Introduction

Arctic sea ice plays a crucial role in the climate system due to its ability to insulate exchanges of radiation, heat, momentum, and moisture between the atmosphere and ocean. In recent decades, the rapid decline of Arctic sea ice and the accelerated warming of the Arctic atmosphere (termed Arctic Amplification), have emerged as prominent features of the global climate system1,2. The reduction of Arctic sea ice, especially in the Barents-Kara Seas, usually leads to an intensification of the Ural blocking and the East Asian trough in boreal winter. At the surface, this manifests as a strengthening of the Siberian High and the Warm Arctic Cold Eurasian (WACE) pattern3,4,5,6,7,8,9,10,11. The tropospheric pathway has been proposed to be an important mechanism in linking the Arctic and the mid-latitude. In autumn with less sea ice, more heat is released into the atmosphere, increasing atmospheric thickness over the Arctic. This results in a reduction in the zonally averaged geopotential height gradient, thereby weakening the westerlies in the mid-latitudes. The weakening of the zonal flow in turn leads to a slower propagation of Rossby waves, favoring the occurrence of more quasi-stationary blocks which affects the mid-latitudes12,13,14,15. The storm track potentially acts as another tropospheric bridge connecting the Arctic and mid-latitude regions by redistributing the momentum, moisture, and heat flux16,17. The Siberian storm track is located in the central Eurasian continent and is also geographically close to the WACE pattern and the Siberian High18. The Arctic warming may influence the Siberian storm track by modifying the meridional temperature gradient and mid-latitude jet. However, how the changes in the Siberian storm track caused by Arctic warming affect mid-latitude climate remains unknown.

Given the complexity of the climate effects of Arctic sea ice, there is still much debate about its impact19,20,21,22,23. Establishing the dynamical causal relationship between sea ice melt and its influence on mid-latitudes has to rely on numerical simulation experiments. However, there is a lack of consensus on the impacts of reduced sea ice in model simulations. Atmospheric responses exhibit great uncertainties and span a wide spectrum from no response to warming and cooling of mid-latitudes24,25. This uncertainty hinders our deeper understanding of the mechanisms connecting the Arctic and mid-latitudes. Previous studies proposed that the background conditions26,27, the nonlinear processes28,29,30, the snow cover31,32,33, the summer circulation condition34,35,36, the low-frequency variability37,38, and the sea ice-ocean coupling relationship27,39,40 all contribute to the sea ice influence. Smith et al.41 have provided a systematic overview of these causes and introduced the Polar Amplification Model Intercomparison Project (PAMIP), aiming to understand and reduce the model spread.

The surface energy budget after sea ice reduction is a vital physical process in model simulations. The upward turbulent heat flux (THF, sensible heat flux, and latent heat flux) after sea ice loss can warm and moisten the atmosphere, leading to large-scale atmospheric circulation anomalies. Blackport et al.19 contended that the sign of the sea ice surface THF anomalies provide physical insight into the predominant direction of ice-atmosphere interaction. Jiang et al.42 found that only the sea ice decline events characterized by anomalous upward THF have the potential to influence the atmosphere. They suggest, when designing numerical experiments, it would be best to use sea ice concentration (SIC) anomalies only from those periods when the anomalous THF is upward. Cohen et al.43 set a functional form of the surface heat transfer in the Barents-Kara Seas and Chukchi Sea altering the heat flux by 70 W/m2. In this way, they were able to amplify the model responses to sea ice reduction and thoroughly investigate the effects of diminished sea ice on the stratospheric polar vortex. However, this method has limitations as the functional form of the surface heat flux is only an idealized scenario and does not represent the real situation of sea ice. The uncertainty in model surface energy budget likely stems from THF. To reduce the uncertainty in model response to sea ice forcing, this study designs a novel THF forcing experiment that incorporates reanalyzed sea ice surface THF data to improve the modeled THF. By comparing the THF forcing experiment with the SIC forcing experiment, we elucidate the role of Arctic sea ice surface THF in simulating the Arctic-Eurasian connection. The simulation error of THF over sea ice regions may be one of the reasons why the model cannot capture the Arctic-Eurasian connection. In this paper, unless otherwise stated, autumn refers to September-October-November (SON), and winter refers to December-January-February (DJF), and spring refers to March-April-May (MAM).

Results

THF over the Arctic sea ice surface

The Specified Chemistry Whole Atmosphere Community Climate Model Version 4 (SC-WACCM4) is utilized for conducting experiments. To explore the different roles of SIC and THF in simulating the Arctic–Eurasia connection, three large-ensemble model experiments are designed. The control run (CTRL) spans 100 years, using prescribed climatological SIC and sea surface temperature (SST) averaged from 1982 to 2001, while other forcings are held constant at the levels of the year 2000. The light SIC forcing experiment (LSIC) utilizes the reduced Arctic SIC averaged from 2005 to 2015. The turbulent heat flux forcing experiment (LTHF) is conducted under the same boundary conditions and external forcings as LSIC, but the model-calculated THF over Arctic sea ice is replaced with the European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) THF data (averaged from 2005 to 2015) using a nudging method (see “Methods” and Supplementary Fig. S1). Given the large spread in reanalysis THF data, we initially assess the annual variability and spatial distribution of THF from four different reanalysis datasets (the Modern-Era Retrospective analysis for Research and Applications Version 2, MERRA2, the National Centers for Environmental Prediction Reanalysis 2, NCEP2, the Japanese 55-year Reanalysis, JRA55, and ERA5). Our analysis reveals pronounced seasonal variations in turbulent heat transport across the Arctic sea ice boundary (Supplementary Fig. S2), with minimal transfer during the warm season and maximal transfer during the cold season. In three out of the four datasets, the turbulent heat transport is consistently upward throughout the year, indicating that the surface warms and moistens the atmosphere. All four reanalysis datasets show upward THF in the Arctic marginal seas during winter (Supplementary Fig. S3). However, there is inconsistency in the central Arctic Ocean (Supplementary Fig. S3), with the ERA5 and MERRA2 datasets showing upward THF, while the NCEP2 and JRA55 datasets indicate the opposite, highlighting the considerable uncertainty in these regions. Kong et al.44 compared the ERA5 THF data with Arctic expedition data from 2 buoys and 11 cruises, affirming the relatively high quality of the ERA5 dataset. Renfrew et al.45 evaluated the ERA5 surface fluxes over the Iceland and Greenland Seas using observations from meteorological buoy, research vessel, and research aircraft. They suggest that ERA5 performs well and that the biases are less than the observed standard deviations for THF. Based on these analyses, we believe that the ERA5 data accurately reflects the THF exchange between sea ice and the atmosphere and is currently a suitable dataset. Hence, ERA5 THF data is predominantly used in our simulations, complemented by MERRA2 data for additional validation and comparison.

During autumn, both LSIC and LTHF experiments exhibit positive THF anomalies within the Arctic margin areas, particularly the Barents-Kara Sea, Laptev Sea, East Siberian Sea, Beaufort Sea, and Baffin Bay (Fig. 1a, d). This is in line with the autumn sea ice reduction in these regions. In winter and spring, the LSIC experiment reveals that the positive THF anomalies are confined to the Barents-Kara Sea, Okhotsk Sea, and northern Canada (Fig. 1b, c). However, the LTHF experiment reveals a distinct pattern. Positive anomalies occupy the entire Arctic Ocean (Fig. 1e, f), indicating that the integration of reanalysis data greatly enhances the THF transfer from the sea ice surface to the atmosphere by approximately 20 W m−2. In Fig. 1, compared to the LSIC experiment, the LTHF experiment shows an increase about 10 W m−2 in THF over the central Arctic region, which is approximately 100% of the ERA5 climate value (Supplementary Fig. S3a, e). Consequently, surface air temperatures (SAT) experience marked amplification (Supplementary Fig. S4). In the LTHF experiment, the average SAT across the boundary of the Arctic sea ice is 3.8 K higher than that in the CTRL experiment. In contrast, the LSIC experiment shows only a 1 K increase compared to CTRL. The findings shed light on the underestimation of Arctic warming in the LSIC experiment.

Fig. 1: THF response (perturbation experiment minus control experiment) across the boundary of the Arctic sea ice.
figure 1

a autumn THF response (W m−2) in the LSIC experiment. b winter THF response (W m−2) in the LSIC experiment. c spring THF response (W m−2) in the LSIC experiment. d−f same as a−c, but for response in the LTHF experiment. The black solid lines denote 1% SIC. Stippling indicates anomalies at the 95% confidence level according to the two-tailed Student’s test.

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Atmospheric circulation response

Figure 2a–c depict the 700 hPa zonal wind anomalies derived from model simulations and ERA5 reanalysis data. Over Siberia, there exists the East Asian polar jet (EAPJ, also known as the eddy-driven jet) during the cold season. Owing to its transient characteristic, it is difficult to determine the location of EAPJ in the monthly mean zonal wind field. According to previous studies46,47,48, the regions spanning 42.5°−62.5°N and 50°−100°E (the black boxes in Fig. 2a–c) are identified as key areas of EAPJ, based on the distribution of jet core numbers. The zonal wind response to THF data is very similar to the observed circulation anomalies, with the EAPJ weakened over the northern Eurasian continent (Fig. 2a, b). A negative-positive-negative tripole wave train is evident across the Eurasian continent in the 500 hPa geopotential height field (Fig. 2d, e). This Eurasian-teleconnection wave train amplifies the Ural High and East Asian Trough. However, the SC-WACCM4 model failed to capture the prominent positive geopotential height anomalies observed over the North Pacific (Fig. 2d, e). In both the LTHF experiment and the observational data, pronounced warm temperature anomalies span the entire Arctic and the Arctic Archipelago (shade in Fig. 2g, h). The strengthened Siberian High is evident at the surface (contour in Fig. 2g, h), intensifying the East Asian winter monsoon and leading to negative temperature anomalies in the central Eurasian continent. In the surface pressure field of the Arctic, both the THF experiment response and the observational anomalies indicate anomalous high pressure in Greenland (contour in Fig. 2g, h). These results are also observed when the model is forced with MERRA2 THF data (Supplementary Fig. S5) though they are slightly different from those forced with ERA5 data. The warm Arctic cold Eurasian pattern and weakened jets are clear, although their positions have changed, indicating the sensitivity of the model to THF.

Fig. 2: Winter atmospheric response (perturbation experiment minus control experiment) in the Northern Hemisphere.
figure 2

a 700 hPa zonal wind response (m s−1) in the LTHF experiment. b Difference in the 700 hPa zonal wind (m s−1) between means averaged over 2005–2015 and 1982–2001 based on ERA5 reanalysis data. c 700 hPa zonal wind response (m s−1) in the LSIC experiment. d−f same as a−c, but for 500 hPa geopotential height response (gpm). g−i same as a−c, but for surface air temperature (°C, shade) and sea level pressure (hPa, contour) response. The contour intervals are 0.5 hPa in g, h and 1 hPa in (i). Black boxes indicate the region over 42.5°−62.5°N, 50°−100°E. Solid and dashed contours represent positive and negative anomalies, respectively, omitting the zero contours. Stippling as in Fig. 1.

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When the model is forced with SIC, the atmospheric response deviates from observational data. There is an increase in zonal winds between 60–80°N, which is contrary to the observed results (Fig. 2b, c). Although some previous studies have simulated the weakening of the mid-latitude jet using the SC-WACCM4 model, the sea ice boundary condition they used is not the magnitude in the present observations, but rather a future 2 °C warming scenario which far exceeds the reduction of sea ice observed at present day49. This artificial enhanced magnitude of sea ice loss may favor an amplified surface forcing. In the 500 hPa geopotential height field, compared with the ERA5 data, the negative anomalies (≤ −4.0 gpm) are missing in East Asia (Fig. 2e, f). At the surface, there is a noticeable increase in the Arctic temperature, particularly in regions such as the Barents-Kara Sea, the Arctic Archipelago, northern North America, and the Okhotsk Sea (shade in Fig. 2h, i). However, the intensity of the warming is relatively weak, and the cold anomalies in the central Eurasian are insignificant. Besides, there is no indication of an intensified Siberian High at the surface (contour in Fig. 2i). The surface pressure exhibits negative anomalies in the Arctic, accompanied by positive anomalies in the North Pacific and western Europe, similar to the positive phase of the Arctic Oscillation. These discrepancies are related to the vertical structure of Arctic warming.

The large-scale zonal mean responses during winter are illustrated in Fig. 3. In the LTHF experiment, the most striking feature over the Arctic is the profound warming from the surface to the upper atmosphere, characterized by two warming maximums (Fig. 3a). The most intense warming is detected in the lower troposphere below 400 hPa, which is consistent with direct heating by the THF associated with sea ice loss (Fig. 1e). The second warming maximum, identified at around 70 hPa, indicates a weakening of the stratospheric polar vortex. Some studies suggest that this stratospheric warming is influenced by energy transportation from below25,50. The simulated deep warming structure with two maxima in the Arctic closely resembles that in the reanalysis data (Fig. 3d). Previous studies highlighted the important role of the vertical structure of Arctic warming. Eurasian cooling tends to occur during winter with Arctic deep warming, whereas shallow warming might be insufficient to generate comparable remote impacts through the same pathway22,51,52,53,54. Corresponding to the deep warming structure, an entire increase in the geopotential height is observed over the Arctic (Fig. 3b, e). The zonal winds around 60°N demonstrate a notable weakening of eddy-driven jet extending from the surface to the stratosphere (Fig. 3c, f). The Arctic deep warming caused by imposed THF weakens the polar-equator temperature gradient. This leads to a slowdown of the westerly jet through the thermal wind relationship, which in turn influences the climate of the mid-latitudes.

Fig. 3: Meridional cross-section of the zonal mean response (perturbation experiment minus control experiment) in winter.
figure 3

a Temperature response (°C) in the LTHF experiment. b Geopotential height response (gpm) in the LTHF experiment. c Zonal wind response (m s−1) in the LTHF experiment. d−f same as a−c, but for differences between means averaged over 2005–2015 and 1982–2001 based on ERA5 reanalysis data. g−i same as a−c, but for response in the LSIC experiment. Stippling as in Fig. 1.

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In the LSIC experiment, the response differs markedly from those results in LTHF and ERA5. The influence of light sea ice forcing primarily results in warming of the tropospheric temperature, while cold anomalies prevail above 300 hPa (Fig. 3g). These pronounced cold anomalies in the stratospheric atmosphere are associated with the negative geopotential height anomalies above 300 hPa over the Arctic (Fig. 3h) and drive the increase in mid-latitude zonal winds (Fig. 3i). This anomalous pattern has been rarely reported in previous studies. Due to the shallow Arctic warming structure, the cold anomalies over the Eurasian continent and strengthened Siberian High are not reproduced (Fig. 2i).

This disparity highlights the model uncertainty when forced with SIC, indicating that the model cannot always capture the atmospheric circulation patterns following sea ice loss. As analyzed previously, this may stem from the incorrect simulation of THF over the sea ice surface due to the oversimplified representation of sea ice processes. The rough representation of the Arctic sea ice state within the Atmospheric General Circulation Model (AGCM) may lead to inaccurate simulation of THF. The sea ice thickness of AGCM is usually set at 2 meters, which weakens the surface THF associated with sea ice reduction. Sea ice features such as sea ice age, melt ponds, as well as sea ice physical processes like sea ice ridging, and sea ice sliding cannot be depicted by the AGCM model. Additionally, the SIC-SST coupling relationship in newly open water areas cannot be accurately characterized55. The model-calculated THF is also influenced by the atmospheric conditions over the sea ice. Therefore, accurately simulating the THF over the sea ice surface is a highly complex issue. How well the THF is simulated is crucial to understanding the impact of sea ice on mid-latitudes.

Quasi-linear tropospheric response

After introducing the observed THF, which enhances heat transfer over the Arctic sea ice surface, the model response is closer to the reanalysis data than simply using SIC forcing. This prompted us to question whether AGCM’s lack of consensus could be attributed to relatively weak Arctic forcing. THF, as a boundary forcing, has an important characteristic. If a positive upward THF boundary forcing is further increased, such as by 2 or 3 times, and the atmospheric temperature will be further enhanced to balance this increased THF. However, if the boundary conditions are fixed and the temperature of the atmosphere increases through some ways, it may not necessarily lead to an increase in surface THF, and may even suppress THF. To investigate this, we increased the THF to two, three, and four times its observed values, leading to the design of the LTHF2X, LTHF3X, and LTHF4X experiments. We observed that while the model’s response pattern remained unchanged (Fig. 4), the intensity of anomalies in the WACE pattern, the Siberian High, the Eurasian teleconnection, and the EAPJ increased with THF enhancement. This not only confirms the stability of THF forcing experiments but also suggests a quasi-linear relationship between tropospheric response and THF intensity. Importantly, it implies that accurately capturing the spatial distribution of THF is crucial, more so than simply amplifying its intensity.

Fig. 4: Winter atmospheric response (perturbation experiment minus control experiment) in the LTHF2X, LTHF3X, and LTHF4X experiments.
figure 4

a SAT (°C, shade) and SLP (hPa, contour) response in the LTHF2X experiment. b 500 hPa geopotential height response (gpm) in the LTHF2X experiment. c 700 hP zonal wind response (m s−1) in the LTHF2X experiment. d−f same as a−c, but for response in the LTHF3X experiment. g−i same as a−c, but for response in the LTHF4X experiment. Solid and dashed contours represent positive and negative anomalies, respectively, omitting the zero contours. The contour interval is 1 hPa in a, d, g. Stippling as in Fig. 1.

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The underlying mechanism

In this section, we explain one possible mechanism of the Arctic-Eurasian connection. The storm track plays a pivotal role in modulating large-scale atmospheric circulation by redistributing momentum, moisture, and heat flux, serving as a potential bridge in linking the Arctic and Eurasia. First, we extract synoptic-scale (2.5–8 days) transient eddies using the Lanczos bandpass filter. We calculated the eddy kinetic energy (Fig. 5a) and found that the Siberian Storm track was reduced in the LTHF experiment, indicating weaker cyclonic activity over the Eurasian continent. The negative Eady growth rate (EGR) anomalies, which measure baroclinic instability in relation to the vertical wind shear, were revealed over mid-latitudes, signifying a reduction in baroclinic instability (Fig. 5b). This is in line with the observed weakening of eddy-driven jet in the same area (Fig. 2a, b).

Fig. 5: Response (perturbation experiment minus control experiment) of storm track, atmospheric baroclinicity, and geopotential height tendency.
figure 5

a Winter response of EKE (m2 s−2) at 300 hPa. b Zonal mean EGR response (1 s−1) along the latitude-pressure cross-section from 30°−120°E. c Winter response of geopotential height tendency (m s−1) related to synoptic-scale transient vorticity forcing at 925 hPa. d Winter response of geopotential height tendency (m s−1) related to synoptic-scale transient thermal forcing at 925 hPa. Stippling as in Fig. 1.

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To quantify the influence of the reduced Siberian storm track on mid-latitude climate, we diagnosed the interaction between transient eddy and time mean flow using the quasi-geostrophic potential vorticity (QGPV) equation56. We employed the Successive Over-Relaxation (SOR) method to numerically solve for geopotential height tendency related to eddy forcing48. Figure 5c, d display the differences in geopotential height tendency due to synoptic-scale transient eddies between LTHF and CTRL experiments. We have identified an impact of synoptic scale transient vorticity forcing on the Eurasian continent. Through the redistribution of the disturbed momentum, the synoptic scale transient vorticity forcing leads to the enhancement of the Siberian High, subsequently causing temperature advection and the Eurasian SAT cold anomalies. Conversely, the influence of synoptic-scale transient thermal forcing on mid-latitude Eurasia is relatively limited, primarily causing localized increases in geopotential height tendency in the Arctic marginal regions through the redistribution of disturbed air temperature. In summary, one Arctic-Eurasian connection mechanism unfolds as follows. Due to the enhancement of THF associated with sea ice loss, the entire atmosphere over the Arctic is heated, forming a deep warming structure with two warming maxima. This deep Arctic warming structure, according to the thermal wind relationship, leads to the weakening of the meridional temperature gradient and EAPJ, resulting in a decrease in atmospheric baroclinicity in mid-latitude. The weakening of atmospheric baroclinicity in mid-latitude affects the Siberian storm track and eddy activities, which in turn provide feedback on the time mean atmospheric circulation through the barotropic eddy forcing feedback accompanied by transient eddy-induced geopotential height tendency. The synoptic-scale transient vorticity forcing is pivotal in forming the anomalous Siberian high during winter.

Discussion

This study utilized the state-of-the-art SC-WACCM4 model to investigate the role of Arctic sea ice THF in the Arctic-Eurasia connection. By contrasting the LTHF experiment with the LSIC experiment, we found that the LTHF experiment enhances the THF in the central Arctic Ocean region by approximately 20 W m−2. This increase in THF led to a notable temperature rise of about 3.8 K on the Arctic surface, compared to only a 1 K when using SIC data. The LTHF experiment effectively captured the atmospheric circulation patterns observed in ERA5 data (differences between means averaged over 2005–2015 and 1982−2001), including the weakened EAPJ over northern Eurasia, the negative-positive-negative Eurasian teleconnection wave pattern at 500 hPa geopotential height field, the WACE temperature distribution, and the strengthened Siberian High. From the zonal mean response, the LTHF experiment exhibited a deep Arctic warming structure with two warming maxima and a weakening of mid-latitude westerlies. In comparison, the LSIC experiment showed warming only at the Arctic troposphere, with cold anomalies prevailing above 300 hPa, and positive zonal wind anomalies at mid-latitudes. The incorporation of sea ice THF improved the model’s ability to simulate the Arctic-Eurasian connection.

This prompted us to question whether AGCM’s lack of consensus could be attributed to relatively weak Arctic forcing. To investigate this, we designed experiments with varying intensities of THF. Our findings revealed the enhancements in the tropospheric atmosphere as the applied THF intensity increased. The enhancements were observed in the tropospheric atmosphere, including the 500 hPa geopotential height, the 700 hPa zonal wind field, the Arctic-Eurasia surface temperature, and the Siberian High. The main response pattern remains robust.

We then elucidated the mechanisms linking the Arctic and mid-latitudes. By introducing reanalyzed THF data, the Arctic atmosphere in the model is strongly heated, forming a deep warming structure. The deep warming in the Arctic, by weakening the meridional temperature gradient, slows down the EAPJ, leading to a reduction in atmospheric baroclinicity and the weakening of the Siberian storm track. The synoptic-scale transient vorticity eddies, through the redistribution of the disturbed momentum, cause an enhancement of the Siberian High, thus strengthening the connection between the Arctic and Eurasia.

These results underscore the critical role of THF, suggesting current models might underestimate the influence of sea ice. Given the rapid warming of the Arctic, there is an urgent need for superior modeling capabilities to accurately capture the atmospheric response to sea ice loss. The refinement of the physical processes related to sea ice THF is crucial for enhancing our understanding of these vital climatic interactions.

Methods

Datasets

The monthly mean data used in this study is obtained from the European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) dataset57 with a horizontal resolution of 0.25° × 0.25° from 1979 to 2015, including geopotential heights (HGT), zonal winds (U), air temperature (T), sea level pressure (SLP), 2 m surface air temperature (SAT). Additionally, 6-hourly ERA5 reanalysis data, including surface sensible heat flux and latent heat flux, is also used for the turbulent heat flux forcing experiments. Surface sensible heat flux and latent heat flux from three sets of reanalysis data, namely the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA2) dataset58, the National Centers for Environmental Prediction Reanalysis 2 (NCEP2) dataset59, and the Japanese 55-year Reanalysis (JRA55) dataset60, are utilized to compare the uncertainty of turbulent heat flux in reanalysis data.

Models

SC-WACCM4 (Specified Chemistry Whole Atmosphere Community Climate Model version 4) that has a finite-volume dynamic core and an active Community Land Model version 4 (CLM4) is the atmospheric component of the National Center for Atmospheric Research (NCAR) Community Earth System Model version 1.2 (CESM1.2). SC-WACCM4 model is a high-top model with 66 vertical layers and its model lid is at 5.1 × 10−6 hPa (extending from the surface to approximately 140 km), which makes this model a good representation of the stratosphere and a suitable tool for simulating the stratosphere-troposphere dynamical coupling. In this study, SC-WACCM4 is conducted using a 1.9° × 2.5° horizontal resolution. SST and SIC data in the model are compiled by Hurrell et al.61 from https://svn-ccsm-inputdata.cgd.ucar.edu/trunk/inputdata/atm/cam/sst/.

Experimental design

The control run (CTRL) spans 100 years, employing a prescribed climatological SIC and SST averaged over the period 1982–2001. Other forcings, such as solar radiation, aerosols, greenhouse gases, etc., are held constant at the levels of the year 2000.

The light SIC forcing experiment (LSIC) utilizes the same climatological SST boundary condition and other external forcings as CTRL, but the climatological SIC boundary condition is the reduced Arctic SIC averaged from 2005 to 2015. In order to facilitate verification and comparison with observed data, we added sea ice forcing in all seasons of model operation to avoid any complex, diverse and inexplainable model results. Furthermore, if the Arctic SIC averaged over 2005–2015 deviated from the climatological mean (1982–2001) by more than 10% (in absolute terms), the warmer SST values (2005−2015 averaged) were used in these sea ice retreat regions, a similar method has been employed in previous research55.

The turbulent heat flux forcing experiment (LTHF) is forced by the same boundary conditions and external forcings as LSIC, but the 6-hourly ERA5 reanalysis THF data over the sea ice surface is integrated into SC-WACCM model using a nudging method. This study refers to grid points with SIC greater than 1% as grid points containing sea ice. When the SIC of the model grid point exceeds 1%, the model-calculated THF at that grid point is replaced with the reanalysis THF data. This THF data, taken at four specific daily intervals: 00:00, 06:00, 12:00, and 18:00, is averaged across the 11 years (2005–2015), producing an annual dataset with a 1460-time demission (365 days multiplied by 4 daily intervals). The contribution of observed THF over the Arctic sea ice to boreal circulation can be obtained by differencing experiments LTHF and LSIC.

Equation

To explore the effects of synoptic scale transient eddy, 2.5–8 day bandpass filter is used to extract synoptic-scale from daily anomalies. In this study, the overbar and prime denote the average over wintertime and synoptic scale transient eddy.

Following quasi-geostrophic potential vorticity (QGPV) equations, the geopotential tendency forced by transient eddy56 can be written as:

$$\left\{\frac{1}{f}\right.{\nabla }^{2}+\left.f\frac{\partial }{\partial p}\left (\frac{1}{\sigma }\frac{\partial }{\partial p}\right )\right\}\frac{\partial \Phi }{\partial t}=-f\frac{\partial }{\partial p}\left(\frac{\alpha }{\sigma }\frac{\overline{{Q}_{{te}}}}{\bar{T}}\right)+\overline{{F}_{{te}}}+{RES}$$
(1)

Where \(\Phi\) \(T\) \(\sigma\) \(\alpha\) represent geopotential height, air temperature, static stability parameter, and specific volume, respectively. \(\overline{{Q}_{{te}}}\) is defined as the time-mean transient eddy heating determined by the convergence of heat flux transported by transient eddy, which can be calculated as follows,

$$\overline{{Q}_{{te}}}=-\nabla {{{\rm{\cdot }}}}\overline{\overrightarrow{{V}_{h}^{{\prime} }}{T}^{{\prime} }}-\frac{\partial \overline{{\omega }^{{\prime} }{T}^{{\prime} }}}{\partial p}+\frac{R}{{c}_{p}p}\overline{{\omega }^{{\prime} }{T}^{{\prime} }}$$
(2)

where,\(\,\overrightarrow{{V}_{h}^{{\prime} }}\) \(\omega\) \(R\) \({c}_{p}\) and \(p\) mean the horizontal and vertical velocity, the gas constant, the specific heat capacity, and the pressure, respectively. The transient eddy vorticity forcing, \(\overline{{F}_{{te}}}\), is determined by the convergence of vorticity flux transported by transient eddy,

$$\overline{{F}_{{te}}}=-\nabla {{{\rm{\cdot }}}}\overline{\overrightarrow{{V}_{h}^{{\prime} }{{{{\rm{\zeta }}}}}^{{\prime} }}}$$
(3)

where ζ refers to the relative vorticity. The term RES denotes the residual of the remaining components.

The maximum Eady growth rate (EGR) is given by

$${{{\rm{EGR}}}}=0.3098\left|\frac{f}{N}\right|\left|\frac{\partial U}{\partial z}\right|$$
(4)

Where \(f\) is the Coriolis parameter, \(U\) is the vertical profile of daily zonal wind, \(z\) is the vertical coordinate and \(N\) is the Brunt-Vaisala frequency.

The eddy kinetic energy (EKE) is given by:

$${{{\rm{EKE}}}}=\,\frac{1}{2}\overline{({u}^{{\prime} 2}+{v}^{{\prime} 2})}$$

Where \(u\) and \(v\) are the zonal and meridional wind components.