Effectiveness of wind-constrained sea-ice momentum on formation of sea-ice distribution and upper halocline of Arctic Ocean in climate model

Initialization of sea ice and the upper halocline in the Arctic Ocean is crucial for sea-ice prediction, but their representation in climate models still remains biased. Here, using historical and four different simulations by a single climate model, we find that constraining the sea-ice momentum by surface wind stress contributes to a better representation of the sea-ice velocity, area, and concentration. Moreover, the wind-constrained sea-ice drift modifies the underlying ocean structure via ice-ocean stress, leading to an improved climatological halocline’s vertical structure in the Canada Basin. This is because the excessively represented negative wind and ice-ocean stress curl in the climate model is weakened when constraining the sea-ice momentum and consequently the downward vertical speed, including the Ekman pumping, is also weakened at depths of 0–500 m, alleviating the deepening of isohalines. From these results, the improvement of sea-ice and ocean states by constraining sea-ice momentum is expected to make sea-ice prediction more accurate.


Introduction
The Arctic region has undergone rapid climate changes over the past several decades (e.g.Serreze et al 2000).Surface and lower-tropospheric temperatures increase at a rate faster than the global-mean temperature (e.g.Screen andSimmonds 2010, Rantanen et al 2022).This warming is accompanied by a reduction in Arctic sea ice (Stroeve and Notz 2018).The warming signal is also observed in the Arctic Ocean interior (e.g.Polyakov et al 2017, 2023, Timmermans et al 2018).The Arctic changes in turn influence the climate system not only in the Arctic but also the mid-latitudes (e.g.Cohen et al 2014, Mori et al 2014, 2019, Coumou et al 2018, Blackport et al 2019) and economic activity via the Northern Sea Route (e.g.Khon et al 2010, Liu andKronbak 2010).Therefore, sea-ice prediction is highly important for both climate science and various socio-economic sectors.
Before predicting seasonal-to-decadal changes in climate states, including sea ice, a climate model needs to be initialized by assimilating observations to consider the natural internal climate variability (e.g.Meehl et al 2009) together with anthropogenically forced climate change.Regarding sea-ice predictions, initialized climate models have shown that the observed summer and winter Arctic sea-ice extent can be predicted up to 2-7 and 5-11 months ahead, respectively (e.g.Chevallier et al 2013, Sigmond et al 2013, Wang et al 2013, Msadek et al 2014, Peterson et al 2015, Guemas et al 2016b, Sigmond et al 2016, Bushuk et al 2017, Ono et al 2018).Subsurface water temperature and sea-ice thickness can be sources of Arctic sea-ice predictability (Day et al 2014a, 2014b, Ono et al 2020).Indeed, incorporating sea-ice thickness data into climate model initialization improves the accuracy of sea-ice predictions in the Arctic Ocean (Blockley andPeterson 2018, Allard et al 2020) as well as the Southern Ocean (Morioka et al 2021).
In dynamical forecasts with climate models, the sea-ice prediction error is relatively large in marginal ice zones due to advective processes compared with thermodynamic processes (Tietsche et al 2014).Because advection of sea ice is closely related to the velocity field and its error affects the reproducibility of sea-ice concentration and thickness through dynamical processes, the sea-ice velocity is a key variable for improving sea-ice reproducibility.The observed sea-ice velocity is assimilated into the ice-ocean coupled models (Zhang et al 2003, Lindsay and Zhang 2006, Dulière and Fichefet 2007, Caya et al 2010) and climate model (Mu et al 2022), leading to an improvement of sea-ice reproduction.
Sea-ice circulation in the Arctic Ocean is mainly driven directly by surface winds (e.g.Thorndike and Colony 1982, Kimura and Wakatsuchi 2000, Kwok et al 2013, Dong et al 2021, Wang et al 2021), influencing the underlying ocean structures through ice-ocean drag.The upper Arctic Ocean has a strong halocline that is formed and modified by various factors: inflows from the Pacific Ocean, sea-ice processes, river runoff, and net precipitation (e.g.Aagaard et al 1981).Temporal and spatial variations in this stratification modify the distributions of water mass, heat, salt, and nutrients via changes in ocean circulation, and thereby also influence the sea ice.Thus, the initial states of not only the sea ice but also the ocean stratification are important for prediction.Given that wind stress is a dominant term in the sea-ice momentum equation (e.g.Leppäranta 2011), in particular near the low sea-ice concentration region where internal ice stress is negligible, constraining the sea-ice momentum by wind stress would better represent the sea-ice velocity and consequently the sea-ice distributions as well as conditions in the upper halocline.
In this study, to evaluate the impact of the sea-ice momentum constraint on the reproducibility of sea-ice fields, we conducted three climate simulations using a single climate model: the first simulation assimilated only sea-ice concentrations into the climate model, the second added the sea-ice momentum constraint to the first experimental design, and the third added the ocean anomaly assimilation to the second experimental design (see section 2.1 for details).We then compared these three experiments with the two previous experiments, along with observational data.Furthermore, we investigated how the impact of the sea-ice momentum constraint appears in the oceanic states under sea ice via changes in sea-ice fields.This study was intended to provide cues for the initialization method to improve the accuracy of dynamical predictions.

Model and experimental designs
The climate model used in the present study is the Model for Interdisciplinary Research on Climate version 6 (Tatebe et al 2019), called MIROC6.The horizontal resolution of the atmospheric component is a T85 spectral truncation (approximately 1.4 grid intervals for both latitude and longitude), and there are 81 vertical levels up to 0.004 hPa.The oceanic component with a tripolar coordinate system (Murray 1996) has a resolution of nominal 1 • south of 63 • N and ∼60 km in the central Arctic Ocean.There are 62 vertical levels with a bottom boundary layer parameterization (Nakano and Suginohara 2002).The sea-ice component implements one-layer thermodynamics (Bitz and Lipscomb 1999), elastic-viscous-plastic rheology (Hunke and Dukowicz 1997) and a subgrid ice thickness distribution (Bitz et al 2001) with five categories.The detailed framework and parameters are described in Komuro et al (2012).
The experiments used in this study are summarized in table 1.The HIST is a MIROC6 unassimilated experiment with a set of external forcing recommended by the Coupled Model Intercomparison Project Phase 6 (CMIP6; Eyring et al 2016) (Tatebe and Watanabe 2018).The SICF.OTSA is a MIROC6 assimilation experiment performed under the Decadal Climate Prediction Project (Kataoka et al 2020).The HIST experiment showed a decreasing trend in sea-ice area but did not accurately replicate the interannual variability, which is successfully addressed in the SICF.OTSA experiment by assimilating temperature and salinity anomalies as well as sea-ice concentration (Kataoka et al 2020).However, it should be noted that biases still exist in the reproducibility of sea-ice velocity and Arctic basic stratification, as will be in section 3.In this study, to further investigate the impact of assimilated data and the sea-ice momentum constraint on the reproducibility of the atmosphere-ice-ocean states, we performed three experiments (SICF, SICF.WIND, and SICF.OTSA.WIND).The results of these experiments were then compared with those of two previous HIST and SICF.OTSA experiments.(Tatebe and Watanabe 2018), SICF: sea-ice concentration full assimilation, SICF.OTSA: sea-ice concentration full assimilation and Ocean Temperature and salinity anomalies assimilation (Kataoka et al 2020), SICF.WIND: sea-ice concentration full assimilation with WIND-constrained sea-ice momentum, SICF.OTSA.WIND: sea-ice concentration full assimilation and Ocean Temperature and salinity anomalies assimilation with WIND-constrained sea-ice momentum.T: ocean temperature anomaly, S: ocean salinity anomaly, SIC: sea-ice concentration, WIND: diagnosed wind stress.The frequency of assimilation is shown in parentheses.1960-2014 1950-2014 1960-2018 1960-2018 The assimilation procedure for the oceanic component of MIROC6 in the SICF.OTSA.WIND experiment is the same as that used in previous studies with MIROC5 (Tatebe et al 2012, Imada et al 2015) and MIROC6 (Kataoka et al 2020).A simplified incremental analysis update scheme (Bloom et al 1996, Huang et al 2002) was used to assimilate the observed monthly temperature and salinity anomalies, which were obtained from the gridded monthly objective analysis (Ishii et al 2006, Ishii andKimoto 2009), relative to the 1961-2000 mean to the upper 3000 m of the ocean at 1 day intervals except in ice-covered regions.For the sea-ice concentration, the full values of the observed monthly sea-ice concentration (Ishii et al 2006, Ishii andKimoto 2009) based on satellite data (Armstrong et al 2012) were assimilated at 1 day intervals following Lindsay and Zhang (2006) and Stark et al (2008).

HIST
To constrain the sea-ice momentum in the SICF.WIND and SICF.OTSA.WIND experiments, we used the daily-mean wind stress from 1958 to 2018 diagnosed in a MIROC6-COCO4.9simulation under phase 2 of the Ocean Model Intercomparison Project (OMIP2) (Tsujino et al 2020), in which the ice-ocean component of MIROC6 was forced by the JRA55-do atmospheric dataset.The sea-ice momentum equation is written as (e.g.Komuro et al 2012) where m is the ice mass per unit area, f is the Coriolis parameter, η is the sea surface height, τ a is the wind stress over sea ice, τ 0 is the stress at the ice-ocean interface, and F is the divergence of the ice internal stress.In the SICF.WIND and SICF.OTSA.WIND experiments with the sea-ice momentum constraint, the wind stress term in equation ( 1) was replaced with the diagnosed daily-mean wind stress.The period of analysis was from 1979 to 2014, while the simulated periods are different in each experiment, to take into account the beginning of satellite observations.

Observational data and reanalysis product
The observed sea-ice area and concentration were derived from the monthly 1  (Hirahara et al 2014).The monthly sea-ice area was defined as the sum of the grid cell area multiplied by the monthly sea-ice concentration (>0%) over the Northern Hemisphere for reanalysis and model, respectively.For comparison of spatial distribution, the simulated sea-ice concentration in the tripolar coordinate is interpolated on a 1 • × 1 • grid area, which is the same grid as the COBE-SST2.Then, to extract internal variations in seasonal to interannual timescales, the linearly-detrended components for the monthly sea-ice area and concentration were calculated by subtracting monthly linear trends during 1979-2014.We used the Polar Pathfinder Daily 25 km EASE-Grid Sea Ice Motion Vectors, Version 4 (Tschudi et al 2019), available from the NASA National Snow and Ice Data Center (NSIDC) from 1979 to 2014, hereafter referred to as NSIDC.To compare with NSIDC, the simulated sea-ice velocities were remapped to the EASE-Grid.In addition, daily sea-ice velocity data derived from Kimura et al (2013), which is one of the reliable Arctic ice drift products (Sumata et al 2014), were also used to compare sea-ice velocity fields.Hereafter, we referred to the dataset as KIMURA.The horizontal resolution of the data is 60 km and the period is from 2003 to 2014.For comparison with KIMURA, the simulated sea-ice velocities were converted to those in polar stereographic coordinates.

Statistics
The statistical significance for correlation coefficients was evaluated using a two-tailed Student's t-test.For the root-mean-square error (RMSE) between the observational or reanalysis data and the model data, we judged that the RMSE is sufficiently small when it had a value smaller than the standard deviation for the detrended component of observation.

Reproducibility of sea-ice fields
We investigated the reproducibility of sea ice with three experiments (SICF, SICF.WIND, and SICF.OTSA.WIND) and compared them with two previous experiments (HIST and SICF.OTSA).For evaluating the reproducibility, we used the correlation coefficient (CORR) and the RMSE between the observations and the simulations, following previous studies (Tatebe et al 2012, Kataoka et al 2020).
Figure 1 shows the climatological sea-ice velocity fields in March and September from the observation (NSIDC) and three simulations.In the SICF experiment (figure 1), the sea-ice velocity tended to be large over the whole Arctic Ocean in both March and September.The magnitude is somewhat small, but the same feature is also found in HIST and SICF.OTSA experiments (supplementary figure 1).However, by constraining the sea-ice momentum by wind stress (SICF.WIND and SICF.OTSA.WIND), the winter and summer sea-ice velocities are more realistically reproduced (figure 1).Similar results are also found in the comparison with sea-ice velocity by KIMURA (supplementary figures 2 and 3), and the Beaufort Gyre and Transpolar Drift Stream, which are mainstream characterizing the Arctic sea-ice circulation, are also represented.
We then calculated CORRs and RMSEs for zonal and meridional velocities using daily mean data from observation (NSIDC) and model from January 1979 to December 2014 only when both data were available.In the SICF.WIND and SICF.OTSA.WIND experiments, the reproducibility of the sea-ice velocity fields is drastically improved in the Pacific (figure 2) and Atlantic (supplementary figure 4) sectors.Higher CORRs and lower RMSEs are found in all months during the analysis period.In the Pacific sector, the reduction in RMSE for the above two experiments appears to be more remarkable in September-January than in February-April, compared to the historical experiment.This might be explained as follows: in winter to late spring, there are regions of higher sea-ice concentrations where the internal stress is more dominant in the sea-ice momentum balance, and thus the constraint by wind stress is ineffective in such a case.The CORRs and RMSEs using the sea-ice drift product by KIMURA also show an improvement from 2003 to 2014 in the experiments with the sea-ice momentum constraint (supplementary figures 5 and 6), meaning that our results are robust.
Figure 3 shows the time series of the linearly-detrended sea-ice area.For March, all the experiments (SICF, SICF.WIND, and SICF.OTSA.WIND) conducted in this study showed higher CORRs and lower RMSEs compared to those for the HIST and SICF.OTSA experiments.In particular, the CORRs and RMSEs for the SICF.OTSA.WIND experiment are best among the climate model simulations and are comparable to those for the OMIP2 experiment.Meanwhile, the difference between the CORR and RMSE among the SICF, SICF.OTSA, and SICF.OTSA.WIND experiments is relatively small.These results suggest that internal variations in the winter sea-ice area on inter-annual timescale can be more realistically represented by constraining the sea-ice momentum together with sea-ice concentration and ocean anomalies assimilation.This is because both atmospheric and oceanic processes are important for sea-ice variability in the Barents Sea, which is one of the regions with the largest winter sea-ice variability, as will be discussed later.For September, the RMSE values (0.219 and 0.238, respectively) for the SICF.WIND and SICF.OTSA.WIND experiments are small compared to those for the SICF.OTSA experiment, though the CORR does not exceed that for the SICF.OTSA experiment.In contrast, the OMIP2 experiment has a lower CORR and a higher RMSE compared to all experiments except the historical experiment.This is due to several remarkable overestimations of amplitude and phase lag with observations, which, for example, are found in 1980, 1990, and 2003.
Figure 4 shows the CORRs and RMSEs for the sea-ice area in each month.When constraining the sea-ice momentum (SICF.WIND and SICF.OTSA.WIND), CORRs higher than those in the SICF.OTSA experiment are found in February and March, and also in May for the SICF.OTSA.WIND experiment (figure 4(a)).However, the RMSE values are low in May-October for SICF.WIND and in February-October for SICF.OTSA.WIND (figure 4(b)).Moreover, the period with lower RMSE values is longer for SICF.OTSA.WIND by 3 months (February-April) than in the SICF.WIND, indicating that a combination of the sea-ice momentum constraint and the ocean anomaly assimilation is effective for reproducing winter sea-ice states.In general, large winter sea-ice variability is found in the Barents Sea (e.To compare the sea-ice spatial distribution, the CORR and RMSE for the linearly-detrend sea-ice concentration were calculated only when both data were available (i.e.not ice-free) in the Northern Hemisphere.Indeed, a closer look at the sea-ice concentration reproducibility reveals that both the CORR and RMSE in March are better for the Barents and GIN Seas in the SICF.OTSA.WIND experiment (figures 5(a) and (b)), leading to an improved reproduction of the winter sea-ice area (figure 3  (figure 4(b)).These are related to the lower sea-ice concentration CORR near the North Pole (figure 5(c)) and to a 4%-8% improvement in the RMSE in the East Siberian Sea (figure 5(d)).
The observed negative trend for the sea-ice area is better reproduced when constraining the sea-ice momentum (i.e.SICF.WIND and SICF.OTSA.WIND) (supplementary figure 7(a)).This is partly attributed to the improved negative trend pattern of sea-ice concentration in the Barents Sea for winter and in the Pacific sector for summer (supplementary figures 7(b) and (c)).However, the positive trend in the winter Pacific sector and the negative trend in the summer Beaufort Sea were not reproduced.This is one of the factors contributing to the under-or over-estimation of the observed sea-ice area trend.
The above comparisons among experiments showed that more realistic winter and summer sea-ice fields (velocity, area, and concentration) are reproduced in the SICF.WIND and SICF.OTSA.WIND experiments.This suggests that, in addition to the conventional assimilations of temperature and salinity anomalies and sea-ice concentration, constraining sea-ice momentum by wind stress is an effective method for reducing the bias of the sea-ice fields.

Improved climatological upper ocean states
Because sea-ice motion is strongly coupled to upper ocean currents via ice-ocean stress (e.g.Leppäranta 2011, Wang et al 2021), the impact of the improved reproducibility of the sea-ice fields is likely to appear in the ocean rather than the atmosphere.Thus, in the present study, we focused on the influence to the oceanic field.and OMIP2) and reanalysis (COBE-SST2) for each month.CORRs higher than 0.33 denote a statistical significance at the 95% level with 34 degrees of freedom based on a two-sided Student's t-test.Black dots indicate RMSE values smaller than the standard deviation for the observed detrended sea-ice constraint (HIST, SICF.OTSA, and SICF), is suppressed to a depth of 400 m, maintaining the stratification structure including the halocline layer.As in summertime, the climatological structure of potential temperature and salinity in wintertime (January-March; JFM) is also better reproduced when constraining the sea-ice momentum (supplementary figure 9).
To clarify the effect of sea-ice momentum constraint, we further analyzed experiments with and without the sea-ice momentum constraint by wind stress, namely the SICF and SICF.WIND experiments.Because the other experimental settings are the same, the comparison of these two experiments can isolate the effect.Figure 7 shows the climatological summertime salinity at 0-600 m depth of the Canada Basin.At a depth range of 0-100 m, water with salinity less than 31 psu spreads northward too far over the southeastern Canada Basin in the SICF.WIND experiment.The freshwater surface flux difference between the two experiments is primarily due to river runoff, evaporation, and snowfall, rather than freshwater fluxes induced by sea ice (see supplementary figure 10).From these results, we speculate that the improved sea-ice fields by the sea-ice momentum constraint also influence the atmospheric circulation in and/or beyond the Arctic region, resulting in increased snowfall in the southern Canadian Basin and increased river water near the mouth of the Mackenzie River through reduced evaporation in the Canadian Basin and Alaska to northern Canadian land areas (supplementary figure 11).However, in the present study, we were not able to find the evidence that can clearly explain to the upper salinity change, which remains as future work.Meanwhile, the ratio of water with a salinity range of 31-31.5 psu is better than that in the SICF experiment (figure 7(a)).For a depth range of 100-200 m, the distributions for water with a salinity of 33.1-33.4psu are relatively well represented in the SICF.WIND experiment, compared to the SICF experiment where water fresher than 33.1 psu dominants (figure 7(b)).For a depth range of 200-600 m, a large region of the Canada Basin is occupied by water fresher than 34.3 psu in the SICF experiment, while is occupied by water higher than 34.3 psu in the SICF.WIND experiment and is relatively close to the observation compared to the SICF experiment (figure 7(c)).Overall, these results indicate an improvement in the reproducibility of climatological ocean structures in the Canada Basin when constraining the sea-ice momentum, although biases still remain.
Why are the climatological oceanic structures, including the halocline layer in the Pacific sector of the Arctic Ocean, better reproduced by constraining the sea-ice momentum, as in the SICF.WIND experiment?In the Pacific sector, the anticyclonic Beaufort Gyre, which is one of the main wind-driven circulations in the Arctic Ocean, forms the dominant ice and ocean circulation in the Canada Basin (e.g.Proshutinsky et al 2009, Timmermans andMarshall 2020) and contributes to formation of the halocline layer there (Timmermans et al 2017).The driving force is the anticyclonic winds associated with the atmospheric Beaufort High (Steele et al 2004, Timmermans andToole 2023).Therefore, it is inferred that wind stress for constraining the sea-ice momentum improved the reproducibility of the sea-ice fields and in turn affected the ocean circulation beneath the sea ice in the Canada Basin.
Figure 8 shows the climatological summertime total stress curl and the Ekman transport and pumping in the Canada Basin.In the ice-covered ocean, the total stress acting on the ocean is a sum of wind stress in the open-water area (τ ao ) and ice-ocean stress in the ice-covered area (τ io ), τ = Aτ io + (1 − A) τ ao , where A is the sea-ice concentration (e.g.Yang 2006, Dong et al 2021).In the SICF experiment, the Canada Basin is characterized by a negative stress curl except near the coast, where it is positive (figure 8(a)).Correspondingly, the Ekman transport is offshore and is particularly strong in the southwestern Canada Basin, and the accompanying Ekman pumping is upward near the coast due to the Ekman transport divergence and is downward over most of the Canada Basin due to the Ekman transport convergence (figure 8(b)).In the SICF.WIND experiment, the negative stress curl and the associated offshore Ekman transport are overall weakened in the Canada Basin and there are some positive stress curl (upwelling) patches in the region north of 75 • N. The Ekman transport based on observations (see figure 9 in Yang (2006)) suggests that the transport pattern in the SICF.WIND experiment is somewhat more realistic than in the SICF experiment.Namely, the sea-ice momentum constraint by wind stress reproduces more realistic sea-ice velocities and further modifies the ice-ocean stress through the physics in the climate model.
Figure 9 shows the climatological summertime zonal-averaged vertical velocity and salinity depth sections in the Canada Basin.In the SICF experiment, the isohalines of 33-34.5 psu are deepened poleward and the 34.5 isohaline is located at a depth of 500 m, which is 100 m deeper than in the SICF.WIND experiment as in figure 6(b).The vertical velocity is downward in the upper 600 m north of 75 • N.Although the vertical velocity includes other effects besides Ekman pumping, the excess negative stress curl over the Canada Basin (figure 8) and thus the strong Ekman downwelling is thought to be related to the deepening of the isohalines.In the SICF.WIND experiment, the vertical velocity in the upper 200 m is weakly upward north of 75 • N, which is consistent with the positive stress curl (upwelling) patchy areas (figure 8), and the deepening of isohalines is alleviated compared to the SICF experiment.On the other hand, it is difficult to believe that the Ekman dynamics directly contributes to push the lower isohalines deeper.However, at least, the difference in the vertical velocity between two experiments reveals that the downward speed is weak at depths of 0-500 m north of 75 • in the SICF.WIND experiment.To clarify the mechanism for connecting between the Ekman dynamics and the lower isohaline structure, further analysis and/or modeling to isolate the other processes besides the Ekman dynamics are required.
From the above results, we speculate the reason for the improvement of halocline's vertical structure as follows: the negative wind and sea-ice stress curl over the Canada Basin, which are relatively strong in the experiments without the sea-ice momentum constraint, is weakened when constraining the sea-ice momentum, alleviating the deepening of not only the upper layer (∼200 m) via the Ekman dynamical process but also the lower layer (200-600 m), leading to a better representation of climatological ocean structure in the Canada Basin.

Conclusion
Using the climate model MIROC6, we conducted three sea-ice initialization experiments with 10-member ensembles for each.The aim of this study was to assess which initializations are most effective in reproducing the sea-ice area, concentration, and velocity and also to clarify how the difference in the reproduced sea-ice fields influences the reproduction of the climatological ocean state.The reproduction of sea-ice fields throughout the year was improved by constraining the sea-ice momentum by wind stress.Furthermore, its effects led to a more realistic reproduction of the climatological upper ocean states in winter and summer via physical processes within the climate model.Although biases still remain in the sea ice and the ocean states beneath the sea ice, the results suggest that constraining sea-ice motion by wind stress, which was first implemented in this study, is an effective method for initializing sea ice.
Notably, the SICF.OTSA.WIND experiment, which constrained sea-ice motion by wind stress together with ocean anomalies and sea-ice concentration assimilations, further reduced the winter to spring (March-June) sea-ice bias compared to the SICF.OTSA experiment (Kataoka et al 2020).This improvement implies the possibility of extending the predictable period for summer (September) sea ice using the climate models.To verify this, as the next step, we are planning to conduct ensemble prediction initialized with the above method.In addition, the impact of improved sea-ice reproduction is expected to emerge in the atmospheric fields in and/or beyond the Arctic region (e.g.Guemas et al 2016a), which was not investigated in this study.To detect the signal of an atmospheric response to the improved sea-ice fields, climate model simulations with large ensembles are required due to the large internal fluctuations of atmospheric circulation.Therefore, we intend to perform further simulations with not only the sea-ice momentum constraint but also with sea-ice concentration assimilation (i.e.SICF.WIND), and then compare the results with those of historical experiment to isolate the impact of only sea-ice reproducibility on the atmospheric response.

Figure 1 .
Figure 1.Climatological (36 year mean of 1979-2014) sea-ice velocity fields on (a) March and (b) September, using the Polar Pathfinder Daily 25 km EASE-Grid Sea Ice Motion Vectors, Version 4 available from the NSIDC (Tschudi et al 2019) and simulated with MIROC6 climate model (SICF, SICF.WIND, and SICF.OTSA.WIND).White and gray areas indicate ice-free and land.
g. Smedsrud et al 2013), which is mainly determined by two processes: oceanic heat transport from the North Atlantic (e.g.Årthun et al 2012, 2019, Nakanowatari et al 2014, Yamagami et al 2022) and atmospheric circulation (e.g.Sato et al 2014, Liu et al 2022).
(a)).In summer, the CORRs in the SICF.WIND and SICF.OTSA.WIND experiments are lower than those in the SICF.OTSA experiment (figure 4(a)), but the RMSEs in both experiments are reduced in July-October

Figure 6
Figure 6 and supplementary figure 8 show the climatological summertime (July-September; JAS) potential temperature and salinity in a trans-Arctic section from the Atlantic to the Pacific.In the Atlantic sector, a warm bias with a range of 1 • C-4 • C still remains south of 85 • N for all experiments (figure 6(a)), and also a low-salinity bias of ∼1 psu is found from the surface to a depth of 400 m north of 80 • N (figure 6(b)).In contrast, in the Pacific sector, the low-salinity water spreading near the surface is reproduced in the SICF.WIND and SICF.OTSA.WIND experiments.In addition, the location of the low-salinity water extending to a depth of 600 m, which was found in the experiments without the sea-ice momentum

Figure 4 .
Figure 4. (a) CORRs and (b) RMSEs (million km 2 ) in sea-ice area between model experiments (HIST, SICF, SICF.OTSA, SICF.WIND, SICF.OTSA.WIND, and OMIP2) and reanalysis (COBE-SST2) for each month.CORRs higher than 0.33 denote a statistical significance at the 95% level with 34 degrees of freedom based on a two-sided Student's t-test.Black dots indicate RMSE values smaller than the standard deviation for the observed detrended sea-ice

Figure 5 .
Figure 5. (a) CORRs and (b) RMSEs (%) in sea-ice concentration between model experiments (HIST, SICF, SICF.OTSA, SICF.WIND, SICF.OTSA.WIND, and OMIP2) and reanalysis (COBE-SST2) for March.(c), (d) Same as (a), (b) but for September.CORRs and RMSEs for regions where the standard deviation of the linearly-detrended sea-ice concentration is less than 3% in both the reanalysis data and simulations were masked by gray color, following Kataoka et al (2020).Stippling for CORR values indicates regions with a statistically significant value at the 95% level with 34 degrees of freedom based on a two-sided Student's t-test.Stippling for RMSE values denotes regions with values smaller than the standard deviation for the observed detrended sea-ice concentration.

Table 1 .
Experimental design for climate simulations used in this study.HIST: historical