Precursory atmospheric circulations with Rossby wave trains leading to Eurasian extreme cold events

This work examines precursory atmospheric circulations with various wave trains contributing to extreme cold weather over central Eurasia in boreal winter from 1979 to 2019. By conducting extended empirical orthogonal function (EEOF) on the preceding propagation circulation fields 2 weeks before the onset of extreme cold event (ECE) cases, three types of ECEs with different disturbance origins are classified and analysed. Type 1 denotes the positive phase of EEOF mode 1, shows as negative phase of Arctic Oscillation‐like pattern. The outbreak of this type of ECE is affected by a wave train originating from Baffin Bay, where an anomalous anticylonic system persisted under a background of weakened westerlies over middle‐high latitudes. Type 2 is picked from positive phase of EEOF mode 2, manifests as a developing blocking system that forms over Scandinavia and shifts to the Barents area. It is found that the blocking system is mainly strengthened by the downstream dispersion process of wave packets that are generated at the northern exit area of the North Pacific westerly jet, where exist anomalous cyclonic zonal wind shear and precipitation. Type 3 is selected from the negative phase of EEOF mode 2, which has a similar origin to type 2 but with the North Pacific jet exit more southward. Then, the generated wave packets propagate to Europe along the northerly jet stream over the North Atlantic, which acts as a waveguide and extends the wave train to downstream. In a word, these three types of precursory atmospheric wave train patterns that bring extreme cold anomalies to Eurasia possess diverse disturbing sources and downstream development mechanisms, and the essential role of the westerly jet is further highlighted. The results, which are investigated based on a quasi‐biweekly time scale, may deepen our understanding of the atmospheric genesis of extreme weather and improve extended‐range weather forecast.


| INTRODUCTION
Frequent extreme cold events (ECEs) occurred in the boreal winter over mid-latitude continents in recent years in spite of the global warming phenomenon (Cohen et al., 2014;Lu et al., 2016;Ma et al., 2018;Mori et al., 2019;Rudeva & Simmonds, 2021), such as the persistent cold surges in Asia in 2012 (Wu et al., 2017), the "boss level" cold wave in 2016 (Ma & Zhu, 2019), cold weather that simultaneously invaded North America and Asia in 2017-2018 (Tachibana et al., 2019), and successive cold outbreaks hit China in 2021 (Yao et al., 2021). It is known that extreme weather prediction is a difficult issue hampered by the variability and indeterminacy of atmosphere circulation (Hoskins, 2013;Luo & Wang, 2017;Wirth et al., 2018), hence the mechanism of the corresponding circulation system generation is an essential issue to investigate.
Many atmospheric circulations can induce extreme climate anomalies over the Eurasian continent. For example, the North Atlantic Oscillation (NAO) pattern can exert an influence on the weather over the Eurasian continent after its mature phase (Bollasina & Messori, 2018;Cheung et al., 2012); the Scandinavian (SCAND) pattern (Barnston & Livezey, 1987), which is typically generated from the North Atlantic (Wang & Tan, 2020), can exert cold temperature in Eurasia (Liu et al., 2014). Park et al. (2014) divided the circulation pattern that results in East Asian cold surges into wave-train and blocking types, pointing out the efficient role of the blocking system on the temperature drop. Many researchers have emphasized the role of Ural blocking on the cold surges of Eurasia (He & Wang, 2016;Tyrlis et al., 2019;Yao et al., 2017), which is deemed as a critical bridge linking Arctic warming and cold Eurasian continent (Luo et al., 2016;B. Luo et al., 2019). The blocking-type circulation occurs more frequently under the negative phase of the Arctic Oscillation (AO − ) pattern (Cheung et al., 2012;Park et al., 2011), which increases the frequency of cold surge occurrence (Jeong & Ho, 2005). In addition to the circulation over the mid-latitude, the cold extremes in midlatitudes can also be influenced by the circulation anomalies in both the Arctic and tropics (Rudeva & Simmonds, 2021). Yang et al. (2020) have pointed out that the atmospheric system affected cold surge in East Asia presents interdecadal variation, which transitioned from zonal wave train type to blocking structure. Therefore, a systematic examination of the circulation mechanism of extreme cold occurrences is necessary.
Besides, on some occasions, the atmospheric wave trains can propagate along the strong westerly jets (Hoskins & Ambrizzi 1993), which can serve as the efficient Rossby waveguides (Branstator, 2002;Chang, 1999). When a wave train extracts energy from mean flow, it promotes the advancement of the Rossby wave (Hu et al., 2018;Kosaka et al., 2009), and extreme weather occurs under the configuration of mature atmospheric circulation. In other words, the Rossby waves can propagate from upstream to downstream along with the westerlies as wave packets, which can be observed in the upper troposphere. Therefore, in addition to the typical teleconnection circulation and blocking system, the evolution of Rossby wave itself can also be a precursor to extreme weather (Fragkoulidis et al., 2018;Wirth et al., 2018;Wirth & Eichhorn, 2014). Certainly, not every extreme weather event is necessarily related to a wave packet precursor (Barton et al., 2016;Wirth et al., 2018), and the situation of wave packets that may induce cold extremes remains unknown. These issues motivate us to wonder whether there is potential forecast value for precursory wave packets of extreme cold events in Eurasia.
This work will focus on the formation and evolution mechanisms of circulation that lead to Eurasian cold events, which commence with precursory signals of different types of cold events. Generally, the classification of cold occurrences can be based on different factors, such as the cold air pathways (Abdillah et al., 2021), the duration of cold surges (Pang et al., 2020;Xie & Bueh, 2017), or the weather type of cold seasons by clustering methods (Gerlitz et al., 2018;Park et al., 2014). Here we decide to use the Extended Empirical Orthogonal Function (EEOF; Weare & Nasstrom, 1982) method, which can extract the dominant evolution pattern and avoid some subjective choices of clustering methods in determining the number of classification, to make the classification based on the corresponding precursory propagating signals of cold events. The dataset and methods are shown in Section 2. The classification details will be described in Section 3, including basic features of the corresponding circulation of each type. The development mechanisms of each type of cold event are discussed respectively in Section 4. Conclusions and discussions are presented in Section 5.

| DATA AND METHODS
The daily mean European Centre for Medium-Range Weather Forecasts reanalysis version 5 (Hersbach et al., 2020) for boreal winter (December-February [DJF]) from 1979-2019 is used, with a horizontal resolution of 1 latitude × 1 longitude. Variables include the 2-m surface air temperature (SAT), sea level pressure (SLP), geopotential height, zonal (u), meridional (v) winds and total precipitation. Anomalies of each variable are calculated by subtracting the 1979-2019 climatological mean for each calendar day at each grid point.
To investigate the mechanisms of Eurasian cold weather, 33 extreme cold events are identified over central Eurasia (40 N-60 N, 60 E-120 E), where manifested a cooling trend over recent years (Cohen et al., 2014;Mori et al., 2019) and increased trend of extremely cold winters (Luo, Chen, et al., 2019). An extreme cold event is defined as at least three consecutive days during which the domain-averaged SAT of central Eurasia is below the 10th threshold (namely, 253.65 K or −19.5 C). Besides, the interval between two cold events needs to exceed 15 days to avoid non-independent circulation systems (Wu et al., 2017). Lag 0 for a cold event is defined as the onset day that the domain-averaged SAT index first reaches its criterion, and the life cycle of each event refers to the number of consecutive days that meet the standard. The detail of the classification of cold events will be introduced in the next section. The wave activity flux (WAF) following Takaya and Nakamura (2001), which is parallel to the local group velocity of stationary Rossby wave and can be used to describe the propagation of the atmospheric wave train, is calculated and expressed as follows: where φ, λ, and z denotes latitude, longitude, and vertical coordinate, respectively; a is Earth' radius, f 0 is Coriolis parameter, p is pressure, N 2 is buoyancy frequency squared; U, V denotes the climatological zonal and meridional horizontal wind, and ψ 0 is anomaly of stream function.
Finally, a two-tailed Student's t-test is used for statistically significant levels.

| Classification of Eurasian ECEs
To extract different precursory features of circulation before the outbreak of ECEs, we conduct EEOF analysis on the pentad-mean anomalous SLP fields over the northern hemisphere during lag −14 to lag 0 days of all ECE cases. Unlike the conventional EOF approach, which assumes spatial stationery, the EEOF method can capture the spatial and temporal characteristics of the atmospheric mode simultaneously, making it more amenable to our study. A similar way is also applied in many studies that analyse atmospheric teleconnection circulation in the intra-seasonal time scale (Baxter & Nigam, 2013;Bollasina & Messori, 2018). Figure 1 presents two leading EEOF modes and corresponding principle components (PC). In the EEOF mode 1 (Figure 1a), a negative Arctic oscillation (AO − ) -like pattern can be recognized in three pentads. In the meanwhile, positive SLP anomalies with progressively stronger amplitude appear over southern Greenland. For EEOF mode 2 (Figure 1b), prominent anticyclonic anomalies present over Scandinavia in the first pentad (lag −14 to −10), gradually shifting to Barents-Kara Seas with increased amplitude. These two leading circulation modes are similar to the patterns, namely wave train under the background of AO − pattern and blocking system pattern, which many researchers have emphasized can affect Eurasian cold winter (He & Wang, 2016;Luo, Chen, et al., 2019;Park et al., 2011Park et al., , 2014. In addition, as can be seen in Figure 1c,d, several cases perform as negative PC values. Note that here both the positive and negative phase of EEOF modes are related to cold outbreaks over Eurasia. We next classify all the cold cases according to the maximum absolute value of PC. As shown in Figure 1c,d, there are 11 cases in PC 1 that are attributed to type 1 (green bar in Figure 1c), 15 cases in PC 2 as type 2 (green bar in Figure 1d), and 5 cases in negative PC 2 as type 3. Two cases shown as negative PC 1 (blue bar in Figure 1c), indicating a direct influence of the Arctic polar vortex southward instead of wave train impacts, are excluded temporarily due to the small sample size. In this way, all the cases are classified into three types of events with different precursory evolutional signals. Figure 2 depicts the distribution of the cumulative negative temperature (multiplied by −1) during the lifecycle of each ECE with the corresponding classification. In general, it can be seen that the cold cases occurred more frequently after the winter in 1999/2000. This phenomenon, namely the frequent cold winter in Eurasia after 2000, has attracted many scholars' attention (Cohen et al., 2014;Kug et al., 2015;Lu et al., 2016;Luo, Chen, et al., 2019;Ma et al., 2018;Mori et al., 2019). In the meanwhile, an upward trend in cumulative temperature can be observed from 1990 to 2010, demonstrating the extreme extent of cold events increased during this period. In the following, the basic atmospheric feature over the troposphere after composite analysis of these three groups of events will be shown.
3.2 | Corresponding atmospheric circulation anomalies Figure 3 shows the evolution of the composite anomalous 500-hPa geopotential height and SAT fields of the three types of ECEs. It can be seen that the strong cold anomalies over central Eurasia can last at least 5 days in all types of events (lag 0-4 days in Figure 3). In type 1 event ( Figure 3a), a positive anomalous action centre is located around southern of the Greenland at lag −14 days, developing at maximum amplitude around lag −2 days. In the meanwhile, negative SAT anomalies present over the mid-Siberia and move southward. After that, the cold anomalies strengthen and intrude into Eurasia at lag 0, while the positive height anomalies upstream decay. It should be noted that the anticyclonic anomalies over F I G U R E 1 Spatial patterns (a,b) and normalized principle components (PC) (c,d) of two leading EEOF modes on the three pentadmean anomalous SLP (units: hPa) fields during lag −14 to 0 days based on 33 cold events, explaining 16.6% and 10.3% of the total variance, respectively. Dotted are in a,b indicate the anomalies are statistically significant above the 95% level of confidence. Green bar in c (d) denotes the case is attributed to type 1 (2), blue bar in d denotes the case is classified as type 3. Two cases shown in blue bar in c are discarded temporarily. The grey bar in c,d denotes the PC value performs better in the other mode.
Greenland last a considerable period, almost throughout the whole process, which may due to positive feedback of sea ice loss over Baffin Bay (figure omitted). In type 2 (Figure 3b), a wave train can be clearly observed at lag −14 days, stretching from the middle North Pacific across north of the North Atlantic to Greenland. After that, an anomalous anticyclonic centre begins to develop over Scandinavia at lag −10 and propagates to Barents-Kara Seas at lag −2 days, forming a strong blocking system and leading cold air intruding into Eurasia at lag 0. The evolution of circulation in type 2 is similar to the Scandinavian pattern, which usually manifests itself as Rossby wave trains arising from disturbances over the North Atlantic (Wang & Tan, 2020). Type 3 is selected from negative PC 2, however, the daily evolving circulation fields do not show a completely symmetrical opposite feature to type 2, as shown in Figure 3c. A wave train beginning from southern North America across the North Atlantic and propagating to Barents Sea can be observed at lag −14. Then, the anticyclonic anomalies begin to form and develop over north of the Siberia, which results in a cold outbreak over Eurasia. According to the above analysis, we know the basic characteristic of circulation evolution.
In the next section, the source and generation mechanisms of atmospheric circulation in these three kinds of ECEs will be explored by examining the situation of Rossby wave packets and westerlies.

| THE FORMATION MECHANISMS OF THE THREE TYPES OF WAVE TRAINS
To exhibit the propagating process of wave trains, Figure 4 shows the pentad-mean averaged composite fields of 250-hPa meridional wind and WAF of three types of ECEs.
In type 1 (Figure 4a), two wave trains can be recognized from the Bering strait to south of the North America and from the Baffin Bay to the European continent at first pentad (lag −14 to −10 days). Obviously, it is the wave train originating from the Baffin Bay that affects the Eurasia ECEs since the wave train originating from the Bering strait almost decays in the second pentad (lag −9 to −5).
In the meanwhile, there are WAFs propagating from the wave packets over the Baffin Bay downstream, which induce a wave packet generated downstream. After that, the WAFs propagate into Eurasia, leading to the outbreak of ECEs, with the upstream wave packets gradually decaying. In type 2 (Figure 4b), a wave train presents over the North America across Greenland to the Barents Sea in the first pentad; then, the wave packets develop downstream with the propagation of upstream WAFs. Interestingly, in type 3 (Figure 4c), there is a succession of wave packets present around 30 N in the first pentad, which is at lower latitude compared with that of type 2. Furthermore, it seems that the disturbance origin of wave packets is also arriving from the middle North Pacific. After that, the wave packets propagate downstream in the northeastern direction along with the transportation of WAFs. Besides, it can be seen that the amplitude of wave packets in type 3 is stronger than that of type 2, which may be due to the smaller number sample size of type 3. According to above analysis, we know the different paths of the wave train evolution in these three type of ECEs. It is known that the development of Rossby wave packets is closely related to energy dispersion and waveguide (Fragkoulidis & Wirth, 2020;Wirth et al., 2018). To learn more about the development process of wave trains of each type, we will further examine the process of energy dispersion and the role of the westerly jet.
It is known that the process of energy dispersion on downstream development can be better observed from the Hovmöller diagram of meridional wind over the upper troposphere (Chang, 1999;Glatt et al., 2011). Figure 5 presents the Hovmöller diagram of 250-hPa meridional wind of the three types of ECEs, which averaged based on the latitude range of the wave packets located in Figure 4. Here the meridional wind is zonally filtered to extract wave numbers 1-7, thus eliminating unimportant local signals (Fragkoulidis et al., 2018). For type 1 event (Figure 5a), the positive meridional wind anomalies arise from around 60 W, where the wave packet over Baffin Bay located in Figure 4a, appears as early as lag −18 days. However, clear energy dispersion signals with faster group velocity than phase velocity present until lag −10, as indicated by the green arrow. These strong successive wave packet signals are suddenly weakened around lag −1, demonstrating the dispersion of F I G U R E 2 Time series of cumulative negative temperature (units: K; multiplied by −1) of 33 ECE cases and corresponding classification. energy due to the outbreak of cold events. Similar situations can also be found in types 2 and 3. The first wave packet in type 2 is located at 160 W, which arises almost at lag −20 days (Figure 5b). Around lag −10 days, two successive wave packets around 0 and 60 E begin to develop, with the upstream wave packets gradually decaying. For type 3 event (Figure 5c), however, a prominent dispersion process can be observed until around lag −8. It can be seen that the wave packets also originate from around 160 W, similar to type 2. This prompted us to examine the situation of a westerly jet over the middle North Pacific, where the exit area of the jet located. Figure 6 presents the composite of 200-hPa zonal wind with anomalies averaged of three pentad-mean before the outbreak of the ECEs. It can be seen that the negative anomalous zonal wind basically dominates high latitude areas with gradually increased amplitude in type 1 event (Figure 6a), especially over north of the North F I G U R E 3 Lead-lag composite of anomalous SAT (shading; unit: K) and 500-hPa geopotential height (contour; unit: gpm, CI = 40 gpm) fields for the three type cold events from lag −14 to 4 days. The thick line and shaded area denote that the anomalies are statistically significant above the 95% level of confidence. The green rectangle denotes the Eurasia area we selected cold events, same as in following figures.
Atlantic, which is beneficial to the development and persistence of the anticyclonic system over the Baffin Bay area as shown in Figure 4a. This kind of situation, which usually represents the decrease of the meridional temperature gradient due to the Arctic warming, is conducive to the invasion of cold air from Arctic to midlatitude (Cohen et al., 2014;Lu et al., 2019;Zhang & Luo, 2020). In type 2 (Figure 6b), an anomalous triple structure can be found over the North Pacific in the first two pentads, with strong positive anomalies strengthening the westerly jet. We noted that the northern exit area of the westerly jet, where the cyclonic wind shear exists, coincides with the start position of wave packets (first pentad in Figure 4b). It is known that the growth of disturbance mainly depends on extracting kinetic energy from the basic state, and this process is found to be greatest in the Pacific jet exit region F I G U R E 4 The composite fields of 250 hPa meridional wind (shading, unit: m s −1 ) and WAF (vector, unit: m 2 s −2 ) based on three types of ECEs averaged from lag −14 to −10 days, lag −9 to −5 days, and lag −4 to 0 days, respectively. Dotted area denotes that the meridional wind anomalies are statistically significant above the 95% level of confidence.

F I G U R E 5
The composite Hovmöller diagram of 250-hPa meridional wind averaged between 45 to 80 N for type 1 (a), 55 to 85 N for type 2 (b), 30 to 70 N for type 3 (c). The longitude scope of Eurasia is presented by green line, and the onset day is marked by red line. Green vector signifies the direction of group velocity. Dotted area denotes that the anomalies are statistically significant above the 95% level of confidence. (Simmons et al., 1983). To examine the existence of wave source, here we also present the situation of precipitation anomalies over the crucial jet exit region. In this area, as the vorticity increases with height, upward motion occurs and precipitation is generated. The latent heat release of precipitation can be a wave source of disturbance generation. Therefore, we suggest that the wave packets in type 2, which promote the maturity of anticyclonic system over Scandinavia through the energy dispersion process, are originating from the North Pacific jet exit region. A similar situation also presents in type 3, but with the location of jet exit region more southward. As shown in Figure 6c, anomalous cyclonic wind shear manifest over jet exit area in the pentad 2 and 3, which appears later than type 2. This is consistent with the emergence of signal in the Hovmöller diagram (Figure 5c). The precipitation centre located around 30 N, southward compared with type 1, corresponding with the location of initial wave packets in Figure 4c. Furthermore, positive zonal wind anomalies dominated the middle North Atlantic, which induced the Atlantic jet to extend northeastward, reaching maximum amplitude at the second pentad (lag −9 to −5). Accordingly, it can be seen that the direction of wave packets propagating at pentad 2 precisely matches the way of westerly jet stretch (Figure 4c), which denotes the westerly jet may act as a waveguide here to promote the wave packets developing to downstream. In many studies, the wave packets are usually found in the subtropical westerly jet over Asia (Watanabe, 2004), which can easily affect the precipitation over south China (Hu et al., 2018;Li & Sun, 2015;Sun & Guan, 2020). In this work, however, the westerlies over North Atlantic in type 3 event can also act as a waveguide.
It is known that the jet stream exit area is also deemed as a place where beneficial to the formation of blocking (Nakamura & Huang, 2018), low-latitude wave growth (Fragkoulidis & Wirth, 2020), and the formation of Rossby wave source (McCrystall et al., 2020). In this work, we highlight the role of anomalous westerlies on the mechanisms of Rossby wave development. The development of wave packets in the three types of ECEs is closely related to weakened westerlies over high-latitude, cyclonic wind shear of the Pacific jet exit region, and the waveguide of strengthened westerlies over the middle Atlantic.

| SUMMARY AND DISCUSSIONS
In this study, we categorize the precursory circulation of extreme cold events over central Eurasia into three types F I G U R E 6 The composite 200-hPa zonal wind (black contour, unit: m s −1 ), and anomalies (shading) averaged from lag −14 to −10 days, lag −9 to −5 days, and lag −4 to 0 days based on three types of ECEs. Grey dotted area denotes that the anomalies are statistically significant above the 95% level of confidence. In type 2 and 3 (b,c), the green dots distributed inside blue rectangle denote the composite total precipitation anomalies over the crucial jet exit era.
by conducting an EEOF analysis on the evolutional pentad-mean SLP fields during 2 weeks before the outbreak of cold cases. Accordingly, type 1 is selected from the case of the positive phase of EEOF mode 1, manifested like AO − mode. Type 2 is picked from the case in positive phase of EEOF mode 2, shown as a developing blocking system that formed over Scandinavia and shifted to the Barents area. Type 3 denotes the negative phase of EEOF mode 2, exhibiting asymmetrical opposite evolutional and development features with type 2. The two cases that manifest as negative phase of EEOF mode 1 are discarded here due to small sample size. According to the classification, each type of precursory anomalous atmospheric mode is found to be associated with Rossby wave trains originating from different positions and situations. The development process of wave packets and the role of the westerly jet in each type of event are examined, respectively.
As shown in Figure 7a, in type 1 event, the wave train that affects Eurasia originates from the Baffin Bay area, where located a strong and persistent anomalous anticyclonic system. In the meanwhile, weakened westerlies dominated high-latitude area, leading the anticyclonic system develop. The continuous process of energy dispersion from the anticyclonic anomalies promotes the development of downstream systems, leading to the cold air intruding into Eurasia. The circulation system that affects type 2 event (Figure 7b) is found to be originated from the Pacific jet exit region, where can be deemed as a wave source that was accompanied by anomalous cyclonic wind shear and precipitation, forming a wave train that starts from the middle North Pacific and extends to Greenland along the northeastern direction. The dispersion of this series of wave packets provides the energy source for the anomalous anticyclonic system over Scandinavia, which further develops into a blocking system F I G U R E 7 Schematic diagram showing the development source and propagation path of wave trains before the outbreak of each type of ECE (upper level) and corresponding surface air temperature mode (low-level). In the upper level, the green dot denotes the source of disturbance; the contour indicates 250-hPa meridional wind anomalies; the red (blue) solid arrow denotes strengthened (weakened) westerlies over 200 hPa; the green solid arrow represents the development direction of wave packets; the red dashed arrow signifies the waveguide role of Atlantic jet. In the lower level, the shading area represents the anomalies of surface air temperature during the lag 0 to 4 days, where the blue (red) denote negative (positive) temperature anomalies; the anticlockwise circle in a represents the strong anticyclonic SLP anomalies correspond to wave source; the precipitation circle in b and c correspond to the wave source related to jet exit region. over the Barents Sea. A similar situation is found in type 3 (Figure 7c), whose disturbance is also originating from the exit area of the Pacific jet but with lower latitude. Furthermore, positive zonal wind anomalies dominated the middle North Atlantic, which induced the Atlantic jet to extend northerly, acting as a waveguide leading the southerly wave packets to propagate into the Eurasian continent.
In our analysis, weakened zonal wind over middlehigh latitude with AO − -like patterns are deemed as the background of the first type of cold events, that is, the first main mode of EEOF. This may also represent the mainly precursory pattern of extreme cold surges over Eurasia in the era of Arctic amplification, which decrease the temperature gradient (Francis & Vavrus, 2015;Yuval & Kaspi, 2020). It is known that blocking-induced cold surges are prone to occur in the periods of AO − pattern (Cheung et al., 2012;Park et al., 2011Park et al., , 2014Zhuo et al., 2022). Here we highlighted the persistent anomalous anticyclonic system over the Baffin Bay area under the AO − -like pattern, which can provide continuous energy for the downstream system, resulting in the extreme cold over Eurasia. In the second EEOF mode, the circulation of type 2 and 3 both originated from the anomalous cyclonic wind shear over the Pacific jet exit region, then propagated to Eurasia via the energy dispersion process. Furthermore, it is found that the northerly Atlantic jet can guide wave packets from low latitude to Eurasia over mid-high latitude in type 3. These results further demonstrate the essential role of the westerly jet in the cold outbreak of Eurasia, which is an important source of disturbance generation and a waveguide for the relay effect. Many studies have emphasized the waveguide role of South Asian jet, which can affect the rainfall over Asia (Chang, 1999;Ding & Li, 2017;Ding & Wang, 2005;Li & Sun, 2015). Our results further highlight the function of the Pacific jet exit and Atlantic jet stream. Besides, although the cold events we discussed are focused on central Eurasia, simultaneously cold temperature is found over North America in type 1 and 3 (lower level in Figure 7a,c). Therefore, more circulation mechanisms that can affect multiple continents are worth investigating.
As discussed in Wirth et al. (2018), there is no clear answer yet whether the presence of precursor Rossby wave packets helps to improve the prediction of extreme weather, which lies in the systematic contact between wave packets and extreme weather. In our work, clear wave packets signals were found around 2 weeks before the outbreak of cold events in types 1 and 2, and precursory signals were found only 1 week before in type 3, suggesting that the Rossby wave packets can indeed act as a precursor signal of extreme cold weather to some extent. In other words, the results have some indicative implications for the improvement of the extended-range weather forecast. Certainly, it is not enough to illuminate the connection from a small sample of extreme cases we selected, thus, more possible mechanisms of precursory wave trains that can lead to extreme weather remain to be explored in the future.