HIRHAM–NAOSIM is a coupled regional atmosphere–ocean–sea ice model applied over a circum-Arctic domain using rotated latitude–longitude grids with a horizontal resolution of 1/4° (∼27km) and 40 vertical layers in the atmosphere component HIRHAM and 1/12° (∼9km) and 50 vertical layers in the ocean–sea ice component NAOSIM. Detailed information on the model components and their coupling is given by , and information on the current model version 2.2, particularly regarding recently introduced reparametrizations, is given by in their supplementary material. The simulation used for the present study was run for the period 1979–2021, with the first part of the simulation disregarded to let the model find its own steady state. The analysis was therefore restricted to the period 1991–2020. It is driven by ERA5 reanalysis data at HIRHAM's lateral boundaries and at HIRHAM's lower and NAOSIM's upper boundaries, which are not covered by the domain of the other model component. For NAOSIM's open lateral boundaries in the North Atlantic, ORAS5 reanalysis data were used.

The Regional Arctic System Model (RASM) is a fully coupled atmosphere–land-ocean-sea ice model. It uses the Weather Research and Forecasting WRF; version 3.71 for atmosphere, a regionally configured version of Parallel Ocean Program POP; version 2.1 for the ocean and the Los Alamos National Laboratory Sea Ice Model CICE version 6 for sea ice. Additionally, it uses the Variable Infiltration Capacity (VIC) land hydrology model and the streamflow routing RVIC; model for transporting the freshwater flux from the land to the ocean. The ocean and sea ice have a resolution of 1/12° (∼9km) on a rotated grid with 45 vertical levels for the ocean and 5 thickness categories for sea ice.

The Arctic Ocean physical reanalysis TOPAZ 4B (hereafter TOPAZ) is a regional ocean reanalysis for the polar region north of 50° N . It uses the Hybrid Coordinate Ocean Model version 2.2 HYCOM;, and a single-category version of CICE 3 for sea ice . ERA5 data is used as atmospheric forcing. The model uses the deterministic ensemble Kalman filter (DEnKF) to assimilate multiple ocean and sea ice observations simultaneously , such as SIC and drift from OSI SAF, gridded sea surface temperature (SST) from OSTIA, and in situ temperature and salinity profiles from the CORA database. Additionally, sea ice thickness for the winter months from CS2SMOS and sea surface salinity based on the SMOS satellite are assimilated after 2010. For river runoff, the reanalysis uses a climatology based on ECMWF reanalysis and the TRIP hydrological model . The data are provided at a standard polar stereographic grid with 12.5 km resolution and 40 depth levels.

The Regional Arctic Reanalysis RARE 1.15.2 (hereafter RARE) is a regional reanalysis with a southern boundary at 44.7° N . It uses the GFDL MOM5/SIS1 numerical model and ERA5 as surface forcing. The model assimilates World Ocean Database (WOD) hydrographic profiles as well as satellite and in situ SST profiles . Sea ice thickness estimates of the Pan-Arctic Ice Ocean Modeling and Assimilation System 2.1 PIOMAS; are used to constrain sea ice using a net surface heat flux relaxation term with a 30 d time scale. Areas with thicker sea ice compared to PIOMAS receive more surface heat flux, and thinner areas receive less . The continental discharge is based on a dataset combined from the World Meteorological Organisation Global Runoff Data Centre estimates and discharge estimates from R-ArcticNET and the Arctic Great Rivers Observatory; gaps in the dataset are filled with climatological monthly estimates. The dataset is provided on a regular 0.1° Mercator grid with 75 depth levels.

Ocean Reanalysis System 5 (ORAS5, hereafter ORAS) is a global eddy-permitting ocean-sea ice ensemble reanalysis system by ECMWF. The resolution is 0.25°, and it has 75 vertical levels. ORAS is produced with the OCEAN5 system , which uses NEMO V3.4 coupled to the LIM2 sea-ice model and the NEMOVAR ocean assimilation system. Data assimilated include in-situ T/S profiles from EN4 , and SST and SIC through HadISST2 + OSTIA , which is based on satellite observations. The atmospheric forcing comes from ERA-Interim from 1979–2014 and re-processed observations.

For sea ice, the analysed variables are SIC, sea ice area (SIA), defined as the sum of grid-cell area multiplied by the SIC for all cells with SIC>15%, and Integrated Ice Edge Error (IIEE), defined as the area where the model or reanalysis and OSI SAF satellite observations disagree on the ice concentration being above or below 15 %. The IIEE is calculated following : 1IIEE=O+U with 2O=∫Amax⁡(cm-co,0)dA and 3U=∫Amax⁡(co-cm,0)dA, where O and U stand for over- and underestimation, A is the area of either the Barents or Kara Seas (see Fig. ), c=1 where the sea-ice concentration is greater than 15 % and c=0 elsewhere. The subscript m denotes the model or reanalysis data, and the subscript o denotes the satellite observations.

For the ocean, we focus on the mean temperature of the ML. The depth of the ML is calculated for each month using the density anomaly (σ) criterion, as the depth at which the density difference to the surface (5 m) is equal to 0.03 kgm-3, following the method of . Density at 5 m depth is used as the surface because it is the uppermost depth available in all models. The monthly mean temperature for each grid cell is calculated from the surface to the depth of the ML. The monthly mean temperature for each region is then calculated by taking the area-weighted mean of each grid cell.

In addition to the sea ice and ML temperature datasets, five climate indices are used to analyse potential drivers of sea ice variability and identify inter-product differences.The indices are: North Atlantic Oscillation NAO;, Atlantic Multidecadal Oscillation AMO;, Pacific Decadal Oscillation PDO;, East Atlantic/ Western Russia teleconnection EA/WR;, and the Northern Hemisphere Ocean Heat Content (0–700 m) NH OHC;. We used the AMO and PDO versions based on NOAA Extended Reconstructed SST V5 ERSST v5;. A correlation analysis between these indices and SIC and ML temperature is presented here.

Trends are calculated using a linear least-squares regression. The statistical significance of the trends is assessed using the p value for the null hypothesis that the regression slope equals zero. Trends are considered significant at the p<0.05 level. The significance of the differences between satellite-observed SIA or SIC and models/reanalyses, presented in Sect. , as well as differences between ORAS and other dataset ML temperatures, are calculated using a Student's t test. The Pearson's correlation coefficient (PCC), r, is used to quantify the correlation between the sea-ice area and ML temperature in Sect. , as well as the correlation between climate indexes and sea ice and ML temperatures with: 4r=∑i(xi-x‾)(yi-y‾)∑i(xi-x‾)2∑i(yi-y‾)2, where x‾ is the mean of vector xi, and y‾ is the mean of vector yi. The Fishers z test is used, with a threshold of p<0.05, to determine if differences between the correlations are significant: 5Z=z1-z2SE, where z1 and z2 are calculated from r using the Fisher's transformation 6zn=12ln⁡1+rn1-rn with n∈{1,2}. The standard error SE in () is given by 7SE=1N1-3+1N2-3, where N1 and N2 represent the sample sizes of datasets 1 and 2, respectively.

The mean and trend of the SIA for the seasons with maximum (spring) and minimum (autumn) sea ice are shown in Table . Figure  shows the difference between the mean SIA of each month and the monthly area climatology of each dataset.

Given the good mean SIA agreement of ORAS and TOPAZ with OSI SAF discussed in Sect. , it is not surprising that their integrated ice edge errors (IIEE), relative to OSI SAF, are much smaller than those of the other datasets (Table ). Furthermore, the monthly mean IIEEs for these products show only small variations (Fig. ), both in the Barents Sea and in the Kara Sea. In the Barents Sea, TOPAZ has a higher IIEE from January to June due to a greater underestimation of the ice edge location than ORAS (Fig. a and c). In the Kara Sea, the largest difference between ORAS and TOPAZ occurs in October and November when TOPAZ overestimates the edge while ORAS underestimates it. The ice edge of TOPAZ tends to recede too fast in early summer and refreeze too fast in early winter, which is most likely the reason for this difference . The trend of the annual mean O–U is small for ORAS and TOPAZ and decreases over time, indicating increasing accuracy in their ice edge simulation (Table  and Fig. e). This is consistent with the good agreement in SIA shown in Sect. . Thus, both products perform well not only in representing the total amount of sea ice, but also its spatial extent.

The IIEE of RASM and RARE are similar to each other, with the maximum IIEE in the summer (June or July) (Fig. a and b). RARE has a larger mean IIEE in the Barents Sea and RASM a larger one in the Kara Sea (Table ). The O–U is larger in RARE than in RASM for both regions. The main difference between RARE and RASM is in the O–U trend (Table  and Fig. e and f). The trend is over 5 times larger in RASM than in RARE, because the ice edge in RASM does not change much over the study period (Sect. ), which results in the model underestimating the ice edge at the start of the study period and significantly overestimating it at the end. Although RARE and RASM have similar mean IIEE values, their behaviour differs substantially. RARE captures the observed decrease in SIA (Sect. ), while the larger O–U trend in RASM reflects its lack of a comparable long-term change.

HIRHAM–NAOSIM has the highest mean IIEE and the highest mean O–U (Table ). The error is largest in December in the Barents Sea and in October in the Kara Sea (Fig. a and b). In the Barents Sea, the trend is smaller than the RASM trend, but in the Kara Sea the trend is similar. The variability from year to year in HIRHAM–NAOSIM is larger than in the other models (Fig. e and f). The IIEE results show that a realistic SIA does not necessarily imply a realistic ice edge. For example, RARE reproduces the observed SIA trends better than RASM, while HIRHAM–NAOSIM has a smaller SIA bias than RARE but a larger ice edge error. Evaluating both metrics therefore provides a more complete assessment of model performance.

The SIC difference between the analysed products and OSI SAF is shown in Fig.  for the spring and autumn. The mean SIC and the decadal trends for these two seasons are shown in Figs.  and . The evolution of the SIC over the study period 1991–2020, along with the differences between the reanalysis and model products against the observed OSI SAF concentration, is discussed in Sects.  and .

The mean temperature and trends of the ML are shown in Table  for spring and autumn. In the Barents Sea, the spring mean temperature varies from -0.5°C (HIRHAM–NAOSIM) to 0.6 °C (RARE) between the models. RARE is considerably warmer than ORAS and TOPAZ, while HIRHAM–NAOSIM and RASM are colder. The mean ML temperature in the regions stays mostly below 5 °C, except in RARE, where some warmer waters can be seen (Fig. d). For the other models, the difference in the regional mean seems to depend more on how widespread the warmer waters are than the difference in temperature of the warmer waters (compare Fig. a, c–g, and h). In the Kara Sea, the spring variation is smaller and the ML is close to freezing (Table ). In autumn, the mean ML temperature does not significantly differ between the reanalyses in either the Barents or the Kara Sea, while both models are significantly colder (Table ). The mean ML temperature stays mostly below 10 °C in the Barents Sea, except in the south-west in RASM (Fig. ) and mostly below 5 °C in the Kara Sea, except in the south-west in RASM, RARE, and TOPAZ (Fig. c, d, and h). The reason why the regional mean for HIRHAM–NAOSIM and RASM is similar, even if RASM has these warmer coastal waters, is that many of these are outside of the compared region (Fig. ). The colder mean mixed-layer temperatures in the coupled models relative to the reanalyses, particularly in autumn, are consistent with their tendency to maintain too much sea ice (Sects.  and ). A more extensive ice cover reduces the direct exposure of the ocean to atmospheric forcing and can limit seasonal ocean warming, suggesting that at least part of the temperature bias may be linked to the sea-ice bias rather than to ocean processes alone.

The ML temperature trend is positive and statistically significant in the Barents Sea in both spring and autumn for the reanalyses and for HIRHAM–NAOSIM, being stronger in the autumn (Table ). In spring, the warming trend in HIRHAM–NAOSIM, ORAS, and TOPAZ is highest in the ice-free areas or close to the ice edge (Fig. b, e, and i), while in the autumn ORAS and TOPAZ have a significant warming trend over the whole Barents Sea. The warming trend is weaker and the region of significant warming is smaller in HIRHAM–NAOSIM and does not extend as far north and east. In RARE, the highest spring warming coincides with deeper areas (Fig. ), where Atlantic water enters the Barents Sea . This partly coincides with the area of the strongest decreasing SIC trend in the MIZ east of Novaya Zemlya (Figs. j and k). The trend in spring at these locations is stronger than in ORAS, and the two areas are separated by a nonsignificant cooling trend. In autumn, RARE has two areas with a cooling trend, of which the eastern one at the coast of Novaya Zemlya is statistically significant. These are located close to the same areas where there was the strong warming trend in the spring. The ML temperature in this location is also on average warmer than in the other reanalyses (Fig. d and f). Of these, the eastern one is located west of Novaya Zemlya, in the same location as the strong warming in spring and is statistically significant. In autumn, RARE also shows a statistically significant deepening of the ML west of Novaya Zemlya (not shown). The contrasting spring warming and autumn cooling in this region may indicate differences in how vertical mixing and the seasonal storage and release of ocean heat are represented in RARE compared to the other reanalyses. The present analysis cannot isolate the respective contributions of the ocean model, assimilation scheme, and atmospheric forcing to this behaviour.

In the Kara Sea, the trend is small for all datasets in spring, when the region is ice-covered (Table ). The limited spring warming is therefore consistent with the weak spring SIA and SIC trends, because the compact ice cover (SIC>80%) restricts atmosphere–ocean heat exchange and keeps the ML temperature close to freezing. In autumn, the trend is statistically significant in the reanalyses and close to 1 °Cdecade-1 (Table ). The autumn ML temperature trend is above 1 °Cdecade-1 in large areas of the Kara Sea in all reanalyses and is stronger in the Kara Sea than in the Barents Sea. HIRHAM–NAOSIM shows no statistically significant trend in the Kara Sea where the sea ice is overestimated (Sect.  and Fig. i). RASM has no widespread statistically significant trends in either region in spring or autumn, only small areas of warming in the Kara Sea and cooling in the Barents Sea (Fig. i and j). Thus, HIRHAM–NAOSIM reproduces the Barents Sea warming better than RASM, but neither coupled model captures the pronounced autumn warming in the Kara Sea. For HIRHAM–NAOSIM, the weak Kara Sea warming coincides with its extensive sea-ice cover, which may limit seasonal atmosphere–ocean heat exchange. RASM, by contrast, shows weak ML temperature trends despite a less extensive sea-ice bias, suggesting that its lack of warming cannot be attributed to excessive ice cover alone.

Table  shows the PCC calculated between SIA and ML temperature and between the anomalies (shown in Figs.  and ). The average ML temperature anomalies (MLTa) (Fig. ) follows similar patterns to that of the SIA (Fig. ), discussed in Sects.  and , though in the Kara Sea, the year-to-year variations are only seen in summer and autumn (for all models). The PCC (r) (Table ) between the sea ice and temperature is negative for all datasets and ranges between -0.85 and -0.94. The PCC between the anomalies (rdiff), where the effect of the annual variation is removed, is also negative and ranges between -0.63 and -0.86. These high correlations are in line with previous studies . The consistently strong negative correlations indicate that all datasets capture the expected tight coupling between mixed-layer temperature and sea ice, whereby warmer upper-ocean conditions favour sea-ice loss and reduced ice cover enhances ocean heat uptake. RARE seems to have a higher correlation between the anomalies than the other datasets and is significantly higher than ORAS in both the Barents Sea and the Kara Sea. In the Barents Sea, only the RARE anomaly PCC (rdiff) differs significantly from ORAS, while in the Kara Sea the difference compared to ORAS is statistically significant for RARE and HIRHAM–NAOSIM. The correlation coefficients between the anomalies are slightly lower in the Kara Sea than in the Barents Sea for ORAS and TOPAZ and slightly higher for the other datasets. However, the differences are statistically significant (Fisher's z test, p<0.05) only for RARE and HIRHAM–NAOSIM. The stronger coupling in RARE may indicate that sea-ice variability is more tightly linked to local ML temperature variability than in the other products. One possible explanation is that RARE constrains sea ice indirectly through surface heat flux relaxation based on PIOMAS Sect. ;. This interpretation is consistent with the product-specific spatial temperature behaviour described above, although the present results do not identify the mechanism responsible for the stronger correlation.

PCC of five climate indices (Sect. ) to SIAa and average MLTa were calculated for both regions to explore the teleconnections in the data (Fig. ). Maps for the correlation of the climate indices per gridcell to the SIC anomaly (SICa) and MLTa, from which the SIAa and average MLTa have been calculated, can be found in the appendix (Figs. –). Overall, none of the climate-index correlations differ significantly among OSI SAF, ORAS, and TOPAZ for SIAa, or between ORAS and TOPAZ for MLTa. This agreement is expected given the small differences among these datasets found in the preceding sections.

For NAO, there are no significant differences between the datasets (Fig. ). The positive NAO phase is characterised by a stronger North Atlantic pressure gradient and enhanced westerly circulation, whereas the negative phase is associated with a weaker pressure gradient and weaker or more meridional circulation . A positive NAO leads to warm and humid westerly winds and enhanced heat transport into the Barents Sea region, leading to decreasing sea ice and a statistically significant correlation in SIAa in the Barents Sea (Fig. a). The effect is, however, weaker further away from the Atlantic in the Kara Sea, and there the SIAa correlation is not statistically significant (Fig. b). The correlation map (Fig. a, b, e, f, i, and j) shows that the negative correlation with sea ice is significant mostly in the northern Barents Sea, and a non-significant negative correlation extends into the northeastern Kara Sea. The rest of the Kara Sea is positively correlated but only statistically significant in small areas.

A positive AMO is characterised by warmer-than-average North Atlantic sea-surface temperatures and has been linked to subsequent temperature variability in the Barents Sea , increasing the heat transport to the Barents Sea. Consistent with this relationship, a positive AMO is associated with a negative SIAa and positive MLTa correlation for OSI SAF, ORAS, and TOPAZ, which is about double the correlation with NAO (Fig. a and c). In the Kara Sea, we see a weaker, though still significant, correlation in the SIAa, but not in the MLTa as the effect of the Atlantic is again weaker in the Kara Sea (Fig. b and d). This difference between SIAa and average MLTa may arise because sea-ice variability integrates the cumulative effects of atmospheric and oceanic forcing, whereas the ML is close to freezing and insulated from the atmosphere during the winter and spring months by the ice cover, dampening the correlation. From the correlation map (Fig. a, b, and e) one can see that the negative correlation to SICa is highest for OSI SAF, ORAS, and TOPAZ in the northern Barents Sea. A weaker negative correlation appears in the Kara Sea. A notable feature is an area of positive statistically significant correlation to SICa in the centre of the Barents Sea in OSI SAF, ORAS, and TOPAZ. This could be because currents and winds collects ice here from the surrounding. For MLTa (Fig. d and g), ORAS and TOPAZ have a positive correlation for most of the area – strongest in the western Barents Sea and weakest in the Kara Sea, where only small areas are statistically significant. In RARE (Fig. f and h), the sea ice correlation is similar but weaker than in the other reanalyses. For MLTa, however, there are some areas with strong negative correlation. These regions coincide with the anomalous ML behaviour identified for RARE in Sect. , particularly west of Novaya Zemlya (Figs. d, f and d, f). The negative correlations therefore appear to be associated with the anomalous ML behaviour in RARE, although the underlying cause of this product-specific relationship cannot be determined from the present analysis. For HIRHAM–NAOSIM (Fig. i and k), the SICa correlation looks similar to the reanalyses for the western Barents Sea, but is positive for the eastern Barents Sea and for the Kara Sea. The same pattern, although with opposite correlation, can be seen for the MLTa as well. RASM correlations are generally weaker (Fig. j and l), with Barents Sea SICa divided into negative correlation in the north and positive in the south, and with Kara Sea showing no large areas of statistically significant correlation.

For PDO, a warm (cold) central northern Pacific is related to a negative (positive) PDO phase. When the central northern Pacific is warm (negative PDO), warm-air advection to the Barents and Kara Seas increases, causing a negative SIAa and positive MLTa. This results in a positive (negative) correlation for the SIAa (MLTa). The PDO correlation is opposite to the AMO correlations and of approximately the same size (Fig. ). The correlation patterns are similar to those for AMO too (Fig. ), but with more spread for the SICa correlations in the reanalyses. RARE PDO-MLTa correlation (Fig. h) shows an area of positive correlation, but not as large and strong as for the AMO. HIRHAM–NAOSIM PDO correlations (Fig. i and k) show a similar east–west divide as for AMO, but the divide is more eastward, resulting in only PDO showing a significantly different correlation (Fig. ). RASM is significantly different from OSI-SAF and ORAS for both regions (Fig. j and l). The correlation for both SICa and MLTa to PDO in RASM is generally non-significant and spatially inconsistent.

The positive (negative) EA-WR produces negative (positive) temperature anomalies over eastern Europe, including the Ural Mountains. As a result, a positive (negative) phase pushes more (less) continental air into the Barents and Kara seas, leading to a generally positive EA-WR – SIA correlation and negative EA-WR – MLTa correlation (Fig. ), which is seen in all reanalyses and in the Barents Sea also for the coupled models. In the Kara Sea, however, neither coupled regional model has a statistically significant correlation either for SIAa or MLTa. From the map (Fig. ) we see that the correlations are weaker in the models than in the reanalyses. HIRHAM–NAOSIM has even an opposite, non-significant, correlation in the northeastern Barents Sea and in most of the Kara Seas, while RASM has a non-significant opposite correlation in the northern parts of the study area.

The NH OHC is the climate index that is most affected by the global warming trend and which shows the strongest correlation to both SIAa and MLTa for OSI SAF, ORAS, TOPAZ, and RARE (Fig. ). It is a good indicator for overall climate warming, as 90 % of the global warming heat is absorbed into the ocean . For OSI SAF, ORAS, and TOPAZ, the correlation with SICa is negative and strongest in the northern Barents Sea, whereas the MLTa correlation is positive and strongest in the western Barents Sea (Fig. a, b, d, e, and g). For RARE, the SICa correlation is slightly weaker than for the other reanalyses, but always negative, while in MLTa the biases in the Barents Sea, that was mentioned before in Sect.  and for AMO and PDO, can again be seen (Fig. f and h). The correlations in HIRHAM–NAOSIM in the Barents Sea are in the same direction as in the reanalyses for both SICa and MLTa, but they are weaker and significantly different from those for OSI SAF, ORAS, and TOPAZ (Fig. i and k). In the Kara Sea, however, the HIRHAM–NAOSIM does not show a statistically significant correlation. For RASM the only region with a wider statistically significant correlation is the southeastern Kara Sea, where there is a weak correlation to MLTa (Fig. l).

For the coupled regional models, HIRHAM–NAOSIM does better in the Barents Sea than RASM for both SIAa and average MLTa correlations. In HIRHAM–NAOSIM, only the AMO and NH OHC correlations differ significantly from OSI SAF (or ORAS in the case of MLTa), while for RASM, AMO, PDO, and NH OHC correlations differ significantly. In the Kara Sea, HIRHAM–NAOSIM SICa (MLTa) correlations with the climate indices differ significantly from OSI SAF (ORAS) for all climate indices except NAO, while RASM SICa climate-index correlations differ significantly for the same indices but do not show the opposite AMO and PDO correlations found in HIRHAM–NAOSIM. For MLTa, only the NH OHC correlation differs significantly in RASM. The differences from observations and reanalyses may partly arise because the coupled regional models simulate interactive atmosphere–ocean–sea-ice processes, whereas the ocean reanalyses are driven by prescribed atmospheric forcing and constrained by assimilated observations. However, the differences between HIRHAM–NAOSIM and RASM also indicate model spread arising from their different components and configurations. The significantly different AMO and NH OHC correlations in both coupled models suggest that the influence of North Atlantic variability is not fully represented. This is consistent with the findings of Yamagami et al. (2022), who showed that Gulf Stream warming contributes to Barents–Kara sea-ice decline and that an underestimation of this warming can lead to an underestimation of sea-ice loss.

A plausible interpretation is that biases in the representation of Atlantic-origin warming affect the ability of the coupled models to reproduce the observed decline in sea ice and increase in mixed-layer temperature. Enhanced warming in the North Atlantic can increase heat transport through the Nordic Seas and Barents Sea, contributing to upper-ocean warming and sea-ice retreat in the Barents–Kara region. The weaker mixed-layer warming trends and weaker sea-ice decline seen in the coupled models are therefore consistent with an under-representation of this mechanism. Although the present analysis cannot determine whether the deficiency originates from the simulation of remote North Atlantic processes, the propagation of heat anomalies into the Arctic, or local ocean–atmosphere–sea-ice feedbacks, the results suggest that Atlantic warming signals are not transmitted to the Barents and Kara Seas.