Our study focused on the downstream region of the TPD, i.e., the Barents Sea and the Greenland Sea, to assess the impacts of sea ice outflow from the Arctic Ocean on the sea ice and other marine conditions in this region on a seasonal scale. The north–south boundaries of this region are from 72∘ N to the three passageways of sea ice outflow, and the east–west boundaries are defined as the coastline of the surrounding islands. To quantify the sea ice outflow from the Arctic Ocean, we calculated the sea ice area flux (SIAF) through the passageways, i.e., the Fram Strait, the Svalbard–Franz Josef Land (S-FJL) passageway, and the Franz Josef Land–Novaya Zemlya (FJL-NZ) passageway (Fig. 1), with widths of about 448, 284, and 326 km, respectively.

We used the National Snow and Ice Data Center (NSIDC) Polar Pathfinder version 4 sea ice motion (SIM) vectors and National Oceanic and Atmospheric Administration (NOAA)/NSIDC Climate Data Record passive microwave sea ice concentration (SIC) version 4 (Tschudi et al., 2019; Meier et al., 2021) to calculate the SIAF from the Arctic Ocean to the BGS in the study year and the climatological average in 1979–2020. The choice of this SIM product was motivated by its spatial completeness and temporal continuance. The SIM product is the most optimal merged interpolation result using satellite remote sensing data, buoy observations, and reanalyzed wind data (Tschudi et al., 2020). This product provides daily ice drift components georeferenced to the Equal-Area Scalable Earth Grid (EASE-Grid) with a spatial resolution of 25 km. The SIC product was a rule-based combination of SIC estimates from the National Aeronautics and Space Administration (NASA) Team (NT) algorithm (Cavalieri et al., 1984) and NASA Bootstrap (BT) algorithm (Comiso, 1986), derived from the Scanning Multichannel Microwave Radiometer (SMMR), Special Sensor Microwave Imager (SSM/I), and Special Sensor Microwave Imager/Sounder (SSMIS) radiometers. Daily SIC fields were gridded on a 25 km resolution polar stereographic grid. Both datasets are available from October 1978 to the present. However, there is a gap in the SIC dataset from 3 December 1987 through 12 January 1988. The sea ice area (SIA) was defined as the cumulative area of the waters covered by sea ice with the SIC above 15 %. For the study region, we used the SIC data since 1979 to estimate the SIA anomaly from January to June in the study year of 2020. In addition, we used buoy observation data from MOSAiC and the International Arctic Buoy Programme (IABP) to prove the effectiveness of the reconstructed results of the sea ice backward trajectories in the study year of 2020 and years with extreme atmospheric circulation patterns.

The sea ice thickness (SIT) data used to characterize the sea ice conditions in the region of the BGS were mainly derived from satellite remote sensing observations and were supplemented by the modeling product in early summer. The remotely sensed SIT data were created from the merged CryoSat-2 and Soil Moisture and Ocean Salinity (SMOS) observations, hereinafter referred to as CryoSat-2/SMOS (Ricker et al., 2017). The CryoSat-2/SMOS dataset makes full use of the detectability of SMOS for thin sea ice (<1.0 m) and the measurement capability of CryoSat-2 for thicker sea ice, which ensures obtaining a more comprehensive product of SIT. Weekly CryoSat-2/SMOS SIT data were available on a 25 km EASE-Grid during the freezing season of October to mid-April from 2010 to the present. During the ice melt season from May–June, we used the monthly SIT modeling product obtained from the Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS; Zhang and Rothrock, 2003). PIOMAS is a coupled ice–ocean model assimilation system that has been extensively validated and compared with satellite, submarine, airborne, and in situ observations and has proved it has good performance in sea ice thickness inversion (Zhang and Rothrock, 2003; Schweiger et al., 2011; Stroeve et al., 2014; Wang et al., 2016). The monthly PIOMAS SIT is gridded on a generalized orthogonal curvilinear coordinate system with an average resolution of 22 km. We regridded the monthly SIT data on the 25 km EASE-Grid and calculated the monthly average CryoSat-2/SMOS SIT data to maintain the spatial and temporal consistency of the two SIT datasets. To assess the data consistency of these two SIT datasets, we calculated the SIT anomalies from December to April using the PIOMAS SIT to compare it with the CryoSat-2/SMOS SIT. We found that the spatially averaged difference between the PIOMAS and CryoSat-2/SMOS SIT anomalies from December to April is about 0.09–0.20 m, which is about 6.0 %–13.3 % of the monthly magnitude. The statistical correlation between the spatially averaged SIT anomalies in December–April calculated using the two datasets in 2011–2020 is 0.95 (P<0.05). Thus, we considered the difference between the two datasets to be acceptable for calculating SIT anomalies, and PIOMAS can be used to supplement the SIT data for CryoSat-2/SMOS during the melt season (i.e., May–June), although their absolute values still have deviations that cannot be ignored. Therefore, we used the CryoSat-2/SMOS SIT from December to April and the PIOMAS SIT from May to June in 2011–2020 to estimate the anomaly in SIT during the study year of 2020.

We used sea surface temperature (SST) from 2011–2020 to characterize the anomalies in oceanic conditions over the BGS during the study year, as SST can be used as a proxy for the physical state over a basin scale (Siswanto, 2020). The SST data were obtained from the NOAA Daily Optimum Interpolation SST High Resolution dataset version 2, which assimilated buoy, ship-based, and satellite SST data (Huang et al., 2021). In the ice-covered regions, the proxy SST from SIC is intermixed with in situ and satellite SSTs. The proxy SST is obtained by a simple linear regression with SIC (Reynolds et al., 2007), and when the SIC is above 35 %, the proxy SST is defined as the freezing points of seawater, which in turn is defined using the climatological sea surface salinity (Banzon et al., 2020). This dataset is available on a regular grid of 0.25∘ × 0.25∘.

The fifth-generation reanalysis ERA5 datasets from European Centre for Medium-range Weather Forecasts (ECMWF) provide sea level pressure (SLP), 2 m air temperature, and 10 m surface wind, as well as atmospheric surface net heat fluxes of longwave radiation, shortwave radiation, sensible heat, and latent heat (Hersbach et al., 2020). These variables, with about 30 km horizontal and 1 h temporal resolutions, were used to identify anomalies in surface atmospheric conditions or forcing over the study region. ERA5 uses an advanced 4D-Var assimilation scheme, with improved performance over the Arctic compared to ERA-Interim (Graham et al., 2019). The hourly SLP data from ERA5 were used to calculate the monthly CAI, defined as the difference between SLPs at 84∘ N, 90∘ W, and 84∘ N, 90∘ E. We used the monthly AO and NAO indices provided by the NOAA Climate Prediction Center (CPC). The AO index was constructed by projecting a daily 1000 hPa height anomaly at the 20∘ N poles onto the AO loading pattern (Thompson and Wallace, 1998). The NAO index is defined as the SLP difference between the Azores High and the Icelandic Low (Hastenrath and Greischar, 2001).

The SIAF was defined as the magnitude of the SIA conveyed through a defined gate during a given period. In accordance with Kwok (2009), we estimated the monthly SIAF by accumulating the daily integral of the products between the gate-perpendicular component of the SIM and SIC along the defined passageways. Note that there is no SIM vector when the SIC is below 15 % (Tschudi et al., 2019). In this case, the SIAF is ignored. Positive values correspond to the SIAF towards the BGS, while negative values are the opposite. Prior to the estimation of SIAF, we interpolated the SIC into the SIM projection and retrieved the gate-perpendicular SIM components. According to the trapezoidal rule, the SIAF was estimated as follows: 1SIAF=∑i=1nuiCiΔx, where n is the number of points along the passageway, ui is the gate-perpendicular SIM component, Ci is the SIC at the ith grid cell, and Δx is the width of a grid cell (25 km).

The corresponding error in SIAF depends on the uncertainties in SIM and SIC products, the sampling number along the passageways, and the calculation period. For daily SIM vectors, the error was estimated to be about 4.1 km d-1 (Tschudi et al., 2019). Several assessments indicated an accuracy of about 5 % in the SIC (Peng et al., 2013). Assuming that these two sources of error are independent, the uncertainty (σf) in estimating SIAF across a 1 km wide gate was estimated at about 2.92, 3.80, and 2.68 km2 d-1 for the Fram Strait, S-FJL, and FJL-NZ, respectively. If we assume that the errors in the samples are additive, unbiased, uncorrelated, and normally distributed, the uncertainty in daily SIAF is σD=σfL/Ns (Kwok, 2009), where L is the length of the gate, and Ns is the number of independent samples across the gate. From January to June, the monthly average uncertainties in SIAF through three passageways were estimated to be approximately 1.81 × 103 to 1.96 × 103 km2, which were about 3.7 %–13.9 % of the monthly magnitude and therefore considered negligible. We described the SIAF anomalies relative to the 1988–2020 climatology because differences in satellite data sources could lead to relatively low SIM speeds derived from the SMMR 37 GHz data during 1979–1987 compared to those derived from daily SSM/I 85 GHz data, SSMIS 91 GHz data, and/or Advanced Microwave Scanning Radiometer for EOS (AMSR-E) 89 GHz observations in the later years (Kwok, 2009). To quantify the relative contributions of changes in SIM and SIC to the variability in SIAF on a seasonal scale, we also calculated the correlation between the sum of the monthly SIAF and the mean SIM speeds/SIC through the three passageways for winter (JFM) and spring (AMJ) in 1988–2020.

To identify the source area of sea ice and describe the relationship between the SIAF and the sea ice transport before reaching the defined passageway, we also reconstructed the sea ice backward drift trajectories from the defined passageways (Fram Strait, S-FJL, and FJL-NZ) over the three defined periods with the ice drifting from the north from 1 January and into the passageways by 30 April, 31 May, and 30 June, respectively. The adoption of three periods to restructure the ice backward drift trajectories is conducive to further distinguishing the difference between the anomalies over the winter or the period of winter through spring. In addition, the reconstructed backward trajectory of sea ice from the defined passageway can help to identify the source area of the ice reaching the passageways, thus revealing the relationship between the sea ice outflow and the sea ice conditions in the source area. The sea ice backward drift trajectories were reconstructed according to Lei et al. (2019), and the zonal X and meridional Y coordinates of the backward ice trajectories were calculated as follows: 2Xt=Xt+1-U(t+1)⋅δt3andYt=Yt+1-V(t+1)⋅δt, where U(t) and V(t) are the ice motion components at the time t along the ice trajectories and δt is the calculation time step of 1 d. Thereby, the course of time corresponding to the sea ice backward drift trajectory is reversed from the defined date to 1 January.

In order to reveal the contribution of the surface heat budget to sea ice melting, we calculated the potential change in SIT (Δh) over the time of t caused by anomalies in atmospheric surface net heat fluxes over the BGS, according to Parkinson and Washington (1979): 4-Δh=tρLδFLw↓+δFSw↓+δH↓+δLE↓, where ρ is the density of sea ice (917 kg m-3); L is the latent heat of fusion for sea ice (333.4 kJ kg-1); δFLw↓, δFSw↓, δH↓, and δLE↓ represent the anomalies in atmospheric surface net fluxes of longwave radiation, shortwave radiation, sensible heat, and latent heat, respectively, with positive values denoting the downward heat flux. We note that Eq. (4) focuses on the atmosphere-to-ice heat fluxes but ignores the effects of ocean heat flux. Thus, it can only be used to assess the impact of the atmospheric anomaly on the local sea ice mass balance.

As shown in Table 1, the monthly AO was in an extremely positive phase from January to March 2020, with the values ranging in the top three among the years of 1979–2020. And then, the AO decreased to a smaller value in April and turned to a weakly negative phase in May–June 2020 (Fig. A1). The monthly CAI in January–June 2020 experienced a continuous positive phase with an average CAI of 8.5 hPa, which was the largest in 1979–2020. During winter–spring 2020, there were two peaks of the monthly CAI occurring in March and June, ranging in the first and fourth for 1979–2020, respectively.

In January–March 2020, accompanied by an unusual positive phase of the AO, the entire Arctic Ocean was almost dominated by abnormally low SLP compared to the 1979–2020 climatology (the first column of Fig. 2). In January 2020, a large-scale anomalously low SLP appeared near the Kara Sea, and the high-pressure center was observed in northern North America. This SLP pattern induced a positive CAI and northerly winds from the high Arctic towards the Barents Sea, accelerating the southward advection of Arctic sea ice into the Barents Sea and causing regional negative air temperature anomalies there (the second column of Fig. 2). In February 2020, the abnormally low SLP dominated near the Barents and Kara seas, inducing strong northerly winds in the Atlantic sector of the Arctic Ocean. This SLP and wind pattern continued to promote Arctic sea ice advecting into the BGS and keeping the negative air temperature anomalies in this region. In March 2020, the low SLP anomalies moved deeper into the central Arctic Ocean and induced westerly wind anomalies in the BGS.

In April 2020, the low SLP in the Arctic, centered in the northern Beaufort Sea, caused the sea ice to continue to advect towards the Barents Sea, and there were still small-scale negative air temperature anomalies over the Barents Sea (the third and fourth columns of Fig. 2). Subsequently, the SLP structure over the Arctic Ocean changed greatly in May 2020, with high-pressure anomalies observed in the Beaufort Sea. The air temperature turned into small positive anomalies over the Barents Sea in May–June 2020. The SLP structure in May 2020 was further conducive to Arctic sea ice advection towards northeastern Greenland. This large change in SLP structure led to the prominently enhanced positive CAI, which reached a second peak in June over 1979–2020; even the AO index decreased remarkably during this period (Table 1). Therefore, the AO mainly manifests the SLP structure of the pan-Arctic, regulating the sea ice outflow from the Arctic Ocean to the BGS by changing the axis alignment of the TPD, while the CAI mainly affects the wind forcing and ice speed in the TPD region, especially for the Atlantic sector.

The extremely positive AO in winter (JFM) 2020 induced relatively high wind speeds over the Atlantic sector of the Arctic Ocean (the first column of Fig. 2), which led to the high SIM speeds along the TPD. Significant positive correlations between the monthly SIM speeds and the wind speeds in the Atlantic sector of the TPD have been identified in January–February, April, and June, as shown in Table A1. The 1988–2020 data revealed that the SIM speeds perpendicular to the passageways are significantly correlated with the accumulated SIAF through three passageways in both winter and spring (R=+0.86 and +0.85, respectively; P<0.001), while the corresponding correlation between SIC and the SIAF is only significant in winter (R=+0.42, P<0.05). In January–June 2020, SIC anomalies contributed 3.9 % to SIAF anomalies and SIM speed anomalies contributed 71.7 %. The anomalies of Arctic sea ice outflow through our defined passageways were mainly dominated by SIM anomalies in winter–spring 2020. Compared to the 1988–2020 climatology, the accumulated SIAF values across three passageways were all at the above-average level in January–March and June, with the largest positive anomalies occurring in March 2020.

In winter 2020, the cumulative SIAF through the Fram Strait was 1.19 × 105 km2, which was larger than the 1988–2020 average by about 20 % and was the second largest in 2010–2020. Especially in March 2020, the monthly SIAF through the Fram Strait (5.77 × 104 km2) was the second largest in 1988–2020. The winter cumulative SIAF through S-FJL in 2020 (1.51 × 104 km2) was also the second largest in 2010–2020. However, the winter cumulative SIAF through the FJL-NZ in 2020 (2.76 × 104 km2) was only about 81.0 % of the 1988–2020 average. That is, the extremely positive AO in winter 2020 only significantly facilitated more sea ice outflow through the Fram Strait and S-FJL, while sea ice outflow through the FJL-NZ did not respond significantly to the extremely positive AO. Under the influence of a positive CAI in spring (AMJ) 2020, the cumulative SIAF through the Fram Strait was still at an above-average level, while the spring cumulative SIAF through the S-FJL and FJL-NZ in 2020 was only 67.5 % and 14.1 % of the 1988–2020 average, respectively. Such low SIAF through the FJL-NZ passageway may be related to the enhanced inflow from the Barents Sea into the Arctic Ocean through this passageway (Polyakov et al., 2023). This implies that the SIAF through these two passageways, especially for the FJL-NZ passageway in the east, was not facilitated by a positive CAI in spring 2020.

Overall, the total SIAF anomalies in January–June 2020 were most pronounced in the Fram Strait, followed by those observed in the S-FJL passageway, with positive anomalies of 2.35 × 104 and 1.40 × 104 km2 (Fig. 3), respectively. However, negative anomalies were observed in the FJL-NZ passageway. This indicates that only the SIAF through the Fram Strait and S-FJL responds to both the extremely positive phase of the winter AO and the continuous positive phase of the winter–spring CAI. Furthermore, the values of the total SIAF anomalies in January–June 2020 through these three passageways were not prominent in 1988–2020 (last row of each panel in Fig. 3). This implies such discontinuous extreme AO and CAI values only had a moderate impact on the Arctic sea ice outflow through these three passageways, especially the FJL-NZ in the east.

We further quantified the relationship between SIAF and two atmospheric circulation indices (AO and CAI) from 1988 to 2020 to test the robustness of the influencing mechanism identified in 2020. Here, we chose the Fram Strait as the investigated passageway because, in winter–spring 2020, the Fram Strait contributed the most (77.6 %) to the total SIAF through the three passageways. We calculated the correlation coefficient (R) between the detrended monthly SIAF and the detrended AO and CAI from January to June for the period 1988–2020 (Table 2). During January–June, there was a significant positive correlation between SIAF and the AO identified in February but not in other months. This is consistent with a weak linkage between the AO and SIAF through the Fram Strait in 1979–2014 (Polyakov et al., 2023). There was also a significant positive correlation between the monthly SIAF and CAI in January, March, and April (R=0.61, 0.40, and 0.54, respectively; P<0.05), which suggests that the relatively high CAI could induce a southward advection of Arctic sea ice to the BGS, especially during the period (March–April) with a relatively high ice motion speed in the regions north of the BGS compared to other months (e.g., Lei et al., 2016).

The sea ice backward trajectories can be traced back to the source region of sea ice that advected to the passageways. The broader distribution of the original sea ice area implies that more ice would enter the passageways, leading to an increased sea ice outflow. The reconstructed sea ice backward trajectory in January–June 2020 was similar to that of the MOSAiC ice station (Nicolaus et al., 2021) in the same period, with almost parallel orientation and a very close drift distance between them (Fig. 4c). The slight dislocation was mainly attributed to the inconsistent termination location between the reconstructed backward trajectory and the MOSAiC trajectory on 30 June 2020. Using the endpoints of the two buoys obtained from MOSAiC as the start points of the reconstructed backward trajectories, the Euclidean distance between the termination locations of the reconstructed backward trajectory and the starting locations of the buoy trajectories is averaged out at 63 km, and their trajectories almost overlapped, with the cosine similarity between them reaching 0.85. We also compared the consistency between the reconstructed backward trajectories and the buoys' trajectories, with the data obtained from the International Arctic Buoy Programme, when the extreme positive or negative (±1 standard deviation) phase of the AO and CAI occurred (hereinafter referred to as AO+, AO-, CAI+, and CAI-). As shown in Table A2, in the AO+ and CAI+ cases, the average Euclidean distances between the reconstructed backward trajectories and buoy trajectories were smaller than in the AO- and CAI- cases. This indicates that the sea ice drift distances obtained from the reconstructed backward trajectories are closer to the buoy observations in the AO+ and CAI+ cases than in the AO- and CAI- cases because the tortuous sea ice trajectories were relatively large under the AO- and CAI- compared to under the AO+ and CAI+. However, the cosine similarities were above 0.9 in all AO and CAI cases. This suggests that the orientation of the reconstructed backward trajectories is reliable regardless of the phases of the AO and CAI. It increases our confidence in using this method to reconstruct the ice backward trajectories to identify the source region of sea ice.

Compared to the sea ice backward trajectories reconstructed using the average SIM vector of 1988–2020 (Fig. 4d–f), the sea ice backward trajectories from the Fram Strait in 2020 tended westwards (Fig. 4a–c). This implies that the orientation of the TPD was more favorable for exporting thicker ice from the western Arctic Ocean and northern Greenland to the Fram Strait during winter–spring 2020. For the Fram Strait, the terminations of the sea ice backward trajectories in 2020 were concentrated at 87–90∘ N, which indicates that most of the sea ice advected into this passageway was from the region close to the North Pole. In all three investigation periods, the net distances from the start points at the defined passageways to the terminations of the reconstructed ice backward trajectories in 2020 were the second longest in 1988–2020. In S-FJL, sea ice was mainly advected from the confluence of the Kara Sea and the central Arctic Ocean (Fig. 4), and its backward trajectories were more curved than those from the Fram Strait. Furthermore, no reasonable backward trajectories of sea ice could be acquired for the S-FJL passageway according to the starting points of 31 May and 30 June. This was because the relatively low SIC in this region by late spring had restricted the acquisition of valid SIM data. The sea ice advected through the FJL-NZ passageway was mainly from the Kara Sea. Thus, the identification of the source areas of sea ice that reached the passageways can explain why the changes in SIAF through the S-FJL and FJL-NZ passageways are not as sensitive to changes in the CAI pattern as those through the Fram Strait.

Overall, compared to the 1988–2020 averages, the sea ice backward trajectories through the Fram Strait in winter–spring 2020 were characterized as longer and farther west. Particularly, the net distances between the terminal points on 1 January and the starting points from the Fram Strait on or after 30 April, 31 May, and 30 June of each year in 1988–2020 were significantly positively correlated with the corresponding SIAF (R=+0.80, +0.72, +0.75, respectively; P<0.001). Thus, the enhanced sea ice motion along the TPD during January–June 2020 promoted more Arctic sea ice export towards the BGS, which in turn accelerated the reduction in sea ice over the pan-Arctic Ocean.

SIA in the BGS generally reaches its annual maximum in April each year and then begins to decline as the air and ocean temperatures rise. In April–June 2020, the SIA in the BGS reached the first, second, and fourth largest in 2010–2020. It was much higher compared to the value obtained from the linear decreasing trend from 1979 to 2020, indicating that the SIA in the study year was higher than the expectation. In the Barents Sea, the monthly SIA values for January–April 2020 all ranged in the top three for 2010–2020 (Fig. 5a). The SIA in the Greenland Sea was similar to that in the Barents Sea, with monthly SIA values in April–June 2020 ranking the first or second largest in 2010–2020. Such a large SIA in the BGS during spring 2020 was linked to a more massive sea ice export from the central Arctic Ocean because we found a significant correlation (R=+0.37, P<0.05) between the total SIAF anomalies through the three defined passageways and the SIA in the BGS based on the 1988–2020 data.

As shown in Fig. 6, negative SIT anomalies, i.e., ice thinner than the average, were observed mainly in the Greenland Sea during December 2019. The SIT anomalies were relatively small in the Barents Sea. Since January 2020, more pronounced positive SIT anomalies, i.e., ice thicker than the average, were observed in the Barents Sea and persisted to June. In the Greenland Sea, the positive SIT anomalies gradually increased, particularly on the eastern side from March 2020 and were especially widespread in May–June, while the negative SIT anomalies were mainly observed on the western side. This east–west pattern of SIT anomalies could be attributed to the increased outflow of thicker sea ice from the central Arctic through the Fram Strait.

Furthermore, widespread negative anomalies of SST (-1 to -3 ∘C, Fig. 7) were observed in the BGS in April–June 2020, with monthly SSTs being the lowest for 2011–2020. In addition, the negative SST anomalies over the Greenland Sea persisted until July 2020. The detrended correlations between the monthly SIA and contemporaneous SST in the BGS from April to June over 1982–2020 (Table A3) were significantly negative. Thus, the abnormally large Arctic sea ice outflow in winter–spring 2020 led to an increased SIA and the associated relatively high albedo in the BGS, thereby preventing the absorption of solar radiation by the ocean and suppressing the rise in SST. In turn, relatively cold seawater was not conducive to sea ice melting there. The corresponding correlation coefficients in the Greenland Sea were weaker compared to those in the Barents Sea, which may be due to the relatively complex influencing factors in the SST variations in the Greenland Sea. That is to say, the northwestern Greenland Sea is protected from cooling effects due to sea ice and surface current outflow from the north, while the southeastern part is subject to warming effects from warm Atlantic waters (Wang et al., 2019). Regionally, we found that the negative correlation coefficients between SIA and SST are more significant in the southern BGS (72–76∘ N) than in the northern part (76–80∘ N). This is likely because the SST is more closely correlated with the SIC in areas with less sea ice (Wang et al., 2019). In addition, we examined the statistical relationship between the detrended April SIA and the detrended monthly SST with a lag of 1–3 months in the BGS (Table A4). In the Barents Sea, the April SIA still had a significant negative effect on the increase in SST until July, i.e., with a lag of 3 months, whereas in the Greenland Sea, the significant influence of April SIA on the SST only lasted until June. This difference suggests that the sea ice anomalies in the Barents Sea have a longer memory for the impact on the SST than those in the Greenland Sea.

To explore the changes in sea ice backward trajectories in response to extreme atmospheric circulation patterns, we examined the years in which the AO+, AO-, CAI+, and CAI- occurred in winter, based on which we obtained the mean SIM field and reconstructed the January–June sea ice backward drift trajectories arriving in the Fram Strait in June of the corresponding years (Fig. A2). In the AO+ case, the end of sea ice backward trajectories (blue trajectory in Fig. A2a) extended westwards, which indicated that the TPD originated further west. This suggests that the winter AO+ is more conducive to sea ice outflow from the central Arctic Ocean to the BGS (e.g., Rigor et al., 2002). Thus, we believe the relationship between the positive phase anomalies of the AO and the westward alignment of the TPD identified in 2020, as shown in Fig. 4, is robust, whereas in the AO- case, the sea ice backward trajectories were closer to the prime meridian and relatively eastwards compared to the AO+ case. Under the influence of the AO-, the expanding Beaufort Gyre can weaken the strength of the TPD and reduces Arctic sea ice export (e.g., Zhang et al., 2022). Associated with either the CAI+ or the CAI-, the sea ice backward trajectories were similar to those under the corresponding phase of the AO. However, in the two investigated periods of January–May and January–June, there is a higher positive (negative) correlation between the latitude (longitude) of sea ice backward trajectory endpoints and the CAI compared to the AO (Table A5). This relationship was due to the fact that the CAI+ might directly enhance the TPD by strengthening the straightforward wind forcing, hence favoring sea ice outflow from the central Arctic Ocean into the Fram Strait. However, an insignificant correlation between them was obtained in the investigated period of January–April. This is likely related to the fact that the sea ice backward trajectories reconstructed in this period were relatively short and the variations in the backward trajectory endpoints between the years were relatively small.

The January–June average sea ice backward trajectories in the AO+, AO-, CAI+, and CAI- cases were then used to further check whether extreme atmospheric circulation patterns have influences on the atmospheric forcing of sea ice thermodynamic processes. We obtained the freezing degree days (FDD), which are the temporal integral of air temperature below the freezing point over the freezing season. The results showed that, only the FDD in the AO+ case (2616 K d-1) were lower than the 1988–2020 mean (2695 K d-1). This implies that the endpoint of the backward trajectory corresponding to the AO+ would be further south and east (Fig. A2); the near-surface air temperature over there would be significantly higher than that in the northwest, which is unfavorable for sea ice growth. We also compared the lengths of time that the sea ice backward trajectory was within the region south of 82∘ N before the floe reached the Fram Strait, as sea ice there was affected by strong heat supply from the ocean (Sumata et al., 2022). In the AO+ (CAI-) case, the residence time in the region south of 82∘ N before ice reached the Fram Strait was 54 (57) d, which is longer than in the AO- (CAI+) case (43 (38) d). This suggests that sea ice in the AO+ or CAI- cases was exposed to strong heat from the ocean for a longer period and therefore facilitated larger sea ice melt than in the AO- or CAI+ cases.

The impact of Arctic sea ice outflow on the SIA in the BGS would be weakened by both local atmospheric and oceanic forcing (Frey et al., 2015; Lind et al., 2018). Here, we focus on the effect of atmospheric anomalies on sea ice conditions. The persistence of negative air temperature anomalies in the BGS from February to April 2020 (the second and fourth columns of Fig. 2), roughly 2 to 6 ∘C lower than the 1979–2020 climatology, would restrict the sea ice melting there. Especially in March 2020, negative air temperature anomalies covered almost the entire BGS, and the region with the -6 ∘C anomalies occurred in the coincident region with positive monthly SIT anomalies (Figs. 2 and 6). Moreover, compared to the 1979–2020 climatology, the monthly atmospheric surface heat fluxes showed positive (upward) anomalies over the climatological ice-covered BGS (regions with the SIC above 85 % for the 1979–2020 climatology) in January–March 2020 (Fig. 8), which were mainly dominated by turbulent heat flux (35.7–38.6 W m-2), accounting for 84.2 %–98.9 % of the atmospheric surface heat flux anomalies. Especially in February and March 2020, the upward anomalies in sensible heat flux were 1.7–2.4 times the latent heat flux. This was likely due to the relatively large air–sea temperature difference and relatively high wind speeds in the BGS during this period, which would have resulted in an unstable atmospheric boundary layer and the increased atmospheric heat flux from the ocean to the air (Minnett and Key, 2007). In addition to turbulent heat flux, the net longwave radiation revealed relatively small upward anomalies (0.4–8.9 W m-2) persisting from January to April 2020, which were also favorable for preventing ocean warming and ice melting. From April to June 2020, the direction of monthly anomalies in atmospheric surface heat fluxes shifted from upwards to downwards, but the values are smaller relative to the values in January–March. It is worth noting that upward anomalies in net shortwave radiation were observed in June 2020 over the study region, which coincided with the relatively large SIA and the associated relatively high regional albedo. Over the climatological ice-covered BGS, anomalies in the cumulative monthly atmospheric surface heat flux from January to April 2020 were associated with a reduced decrease of 0.12–0.51 m in SIT, estimated using Eq. (4). This was conducive to the survival of sea ice during spring and early summer 2020.

The NAO did not exhibit an extreme positive phase in 2020. However, we still investigated the relationship between the NAO index and the sea ice conditions in the BGS, considering the regional influence of the NAO on the BGS. In 2020, the NAO index remained positive from January to March, similarly to the positive AO index. It favored Arctic sea ice outflow to the BGS to some extent, as a significant positive correlation (R=0.36, P<0.05) between the NAO index and the SIA in the southern BGS was identified in January. The positive phases of NAO in January–March also induced a stronger northerly wind over the North Atlantic, carrying cold air southwards and thus decreasing the air temperature in the BGS (e.g., Hurrell, 2015), as shown in the second column of Fig. 2, which was not conducive to sea ice melting. Thus, the NAO mainly regulates the wind forcing of the BGS, rather than the atmospheric forcing, before sea ice reaches our defined passageways, as the AO and CAI do.

In the past decade, positive anomalies in the winter–spring SIAF through our defined passageways relative to the 1988–2020 climatology were also identified in 2011, 2017, and 2019, close to the value in 2020 (Fig. 3). Therefore, we also quantified the anomalies of sea ice and ocean conditions in the BGS for these years to assess the robustness of the seasonal feedback mechanisms identified in winter–spring 2020. During these 3 years, the sea ice backward trajectories reconstructed starting 30 April, 31 May, and 30 June were also characterized as longer and farther west compared to the 1988–2020 climatology. This suggests that the ice speeds along the TPD were relatively large and could partially contribute to the positive SIAF anomalies in these years. In the BGS, although small negative SIA anomalies were observed in March–June 2011, 2017, and 2019 compared to the 1979–2020 climatology, their values were still much higher than those estimated from the long-term linear decreasing trends since 1979 by 0.16 × 104–2.95 × 104, 0.33 × 105–1.41 × 105, and 0.71 × 105–1.09 × 105 km2, respectively. During these 3 years, similar upward anomalies in accumulated net atmospheric surface heat fluxes were also identified in January–March, suggesting the potential coupling mechanism between sea ice coverage and the surface heat budget in the BGS. However, compared to the 1979–2020 climatology, there were positive air temperature anomalies in January–March 2011, 2017, and 2019, in contrast to the negative air temperature anomalies in 2020. This may subsequently contribute to the relatively small negative SIA anomalies in these years compared to in 2020. The SIT anomalies were calculated only for 2017 and 2019 since satellite SIT data were not available prior to 2011, and we found that the BGS also showed small positive anomalies from March to June for both years compared to the average since 2011. Furthermore, the sea ice anomalies in these years also had impacts on the oceanic conditions of the BGS in the subsequent April–June. The monthly SSTs in May–June of 2011, 2017, and 2019 all ranked the second to fourth lowest for 2010–2020.

For comparison purposes, the extremely negative SIAF anomalies through the defined passageways in winter–spring should also be taken into consideration; we thus chose the year of 2018 as the case of low Arctic sea ice outflow (Fig. 3). In 2018, the sea ice backward trajectories were all shorter than for the 1988–2020 climatology over all the periods of January–April, January–May, and January–June. This suggested that the southward SIM speeds along the Fram Strait were relatively low from January to June in 2018 (Sumata et al., 2022). In the BGS, the SIA in May–June 2018 was lower by 4.44 × 104 and 3.63 × 104 km2 compared to the SIA estimated from the long-term linear decreasing trends since 1979. In January–June 2018, there were widely negative SIT anomalies in the BGS compared to the 2011–2018 climatological mean, which is consistent with the abnormal SIT reduction in the Fram Strait region confirmed by Sumata et al. (2022). The oceanic conditions in the BGS were also affected. In May, the mean SST in 2018 was higher than that in the high-outflow cases (2011, 2017, and 2019) by 20 %–40 %, consistent with the negative correlation between SIA and SST (Table A3).

We also assessed the impact of the positive AO in summer (JAS) on the BGS, since sea ice motion generally responds more strongly to the atmosphere in summer. Using the year of 2016 in which the AO+ occurred in summer, we found that the SIAF through the Fram Strait in this summer was much larger than the 1988–2020 climatology, ranking the third and fourth for 1988–2020. This suggests that the AO+ also contributes to the enhanced Arctic sea ice outflow to some extent in summer. However, due to local processes, the SIA of the BGS in this summer was even smaller than that estimated from the linear regression of 1979–2020.

Note that we also expect that the influences of abnormally high Arctic sea ice outflow on the sea ice and other marine conditions in the BGS will gradually weaken if the Arctic sea ice continues to thin and the northward Atlantic Ocean heat flow continues to increase because the thinner ice under the increased oceanic heat would not be conducive to the survival of sea ice in the BGS.