice concentration in winter (December to February; DJF) for all possible 20-year periods over the satellite periods (i.e., twenty-three 20-year periods over 1980–2022) and their averages. Arctic sea ice trends on 20-year moving windows are often used in previous studies to demonstrate the fluctuations of bi-decadal sea ice trends over a long period15,59. To obtain the trends, we first interpolate sea ice concentration data to 1° × 1° latitude-longitude grids, and calculate the seasonal (DJF) data by averaging the monthly data. We next calculate the weighted area-averaged indices of sea ice concentration (in %) over the Barents–Kara Sea (70°–82°N, 15°–100°E; see the black box in Fig. 1A)69. During the calculation, all grid points with sea ice concentration less (more) than 15% are considered as having no (full) sea ice cover (this is equivalent to sea ice extent). Linear trends of the sea ice indices are calculated as standard least-squares linear regression. Note that the interpolation procedure introduces a small error for the sea ice indices, but the calculation of linear trends is not affected.

To estimate the anthropogenic component for observed Barents–Kara sea ice trends, we calculate the linear trends of area-averaged Barents–Kara sea ice concentration indices (following the same procedures for observations) for each ensemble member from 12 CMIP6 coupled, forced simulations (each has exactly 10 ensemble members; Table 1) for the periods consistent with observations (all possible 20-year windows within 1980–2022 and their averages). For each individual model, we first isolate the modelled anthropogenic sea ice trend by averaging across its 10 members. We next average these trends across all 12 models to obtain the best estimate of anthropogenic Barents–Kara sea ice trends. To estimate the model sensitivity, we calculate and present half of the standard deviation of the anthropogenic sea ice trends across the 12 models.

To estimate the circulation-driven component for observed Barents–Kara sea ice trends, we use Ridge Regression (a linear machine-learning tool that considers the collinearity of predictors) to set up a regression task to learn relationships between linear trends of high-latitude atmospheric circulation patterns and the weighted area-averaged Barents–Kara sea ice concentration index. The training data are from the same set of 12 CMIP6 coupled, forced simulations with 10 ensemble members each (see Table 1). The inputs of the training data are 20-year linear trends of sea level pressure (spatial maps covering the region of the Euro-Atlantic sector, 54°–87°N and 60°W-102E°, interpolated to 3° × 3° latitude-longitude grids) over four seasons: December to February (DJF), September to November (SON), June to August (JJA) and March to May (MAM). The outputs of the training data are 20-year linear trends of the Barents–Kara sea ice concentration indices in winter (December to February; DJF). The 20-year training data cover the period of 1960–2040 with a five-year interval (i.e., 1960–1980, 1965–1985…2020–2040) from the simulations. These periods are selected to make sure that the model-derived circulation-ice relationships can be applied to the periods of satellite observations (1980–2022) and that there are enough samples for training. For example, the input of the first training data is the linear trends of sea level pressure maps from DJF 1960/61–1979/80, SON 1960–1979, JJA 1960–1979 and MAM 1960–1979, and the output is the linear trend of Barents–Kara sea ice concentration index from DJF 1960/61–1979/80 for the first model’s first ensemble member. There are 1560 training data in total (12 models, 10 ensemble members, 13 20-year periods). For each individual model member and 20-year period, the ensemble mean of the sea ice trend is removed to isolate the sea ice changes not associated with anthropogenic forcing. The inputs and outputs of the training data are further standardised (i.e., removing the mean and dividing by the standard deviation across samples) prior to the training.

We validate the training results using a “take-one-model-out” approach26,29 to avoid overfitting and make sure that the training is successful. Under such an approach, we iteratively take one model out for validation and leave the other remaining models for training. After the training is complete, we input the circulation trends (standardised by the mean and standard deviation from the training data) from the validating model (all 10 ensemble members and 13 20-year periods) into the trained regression model to estimate the circulation-driven Barents–Kara sea ice trends. Such estimated trends are then compared to the actual trends with ensemble mean removed for the validating model. Results show that the training models generally give a good estimation of the Barents–Kara sea ice trends in the validating model that is withheld, although the estimation tends to show a bias that might underestimate the actual trends (Fig. S11). In each iteration when a model is withheld for validation, we also input the observed circulation trends (from MERRA2, ERA5 and JRA55 reanalysis) for all possible 20-year slicing windows from 1980 to 2022 to estimate the circulation-driven Barents–Kara sea ice trends for observations. This results in 12 estimated circulation-driven Barents–Kara sea ice trends for each period. We take the averages of these 12 values as the best estimate. The estimated sensitivity is calculated and presented as half of the standard deviation of errors between the estimated and actual sea ice trends for all validating models, similar to a previous study29.

The “take-one-model-out” validation provides a test bed to test whether circulation trends in autumn, summer and spring are useful to estimate the Barents–Kara sea ice trends in the following winter. This is done by a permutation feature importance test where we remove the information on circulation trends in each season when estimating the sea ice trends for the validating model, and quantify how the errors increase (compared to the actual trends) when the information is removed. The overall results show that the winter circulation has the most information for the winter sea ice trends, followed by the autumn, spring, and summer circulation ahead of the targeted winter (Fig. S6).

The “take-one-model-out” validation also allows us to optimise a hyperparameter (α, a regularisation term to handle the collinearity of predictors and hence reduce overfitting) in Ridge Regression. We iterate through different values of α and find that α = 200 gives the smallest errors for the validation models (Fig. S12). Using Artificial Neural Network (a machine-learning regression tool that does not assume linearity between predictors) can yield very similar results compared with using Ridge Regression (see Fig. S13).

Methods to test the dynamic drivers of the high-latitude atmospheric circulation trends

To test the role of anthropogenic forcing in shaping the high-latitude circulation trends in recent decades, we compare the circulation trend pattern of interest between observations and models. We first calculate the seasonal (DJF) sea level pressure by averaging the monthly data. We next extract the weighted area-averaged indices over the regions of Urals (50–70°N, 25–90°E) and Iceland (52–70°N, 37–1°W, see the red boxes in Fig. 3), and calculate the difference between them (the former minus latter). We finally calculate the linear trend of the indices using standard least-squares linear regression. We compare such linear trends between atmospheric reanalysis datasets (MERRA2, ERA5 and JRA55; DJF 1996–2016 and DJF 1997–2017) and long observational records (20CRV3; all possible 20-year periods over DJF 1836–2015). We also compare the same trends between forced (DJF 1996–2016 and DJF 1997–2017 for each ensemble member) and unforced (all possible 20-year periods over DJF 1–800 years) coupled simulations from CMIP6 (see Table 1).

Similarly, to test the combined role of anthropogenic forcing, sea surface temperature, and Arctic sea ice loss in shaping the winter high-latitude circulation trends, we compare the same linear trends between forced (DJF 1996–2016 and DJF 1997–2017 for each ensemble member) and unforced (all possible 20-year periods over DJF 1–999 years) atmosphere-only simulations that follow the CMIP protocol (see Table 1).