Introduction

One of the most pronounced consequences of global warming is the decline in Arctic sea ice extent. This reduction has been extensively observed1,2 and confirmed through reconstructions3 and model simulations4. The diminishing sea ice brings about a series of ecological environment changes, including increased freshwater reserves5, heightened surface water carbon dioxide levels6 and acidification7, as well as more frequent extreme weather events in mid-latitudes8,9,10. Additionally, it affects shipping and trade routes11,12. Since the late 1970s, satellite observations have indicated a sharp decrease in Arctic sea ice extent during all months of the year, particularly in September, with accelerated decline since the 1990s1,13,14,15 (dashed blue line in Fig. 1a). As Arctic sea ice in September represents the annual minimum extent of ice coverage, its continued decline could lead to the ice-free conditions in the Arctic, which is a matter of great concern due to its significant climate, economic, and geopolitical implications. Arctic sea ice began to melt rapidly after the 1990s, reaching its historical low in 2012. It is worth noting that the past decade since 2014 has been the hottest on record (source: NASA/GISS; https://climate.nasa.gov). Ongoing global warming would have facilitated sustained Arctic sea ice melt. However, Arctic amplification appears to have reached its peak16. As clearly shown by black line in Fig. 1, the Arctic warming rate in the most recent decade has slowed down compared to previous decades. Furthermore, Arctic sea ice has not fallen below the historical record set in 2012 so far. More importantly, observations show no significant decline in Arctic sea ice concentration (SIC) since 2012 (solid blue line in Fig. 1a), revealing a negligible trend of −0.4% per decade and indicating a slowdown in September Arctic sea ice melt over the past decade. The slowdown of sea ice melting mentioned here refers specifically to SIC and does not account for the thickness of the sea ice. The thicker multi-year ice may be still melting, which is likely to lead to a decrease in ice thickness rather than affecting concentration.

Fig. 1: Observed recent slowdown in September Arctic sea ice (ASI) and its association with multidecadal preceding summer North Atlantic Oscillation (NAO) variability.
figure 1

a The time series of regional averaged September sea ice concentration (SIC) across the Arctic region (66.5°–90° N, 180° W-180° E), defined as the ASI index, derived from Hadley (dashed red curve), ERA5 (European Centre for Medium-Range Weather Forecasts Reanalysis v5; dashed yellow curve) spanning 1950–2023, and NSIDC (U.S. National Snow and Ice Data Center; dashed purple curve) spanning 1979–2023, as well as the regional averaged September 2 m temperature across the Arctic region (66.5°–90° N, 180° W-180° E), defined as the surface air temperature (SAT) index derived from ERA5 (dashed grey curve) spanning 1950–2023. The dashed and solid blue curves depict the linear trend of the ASI index (unit: %/decade) averaged over the three datasets spanning 1996-2011 and 2012-2023, respectively. The dashed and solid black curves depict the linear trend of the SAT index (unit: K/decade) spanning 1996-2011 and 2012-2023, respectively. An asterisk (*) indicates statistically significance at p < 0.01, highlighting a statistically significant trend. b The time series of standardized September ASI index derived from Hadley (dashed red curve) and ERA5 (dashed yellow curve) and the preceding summer (June-July-August, JJA) NAO index (grey bar; the primary mode of atmospheric variability in the North Atlantic region) from 1955 to 2018, all de-trended and smoothed with an 11-year sliding average to examine their characteristics and relationships on an interdecadal time scale. The 11-year sliding average of the ASI index in year Y (a specific year) is the average ASI index from year Y-5 to Y + 5. The values r and p denote the correlation coefficients and significant levels between the NAO index and ASI index derived from Hadley and ERA5, respectively. The index is “standardized” by subtracting the mean and then dividing the resulting deviations by the standard deviation.

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Arctic sea ice melt is driven by both long-term climate change and internal climate variability such as interannual and interdecadal variability17,18,19,20. Previous studies have shown that the intensified summer anticyclonic circulation over the polar regions plays a key role in driving the interannual variability and long-term trend of sea ice loss in the western Arctic21,22. Francis and Hunter (2006)23 demonstrated the location of the summer ice edge is strongly correlated with the variability of downwelling longwave radiation (DLR). The extreme loss of Arctic sea ice observed in 2007 was linked to the enhanced summertime radiation balance associated with an anticyclonic atmospheric circulation pattern24,25,26. Furthermore, Ding et al.21 attributed the rapid decline of September Arctic sea ice since 1979 to the sustained strengthening of Arctic anticyclones, which promote warming and moistening of the lower troposphere, along with increased DLR, as supported by model experiments and reanalysis data. Their fingerprint pattern matching method further suggests that internal variability accounts for approximately half of the observed Arctic sea ice decline, which is as crucial as external forcing in influencing Arctic sea ice changes27. However, these studies did not pin point which atmospheric internal variability plays a dominant role in the decadal variability of Arctic sea ice. This study utilizes multiple sets of SIC observational data to reveal that the rapid decreasing trend of September Arctic sea ice since the 1990s has transitioned to a slowdown since the early 2010s. By combining the European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) atmospheric reanalysis dataset and Coupled Model Intercomparison Project Phase 6 (CMIP6) multi-model historical simulations and Shared Socioeconomic Pathway 2-4.5 (SSP245) scenario, we demonstrate that the decadal variability of September Arctic SIC, the transition of rapid melt from the late 20th century to a slowdown since the early 2010s, is closely coupled with the multi-decadal variability of the preceding summer (June–July–August, JJA) North Atlantic Oscillation (NAO). The physical mechanisms coupling the summer NAO and September sea ice melt are diagnosed. In addition, the roles of the Atlantic Multi-decadal Oscillation (AMO) are investigated.

Results

Observed recent slowdown in Arctic sea ice melt

Figure 1 shows three sets of observational September SIC data commonly used in Arctic sea ice research: Hadley, U.S. National Snow and Ice Data Center (NSIDC), and ERA5. Without removing linear trends, the correlation coefficients among the three datasets are approximately 0.99 (Supplementary Table 1); even after removing trends, the correlations among the three remain highly significant (Supplementary Table 2), suggesting the strong consistency of these observational sea ice datasets. Figure 1a shows that the September Arctic sea ice (ASI) index, defined as the regional averaged September SIC across the Arctic region (66.5°–90° N, 180° W-180° E), has generally exhibited a declining trend. However, the decrease rate of ASI varies at different stages. Specifically, from the 1950s to the 1990s, the decline was relatively slow, but after the 1990s, the decrease rate accelerated to a significant trend of −11.3 ± 3.3% per decade, reaching a minimum by 2012, consistent with previous studies28. However, after 2012, despite year-to-year fluctuations in Arctic SIC—with 2020 marking the second-lowest September sea ice extent in recent decades— there has been an insignificant downward trend of only −0.4±6.8% per decade. Supplementary Fig. 1 illustrates the spatial patterns of September Arctic SIC linear trends for the periods of 1996–2011 and 2012–2023. During 1996–2011, Arctic sea ice decreased rapidly in the western Arctic, including the Beaufort, Chukchi, East Siberian and Laptev seas, with some areas experiencing reductions exceeding 60% per decade (Supplementary Fig. 1a). This aligns with previous studies indicating an accelerated decline in Arctic sea ice after the 1990s1,13,14. However, starting from the early 2010s, September Arctic SIC has not shown a significant decline (Supplementary Fig. 1b). Multiple observational SIC datasets confirm a slowdown in September Arctic sea ice melt since 2012. The accelerated decline in the 1990s, followed by a slowdown in September Arctic SIC post-2010, indicates an interdecadal change in the Arctic SIC trend. Additionally, we have observed that the rate of increase in the regionally averaged near-surface air temperature in the Arctic has slowed down from 2012 to 2023 to only half of the rate observed during 1996-2011 (black line in Fig. 1a). The deceleration of the Arctic air temperature trend is consistent with the slowdown in Arctic sea ice melting. Given the limited time span of NSIDC data and the strong consistency among the three observational SIC datasets, the following analysis of interdecadal variability in Arctic SIC is conducted using the Hadley and ERA5 datasets.

To clearly depict the interdecadal variability of Arctic SIC and its correlation with atmospheric circulation on an interdecadal scale, all variables were de-trended and smoothed using an 11-year sliding average, unless otherwise specified. The curve in Fig. 1b illustrates distinct decadal characteristics of ASI, showing a negative phase in the 1950s, a transition to a positive phase from the 1960s, and then reverting to a negative phase from the 1990s. The rapid melting of Arctic sea ice following the 1990s coincided with the phase shift from the peak positive phase to the peak negative phase of ASI interdecadal variation. After the early 2010s, ASI gradually increased from the minimum of the negative phase, aligning with the period of sea ice melt slowdown identified in this study. We believe that the decadal variability relative to the linear trend of Arctic SIC, accelerated the melting of Arctic sea ice since the 1990s and sustained a slowdown in melting observed since the early 2010s.

The physical mechanism

To investigate the connection between low-frequency internal atmospheric variability and multidecadal variability in Arctic sea ice, 500 hPa geopotential height from the preceding summer (JJA) was regressed against the September ASI index (Fig. 2a). Considering the strong link between summer atmospheric circulation and Arctic sea ice variability, as well as the approximately three-month decorrelation timescale of September sea ice anomalies21,29,30,31,32,33, we focus on summer atmospheric circulation in our analysis21. During the positive phase of ASI, significant cyclone and anticyclone anomalies emerge over the Arctic and North Atlantic, forming an anomalous dipole pattern (Fig. 2a). This pattern bears strong resemblance to the NAO pattern, which is the dominant mode of atmospheric variability in the North Atlantic region (Fig. 2a, b)34. Furthermore, the multidecadal oscillations of September ASI closely mirror the observed interdecadal evolution of the summer NAO index (Fig. 1b), particularly concerning the timing of phase transitions and peak values in both positive and negative phases. The correlation coefficient between them reaches 0.92, indicating that the summer NAO is highly coupled with the interdecadal variability in September ASI. Even after adjusting for the reduced degrees of freedom due to the 11-year sliding average applied to both indices, resulting in effective degrees of freedom of 3 and 4 for Hadley and ERA5 datasets, respectively, the correlation remains statistically significant (p < 0.05). We will subsequently explore their relationship on an interannual scale and employ CMIP6 simulation data to increase the sample size to test the robustness of the relationship between the NAO and ASI indices on interdecadal time scales. These findings suggest that the NAO pattern is likely tied to the interdecadal fluctuations in Arctic sea ice, associated with accelerated melting after the 1990s and a recent slowdown in melting over the past decade.

Fig. 2: North Atlantic Oscillation (NAO)-related atmospheric thermodynamic impacts on an interdecadal scale.
figure 2

a summer (June-July-August, JJA) 500 hPa geopotential height (HGT, colored, interval: 2, unit: m) regressed onto the standardized September Arctic sea ice (ASI) index, b summer (JJA) 500 hPa geopotential height (HGT, colored, interval: 2, unit: m), c lower-tropospheric (1000-700 hPa) air temperature (AT, colored, interval: 0.1, unit: K), d total column water vapour (WV, colored, interval: 0.08, unit: kg m−2), e downwelling longwave radiation at surface (DLR, colored, interval: 0.4, unit: W m−2) and f September sea ice concentration (SIC, colored, interval: 2, unit: %) anomalies regressed onto the standardized summer (JJA) NAO index. The white dots indicate statistically significance at p < 0.1. Yellow dashed boxes mark the areas of 66.5°–90° N, 90°–40° W. g The time series of standardized September ASI index (dashed red curve), the summer (JJA) NAO index (dashed blue curve), AT index (dashed grey curve), WV index (dashed yellow curve) and DLR index (dashed purple line) from 1955 to 2018. The values r and p denote the correlation coefficients and significant levels between the ASI/NAO index and AT index, between the ASI/NAO index and WV index, between the ASI/NAO index and DLR index, and between the ASI index and NAO index. For convenience, the NAO index and DLR index have been multiplied by one-third. The ASI index is derived from Hadley. These data have been de-trended and subjected to an 11-year sliding average. The atmospheric reanalysis data are derived from ERA5 (European Centre for Medium-Range Weather Forecasts Reanalysis v5) atmospheric reanalysis dataset.

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To delineate the physical pathway that connects NAO and Arctic sea ice, we examine the interdecadal variability of NAO-induced thermodynamic processes. In the positive phase of the NAO, a significant cyclonic anomaly is observed, accompanied by negative anomalies in summer Arctic air temperature (AT), water vapour (WV) and DLR at surface across the Arctic region (Fig. 2b–e). These factors contribute to positive anomalies in September SIC in the western Arctic (Fig. 2f)21. Furthermore, the summer AT, WV and DLR indices (See Methods) are all significantly correlated with September ASI/summer NAO index, with correlation coefficients of −0.90/−0.94, −0.94/−0.93 and −0.80/−0.67 (Fig. 2g). Specifically, from 1990s to the early-2010s, the NAO evolved towards its peak negative phase and summer anomalies of air temperature, water vapor and downwelling longwave radiation at surface changes from negative to positive, promoting rapid decline of Arctic sea ice (Figs. 1 and 2g). Our finding is consistent with prior research that showed the declining trend in Arctic sea ice was driven by the intensified anticyclonic circulation over the polar, resulting from warming and increased moisture in the lower troposphere21,22. Since the early 2010s, the NAO transitioned from its peak negative phase to a positive phase. During this time, anomalies in air temperature and moisture, as well as downwelling longwave radiation, reversed from positive to negative, leading to an increasing tendency in sea ice extent on interdecadal scale that counteracts the long-term decline caused by persistent global warming (Figs. 1 and 2g). As shown in Fig. 2, the linkage between the NAO and Arctic sea ice comes from the polar cell, which aligns with previous research indicating that the declining trend in Arctic sea ice is driven by intensified atmospheric anomalies over the polar regions21,27, while the mid-latitude cell serves as a gateway that links the source of the low-frequency variability to high-latitude atmospheric circulation.

In addition, to strengthen the robustness of the observed strong interdecadal linkage between NAO and ASI (r = 0.92, p < 0.01), we applied a five-year running climatology removal to isolate interannual variability, following Kapsch et al. (2019)35. This approach, applied to reproduce Figs. 1b and  2, allows us to investigate the relationship between NAO and ASI variability on interannual timescales and the corresponding physical mechanisms (Supplementary Figs. 2 and 3). On interannual timescales, the NAO also exhibits significant correlations with ASI indices obtained from two datasets (r = 0.43 and 0.36; Supplementary Fig. 2). Furthermore, Supplementary Fig. 3 demonstrates that the mechanisms underlying the significant correlation between NAO and Arctic sea ice at interannual timescales are consistent with those at interdecadal timescales (Fig. 2). Overall, the NAO exhibits significant correlation with ASI on interannual scales, strongly supporting the proposed physical mechanism of their tight coupling at the interdecadal scale. This approach also helps address the issue of limited sample size when studying interdecadal-scale phenomena using observational data.

Decadal variability in CMIP6 models

Given the limited timeframe of observed SIC and atmospheric data, there are relatively few effective degrees of freedom available for analyzing their interdecadal characteristics and relationships. Consequently, asserting a strong correlation between Arctic sea ice and the summer NAO on interdecadal timescales over a relative short period may raise questions. To address this limitation, we turned to historical simulations from 24 models in the CMIP6 project (Supplementary Table 3), covering the years from 1850 to 2014, to extend the data length.

The ensemble mean derived from the CMIP6 models reveals a statistically significant correlation of 0.92 between the September ASI index and the summer NAO index (Fig. 3). Notably, after around 1955, there is remarkable consistency in both the peaks of the positive and negative phases, as well as the phase transitions of the ASI and NAO indices. Out of the 24 models examined, 16 replicate the significant positive relationship between the September ASI index and the summer NAO index (Fig. 3). In addition, we also applied a five-year running climatology removal method to analyze the simulated interannual relationship between NAO and ASI in the CMIP6 historical simulation models, as shown in Supplementary Fig. 4. Eight models (out of 24) are still able to reproduce the significant interannual linkage between NAO and ASI. Considering that the CMIP6 historical simulation data only extends to 2014, we used 12 SSP245 models to extend the data length and analyze the interdecadal relationship between the NAO and ASI (Supplementary Table 3). Five SSP245 models (out of 12) reproduced a significant linkage between NAO and ASI (Supplementary Fig. 5). While the majority of CMIP6 models demonstrate consistency with observational data in historical decadal-scale simulations, there are large uncertainties in the simulated NAO-ASI relationships - both in historical simulations and future climate projections. In summary, the results from historical and future scenario generated by CMIP6 models support the observational findings. Considering that the NAO is an atmospheric pressure pattern with little inertia and memory, we further investigate the possible source of NAO on decadal timescales.

Fig. 3: The relationship between the September Arctic sea ice (ASI) index and summer North Atlantic Oscillation (NAO) index on an interdecadal scale in 24 historical simulation models from the Coupled Model Intercomparison Project Phase 6 (CMIP6).
figure 3

The time series of the standardized September ASI index (curve) and the summer (June-July-August, JJA) NAO index (bar) from 1855 to 2009. These data are de-trended and subjected to an 11-year sliding average. Please refer to the subheading for the ensemble mean of the 24 models and the specific model names. The values r and p represent the correlation coefficients and significant levels between the NAO index and the ASI index.

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The interdecadal variability sources

Given that the NAO is an internal mode driven by eddy-mean flow feedback, we have examined the spatial distribution of the NAO-related storm track activity (also known as synoptic-scale eddy activity). During the positive phase of the NAO, significant positive anomalies in Atlantic storm track activity are observed near its climatological maximum region (Fig. 4a). To further characterize the interdecadal variability of the Atlantic storm track activity, we have defined the Atlantic storm track (AST) index as the regional average of the storm track activity within the area indicated by the yellow box in Fig. 4a. Figure 4g demonstrates that the interdecadal variability of the AST is highly consistent with that of the NAO, and their correlation is statistically significant at 0.96. Additionally, we have estimated the barotropic processes in low-frequency atmospheric circulation anomalies forced by transient eddies using the geopotential height tendency equation36,37 (Details in Methods), as shown in Fig. 4b. The transient eddies force a significant cyclonic anomaly to the north and an anticyclonic anomaly to the south over the North Atlantic, which aligns with the spatial pattern of the NAO. Therefore, the interdecadal variability of the NAO is likely driven by the interdecadal variability of transient eddies.

Fig. 4: The possible sources of multidecadal variability.
figure 4

a Summer (June-July-August, JJA) storm track activity anomalies (colored, interval: 4, unit: m) regressed onto the standardized summer North Atlantic Oscillation (NAO) index, along with the climatology of summer storm track activity (contour, interval: 100, unit: m). b Summer (JJA) eddy-induced geopotential height tendency anomalies (colored, interval: 4, unit: m month–1), c sea surface temperature anomalies (SST; colored, interval: 0.1, unit: K) and d their negative meridional gradient (colored, interval: 0.1, unit: K (1000 km)-1), e negative meridional gradient anomalies of 700 hPa air temperature (colored, interval: 0.05, unit: K (1000 km)-1) and f 700 hPa eady growth rate anomalies (colored, interval: 0.1, unit: day−1) regressed onto the standardized summer Atlantic storm track (AST) index. g The time series of standardized September Arctic sea ice (ASI) index (dashed red curve) derived from Hadley dataset, along with the summer NAO index (dashed purple curve), summer AST index (dashed blue curve) and summer Atlantic Multidecadal Oscillation (AMO) index (dashed yellow curve), span the years 1955 to 2018. These data are de-trended and subjected to an 11-year sliding average. The values r and p represent the correlation coefficients and significant levels between the AST and NAO indices, AST and AMO indices, NAO and AMO indices, and ASI and AMO indices, respectively. An asterisk (*) indicates statistically significance at p < 0.1, highlighting a statistically significant relationship. Yellow dashed boxes mark the areas of 55°–75° N, 60° W-20° E. For convenience, the eady growth rate has been multiplied by 100. The white dots indicate statistically significance at p < 0.1 in a–f.

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Numerous prior studies have established a close link between the multidecadal variations in Arctic warming, sea ice melt, and the NAO with the Atlantic Multidecadal Oscillation (AMO)18,38,39,40,41,42,43. Figure 4c and Supplementary Fig. 6 illustrate summer sea surface temperature (SST) anomalies associated with the summer AST, NAO and September ASI, displaying a notable similarity to the AMO pattern. The correlation coefficients between the AMO and AST, AMO and NAO, as well as between the AMO and ASI, are significant at −0.85, −0.83 and −0.74, respectively (Fig. 4g). We have further analyzed that the interdecadal variability of transient eddies may be sourced from AMO.

Previous studies have shown that the intensification of oceanic fronts can enhance atmospheric baroclinicity, which favors the generation of atmospheric transient eddies44,45,46,47,48. The SST anomalies associated with the AST in the south of Greenland exhibit large and significant cold anomalies, which are largely consistent with the spatial distribution of the AMO (Fig. 4c and Supplementary Fig. 6c). These significant cold anomalies likely strengthen the meridional SST gradient to some extent. The oceanic front associated with the AST exhibits some degree of intensification at approximately 50°–70°N over the North Atlantic (Fig. 4d). Correspondingly, there are significant positive anomalies of the low-level meridional air temperature gradient and the atmospheric baroclinicity, contributing to the active atmospheric transient eddy activities (Fig. 4a, e, f). Therefore, the interdecadal variability of atmospheric transient eddies can be partially traced back to the decadal variability of the AMO. The AMO phase change initially alters the synoptic-scale eddy activity through modifying oceanic front and atmospheric baroclinicity. Then, through wave-mean flow interactions, this process ultimately drives NAO decadal variability.

On the other hand, observations and climate prediction systems have highlighted the significance of the stratospheric polar vortex (PV) as a key influence of the NAO49,50. Supplementary Fig. 7 reveals that, on an interdecadal scale, there is a notable strengthening of the stratospheric PV in the preceding February during the positive phases of both the NAO and the ASI indices. In addition, we have examined the temporal evolution of the PV anomaly, as shown in Supplementary Fig. 8. The PV-related anomalies in the tropospheric geopotential height field exhibit a NAO-like pattern in February, March, June, July, and August. However, this NAO-like pattern disappears in April and May, suggesting that the influence of the PV may weaken or become less direct during these months. While this does not completely rule out the impact of polar vortex on the NAO, it indicates that the relationship may involve complex nonlinear processes.

Overall, considering that the correlation coefficient between the NAO and ASI reaches 0.92 and that the timing of the phase transition of the NAO aligns more closely with the ASI, the multidecadal variability of the preceding summer NAO is tightly coupled with the decadal oscillations in September Arctic sea ice, associated with its recent slowdown over the past decade. The AMO plays a primary role in driving the low-frequency variability of the NAO and Arctic sea ice by modulating wave-mean flow interactions, while the polar vortex may also contribute to some extent. Moreover, the multi-model ensemble mean shows considerable consistency in NAO variation simulations across different models, indicating that NAO variability could be not only driven by internal climate variability but could also be driven by external forcings. Beyond the influence of AMO, external forcings may also modulate the decadal variability of both the NAO and ASI, which warrants further investigation in future studies. Also, there may be the intricate interplay among these factors.

Discussion

This study, utilizing three observational sea ice datasets, reveals a recent slowdown in September Arctic sea ice melting over the last decade. This slowdown is closely related to the decadal variation of the summer NAO. Specifically, the shift of the NAO from a negative phase to a positive phase after early-2010s contributes to decreased Arctic air temperature and moisture, followed by an expansion of Arctic sea ice. In this context, the declining trend in Arctic sea ice due to external forcings, such as greenhouse gas emissions, is offset by the sea ice growth on an interdecadal scale, which is strongly correlated with the summer NAO. The combined effect of external forcings and interdecadal variability results in the observed recent slowing of September Arctic sea ice melting over the past decade. Historical simulation and future scenario from the CMIP6 models corroborate this multi-decadal variability in Arctic sea ice and the NAO.

Previous research has shown that global warming and Arctic amplification are modulated by the Interdecadal Pacific Oscillation (IPO); particularly, in a negative phase of the IPO, La Niña events-like interdecadal cooling in the tropical eastern Pacific contributed to a temporary global warming hiatus around 201051,52,53,54. Supplementary Fig. 6a indicates that the SST anomalies pattern associated with ASI does not exhibit a significant IPO-like pattern in the Pacific Ocean but instead displays an AMO-like pattern. Regarding global SST anomalies associated with ASI, the AMO emerges as the most prominent factor in driving the low-frequency variability of the NAO and Arctic sea ice by modulating wave-mean flow interactions. Additionally, the decadal variability in September ASI may also be linked to the stratospheric polar vortex in the preceding February.

Moreover, the spectrum analysis applied to the NAO reveal a typical periodicity of approximately 40 years (Supplementary Fig. 9). The transition from the peak negative phase to the peak positive phase, starting around early 2010s, is likely to extend until roughly 2030–2040. Given the strong coupled relationship between the NAO and Arctic sea ice, the slowdown in the September Arctic sea ice melt is likely to continue until 2030–2040. Nevertheless, a phase of accelerated Arctic sea ice decline may ensue when the NAO passes the peak positive phase after 2030–2040. In the absence of greenhouse gas emission reduction, we may encounter a sequence of climate and environmental crises triggered by a sharp reduction in Arctic sea ice after approximately a decade or so. Fortunately, the impact of internal atmospheric variability provides a climate buffer period of 10–20 years, allowing for the implementation of essential emission reduction measures to address the impending catastrophic challenges.

Methods

Arctic sea ice (ASI) index

ASI index is defined as the regional averaged SIC across the Arctic region (66.5°–90° N, 180° W-180° E).

North Atlantic Oscillation (NAO) index

The NAO index is the principal component time series corresponding to the first empirical orthogonal function (EOF) mode of the 500 hPa geopotential height anomalies over the North Atlantic region, which represents the primary mode of atmospheric variability in the North Atlantic region.

11-year sliding average

The 11-year sliding average of the X (e.g., ASI and NAO) index in year Y (a specific year) is the average X index from year Y-5 to Y + 5.

Air temperature (AT) index

The AT index is defined as the regional averaged 1000-700 hPa air temperature across the region (66.5°–90° N, 90°–40° W) where the cyclone anomalies are the most significantly correlated with the NAO.

Water vapour (WV) index

The WV index is defined as the regional averaged total column water vapour across the region (66.5°–90° N, 90°–40° W) where the cyclone anomalies are the most significantly correlated with the NAO, respectively.

Downwelling longwave radiation (DLR) index

The DLR index is defined as the regional averaged downwelling longwave radiation across the region (66.5°–90° N, 90°–40° W) where the cyclone anomalies are the most significantly correlated with the NAO.

Atlantic Multidecadal Oscillation (AMO) index

The AMO index is calculated as the area weighted average of SST over the North Atlantic, basically 0°–70°N.

Polar vortex (PV) index

The PV index is calculated as a zonal mean zonal wind at 50 hPa over the latitudes 60°–80°N, representing the intensity of the polar vortex50.

Storm track activity

The storm track activity is defined as the root mean-square (RMS) of the 2–8 day bandpass filtered geopotential height at 300 hPa48,55.

Atlantic storm track (AST) index

The AST is defined as the regional averaged storm track across the region (55°–75° N, 60° W-20° E).

Geopotential height tendency

The equivalent-barotropic response of geopotential height tendency to transient eddy vorticity forcing can be diagnosed as follows36:

$$\frac{\partial h}{\partial t}={\nabla }^{-2} \left[-\frac{f}{g} \overline{\nabla \cdot \left( {{\rightharpoonup}\atop{{{{\bf{v}}}_{{\bf{h}}}^{\prime} }}}{\xi}^{\prime }\right)}\right]$$
(1)

Here, \(\frac{\partial h}{\partial t}\) represents the geopotential height tendency, while f and g denote the Coriolis parameter and gravity acceleration, respectively. The variables \({{ \rightharpoonup } \atop{{{\bf{v}}_{\bf{h}}^{\prime} }}}\) and \({\xi }^{{\prime} }\) refer to the 2–8 day bandpass filtered horizontal wind and relative vorticity.