The station data used in this study are from the National Meteorological Information Center of China and contain the daily records of 824 gauge stations in China. A total of 68 out of 635 stations with no missing records during the period 1981–2021 are selected over NEC (42°–52°N, 120°–135°E). The daily observational atmospheric data are from the NCEP/NCAR reanalysis Ⅰ dataset, including sea level pressure (SLP), geopotential height, zonal and meridional wind, and surface air temperature with a horizontal resolution of 2.5° × 2.5°. The surface latent heat net flux and the surface sensible heat net flux are on a Gauss grid (Kalnay et al., 1996). The daily SST and the sea-ice cover (SIC) data are from the NOAA OISSTv2 dataset, with a horizontal resolution of 0.25° × 0.25° (Reynolds et al., 2007). Moreover, the daily AO index data are from the Climate Prediction Center (https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml).

The climatology is defined as the average span of the period 1980–2015. Several indices are employed to estimate the status of atmospheric or oceanic systems in this study, and the definitions are as follows:

The intensity of the Siberian high (SHI) is defined as the mean SLP averaged over the center of the anticyclone (40°–60°N, 70°–120°E) (Gong et al., 2001). The intensity of the EAT (EATSI) is represented by the averaged geopotential height at 500 hPa over (30°–45°N, 125°–145°E) (Sun and Li, 1997). The EAT axis index (EATAI) is calculated as the longitudinal position of the minimum 500 hPa height at each latitudinal step within the index range (25°–50°N, 100°–180°E) (Bradbury et al., 2002; Wang et al., 2009). The daily Northern Annular Mode (NAM) index is calculated by projecting daily geopotential height anomalies onto the leading mode of the empirical orthogonal function of daily geopotential height.

The Rossby wave source and the propagations of wave trains are adopted to reveal the circumstances and physical mechanisms related to the subseasonal reversal of temperature over NEC in winter 2014/2015, as well as the connections to the Arctic sea ice. The functions are as follows:

(1) Rossby Wave Source (RWS):

To diagnose the stationary wave propagation in the troposphere, the horizontal component of WAF generalized by Takaya and Nakamura (2001) is applied: W x = p 2 a 2 | U | { U cos ⁡ ϕ [ ( ∂ ψ ′ ∂ λ ) 2 − ψ ′ ∂ 2 ψ ′ ∂ λ 2 ] + V [ ∂ ψ ′ ∂ λ ∂ ψ ′ ∂ ϕ − ψ ′ ∂ 2 ψ ′ ∂ λ ∂ ϕ ] } , W y = p 2 a 2 | U | { U [ ∂ ψ ′ ∂ λ ∂ ψ ′ ∂ ϕ − ψ ′ ∂ 2 ψ ′ ∂ λ ∂ ϕ ] + V ⁡ cos ⁡ ϕ [ ( ∂ ψ ′ ∂ ϕ ) 2 − ψ ′ ∂ 2 ψ ′ ∂ ϕ 2 ] } , where p = (pressure/1,000 hPa), a is the Earth’s radius (unit: km), U = (U, V, 0) ^T denotes a steady zonally inhomogeneous basic flow, ψ ' is the perturbation geostrophic stream function, and ( ϕ , λ ) are latitude and longitude, respectively.

The vertical component of WAF is also used to diagnose the troposphere–stratosphere interaction. The calculations are based on the functions proposed by Plumb (1985): F z = 2 p Ω 2 ⁡ sin 2 ⁡ ϕ N 2 a ( ∂ ψ ′ ∂ λ ∂ ψ ′ ∂ z − ψ ′ ∂ 2 ψ ′ ∂ λ ∂ z ) where Ω is the angular velocity of rotation, N is the buoyancy frequency, and z = − H ln ⁡ p , where H is a constant scale height (H = 8,000 in this paper).

Moreover, the Fourier transform is also applied in this paper to isolate the wavenumbers.

Despite the warmer condition over NEC in winter 2014/2015, the temperature featured a significant subseasonal reversal around 22–23 December 2014, which was cooler than normal in December but anomalously warmer in January and February (Figure 1; hereafter abbreviated as NECTA_-++). The temperature difference at the monthly scale between January and December exceeded 3°C (Figure 1E). Correspondingly, the strength of the EAWM also changed around 22–23 December 2014 (figures not shown).

The time series of daily indices, including the SHI, EATSI, EATAI, and AO, are calculated to analyze the evolutions of atmospheric circulation systems related to the variations of winter temperature over NEC (Figure 2). The results indicate that these systems all featured subseasonal reversal in late December 2014, which is consistent with the variations of temperature over NEC. The stronger-than-normal Siberian high turned to become weakened around 20 December and sustained to February (Figure 2A). The invasion of cold air from the polar region to NEC is always impacted by the location and strength of the EAT. In winter 2014/2015, the EAT was stronger at the normal location during the early winter, whereas it moved eastwards and faded during the late winter (Figures 2C,D). Thus, the frequencies of cold surges over NEC decreased, favoring a warmer condition during January and February in 2015. In terms of the AO, its negative phase was maintained from November to early December, corresponding to a weakened polar vortex and lower temperature over NEC. The AO converted to a positive phase around 20 December and later strengthened significantly, thereby changing the temperature anomalies over NEC (Figure 2B).

Hence, the atmospheric systems related to the winter temperature over NEC all featured changes at the subseasonal scale corresponding to the subseasonal reversal of winter temperature over NEC. For further analysis, the evolutions of large-scale circulations are investigated in the next part of this paper.

The daily evolution of 500 hPa geopotential height averaged between 30°N and 80°N during winter 2014/2015 is exhibited in Figure 3. It indicates that the atmospheric circulations in the mid-high latitudes featured significant eastward propagation, which further affected the intraseasonal variations of the location and strength of the EAT.

Previous research has pointed out that the heat budget in the lower troposphere is the main cause of the airmass transformation of the Siberian high, and it features marked low-frequency meridional movement with a period of 10–20 days, along with the related cold-air outbreak (Ding and Krishnamurti, 1987; Ding, 1990). Staff Members of Academia Sinica (1958) concluded four categories of cold waves over East Asia and indicated the importance of eastward short waves in affecting the EAT and the Siberian high. Suda (1957) also proved that the eastward shift of the permanent trough in the mid-troposphere is responsible for the cold waves in the Far East. Some other studies have also indicated that the intraseasonal-amplification events of the winter surface Siberian high over central and western Siberia are associated with the formation of blocking bridges in the upper troposphere, which generally form as a quasi-stationary Rossby wave train propagating over the Eurasian continent (Takaya and Nakamura, 2005a; Takaya and Nakamura, 2005b). The significance of low-frequency Rossby waves and synoptic transient eddies in influencing the intraseasonal variation of the strength of the EAT were also revealed by Song et al. (2016). All these studies emphasize the critical role of the eastward wave trains over the Eurasian continent in the winter. Hence, the role of Rossby wave activities in winter 2014/2015 is discussed in the following part of this section.

An anomalous anticyclone formed in the lower troposphere over the midlatitude North Atlantic in early November 2014, and a cyclonic circulation existed to the northeast of it (Figure 4A). This pairing of cyclonic–anticyclonic anomalies maintained throughout December 2014 and propagated eastwards, inducing a train of cyclonic–anticyclonic circulations stretching from the North Atlantic to East Asia. The temperature over NEC decreased with the deepened EAT when the anomalous cyclones reached East Asia. However, the wind anomalies over East Asia in the lower troposphere faded from the second pentad of December 2014 and disappeared in the last pentad (12.26–12.30), corresponding to the timing of the temperature reversal (Figure 4B). The evolution of wind in the lower troposphere indicates the existence of eastward Rossby waves that originated from the North Atlantic and disappeared in late December 2014.

The anomalies of RWS (figures not shown), geopotential height at 500 hPa, and horizontal components of WAF (Figure 5) of each pentad during November–December 2014 are calculated for further investigation of the propagation of the Rossby wave train. It turns out that the RWS over the mid–high latitudes of the North Atlantic oriented east–west anomalies in November 2014, which further induced Rossby waves propagating to East Asia (Figure 5A). The wave train that spread from the North Atlantic to East Asia gradually weakened in early December and vanished in late December, accompanied by a faded pair of RWS anomalies during late November to early December 2014 (Figure 5B). Moreover, the local RWS anomalies over the Barents–Kara Sea enhanced significantly since the third pentad of November 2014, favoring the Rossby waves that originated over the North Atlantic, and then propagated to East Asia via the Barents–Kara Sea (Figure 5A).

Figure 5B exhibits the geopotential height anomalies over the Eurasian continent in December, which can be attributed to the Rossby waves trains that propagated from the North Atlantic to East Asia via the Barents–Kara Sea. Previous studies have identified that the geopotential height anomalies over the Eurasian sector are the source of the vertical development of planetary waves (Plumb, 1985; Kuroda and Kodera, 1999). Charney and Drazin (1961) discussed the propagation of the planetary waves and indicated that the wavenumber-1 and -2 components of the planetary waves dominate the vertical propagation to the stratosphere (Hayashi, 1981). Due to strong negative wind shear in the upper-stratospheric polar jet, the wave packets reflect down from the stratosphere to the troposphere, inducing the stratosphere–troposphere coupling (Kodera et al., 2013; Nath et al., 2016). In particular, zonal wavenumber-1 dominates the downward interaction on the short-term time scale (up to 12 days), forming the wavenumer-1 anomalies in the geopotential height field in the high-latitude troposphere (Perlwitz and Harnik, 2003, 2004; Shaw and Perlwitz, 2013). All these studies emphasize the importance of the wavenumber-1 component of planetary waves. Hence, the planetary wavenumber-1 component averaged over (50°–70°N, 0°–180°E) (Figure 6A) and the NAM index (Figure 6B) are calculated to analyze the daily evolutions of vertical circulations over the Eurasian continent during 1 November 2014 to 28 February 2015.

According to Figure 6A, the downward wave flux in the troposphere extended to the upper stratosphere throughout November 2014. This reflects the fact that the upward planetary wave flux propagating to the stratosphere was depressed, causing less wave energy reaching the stratosphere and a stronger polar vortex (Figure 6B). In early-to-mid December 2014, the upward propagation of wave flux in the troposphere interrupted the downward reflection of planetary wavenumber-1 from the stratosphere. However, the downward wavenumber-1 component of planetary waves dominated the troposphere in late December, strengthening the tropospheric polar vortex and causing a warmer condition over NEC. The planetary wavenumber-1 reflected downward from the stratosphere entirely ever since a minor sudden stratospheric warming occurred in early January 2015 (Manney et al., 2015). As a consequence, the polar vortex enhanced again and the geopotential height anomalies characterized the positive phase of the AO in the stratosphere. The AO pattern propagated downwards to the troposphere, enhancing the warm condition over NEC.

In conclusion, the subseasonal reversal of temperature over NEC in winter 2014/2015 was a combination of the influence of Rossby waves propagating eastwards from the North Atlantic to East Asia in November and the downward reflection of planetary wavenumber-1 from the stratosphere in mid-December 2014. The eastward Rossby waves excited by the anomalous RWS over the North Atlantic propagated through the Barents–Kara Sea in November, strengthening the Siberian high and EAT, which further favored the southward invasion of cold airmass to NEC. However, this eastward Rossby wave train gradually disappeared and slightly affected NEC in late December 2014. Meanwhile, the anomalies of the stratospheric polar vortex propagated downwards with the planetary wavenumber-1, inducing the positive phase of the AO in the troposphere and the subsequent warm condition over NEC from late December 2014.

The Arctic sea ice is always an essential factor for climate changes in China. Dai et al. (2019) determined the combined influences of the sea ice over the Barents–Kara Sea (SIC-BKS) and the Davis Strait–Baffin Bay (SIC-DSBB) in November to the month-to-month variability of winter temperature over NEC on the monthly scale. In this subsection, the daily impacts of the Arctic sea ice are examined based on analysis focused on the monthly variability.

The SIC was anomalously low over the Davis Strait–Baffin Bay, whereas more-than-normal SIC existed over the Barents–Kara Sea in November 2014 (Figure 7A). These anomalies sustained till early December and then returned to the climatology (Figure 7C). SIC-BKS in November increased about 40%–50% compared with that in October, which was much higher than that of SIC-DSBB (Figure 7B). The characteristics of SIC-BKS and SIC-DSBB indicate that the anomalies of sea ice over these two domains partly contributed to the NECTA_-++ event in winter 2014/2015, and the anomalies of SIC-BKS could have resulted in stronger circulation anomalies. The subseasonal variations of SST, RWS, and surface turbulent heat flux are analyzed to elucidate the physical mechanisms on the daily scale by which the Arctic sea ice affected the NECTA_-++ event in winter 2014/2015.

Less-than-normal SIC-DSBB in November 2014 directly induced the regionally warmer SST, and the anomalies of SST expanded to the mid–high latitudes of the North Atlantic via air–sea interactions, characterized as a tripole pattern (Figure 8). This tripole pattern of SST sustained throughout the whole winter of 2014/2015 (figures not shown). Correspondingly, the sea surface heat flux also featured a northeast–southwest tripole pattern over the North Atlantic (Figure 8A). In particular, the downward (upward) flux anomalies corresponded to the negative (positive) SST anomalies. This in-phase configuration of SST and sea surface flux was maintained in early and late November 2014 (Figures 8A,B,E,F), and then reversed in mid-November (Figures 8C,D). The local relationship between flux and SST tendency anomalies has been revealed previously (Cayan, 1992). It denotes that when flux anomalies are in-phase with SST anomalies, suggesting that flux anomalies are driven by the ocean thermal field. Therefore, in the present case, the SIC-DSBB anomalies induced the atmospheric anomalies via a direct influence on the local warming of SST in early November 2014, and these anomalies were maintained with the local air–sea interactions.

The variations and influences of SIC-BKS were different from those of SIC-DSBB. The SIC-BKS grew slightly heavier than normal in the third pentad of November 2014, inducing the local colder SST (Figure 7C, Figure 8C). The regional SST anomalies lasted and strengthened slightly till late November, corresponding to the upward sea surface heat flux. Consequently, positive anomalies of SIC-BKS caused the above atmospheric anomalies to propagate eastwards and affect the downstream circulations in late November 2014.

Since SIC-BKS and SIC-DSBB both have impacts on eastward wave trains over Eurasia, the lead–lag correlations between the RWS and SIC indices over the Barents–Kara Sea and the Davis Strait–Baffin Bay are employed to determine the differences (Figure 9). The SIC indices are defined as the area-averaged values over the Barents–Kara Sea and the Davis Strait–Baffin Bay. Specifically, the interactions between SIC-BKS and SIC-DSBB are removed before calculating the lead–lad correlations. The results indicate that anomalously thinner SIC-DSBB corresponded to the local pair of RWS anomalies, which sustained throughout mid-November and faded in late November 2014 (left-hand column of Figure 9). After excluding the influence of upstream SIC-DSBB anomalies, the anomalous RWS over the BKS could still be attributed to the heavier SIC-BKS in mid-November (right-hand column of Figure 9). The development of regional RWS triggered by SIC-BKS separately were corresponding to the evolutions of RWS and horizontal wave activities over Barents–Kara Sea in November 2014 (Figure 5A). That means the strengthened RWS over Barents–Kara Sea since the third pentad of November 2014 was excited by anomalously heavier SIC-BKS, which further intensified the eastward propagation of Rossby waves originating from the North Atlantic (Figure 5A; right-hand column of Figure 9), enhancing the atmospheric anomalies over Eurasia.

The analyses in this section can be concluded as follows: the thinner SIC-DSBB in November 2014 induced the eastward Rossby waves via regional air–sea interactions, and subsequently caused a stronger Siberian high and deepened EAT. The Rossby waves were later enhanced by heavier SIC-BKS. However, the tropospheric Rossby waves over the Eurasian section triggered by anomalous SIC-BKS and SIC-DSBB became weak and disappeared in mid-to-late December 2014. That was because of the discontinuation of SIC anomalies over the Barents–Kara Sea and the Davis Strait–Baffin Bay in early December 2014. However, the geopotential height anomalies over the midlatitudes of Eurasia due to SIC anomalies depressed the upward propagations of planetary wavenumber-1 and strengthened the stratospheric polar vortex. Later, in mid-December, the stratospheric height anomalies began to reflect downwards, causing the positive phase of the AO in the troposphere from late December.