Thermodynamic and dynamic contributions to the abrupt increased winter Arctic sea ice growth since 2008

Daily sea ice motion (Tschudi et al 2019a) and daily sea ice concentration (SIC) (Cavalieri et al 1996) products on a 25 km grid are obtained from the National Snow and Ice Data Center (NSIDC) and are used in the SIC budget analyses. Weekly sea ice age data on a 12.5 km grid from the NSIDC is also chosen to calculate the fraction of seasonal sea ice (or first-year ice). The ice age data is produced by using the sea ice motion product and tracking parcels in a Lagrangian sense (Tschudi et al 2019b). Due to the availability of ice age data starting in 1984, the analysis in this study is limited to the years 1985–2021.

To further examine the dominate feature of large scale atmospheric circulation, two monthly gridded datasets are used to link the atmospheric variability to the SIC, including the fifth-generation global atmospheric reanalysis (Hersbach et al 2020), and the National Centers for Environment Prediction/Department of Energy (NCEP/DOE) reanalysis (Kanamitsu et al 2002). Monthly 10 m surface winds and sea level pressure (SLP) are derived from these two datasets. Monthly sea surface height (SSH) and speed of sea surface ocean currents are derived from Ocean Reanalysis System 5 (C3S-CDS 2021), to study the oceanic background of the WSIG.

Following Holland and Kwok (2012), this study has diagnosed the concentration budget of WSIG (equation (1))

$$\begin{equation}\frac{{\partial C}}{{\partial t}} = - {\boldsymbol{U}} \cdot \nabla C - C\nabla \cdot {\boldsymbol{U}} + {\text{residual}},\end{equation} \tag{ 1 }$$

where $C$ is SIC and ${\boldsymbol{U}}$ is sea ice drift. The ice tendency ($\frac{{\partial C}}{{\partial t}}$) on the left-hand side is determined by the dynamic and residual processes. The residual term is mainly caused by thermodynamic melting/freezing and mechanical redistribution (Uotila et al 2014, Pope et al 2017). The dynamic process includes convergence/divergence ($- C\nabla \cdot {\boldsymbol{U}}$) and advection ($- {\boldsymbol{U}} \cdot \nabla C$). The former is mass-unconserving, including convergence-caused (forming ridges or rafts by floes collision) and divergence-caused (cracking apart into leads) ice thickening or area increasing, which is only a very small fraction compared to thermodynamics (Holland and Kimura 2016, von Albedyll et al 2022).

Although WSIG in volume reflect the actual ice growth, this volume increase is due to both the thickening of multiyear sea ice and the formation of seasonal sea ice. The concentration of WSIG can largely be regarded as the seasonal sea ice growth arising in open water after summer. Therefore, we choose to conduct the SIC budget analysis considering the climate effect of SIC will be more direct when the Arctic becomes ice-free in summer around the mid-2000s.

The concentration of WSIG (${C_{{\text{WSIG}}}}$) in every grid cell is defined as the difference between the maximum SIC in March (${C_{{\text{Ma}}{{\text{r}}_{\text{0}}}}}$) and the minimum SIC in the preceding September (${C_{{\text{Se}}{{\text{p}}_{ - 1}}}}$). This method can give us more details about WSIG, especially on both temporal and spatial scale in the entire Arctic. This definition comes from the Arctic climatological SIC seasonality which generally reaches a minimum in September and a maximum in the following March (Haine and Martin 2017). As Arctic sea ice freezes in October–February, this preconditional ice growth accumulates, reaching the maximum in March. Accordingly ${C_{{\text{WSIG}}}}$ can be approximated as follows:

$$\begin{equation}{C_{{\text{WSIG}}}} = {C_{{\text{Ma}}{{\text{r}}_{\text{0}}}}} - {C_{{\text{Se}}{{\text{p}}_{ - 1}}}}\sim \int_{{\text{Oc}}{{\text{t}}_{ - 1}}}^{{\text{Fe}}{{\text{b}}_0}} {\frac{{\partial C}}{{\partial t}}} {\text{d}}t,\end{equation} \tag{ 2 }$$

where the last item is calculated as the time integration of daily ice tendency in October–February. This approach uses the daily SIC and excludes grid cells below the 15% threshold because the daily ice motion has a high uncertainty there (Tschudi et al 2019b). Combining equations (2) and (1), we construct the ${C_{{\text{WSIG}}}}$ and obtain its dynamic and thermodynamic contributions.

To understand the WSIG variability in the particular regions, we define the area of WSIG as the sum of the area of each grid cell multiplied by the ${C_{{\text{WSIG}}}}$ in the selected region. The extent of first-year ice is the sum of the ice age grid cells equal to 1 year in the given region. The fraction of the first-year ice extent in the total sea ice extent, averaged in October–March, is combined to discuss the sea ice state of the WSIG.

The statistical significance is evaluated by the two-tailed student's test. The moving t-test method is used to detect the abrupt change in the WSIG variability.

Figure 1(a) shows the time series of the area of Arctic WSIG north of 60°N in the Arctic. The long-term mean area of Arctic WSIG has increased from 7.78 million km² during 1985–2007 to 8.81 million km² during 2008–2021. We use the moving t-test method to study the significant shift and the result is shown in figure S1. Spatially, the abrupt shift of WSIG occurs in the Arctic shelf edge zone (ASEZ) when comparing the distribution of WSIG during 1985–2007 and 2008–2021 (figures 1(e)–(g)). Because the WSIG accuracy is influenced by the SIC accuracy both in winter and summer, we mark the concentration contour at a value of 0.7 as a threshold for active WSIG when considering the largest SIC accuracy (15%, Cavalieri et al 1992). Since winter 2008, the outline of the active WSIG has extended poleward to the Arctic shelf edge (figures 1(e)–(g), black contours). This ASEZ, likewise, displays an apparent shift in the WSIG (figure 1(b)), contributing about 70% to the total change of Arctic WSIG, with a rapidly increasing trend of 0.028 million km² per year at a 95% confidence level during 1985–2007, turning into an insignificantly rising trend of 0.009 million km² per year during 2008–2021. In contrast, the southern Barents Sea and the Greenland Sea show reduced WSIG (figure 1(g), blue shading). Our results of winter sea-ice expansion in the ASEZ after winter 2008 are consistent with previous studies (Hao et al 2020).

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ASEZ is also a transitional region between multiyear ice and first-year ice. Compared to the pan-Arctic, the fraction of the first-year ice in the total sea ice in winter in the ASEZ has increased dramatically from 31% in 1985–2007 to 75% in 2008–2021 (figures 1(a) and (b), lower panels). The rapidly increasing fraction means that ASEZ has transitioned from a multiyear, ice-dominated regime to a seasonal, ice-dominated regime. As notable examples among the ASEZ, we focus on the northwest Beaufort Gyre (BG) and northern Laptev Sea. The reasons are that the northwest of BG has experienced great dynamic change and summer melt (figure 1(c), bottom panel; Maslanik et al 2011, Kwok 2018, Bi et al 2020), and the northern Laptev Sea is considered an 'ice factory' in winter due to its oversized ice production (figure 1(d); Cornish et al 2022). Their locations are shown as yellow rectangles in figure 1(g). Furthermore, they are regionally controlled by the main Arctic Ocean gyre system, the BG, the Transpolar Drift, and the Laptev Gyre. One point should be noted that, when comparing the trend of WSIG during two periods, 1985–2007 and 2008–2021, northwest BG has transitioned to a quasi-stable state, while northern Laptev Sea still retains an insignificant rising in the latter period. To understand this geographic difference, we further evaluate the combined effects of thermodynamic and dynamic processes in a regional scale.

To distinguish the relative thermodynamic and dynamics contributions to the WSIG variability, we diagnosed the concentration budget of Arctic WSIG from October to February during 1985–2021 (see section 3).

Figure 2 shows winter thermodynamic and dynamic growth in the Arctic WSIG. The residual term mainly represents the net concentration of WSIG from thermodynamic. Comparing the two periods of 1985–2007 and 2008–2021, the increased WSIG is dominated by thermodynamics in most parts of the Arctic seasonal ice zone (figures 2(b), (g) and (l)), particularly in Alaska and Siberia marginal seas (figure 2(l)). Notably, the thermodynamic-dominated pattern recedes near the central Arctic ice edge, for example, in the ASEZ (figure 2(l), black contours), and may have a source due to dynamics (figure 2(m), red shading).

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The dynamic term is divided into advection and convergence/divergence to illustrate the respective contribution of the dynamic process. Intensification of winter ice formation caused by strong divergence ($- C\nabla \cdot {\boldsymbol{U}}$, positive value) extends in a zonal band westward from the Canadian Arctic Archipelago to the Laptev Sea (figures 2(e) and (j)). While convergence results in a negative WSIG in most regions, including off the coast of Alaska and Siberia, Baffin Bay, and the central polar region. Advection ($- {\boldsymbol{U}} \cdot \nabla C$) counteracts WSIG only in areas of strong ice transport in concentration gradients, such as the Fram Strait, the Labrador Sea, and offshore Alaska (figures 2(d) and (i)). When comparing two periods, what stands out is the dominance of the divergent/convergent WSIG in the dynamic change (figures 2(m) and (o)). It reflects the maintenance of the newly formed ice and seem to be controlled by the strengthened sea ice drift of the anticyclonic BG, the Transpolar Drift, and the cyclonic Laptev Gyre (figures 2(c), (h) and (m) arrows).

It is complex to interpret the thermodynamics and dynamics in ASEZ because the divergent gain can be offset by a convergent loss in concentration in a chosen region. As examples of good dynamic consistency, the monthly climatologies of the SIC budget items in northwest BG (figure 3(a)) and northern Laptev Sea (figure 3(e)) are compared in detail. There are many similarities between northwest BG and northern Laptev Sea. For example, they both start to melt in April and freeze in September during 1985–2007 (figures 3(a) and (e), bold line). After 2008, rapid summer ice loss and fall ice growth were observed, most frequently occurring in July–August and October–November, respectively (figures 3(b) and (f), bold line). The enhanced thermodynamic process plays a key role (figures 3(b) and (f), light bars), as the melting creates a precondition toward a thinner ice cover that freezes delayed and fast (Stroeve et al 2014), allowing subsequent WSIG to occur in early winter (figures 3(b) and (f)). In contrast to northern Laptev Sea, a thermodynamic-dominated ice growth region, the increase in extent of northwest BG is partly due to thermodynamic growth limited in October and partly to positive dynamic growth from October to the end of winter (figures 3(a) and (e)).

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Considering these preconditions of each month in winter, the constructed area of WSIG variability in northwest BG and northern Laptev Sea during two periods (1985–2007 and 2008–2021) is shown in figures 3(c) and (g). The constructed area of WSIG index (red curves) and the area of WSIG index (lower panel of figures 1(c) and (d), black curves) achieve a good agreement with the correlation coefficitions large than 0.91, though there is some difference in amplitude. The northern Laptev Sea reveals a simultaneous growth in the thermodynamic contribution and the constructed area of WSIG index (R = 0.80, P < 0.05). Mean area of the thermodynamic growth increase significantly from 0.15 to 0.37 million km² in two periods (figure 3(g), yellow bars). Although thermodynamic growth has also strengthened in northwest BG, the dynamic contribution (mean area increased from 0.36 to 0.6 million km²) still predominantly facilitates significant intensification of WSIG in northwest BG, accounting for 84% of the abrupt rise in the area of WSIG. The probability distribution of daily ice motion divergence ($- \nabla \cdot {\boldsymbol{U}}$) is more even since winter 2008, distributing towards stronger divergence (convergence) in the northwest BG (northern Laptev Sea) (figures 3(d) and (h)). This supports our interpretations of ice dynamics related to more mobile seasonal ice convergence/divergence in an emerging new Arctic.

Taken together, these results suggest that although thermodynamic ice growth has concurrently dominated the abrupt shift in WSIG in most ASEZ regions, such as northern Laptev Sea, the enhanced dynamic growth, mainly ice divergence, contributes 84% of the significant expansion of WSIG in northwest BG.

The main feature of large-scale ice drift pattern of Arctic winter climatology during 1985–2021 is first explained (figures 2(c) and (h), arrows). Ice circulates as part of the BG and is transported out of the Arctic through the Fram Strait by Transpolar Drift. The two main wind-driven circulations are under the influence of two major meteorological systems, the Beaufort High and the Icelandic Low. The center of BG, characterized by a maximum in SSH and anticyclonic ocean currents, generally coincides with the overlying Beaufort High center, characterized by a maximum in SLP and anticyclonic winds, forcing the ice divergence/convergence via ocean-ice and air-ice stresses (Timmermans and Toole 2023).

Previous studies have indicated a significant amplification of the Beaufort High during summer and fall and attributed it to the intensification of the BG in the mid-2000s (Giles et al 2012, Moore 2012, Wu et al 2014, Regan et al 2019). Associated with the wind-driven spin-up of the BG, the gyre has expanded northwestward in recent decades (Armitage et al 2017, Regan et al 2019, Bertosio et al 2022). The mechanism of thermodynamic ice growth, attributed to an abrupt shift in the WSIG in the mid-2000s, has been studied in observations including the warming of the atmosphere (Ding et al 2017, Hao et al 2020, Wang et al 2023) and ocean (Timmermans 2015, Ricker et al 2021, Tsubouchi et al 2021, Zhong et al 2022). Hence, we focus on the dynamic change of WSIG as its responses to surface winds and oceanic forcings have increased significantly (e.g. the intensified ice convergence/divergence ($- \nabla \cdot {\boldsymbol{U}}$) in figures 3(g) and (h)).

To determine the large-scale circulation that are associated with the WSIG, we regressed the synchronous atmospheric and oceanic anomalies with the normalized area of WSIG index in ASEZ (figure 4(j), black line) during 1985–2021 (October–February). Corresponding to the increase of WSIG in ASEZ, the positive SSH anomalies and anticyclonic ocean currents at BG are pronounced in figure 4(c). Figure 4(b) shows the enhanced easterly winds anomalies along the Alaska coast and northwesterly winds anomalies across the Laptev Sea, which could speed up the BG and Laptev Gyres. We also regressed the preceding summer (June–September) SLP anomalies with the normalized area of WSIG index in ASEZ during 1985–2021 (October–February, figure 4(a)). As expected, a positive SLP anomaly near the Canadian Arctic Archipelago extending from Greenland to the Beaufort Sea and a negative SLP anomaly overlying the Barents Sea is conducive to enhancing the anticyclonic BG and cyclonic Laptev Gyre in the following winter. Thus, these anomalous patterns indicate the enhanced ice advection off the Akaska coast upstream and the divergence of thinner and more mobile ice packs towards the northwest extent of BG. Meanwhile, the strengthened convergence in northern Laptev Sea and the compensated convergence by newly formed ice in the nearby shallow waters are prevalent.

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This persistent Beaufort High pattern is one of the leading modes of atmospheric circulation, which can be defined as the second leading empirical orthogonal function (EOF) mode of the Arctic and contributes 11.61% of the total variance from 1984 to 2020 (figures 4(d) and S2). The time series of the summer Beaufort High mode exhibited a strengthening during 2005–2012 (figure 4(j)), consistent with the topic of locally strengthened summer anticyclonic circulation mode near the Canadian Arctic Archipelago (figure 4(g); Wang et al 2023). The correlation coefficient of the normalized Beaufort High index with the following normalized area of WSIG index in ASEZ is 0.54 (P < 0.05) during 1984–2020. While the first leading mode is the so-called Arctic Oscillation, it insignificantly correlates to the normalized area of WSIG index (figure S2, R = $-$0.22). Thus, the decadal change of the summer Beaufort High is speculated to be linked to the abrupt rise of WSIG over the ASEZ. To provide more evidence, we regressed the atmospheric and oceanic circulation during October–February to the preceding summer (June–September) Beaufort High index during 1985–2021 (figures 4(e) and (f)). As expected, the SSH and ocean currents response to summer Beaufort High variability shows general resemblances to these respondence to WSIG variability in ASEZ, but with half of the magnitude (figures 4(c) vs (f)). One exception is the winter surface wind pattern (figures 4(b) vs (e)). This suggests a short memory of the atmosphere and confirms the lasting memory of summer winds on winter ice through the ocean's memory (Wang et al 2021). We also use NCEP/DOE data sets to examine the SLP leading mode and quite similar results are shown in figure S3.

Considering the background change in Arctic climatology, we displayed the composite differences of atmospheric and oceanic circulation between the 2008–2021 and 1985–2007 periods (figures 4(g)–(i)). By comparing three columns of figure 4, we found good agreement in spatial patterns, suggesting that the strong summer Beaufort High and anticyclonic winds (figure 4(g)), as well as the following wind-driven spin-up of BG (figure 4(i)) after 2008 may provide a beneficial background for the abrupt increase of WSIG.