Mechanism of the wintertime subseasonal surface air temperature variability over Eurasia

The formation mechanism responsible for the leading mode of the subseasonal variability of wintertime surface air temperature (SAT) over Eurasia is investigated. The leading SAT mode over Eurasia is characterized by a triple pattern with strong cold anomalies centered over northern Eurasia and weaker warm anomalies over the Arctic and East Asia, respectively, which has a deep barotropic structure and extends from the surface to the upper troposphere. It is tightly coupled to a wave-like atmospheric circulation, which stretches from the North Atlantic to East Asia and resembles the Scandinavia teleconnection pattern. Its formation mechanism is further revealed through the analysis of the temperature budget. The atmospheric circulation-induced horizontal advection is found to be the primary driver of the cold anomalies over northern Eurasia associated with the leading SAT mode in two steps. First, the advection of the climatological temperature by the mode-associated meridional wind anomalies triggers the cooling in the western part of Eurasia. Second, the advection of the above cold anomalies by background westerly winds from west Eurasia to the east further redistributes the cold anomalies. The meridional and zonal advection eventually causes the mode-associated strong cold anomalies over northern Eurasia.


Introduction
The wintertime surface air temperature (SAT) exhibits pronounced subseasonal variability over the mid-to high latitudes of the Northern Hemisphere (Yang and Li 2016, Lin 2018, Guan et al 2020, Xiu et al 2022, which is closely related to extremely warm and cold events over Eurasia , Xiu et al 2022 and North America (Lin 2014, Guan et al 2020, Sung et al 2021. An improved understanding of the mechanism regulating the subseasonal SAT variability is essential because it may provide guidance for the subseasonal-to-seasonal predictions (Vitart and Robertson 2018, Xiang et al 2019, Cui et al 2021. Eurasia has a large population, and its wintertime SAT shows pronounced subseasonal variability with several leading modes (Yang and Li 2016, Lin 2018, Xiu et al 2022. The first mode is characterized by a triple pattern with three centers over the Arctic, northern Eurasia, and East Asia, and the second mode is featured with a warm Arctic-cold Eurasia (WACE) pattern. Their evolutions, climate impacts, and mechanism have been extensively documented (Sorokina et al 2016, Yang and Li 2016, Tyrlis et al 2020, Kim et al 2021, Xiu et al 2022. The triple mode attracts less attention than the WACE pattern, likely because the latter's interannual counterpart is closely related to the changes in the Arctic sea ice (Mori et al 2014, Labe et al 2020, Ye and Messori 2020. It also has a significant, though not strong, lead-lag correlation with the WACE pattern, reflecting the same propagation mode at different phases to some extent (Yang and Li 2016). This significant but not strong correlation suggests that the two modes have distinct mechanisms, although they share some common physical processes (Yang and Li 2016, Kim et al 2021, Xiu et al 2022. Yang and Li (2016) investigated the mechanism for the propagation of the triple mode. They noted that the advection of subseasonal temperature perturbation by the mean meridional flow drives the southeastward propagation of the alternative triple mode and WACE pattern. Their results are illuminating, but it is the propagation mechanism of the triple mode that is addressed. In contrast, it remains open what controls the subseasonal growth and decay of the triple mode, and this issue will be addressed in this study. Section 2 describes data and methods. Section 3 explores the evolution characteristics and key processes for the formation of the triple mode. Section 4 summarizes the conclusions and discusses some remaining issues.

Data and methods
The daily-mean reanalysis data from the European Centre for Medium-Range Weather Forecasts reanalysis version 5 (ERA5) dataset (Hersbach et al 2020) are used in this study. They are averaged from the hourly data and have a 1 • by 1 • horizontal resolution. The variables used include SAT and sea level pressure (SLP) at a single level and geopotential height, zonal and meridional winds (u, v), and air temperature (T) at pressure levels. Subseasonal anomalies of each variable were obtained by first removing the climatological annual cycle, defined as the annual mean plus the first three harmonics, and then filtering using a 10-90 days Lanczos bandpass filter. This study uses data from 41 winters (November to March) for 1979-2020, where the 1979 winter denotes 1979/80 winter.
Temperature tendency equation in pressure coordinates is diagnosed (Holton and Staley 1973) to elucidate the key processes that drive the formation of the subseasonal T anomalies, which can be expressed as where α is the specific volume, c p the specific heat of air, andQ the rate of diabatic heating. u, v are the zonal and meridional wind velocities, respectively. ω is the vertical velocity in pressure (p) coordinates. Primes denote the subseasonal time-scale variability with a period between 10 and 90 days. The terms on the right-hand side are anomalies of horizontal temperature advection, vertical temperature advection, adiabatic warming, and diabatic heating, respectively. The diabatic heating term is not directly provided in the ERA5 dataset, so it is calculated as the residual of the temperature tendency equation.
To further diagnose the contributions of different time-scale processes to the temperature advection, we follow the approach of Yang and Li (2016) and divide any variable A into three different time scales ( A =Ā + A ′ + A ′ ′ ). Here,Ā, A ′ , A ′ ′ denote the background state with a period greater than 90 days, the subseasonal time-scale variability with a period between 10 and 90 days, and high-frequency variability with a period shorter than 10 days. After decomposing u, v and T into the three components, the zonal and meridional temperature advection terms can be expressed as Figure 1(a) shows the standard deviation of daily SAT anomalies during boreal winter. Pronounced day-to-day SAT variability is observed over the mid-to high latitudes of the Northern Hemisphere. Large values of the standard deviation of 10-90 days filtered SAT anomalies are also found over many regions of Eurasia, North America, Greenland, and the Arctic, with a local maximum over northern Eurasia ( figure 1(b)). The ratio of 10-90 days SAT variability to the total daily standard deviations averaged over the Eurasia sector (blue box in figure 1(b)) exceeds 70%, indicating the importance of the subseasonal component in the daily SAT variability. The empirical orthogonal function (EOF) analysis is applied to the wintertime subseasonal SAT anomalies over 30 • -90 • N, 30 • -140 • E (blue box in figure 1(b)) to extract the dominant subseasonal SAT variability mode over the Eurasia sector. Before the EOF analysis, SAT anomalies were weighted by the square   North et al (1982). (d) Lead-lag correlation coefficients between PC1 (i.e. triple SAT index) and PC2. A positive lag denotes PC2 leads PC1. Two red dash lines denote the 95% confidence level based on the two-tailed Student's t-test. root of the cosine of the latitude. The two leading EOF modes (EOF1 and EOF2) explain 21.9% and 15.2% of the total variance of the subseasonal SAT variability, respectively, and are adequately separated from each other and remaining modes according to the North et al (1982) criteria (figure 2(c)). The EOF1 is characterized by a triple pattern with strong cold anomalies centered over the northern Eurasia continent and relatively weak warm anomalies over the Arctic and East Asia (figure 2(a), referred to as triple SAT pattern hereafter). The EOF2 features the WACE pattern, with two anomalous centers of the opposite sign over central Eurasia and the Arctic (figure 2(b)). The sequences of the two EOF modes may switch if a larger or smaller domain over Eurasia is used in the EOF analysis, but their spatial patterns are insensitive to the domain and remain almost identical (Xiu et al 2022). As such, the two leading EOF modes shown in figures 2(a) and (b) quite resemble those reported in previous studies (e.g. Yang and Li 2016), although different time filter (e.g. 10-60 days in Yang and Li 2016) was applied. Lead-lag correlations between PC1 and PC2 show that PC1 leads PC2 by about four days, and negative PC1 lags PC2 by four days (figure 2(d)), consistent with Yang and Li (2016). In the following, we focus on the triple SAT pattern (i.e. EOF1) and investigate its evolution characteristics and the underlying mechanism.

The leading subseasonal SAT modes over Eurasia
To explore how often this triple SAT pattern exists climatologically, we select positive and negative events based on the normalized PC1 (referred to as the triple SAT index hereafter). A positive or negative event is identified when the normalized triple SAT index is above or below the threshold of 1.5 or −1.5 for more than  Figure 4 shows the evolution of the SAT and SLP anomalies associated with the triple SAT pattern obtained via lead-lag regressions of the 10-90 days filtered SAT anomalies onto the normalized triple SAT index from days −9 to 6 at a 3 day interval. Visible warm anomalies appear over northern Eurasia on day −9 and intensify gradually (figures 4(a) and (b)). They propagate southeastward and become a triple pattern on day −3, with cold anomalies over northern Eurasia and warm anomalies over the Arctic and East Asia (figure 4(c)). The triple SAT pattern peaks on day 0 and decays afterward (figures 4(d)-(f)). From day −3 to day 3, the triple pattern-associated temperature anomalies move little and are coupled with an anomalous surface high over the Arctic and low over East Asia (figure 4(c)).

Evolution characteristics of the triple SAT pattern
To further depict the evolution of the triple SAT pattern, figure 5 shows the time-latitude and time-longitude cross-sections of SAT and SLP anomalies along the axis linking the three anomalous SAT centers in the triple pattern (i.e. the green lines in figure 4(d)). The SAT anomalies on day 0 capture the triple structure of the leading SAT mode, and they are bridged by an anomalous high over the Arctic and low over East Asia (figures 5(a) and (b)). The southeastward propagation of both SAT and SLP anomalies can be clearly seen from their temporal evolutions, consistent with the features reported by Yang and Li (2016). Note that the maximum SLP anomalies near the Arctic lead the cold anomalies over northern Eurasia by about two days ( figure 5(c)). It implies an active role of the atmospheric circulation in driving the triple SAT pattern, where anomalous circulation is expected to sustain the SAT pattern by advecting cold air from the Arctic into Eurasia. Figure 6 further illustrates the triple SAT pattern-associated 300 hPa geopotential height anomalies and horizontal wave activity fluxes (Takaya and Nakamura 2001). Visible wave activity fluxes originating from the North Atlantic are observed from day −9 to day −3 (figures 6(a)-(c)). They lead to the intensification of an anomalous anticyclonic geopotential height center over the Arctic near Svalbard from day −6 to day 0 (figures 6(b)-(d)). In this process, the wave pattern weakens and disappears over the North Atlantic and The triple SAT pattern shown in figure 2(a) is similar to the leading interannual SAT mode over Eurasia identified by Mori et al (2014), which is strongly associated with Arctic Oscillation (AO) on the interannual timescale. Motivated by the possible connection between AO and the triple SAT pattern, we also examined the lead-lag correlation between the triple SAT index and the daily AO index that is obtained from the National Oceanic and Atmospheric Administration's Climate Prediction Center. A significant correlation between the triple SAT index and the 10-90 days filtered AO index (r = 0.3, figure 7) is found when the AO index leads the triple SAT index by 2 days, but this value is weaker than that between the Scandinavia index and the triple SAT index. Thus, the Scandinavia pattern is more important than AO in modulating the triple SAT pattern. Note that the triple SAT pattern is also linked with a weakened stratospheric polar vortex (figure 8). This is consistent with previous studies that reported a role of the stratospheric polar vortex in the Eurasian cold events (e.g. Kim et al 2014, Zhang et al 2016, 2018, Xu et al 2023. Figure 9 presents the triple SAT pattern-associated 1000 hPa T anomalies and their tendencies from day −9 to day 6 with a 3 day interval. The evolution of 1000 hPa T anomalies is highly consistent with that of the SAT (figure 4). It suggests that the mechanism of the triple SAT pattern can be understood through the diagnosis of the 1000 hPa T anomalies. Negative T tendencies are observed over northern Eurasia before day 0 (e.g. figures 9(b) and (c)) and account for the establishment of cold anomalies over northern Eurasia on  day 0. In contrast, positive T tendencies there correspond to the decay of cold anomalies after day 0 (figures 9(d) and (e)). As such, the development and decay of the triple SAT pattern can be revealed via diagnosis of the associated T tendencies. Figure 9. (a) Regression coefficients of the 10-90 days filtered 1000 hPa T (shading, SI = 0.5 K) and T tendency (contour, CI = 2 × 10 −6 K s −1 ) onto the normalized triple SAT index from (a) day −9 to (f) day 6 with an interval of 3 days. Dots indicate values exceeding the 95% confidence level based on the two-tailed Student's t-test for shading. Red boxes denote the triple SAT pattern's cold center over northern Eurasia, consistent with figure 4(d).

Mechanism of the triple SAT pattern
To investigate the factors responsible for T tendencies, the temperature tendency equation is diagnosed over northern Eurasia (55 • -75 • N, 60 • -120 • E), where the strongest center of the triple SAT pattern is located. The cold anomalies over Eurasia extend from the surface to the upper troposphere and have a decreasing amplitude with height ( figure 10(a)). Strong negative and positive T tendencies are observed before and after day 0, respectively. These tendencies are primarily driven by horizontal temperature advection, especially the advection of background temperature by subseasonal meridional wind anomalies and the advection of subseasonal temperature anomalies by background zonal wind (−ū ∂T ′ ∂x ) ( figure 10(b)). They are also accounted for by diabatic processes near the surface ( figure 10(c)). In contrast, the role of vertical advection and adiabatic processes is negligible ( figure 10(d)). These results suggest that the growth and decay of the triple SAT pattern in a deep-tropospheric layer are primarily driven by horizontal temperature advection. To quantify the contributions of the above processes to the observed T tendency, each of the above processes in the time-height cross-section (e.g. figure 10(b)) is projected onto the observed T tendency (i.e. figure 10(a)). The polarity and magnitude of the projection coefficients can measure the contribution quantitively, as suggested in Xiu et al (2022). In agreement with previous discussions, horizontal temperature advection plays a dominant role in the evolution of the triple SAT pattern, with a minor contribution from vertical advection, adiabatic and diabatic processes ( figure 11(a)).
The zonal and meridional temperature advection and their decompositions (see equations (2) and (3)) are further examined to illustrate the relative role of zonal and meridional temperature advection and their mechanism. All these terms are then projected onto the time-height cross-section of the observed T tendency in figure 10(a), like the process to obtain figure 11(a). Apparently, the meridional temperature advection Figure 10. Time-altitude evolution of the triple SAT pattern's (a) observed T tendency (shading) and T anomalies (contour, CI = 0.5 K), and T tendency caused by (b) horizontal advection (shading) and (−ū ∂T ′ ∂x − v ′ ∂T ∂y ) term (contour, CI = 5 × 10 −7 K s −1 ), (c) diabatic processes, and (d) vertical advection plus adiabatic processes averaged over northern Eurasia (55 • -75 • N, 60 • -120 • E). SI = 5 × 10 −7 K s −1 in (a)-(d).
plays a more important role than the zonal temperature advection (figures 11(b) and (c)). The decomposition (figures 11(b) and (c)) suggests that zonal advection is dominated by the advection of subseasonal temperature anomalies by background zonal wind (−ū ∂T ′ ∂x ), whereas meridional advection is dominated by the advection of background temperature by subseasonal meridional wind anomalies . The mechanism of the above two processes can be further understood visually from figure 12. The cold center of the climatology of the winter mean 1000 hPa T field is located over northeastern Siberia, and it forms a clear northeast-southwest-oriented T gradient over the mid-to high latitudes of Eurasia ( figure 12(a)). As such, the northerly wind anomalies of the west portion of the triple SAT pattern efficiently advect cold air from the Arctic to Eurasia and lead to a cooling tendency center over west Eurasia near 70 • E, 65 • N ( figure 12(a)). This cooling tendency center contributes substantially to the formation of the central and western portion of the triple SAT pattern's anomalous cold center over northern Eurasia (figures 9(d) and 12(b)). Meanwhile, the background zonal wind is westerly over most parts of Eurasia ( figure 12(b)), and it redistributes the triple SAT pattern's anomalous cold center over northern Eurasia by advecting cold anomalies from west to the east of 90 • E ( figure 12(b)). Hence, the cooling effect of −v ′ ∂T ∂y on the western portion and the redistribution effect of −ū ∂T ′ ∂x to the eastern portion together explains the formation of the triple SAT pattern over northern Eurasia.
The above effects are not only confined in the lower troposphere but also extend into almost the whole troposphere. Figure 12(c) shows that the northerly wind anomalies (v ′ < 0) over northern Eurasia are evident deep in the troposphere to the west of 90 • E. In the presence of negative background temperature gradients ( ∂T ∂y < 0), these wind anomalies can result in cooling tendency (−v ′ ∂T ∂y < 0) and cold anomalies over west Eurasia. The resultant cold anomalies to the west of 90 • E create positive zonal temperature gradient anomalies ( ∂T ′ ∂x > 0) to the east of 90 • E over northern Eurasia ( figure 12(d)). As such, the background westerly winds (ū > 0) lead to cooling tendency (−ū ∂T ′ ∂x < 0) and cold anomalies over east Eurasia.

Conclusions and discussions
The formation mechanism of the dominant subseasonal SAT mode over the Eurasia sector during boreal winter is investigated in this study. The leading subseasonal SAT mode is identified by the EOF analysis on the 10-90 days filtered SAT anomalies during 41 boreal winters (November-March, 1979-2020. It exhibits a triple pattern with a strong cold center over northern Eurasia and two relatively weak warm centers over the Arctic and East Asia, respectively. The triple SAT pattern moves southeastward with time, and it remains quasi-stationary from day −3 to day 3 and is coupled with an anomalous surface high over the Arctic and low over East Asia. This near-surface circulation configuration is attributed to a Rossby wave train emanating from the North Atlantic and propagating towards East Asia, which quite resembles the Scandinavia pattern. The triple SAT pattern is not only confined near the surface but also extends deep into the troposphere, with a decreasing amplitude with height. The analysis of the temperature tendency equation indicates that the tropospheric temperature anomalies associated with the triple SAT pattern are primarily caused by horizontal temperature advection via two processes. First, the northerly wind anomalies in the western flank of the triple SAT pattern-associated cyclonic center over northern Eurasia advect cold air from the Arctic toward Eurasia and trigger cold anomalies over west Eurasia. Second, the above-mentioned cold center-resultant zonal temperature gradient is advected by background westerly wind, generating cold advection from west Eurasia to the east and further leading to cold anomalies over east Eurasia. As such, both the advection of climatological temperature by subseasonal meridional wind anomalies and the advection of subseasonal temperature anomalies by climatological zonal wind play a crucial role in the formation of the subseasonal triple SAT pattern. The above mechanism seems in contrast to Yang and Li (2016), which suggests that the advection of subseasonal temperature anomalies by climatological meridional wind is dominant, but it is not the case. Yang and Li (2016) investigated the southeastward propagation of the triple SAT pattern. In contrast, the current study investigates the growth and decay. These two aspects together portrait a full picture on both the formation and propagation of the leading wintertime subseasonal SAT variability over Eurasia. Last but not least, the Scandinavia pattern is found to account for the subseasonal triple SAT pattern. Although the triple SAT pattern-associated temperature anomalies are confined in the troposphere, the Scandinavia pattern can be coupled to stratospheric processes (Pang et al 2021). It is well known that the stratosphere is an important source for the tropospheric intraseasonal variability in the mid-and high latitudes. Therefore, it is meaningful to investigate the possible role of the stratosphere and its interactions with the tropospheric circulations in the formation of the subseasonal triple SAT pattern over Eurasia.
No new data were created or analyzed in this study.