Nonstationary thermodynamic and dynamic contributions to the interannual variability of winter sea ice growth in the Kara–Laptev Seas

The Kara–Laptev Seas (KLS), known as the ‘Ice Factory of the Arctic’, witnesses rising instead of falling winter sea ice growth (WSIG) under the shrinkage of Arctic ice. However, knowledge of the large year-to-year variation is still unclear. Combining a seasonal ice concentration budget, a composite analysis, and a typical case study, we study both the interannual variability of WSIG in the KLS and the associated air-sea forcings during 1985–2021. Results quantitatively reveal that, during 1985–2021, thermodynamic melt in the melting season (April–August) contributed 80.3% to the interannual ice loss difference and promoted the subsequent WSIG by the recovery mechanism in the KLS. This consistent thermodynamic melt is caused by the strengthened summer Beaufort High, transporting heat and introducing a locally positive ice-albedo feedback. However, since 2010, the dynamic growth during the freezing season (October–February) has increasingly stimulated the WSIG. Typical cases in 2013 and 2017 indicate that the overlying anticyclonic atmospheric regime restricts the ice drift from the KLS and contributes to the dynamic growth of 41.6% of the WSIG difference, while the turbulent-heat-induced thermodynamic growth in winter is down to 58.4%. In short, we reveal an unstable relationship between the summer ice loss and the subsequent WSIG under the background of Arctic warming. Our study points out that the distinct dynamic ice growth driven by surface winds or ocean currents during the freezing season is likely to increase in the near future, with thinner and more mobile seasonal ice predominating in the Arctic.


Introduction
Over the past 40 years, the Arctic has witnessed a continuous decline in sea ice extent, which leads to more open water in summer and thinner as well as younger ice in winter (Comiso et al 2008, Polyakov et al 2012, Jeffries et al 2013).Sea ice concentration (SIC) exhibits significant seasonal variation, reaching its peak in March and its lowest point in September during a boreal year.Although there are ongoing losses in the Arctic in all seasons, they are more severe in September (about −25% decade −1 ) than in March (about −15% decade −1 ) (Onarheim et al 2018, Stroeve andNotz 2018).These seasonal trends suggest a boost of winter sea ice growth (WSIG) in recent years to compensate for its summer loss, which is expected to last until the mid-21st century (Stroeve and Notz 2015, Petty et al 2018, Ricker et al 2021).
A recent study has indicated a new era of boosting WSIG and a strengthened Arctic ice recovery, which is associated with the abrupt shift of intensified summer Beaufort High since 2008 (Yi et al 2024).According to their study, the WSIG represents the net accumulation of SIC during an entire freezing season.In this regard, the interannual variability of Arctic WSIG during the freezing season (October-February) is a good indicator of the interannual variability of ice growth.However, on the interannual timescale, the influencing factors of Arctic WSIG that should receive more attention still remain unclear.Benefiting from its definition, WSIG can better capture cumulative climate effects than the SIC used to be adopted, as the SIC can only describe ice cover in a given month.Alternatively, the WSIG could potentially reflect local heat exchange in the sea-ice-air interfaces, which profoundly affects the climate of the local Arctic and mid-high latitudes (Francis et al 2009, Vihma 2014, Wunderling et al 2020).
The Kara-Laptev Seas (KLS, 70 • N-83 • N, 55 • E-150 • E) has the largest sea ice growth rate (Cornish et al 2022).In winter, southerly winds and offshore ocean currents prevail in this area, transporting locally newly formed sea ice north into the Arctic central basin.The ice loss in other areas caused by the Transpolar Drift is then compensated (Rigor andColony 1997, Alexandrov et al 2000).Thus, KLS is known as the 'ice factory' of the Arctic (Reimnitz et al 1994).The newly formed sea ice in the KLS keeps a continuous positive trend (Yi et al 2024), making the KLS an area dominated by seasonal ice that cannot survive a summer (figure 1(b)).Thus, WSIG in the KLS has large interannual variability compared with in other Arctic areas (figure 1(c)).These features are consistent with a new Arctic covered by thinner, seasonal sea ice along with increasing WSIG, as described above, making KLS a potential hotspot for future sea ice development.
Given the importance of the Arctic WSIG, some studies have examined its linear long-term trend, decadal variability, and mechanisms (Hao et al 2020, Ricker et al 2021, Zhao et al 2023).Previous studies also revealed that ice growth can be understood from thermodynamic and dynamic processes.Thermodynamic factors such as cold sea surface, as well as dry and cold air advection, can both contribute to local sea ice growth (Onarheim et al 2014, Polyakov et al 2017, De Steur et al 2023).Dynamic factors such as near-surface winds and ocean currents (e.g.Beaufort Gyre and Transpolar Drift) may lead to ice thickening or area increase, as well as spatial redistribution (Kimura 2004, Heorton et al 2018).Particularly, Tietsche et al (2011) proposed a sea ice recovery mechanism, suggesting that the preceding intensified ice melt is beneficial to the following increase in WSIG.Focusing on the KLS, Cornish et al (2022) performed regional projections using a CESM-LE model and attributed the linear trend of WSIG to internal variability of models and external forcings such as snow depth and September sea surface temperature (SST).They emphasized the decadal variability of WSIG in the KLS, but its interannual variability of WSIG and the driving forces remain entangled.
In this study, we aim to examine the interannual variability of WSIG in the KLS by quantitatively diagnosing the thermodynamic and dynamic contributions.We also seek key influencing factors including air-sea heat exchange and dynamical processes in terms of seasons, as these external forcings have longlasting effects on ice growth.The rest of the paper is arranged as follows.Section 2 describes the data and methods used in the study.Section 3 introduces the spatiotemporal features of interannual variability of WSIG in the KLS.Thermodynamic and dynamic contributions to the WSIG during the melting and freezing seasons are analyzed separately.Finally, the main conclusion and discussion are presented in section 4.

Data and methods
In this study, we use daily SIC (Cavalieri et al 1996), daily sea ice motion (Tschudi et al 2019a), and weekly ice age data (Tschudi et al 2019b) provided by the National Snow and Ice Data Center (NSIDC).Monthly atmospheric circulation reanalysis data is provided by the National Centers for Environmental Prediction/the National Center for Atmospheric Research (NCEP/NCAR) (Kalnay et al 1996) and the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) (Hersbach et al 2020), involving geopotential heights, 10 m wind, 2 m air temperature, specific humidity and net heat fluxes.The weekly SST is derived from the National Oceanic and Atmospheric Administration (NOAA) (Reynolds et al 2002).Analysis in this study is constrained to 1985-2021 since ice age data is available from 1984.
The phase-consistent pattern of WSIG is the first empirical orthogonal function (EOF) leading mode in the KLS, accounting for 30.61% of the total variance (figure S1).Therefore, the KLS has been chosen as a representative for further analysis.Figure 1(d) shows the annual cycle of the monthly increment of SIC since the beginning of the freezing season (SIC mon -SIC Sep ) averaged in the KLS from 1985 to 2021 (blue line).Note that we define the preceding April (ice starts to decrease) to March of the current year as a whole annual cycle, covering the melting and freezing seasons of sea ice in sequence.For example, the 2013 sea ice evolves from April 2012 to March 2013.Therefore, according to Yi et al (2024), we have, (1) A WSIG index is defined as the detrended, standardized, and area-weighted averaged WSIG in the KLS from April 1984 to March 2021.
To determine the thermodynamic and dynamic contributions to the ice growth, we follow the ice concentration budget method in previous studies (Holland andKwok 2012, Uotila et al 2014), where C is SIC and U is sea ice motion.Dynamic processes contributing to SIC tendency ( ∂C ∂t ) include advection (−U • ∇C) and convergence/divergence (−C∇ • U).The residual term is approximately regarded as a thermal term.
Previous studies have worked on long-time integrals for seasonal analysis (Lecomte et al 2016, Nie et al 2022).Inspired by them, we reorganize SIC variation by integrating it from October to February to separate the thermodynamic ice growth and dynamic ice growth quantitatively (Yi et al 2024), We end the integral in every February to ensure each grid in the KLS is undergoing an ice increase simultaneously.The approximation is acceptable because ice growth is close to stopping in March.And the plausibility of the above approximation is also confirmed by the similarities in the spatial pattern of WSIG and the constructed pattern of the budget terms (figure S2).Similarly, the reconstructed budget term for ice melt in the preceding summer is defined as follows.The approximation is also acceptable because ice cover has mostly been replaced by open water in the KLS in September.
Ice melt in the preceding summer To quantify local dynamic and thermodynamic processes in the KLS for the SIC variation, we calculate their contributions separately, following Lukovich et al (2021), where D = −U • ∇C − C∇ • U refers to dynamic processes, and T = residual represents thermodynamic processes.The relative fraction with a value of 0.5 indicates equal influences of dynamic and thermodynamic processes.

Spatiotemporal features of interannual variability of the WSIG
Figure 1(a) shows the climatological spatial pattern of the Arctic WSIG during 1985-2021.The WSIG predominantly lies around Arctic marginal seas with a value close to 100%, while it exists less in the central Arctic with a value less than 30%.Higher interannual variation of WSIG can be found in the marginal seas along the coasts of the Eurasian continent, whose detrended standard deviation is more than 30%.In contrast, insignificant ice growth is mainly located in the Western Hemisphere, with a detrended standard deviation of less than 10% (e.g.Northern Canadian Arctic Archipelago, figure 1(c)).We show the monthly increment of SIC in the black sector, which accumulates from fast to slow and finally hits its maximum at 72% in March, namely the WSIG in the KLS (red dot in figure 1(d)).
To address the interannual variation of WSIG in the KLS, we performed a composite analysis of WSIG anomalies.First, high and low WSIG years are defined by using the criteria of 0.5 standard deviation of the WSIG index mentioned above, with 13 high WSIG years and 11 low WSIG years, respectively (figure 2(a)).Results of higher criteria also show good agreement in spatial patterns (e.g.0.8 standard deviation, figures S3 and S4).
Spatially, composite anomalies of the WSIG in the KLS during 1985-2021 are shown in figures 2(b)-(g).In high WSIG years, the WSIG in the KLS extends from the continental shelf to the Arctic basin northwards (figure 2(b)), while in low WSIG years, the newly formed sea ice grows mainly close to the coastline (figure 2(c)).When compared to the climatological mean (figure 2(d)), the spatial maps exhibit an almost symmetric anomaly in figures 2(e) and (f), with one exception that there is significantly less ice growth than normal in the western Kara Sea.Overall, newly formed covers more surface area in the Arctic basin in the positive WSIG anomalous years, at a 90% confidence level (figure 2(g)).

Nonstationary relationship between the WSIG and sea ice melting or freezing
Since ice growth is seasonally dependent, to further investigate the seasonal causes of the interannual WSIG differences in the KLS, we calculate the regional averaged 9 year sliding correlation between the WSIG, the SIC in March (SIC Mar ) and in September (SIC Sep ) during 1985-2021 (figure 2

Consistent thermodynamic contribution of interannual variability of the WSIG during the melting season
The close linkage between the WSIG and SIC Sep in the KLS inspired us to further examine the driving of the interannual variability of the WSIG.Therefore, we performed an ice concentration budget analysis in the melting season (April-August) during 1985-2021 equation (5).
Figure 3 shows the composite results of the ice concentration budget analysis and relevant atmospheric and oceanic circulation anomalies over the KLS during the melting season in high and low WSIG years from 1985 to 2021.Ice melt occurs primarily along the Eurasian continental shelf, however, it expands toward higher latitudes in high WSIG years (figures 3(a) and (b)).The difference in ice loss between high and low WSIG years in the KLS is more than 30%, which can be attributed to the intensification of thermodynamic melting (figures 3(c) and (f)), with 80.3% contribution to the interannual ice loss difference equation ( 7).Meanwhile, during the melting season, the floe ice diverges in the northern Kara Sea but converges in the western Laptev Sea (figures 3(g) and (h)).Composite difference of dynamic items shows positive SIC anomalies in the northern Kara Sea (figure 3(i)), suggesting that an anomalous convergence accumulates the floe ice (figure 3(i), or −C∇ • U, figure S5).And in the west of the Laptev Sea, a stronger northward advection stimulates a stronger meridional ice drift in the KLS (−U • ∇C, figure S5), partially offsetting the SIC decline caused by thermal melt.Dynamic forcing contributes 19.7% to the interannual ice loss equation ( 6).
Previous studies have indicated a recovery mechanism of ice melt (Tietsche et al 2011).On one hand, it recovers through restricting the heat transport from lower latitudes to the pole by the excessively stored ocean heat.On the other hand, this mechanism encourages redundant heat-releasing by outgoing longwave radiation in the early winter (figure S6(a)), allowing ice to recover after experiencing a stronger melting season, served as an explanation for the negative correlation between WSIG and SIC Sep in the KLS.
Following this recovery mechanism, we further performed a composite analysis of the atmospheric and oceanic circulation over the KLS during the melting season of 1985-2021.As expected, the composite anomalies favor thermodynamic and dynamic ice loss (compare figures 3(f), (i) and (j)).For example, on the sea surface of the KLS (figure 3(j), bottom panel), increased downward net heat flux (dominated by the downward shortwave radiation flux, shading), reduced sea surface albedo (not shown), and warm SST anomalies (contours) are found during the melting season, resulting in an ice-albedo positive feedback to accelerate ice melting (Curry et al 1995).Meanwhile, overlying the Arctic basin (figure 3(j), middle and top panels), a significant positive geopotential height anomaly from 500hPa to the surface is observed, implying a quasi-barotropic vertical structure over the Canadian Archipelago-Beaufort Seas, that is, an anomalous westerly center of the Arctic polar vortex and a strengthened summer Beaufort High.This positive anomalous sea level pressure (SLP), together with the negative SLP anomalies over the Barents-Kara Seas enhanced the southerly wind anomalies prevailing in the KLS and led to warm and humid air from the Eurasian continent northwards (figures S6(b) and (c)).In general, these background atmospheric circulation anomalies intensify ice melting and northward ice transporting in the KLS (figure 3(k)).

Distinct dynamic contribution of interannual variability of the WSIG during the freezing season since 2010: a study of typical cases
From 2010 to 2021, it is derived that the interannual variability of WSIG in the KLS could be positively related to the unstable growth in the freezing season (October-February).Why has their relationship become stronger since 2010?What are the interannual forcings and their contributions?Because of the limited observational samples, we further performed a typical case study by estimating the WSIG in an extremely high WSIG year (2013) and an extremely low WSIG year (2017) since 2010.
Likewise, an ice concentration budget analysis is applied to examine the thermodynamic and dynamic processes during the freezing season equation (4).Diagnose result shows that more than 30% of regional increases of WSIG appear in 2013 than in 2017, which are mainly observed in the northern KLS (figure 4(c).Among them, thermodynamic growth accounts for 58.4% while dynamic growth accounts for 41.6% of the WSIG difference between the two years (equations ( 6) and ( 7), figures 4(f) and (i)).This comparable thermodynamic and dynamic growth emphasizes the dynamic contribution because it only accounts for about 26.5% during the freezing season To deeply understand the distinction above, we estimate the atmospheric circulation differences during the freezing season between 2013 and 2017.The result is conducive to the thermodynamic and dynamic ice growth (compare figures 4(f), (i) and (j)).For example, during the freezing season, on the sea surface of the northern Laptev Sea (figure 4(j), bottom panel), strengthened upward net heat flux (dominated by the upward turbulent flux, shading), warm SST anomalies (contour), and more open water (not shown) are found in 2013 (Parkinson and Comiso 2013, Zhang et al 2013, Jeong et al 2022), echoing the recovery mechanism and consistent thermodynamic growth.However, it should be noted that an anticyclonic anomaly from 500 hPa to the surface controls the polar atmospheric circulation (figure 4(j), middle and top panels), favoring an anticyclone wind-driven ice drift (not shown) and a southwestward ice motion anomalous in the northern KLS (arrows).Thus, due to the long-lasting anticyclonic anomaly background, the anomalous along-shore ice convergence helps maintain more ice in the KLS in 2013 (figure 4(k)).
It is not only a case study in 2013, but an example reflecting the more flexible and more mobile ice in the freezing season the background of a looser ice pack in the KLS since 2010, especially near the ice margins (Li et al 2014, Wagner et al 2021).Therefore, contributions of dynamic growth to the WSIG increase as thinner ice may have a stronger response to anomalous surface wind forcing, especially in winter (Zhang et al 2012, Zhang et al 2021).

Discussion and conclusion
Using observations and reanalysis data, the interannual variation of Arctic WSIG and its associated atmospheric and oceanic forcings are investigated during 1985-2021.We conclude that the interannual variability of the WSIG is primarily active in the KLS.Moreover, we emphasize the unstable thermodynamic and dynamic contributions to the year-toyear variation of the WSIG in the KLS by diagnosing its seasonal SIC budget.During 1985-2021, the thermodynamic melt is the primary factor driving increasing ice loss during the melting season, affected by the strengthened summer Beaufort High, transporting heat to intensify summer melt, and introducing a locally positive ice-albedo feedback.It contributes 80.3% to the interannual ice loss difference and promotes the subsequent expansion of WSIG by the recovery mechanism in the KLS.While buried dynamic growth during the freezing season outstands from 2010 to 2021.Typical cases in 2013 and 2017 indicate that the overlying anticyclonic atmospheric regime in the Arctic restrains ice exportation from the KLS, contributing 41.6% to the WSIG difference.Thermodynamic growth also accounts for 58.4% of the case difference by increasing locally upward turbulent heat release.Results calculated by ERA5 also show good agreement (figures S8-S10).
Recent studies have revealed the summer ice loss since 2012 and examined the related weakened summer atmospheric forcing in the last decade (Ding et al 2017, Francis andWu 2020).Besides, the abrupt decline of the Arctic summer ice extent occurred since 2008 (Comiso et al 2008, Stroeve et al 2012).In this study, the no longer falling and low-keeping floe ice in September KLS since around 2010, as well as the unstable and rising WSIG (figure 2(i)) not only confirms the above studies but also points out this new ice-loss slowdown state may reduce linkage of summer processes with WSIG.Accordingly, we can reasonably speculate that the ice dynamic growth driven by surface winds or ocean currents during the freezing season is likely to increase in the near future, with the dominance of thinner and mobile seasonal ice in the Arctic (Park et al 2018).
Overall, the interannual variability of WSIG in the KLS is consistently controlled by the thermodynamic growth as well as the increasingly important dynamic growth, which may not yet be stopped by the general Arctic warming during the recent decade.The interannual forcings of WSIG unveiled in this paper depend on the local atmospheric variabilities, contributing to understanding its future changes in the context of increasing Arctic WSIG.Further work is needed to fully comprehend the external forcing of WSIG, such as the remote regulation from the tropical and mid-latitudes.

Figure 1 .
Figure 1.Spatial distribution of (a) the climatological mean of the WSIG (%), (b) the climatological mean of ice age (yr), and (c) the interannual variability of the WSIG (%) in the Arctic during 1985-2021.The black dashed sectors indicate the location of the Kara-Laptev Seas (KLS).(d) The seasonal cycle of the sea ice concentration (SIC, unitless, black line) and accumulated increment of SIC (blue line) averaged in the KLS during 1985-2021.The shadings represent the range of one standard deviation.The red dot denotes the long-term mean WSIG value in the KLS from 1985 to 2021.
(h)).The results show that the WSIG is insignificantly correlated with SIC Mar and reverses from negative to positive around 2010, thereafter exhibits rising positive correlation from 2010 to 2021.From 2010 to 2021, their Pearson correlation coefficient equals 0.78 (p < 0.01).On the contrary, over this period the Pearson correlation of WSIG and SIC Sep has weakened slightly to −0.78 (2010-2021, p < 0.01), despite WSIG has a steady negative correlation with SIC Sep from 1985 to 2021 and their Pearson correlation is −0.99 (1985-2009, p < 0.01).These results indicate that sea ice melting may dominate the interannual variability of WSIG in the KLS over the entire period of 1985-2021, but after 2010, the hidden contributions of freezing season processes started to stand out.This nonstationary relationship between the WSIG and sea ice melting or freezing should be considered in the climate context.The time series of SIC Mar and SIC Sep with linear trend have been shown in figure 2(i).It reveals a wider open water in September (figure 2(i), red line) and a not fully icebound surface in March (blue line) since around 2010 in the KLS.The gradually synchronized fluctuation and closer amplitude in SIC Mar and WSIG support our interpretations of the interannual variability of WSIG related to unstable growth in the freezing season since 2010.

Figure 3 .
Figure 3. Ice concentration budget terms in the KLS during the melting season (April-August, 1985-2021).(a), (d) and (g) are respectively the total summer ice melt, thermodynamic melt, and dynamic melt in high WSIG years.Similarly, (b), (e), and (h) are the corresponding terms in low WSIG years.(c), (f) and (i) are the corresponding terms of differences between high and low WSIG years.Gray contours denote 200 m isobath.Black arrows show mean ice drift during the melting season.(j) shows the ice melt mechanism by indicating the related air-sea circulation anomaly between high and low WSIG years.Bottom panel: net shortwave radiation flux anomaly (w • m −2 , upward positive, shaded), positive sea surface temperature anomaly ( • C, contours) and ice drift anomaly (cm • s −1 , black arrows) in the KLS; Middle panel: sea level pressure anomaly (mb, shaded) and 10 m wind anomaly (m • s −1 , gray arrows); Top panel: 500 hPa geopotential height anomaly (m, shaded) overlying the KLS.Black dots indicate anomalies at a 90% confidence level.

Figure 4 .
Figure 4. Ice concentration budget terms in the KLS during the freezing season (October-February) in 2013 and 2017.(a), (d) and (g) are respectively the total winter ice growth, thermodynamic growth, and dynamic growth in 2013.Similarly, (b), (e), and (h) are the corresponding terms in 2017.(c), (f) and (i) are the corresponding terms of differences between 2013 and 2017.Gray contours denote 200 m isobath.The black arrows show ice velocity averaged during the freezing season.(j) shows relevant ice growth mechanisms by indicating the related air-sea circulation anomalies between 2013 and 2017 (2013 minus 2017).Bottom panel: net turbulent heat flux anomaly (w • m −2 upward positive, shaded), positive sea surface temperature anomaly ( • C, contours) and ice drift anomaly (cm • s −1 , black arrows) in the KLS; Middle panel: sea level pressure anomaly (mb, shaded) and 10 m wind anomaly (m • s −1 , gray arrows); Top panel: 500 hPa geopotential height anomaly (m, shaded) overlying the KLS.Black dots indicate anomalies at a 90% confidence level.
sea ice growth since 2008 Environ.Res.Lett.19 014048 Zhang J 2021 Recent slowdown in the decline of Arctic sea ice volume under increasingly warm atmospheric and oceanic conditions Geophys.Res.Lett.48 Zhang J, Lindsay R, Schweiger A and Rigor I 2012 Recent changes in the dynamic properties of declining Arctic sea a model study Geophys.Res.Lett.39 Zhang J, Lindsay R, Schweiger A and Steele M 2013 The impact of an intense summer cyclone on 2012 Arctic sea ice retreat: cyclone impact on 2012 arctic sea ice Geophys.Res.Lett.40 720-6 Zhao J, He S, Fan K, Wang H and Li F 2023 Projecting wintertime newly formed Arctic sea ice through weighting CMIP6 model performance and independence Adv.Atmos.Sci.accepted (https://doi.org/10.1007/s00376-023-2393-2)