1. Introduction
Observations show that under the background of global warming, the near-surface air temperature in the Arctic has risen rapidly, with the rate of warming reaching more than twice the global average (Polyakov et al. 2002; Screen and Simmonds 2010) and most recently exceeding the global average surface temperature trend by more than 3 times (Chylek et al. 2022; Thoman et al. 2022). However, in recent decades, the Eurasian continent has been frequently attacked by cold air, and there is a widespread cooling trend (Cohen et al. 2012; Mori et al. 2014; Zhang et al. 2012). Although the cooling trend may not necessarily be robust (Blackport and Screen 2020; Cohen et al. 2023), this counterintuitive phenomenon of the Arctic and midlatitude Eurasia exhibiting opposite temperature trends is known as the “warm Arctic–cold Eurasia (Siberia or continent)” (WACE) pattern (Inoue et al. 2012; Luo et al. 2016; Overland et al. 2011). Weather-related disasters or extremes such as cold surge, blizzard, and freezing rain accompanied by the WACE pattern have had serious impacts on the social economy and living environment (Ding et al. 2008; Ma and Zhu 2019). Therefore, it is important to investigate and understand variations in the WACE pattern.
The WACE pattern has prominent intraseasonal, interannual, and interdecadal variations (e.g., Cohen et al. 2014; Luo et al. 2022; Sung et al. 2018; Tyrlis et al. 2020; Wegmann et al. 2018; Yao et al. 2017; Ye and Messori 2020). With respect to the interannual time scale, numerous previous studies have extensively explored the reasons for the variation in the WACE pattern. Some studies have focused on the role of external forcing. For example, the sea ice loss in the Barents-Kara Seas might contribute to the WACE pattern through intensified turbulent heat flux (Honda et al. 2009; Sorokina et al. 2016). The snow cover reduction in northern Eurasia may favor the WACE pattern by quasi-stationary planetary wave activity via stratospheric processes (Xu et al. 2018). Additionally, the meridional shift of a sea surface temperature front over the Gulf Stream results in the WACE pattern through the excited planetary wave (Sato et al. 2014). However, the impact of sea ice conditions on the WACE pattern is considered to be less significant (Blackport et al. 2019; McCusker et al. 2016; Peings et al. 2023) and some numerical experiments have argued that the decrease in Arctic sea ice is not significantly linked to the WACE pattern (Boland et al. 2017; Labe et al. 2020; Sun et al. 2016), which suggests that the internal atmospheric variability should be taken seriously in the variation in the WACE pattern (Peings et al. 2021).
In contrast, some studies have emphasized the role of internal atmospheric variability. The weakening of the zonal flow and the strengthening of the wave amplitude may benefit the warm air entering the Arctic region and the cold air invading Eurasia, thereby leading to the variation in the WACE pattern (Francis and Vavrus 2012; Outten and Esau 2012; Screen and Simmonds 2013; Cohen et al. 2020; Overland et al. 2021). Furthermore, the persistent Ural blocking associated with the positive phase of the North Atlantic Oscillation (NAO) is thought to significantly impact the WACE pattern (e.g., Luo et al. 2016; Tyrlis et al. 2020; Wegmann et al. 2018; Yao et al. 2017). However, a recent study indicated that a stronger-than-normal Ural blocking followed by a WACE pattern is modulated by the significantly weakened midlatitude westerly jet over Eurasia (Xu et al. 2022). In addition, Inoue et al. (2012) reported that the change in cyclone activity paths over the Barents Sea is the dominant mechanism for the WACE pattern by focusing on the role of sea ice. In view of the intimate linkage between the zonal wind and the storm track, as well as the latter also referring to migratory transient eddies traveling in the prevailing westerlies, variations in the WACE pattern may be understood from the perspective of the storm track.
The synoptic-scale disturbances in Siberia are the most active in the Northern Hemisphere during boreal winter apart from the North Pacific storm track and the North Atlantic storm track (Blackmon 1976; Bengtsson et al. 2006; Hoskins and Hodges 2019). Hoskins and Hodges (2002) referred to it as the Siberian storm track. It is located between the two major storm tracks over the oceans, deep in the central part of the Eurasian continent, and has a more complex geographical environment (Ma et al. 2017). The Siberian storm track is also geographically close to the WACE pattern and Ural blocking. Considering that the storm track can interact with the atmospheric blocking (Holopainen and Fortelius 1987; Hwang et al. 2020; Shutts 1983), there may be a possible relationship between the Siberian storm track and the Ural blocking. On the other hand, the WACE pattern may influence the Siberian storm track by modifying the meridional temperature gradient. Therefore, focusing on the Siberian storm track may provide new insights into the interannual variations in the WACE pattern.
In this study, we aim to investigate the relationship and interactions between the Siberian storm track and the WACE pattern on the interannual time scale and further explore the underlying physical mechanism on the intraseasonal time scale. The present study is organized as follows: descriptions of the data and methods are presented in section 2; the relationship between the Siberian storm track and the WACE pattern is addressed in section 3; the association among the Siberian storm track, WACE pattern, and Ural blocking on the intraseasonal time scale is investigated in section 4; and a summary and discussion are given in section 5.
2. Data and methods
a. Data
Daily and monthly mean atmospheric variables, including the geopotential height, horizontal winds, air temperature, and sea level pressure, were obtained from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) global atmospheric reanalysis datasets (Kalnay et al. 1996). The horizontal resolution was 2.5° × 2.5°, and the time span was from 1948 to 2022. Monthly sea ice area fraction was provided by the Hadley Centre Global Sea Ice and Sea Surface Temperature (HadISST) dataset version 1.1 (Rayner et al. 2003) with a horizontal resolution 1° × 1°. Winter was defined as the period from 1 December to 28 February (90 days). The linear trend of all variables is removed. The fast Fourier transform is applied to extract interannual signals that have periods less than 10 years. When calculating the regional average, the box-averaged indices are weighted by the cosine of the latitude to avoid overweighting the high latitudes.
b. Representation of the storm track
To conveniently measure the intensity variation in storm track activities, the box-averaged variance of 24-h difference-filtered geopotential height at 500 hPa over 50°–70°N, 30°–80°E is defined as the Siberian storm track index (SSTI). In addition to the interannual time scale, this study also focuses on the intraseasonal time scale, which involves activity identification. If the detrended SSTI for two consecutive days is greater than the standard deviation of the daily SSTI encompassing all winters, it is identified as a Siberian storm track activity. Since synoptic-scale disturbances have a life cycle shorter than a week, we assume that an activity lasts for no more than 6 days, and the day with the maximum SSTI is regarded as the peak day. A total of 194 Siberian storm track activities are identified during the wintertime from 1948/49 to 2021/22.
c. WACE index
The difference in the box-averaged winter-mean near-surface air temperature anomalies at 2 m between the Barents-Kara Seas (65°–85°N, 30°–90°E) and central Eurasia (40°–60°N, 60°–120°E) is defined as the WACE index (WACEI; Luo et al. 2022).
d. Detection of the atmospheric blocking
3. Interannual relationship between the Siberian storm track and the WACE pattern
a. Statistical analyses
Figure 1a shows the regressed pattern of the winter-mean near-surface air temperature against the standardized interannual SSTI. There is a meridional dipole with prominent cooling over the Barents and Kara Seas and Novaya Zemlya, and remarkable warming over central Eurasia. This anomalous temperature pattern related to the SSTI is almost similar to the WACE pattern (Fig. 1b), albeit with reversed signs and reduced magnitude. The main body of the climatological winter-mean Siberian storm track (contours in Fig. 1c) lies to the middle of the meridional dipole of the anomalous temperature. The intensified WACE pattern is associated with significantly negative storm track anomalies over western Russia and Kazakhstan (Fig. 1c), which suggests a weakened Siberian storm track. To avoid the possible effects of filtering on characterizing the storm track activity, Fig. 1d shows the results based on the Lanczos bandpass filter (Duchon 1979) by isolating synoptic-scale (2–8-day) disturbances. We can see that both the climatological winter-mean Siberian storm track and the WACE-related regression pattern correspond well with those derived from the 24-h difference filter, albeit with different magnitudes. Thus, it can be inferred that the Siberian storm track anomalies associated with the WACE are independent of the filter to a large extent.
The standardized interannual time series of the winter-mean WACEI and SSTI are shown in Fig. 2a. It can be seen that in most years, a positive WACEI corresponds to a negative SSTI. The correlation coefficient between the WACEI and the SSTI is −0.62, with statistical significance at the 1% level, indicating a significant out-of-phase relationship between them. To examine whether the out-of-phase relationship between the WACE pattern and the Siberian storm track is robust during the period, Fig. 2b displays the 21-yr sliding correlation coefficients between the WACEI and the SSTI. Their 21-yr correlation coefficients are significant at the 1% and 5% levels most of the time and at the 10% level in the late 1990s and early 2000s. Furthermore, to eliminate the possible influence of the different storm track characterizations, Fig. 2b also exhibits the results based on some other commonly used Eulerian eddy metrics, including the variance of 24-h difference-filtered sea level pressure, the meridional eddy heat flux at 850 hPa, the eddy kinetic energy at 500 hPa, and the variance of filtered meridional wind at 250 hPa. Almost all the sliding correlation coefficients are significant at the 10% level, which reveals a robust out-of-phase relationship between the WACE pattern and the Siberian storm track. Therefore, it is suggested that the WACE pattern may potentially weaken due to the amplified Siberian storm track. The subsequent section will explain their negative correlation from the perspective of interactions between high-frequency transient eddies and the time-mean flow.
b. Physical interpretations
1) Atmospheric circulation and baroclinicity
Given that the storm track activity is symbiotic with the planetary-scale flow (Cai and Mak 1990), the WACE pattern may correlate to the Siberian storm track through the associated atmospheric circulation. Figure 3a shows the regressed specific humidity and horizontal wind anomalies at 850 hPa against the WACEI. In the lower troposphere, there is a noticeably anticyclonic circulation anomaly accompanied by the enhanced WACE pattern, with the anomalous center appearing over the south side of Novaya Zemlya. The southerly wind anomalies on the western flank of the anomalous anticyclone carry a large amount of heat and moisture northward. The Arctic can be warming directly by the warm advection and indirectly by the wet advection through the consequent increased downward longwave radiation and the release of latent heat. In contrast, cold and dry advections on the southeastern flank of the anomalous anticyclone can contribute to the cooling of the Eurasian continent.
In the middle troposphere, the prominent WACE pattern is associated with significantly positive geopotential height anomalies over northern Europe and northern Russia and negative anomalies over central Eurasia (Fig. 3b). The maximum amplitude of the positive anomalies is obviously larger than that of the negative anomalies, with the anticyclonic anomaly stronger than the cyclonic anomaly. The anomalous easterly wind on the southern side of the anticyclonic anomaly tends to weaken the prevailing westerly wind. In the upper troposphere, there is a band of easterly wind anomalies at the midlatitudes extending zonally across western Eurasia (Fig. 3c), which suggests attenuated atmospheric baroclinicity and is basically consistent with the storm track anomalies related to the WACE pattern (Fig. 1c). According to the linear theory of baroclinic instability (Charney 1947; Eady 1949), the storm track activity is shaped by the atmospheric baroclinicity. To investigate the variation in low-level atmospheric baroclinicity, Fig. 3d shows the regressed pattern of the low-level tropospheric maximum Eady growth rate (Lindzen and Farrell 1980) against the WACEI. Significantly negative atmospheric baroclinicity anomalies associated with the strengthened WACE pattern broadly coincide with the storm track anomalies, which indicates that the WACE pattern can suppress the Siberian storm track by attenuating the atmospheric baroclinicity over midlatitude Eurasia.
2) Feedback forcing from synoptic-scale eddies
c. Association with the Ural blocking
1) Interannual time scale
Note that the markedly positive geopotential height anomalies related to the strengthened WACE pattern (Fig. 3b) are also basically located in the climatological region of the Ural blocking (contours in Fig. 6). If the box-averaged blocking amplitude over 50°–75°N, 40°–90°E is defined as the Ural blocking index (UBI), Fig. 2a shows the standardized interannual time series of the wintertime UBI. The UBI is highly correlated with the WACEI, and their interannual correlation coefficient is 0.71. The significant in-phase relationship between the UBI and the WACEI conforms to previous results that the WACE pattern can be strengthened by the Ural blocking (e.g., Luo et al. 2016; Tyrlis et al. 2020; Yao et al. 2017; Zhao et al. 2022). In addition, the accelerated midlatitude westerlies due to the feedback forcing from the intensified Siberian storm track tend to suppress the Ural blocking. If one standard deviation of the SSTI is taken as the criterion, there are 10 and 15 selected winters with strong and weak Siberian storm track (Table 1), accompanied by 10 and 18 Ural blocking events, respectively. Figure 5 shows the time–longitude evolution of the composite Ural blocking-related geopotential height anomalies at 500 hPa. During the winters with strengthened Siberian storm track, the Ural blocking amplitude is weaker and the duration of Ural blocking events is shorter than those with weakened Siberian storm track.
Distributions of winters for the strong and weak SSTI from 1948/49 to 2021/22.
There seems to be a close connection among the WACE pattern, Siberian storm track, and Ural blocking. To further reveal the association of the Siberian storm track with the Ural blocking, Fig. 6 shows the regressed instantaneous blocking frequency and blocking amplitude against the SSTI. The intensified Siberian storm track is significantly accompanied by the reduced instantaneous blocking frequency (Fig. 6a) and weakened blocking amplitude (Fig. 6b) over the Ural Mountains. The interannual correlation coefficient between the SSTI and the UBI is −0.29 with statistical significance at the 5% level. If the storm track activity is characterized by other aforementioned Eulerian eddy metrics, their out-of-phase relationship is significant at the 1% level; for example, their correlation coefficient is −0.53 when the SSTI is derived from the variance of 24-h difference-filtered sea level pressure. In addition, the Siberian storm track is significantly positively correlated with the European blocking. If we define the European blocking index as the box-averaged blocking amplitude over 40°–65°N, 20°W–40°E, the correlation coefficient between the European blocking index and the SSTI is 0.42. The strengthened European blocking is accompanied by the accelerated upper-tropospheric westerly wind over the Norwegian Sea and Scandinavian peninsula (Yang et al. 2021b), which is associated with the enhanced Siberian storm track (Fig. 4d).
Previous studies suggested that the forcing of synoptic-scale eddies plays a crucial role in the generation and maintenance of atmospheric blocking (e.g., Hwang et al. 2020; Nakamura et al. 1997). Thus, the underlying dynamics behind the relationship between the Siberian storm track and the Ural blocking may be attributed to the feedback forcing from high-frequency transient eddies. Figure 7a shows the regressed pattern of transient eddy-induced geopotential height tendencies at 500 hPa against the UBI. Prominently positive anomalies over the east of the Scandinavian peninsula are significantly associated with the augmented Ural blocking amplitude. The negative geopotential height tendency anomalies above that position related to the intensified Siberian storm track (Fig. 4a) contribute to the negative interannual connection between the Siberian storm track and the Ural blocking. Meanwhile, the altered atmospheric baroclinicity that is associated with the Ural blocking is also anticipated to connect the Siberian storm track with the Ural blocking. However, it is difficult to identify causality between the feedback forcing from high-frequency transient eddies and the Ural blocking on an interannual time scale. Next, we will attempt to reveal their causal relationship on an intraseasonal time scale by focusing on blocking events.
2) Intraseasonal time scale
In this subsection, the association of the Ural blocking with the feedback forcing from transient eddies is investigated based on composite blocking events. There are a total of 83 Ural blocking events in all wintertime period from 1948/49 to 2021/22. In our composite time evolution, the high-frequency transient eddy-induced geopotential height tendencies are significantly intensified upstream of the initial blocking embryo (Fig. 7b), which corresponds to the interannual regressed peak region (Fig. 7a). Significantly positive forcing from high-frequency transients 2 days before the peak time can also be found in a previous study (Takaya and Nakamura 2005) that focused on the blocking events targeted at 57°N, 80°E. With the significant feedback forcing from transient eddies remaining almost stationary, the composite geopotential height field exhibits an omega-shaped blocking 1 day before the peak time (Fig. 7c). When the Ural blocking reaches its peak amplitude, the feedback forcing from transient eddies becomes the strongest (Fig. 7d). After the peak time, however, the amplitude of the Ural block is observed to decrease gradually accompanied by almost insignificant feedback forcing from transient eddies (Figs. 7e,f). From the composite time evolution of the Ural blocking events, it can be suggested that the feedback forcing from high-frequency transient eddies contributes to the formation and development of the Ural blocking. The results are consistent with previous observational and theoretical studies that emphasized the intimate relationship between the blocking and high-frequency transient eddies embedded in storm tracks (e.g., Luo et al. 2001; Nakamura and Wallace 1993; Trenberth 1986).
4. Association among the Siberian storm track, WACE pattern, and Ural blocking on the intraseasonal time scale
To better understand the relationship between the Siberian storm track and the WACE pattern on an intraseasonal time scale, we present a composite time evolution of near-surface air temperature anomalies (Fig. 8) based on 194 peaks in Siberian storm track activity (see Fig. A1 in the appendix). Two days before the peak time, modest negative air temperature anomalies are observed over the Barents and Kara Seas, while warm anomalies are observed over central Eurasia (Fig. 8a). A peak in Siberian storm track activity tends to be preceded by a weak cold Arctic–warm Eurasia pattern, which is associated with enhanced low-level atmospheric baroclinicity and provides favorable conditions for storm track activities. The spatial distribution of anomalous near-surface air temperature remains largely unchanged on the following day (Fig. 8b). However, the amplitude of air temperature anomalies increases significantly when the Siberian storm track reaches its peak (Fig. 8c). After the peak, the cold Arctic–warm Eurasia pattern becomes increasingly prominent, particularly 2–3 days after the peak time (Figs. 8e,f). Our results indicate that the peak time of the Siberian storm track activity precedes that of the cold Arctic–warm Eurasia pattern. The time evolution of near-surface air temperature anomalies suggests that the significant interannual out-of-phase linkage between the WACE pattern and the Siberian storm track results from the latter weakening the former.
Section 3c identifies the close connection among the Siberian storm track, WACE pattern, and Ural blocking on an interannual time scale. Given the contribution of the feedback forcing from synoptic-scale eddies to the formation and development of the Ural blocking (Fig. 7), it is necessary to explore the correlation between the Siberian storm track and the Ural blocking on the intraseasonal time scale. Figure 9 shows the composite time evolution of the geopotential height and horizontal wind at 500 hPa based on Siberian storm track activities. Due to the significant negative correlation of the Siberian storm track with the Ural blocking on the interannual time scale, there is a persistent anomalous cyclone circulation, or blocking low, over the vicinity of the Ural Mountains, which runs through the entire Siberian storm track activity. In general, the northerly wind anomalies in the rear of the anomalous cyclone transport polar cold air to the Barents and Kara Seas and cause the region to become colder. The southwesterly wind anomalies and the resulting warm advection on the southeast side of the anomalous cyclone circulation directly contribute to the positive air temperature anomalies over central Eurasia. For 2 days before the peak time of Siberian storm track activities, the amplitude of this cyclone circulation is relatively weak (Fig. 9a). The anticyclonic circulation over the Scandinavian peninsula may result from the European blocking. Then, the center of the cyclone strengthens on the following day (Fig. 9b). When the Siberian storm track activity attains its maximum intensity, the anomalous cyclone circulation becomes more intense (Fig. 9c). It is worth noting that the maximum amplitude of the anomalous cyclone continues to increase, reaching its peak 1 day after the peak time of Siberian storm track activities (Fig. 9d). The Siberian storm track activity preceding the Ural cyclonic circulation means that the preexisting incident synoptic-scale eddies may play a key role in the life cycle of blocking, which conforms to the nonlinear multiscale interaction model for atmospheric blocking established by Luo and Zhang (2020).
To check the possible role of the Siberian storm track activity in the Ural cyclonic circulation on the intraseasonal time scale, Fig. 10 shows the composite time evolution of feedback forcing from synoptic-scale eddies. A high-frequency transient eddy-induced intensification in anomalous cyclonic circulation is expected to be accompanied by the feedback forcing manifested as negative geopotential height tendencies. However, the slightly negative geopotential height tendencies induced by high-frequency transient eddies are observed over the Barents Sea until 1 day before the Siberian storm track activity attains its maximum amplitude (Fig. 10b). These negative geopotential height tendencies grow rapidly on the peak day (Fig. 10c) and expand downstream on the next day (Fig. 10d). These strong negative anomalies continue to persist until 1 day after the peak time, and then begin to dissipate on the second day (Fig. 10e). Looking back at the temporal evolution of the Ural cyclonic circulation, it also reaches its maximum approximately 1 day after the peak of the Siberian storm track activity, and then decays. It can be concluded that the feedback forcing resulting from the Siberian storm track activity is beneficial to the enhanced Ural cyclonic circulation.
Taking the peak day of the Siberian storm track activity as a reference, Fig. 11 exhibits the composite temporal evolution of box-averaged relevant variables. We can see that the maximum temperature difference between the Arctic region and central Eurasia occurs approximately 2–4 days after the peak of Siberian storm track activities. The box-averaged Ural cyclonic circulation associated with the Siberian storm track activity can maintain its intensity 1 day after the maximum Siberian storm track amplitude due to the high-frequency transient eddy-induced geopotential height tendency that can persist at full strength for 2 days. One may think that Ural cyclonic circulation is not directly corresponding to Ural blocking; in fact, both the frequency and strength of the Ural blocking reach their minimum values on the peak day of the Siberian storm track activity and remain relatively stable on the following day. The composite time evolution of Ural blocking is basically consistent with the feedback forcing associated with the Siberian storm track activity. Therefore, the Siberian storm track activity is a precursory signal for the weakened Ural blocking and WACE pattern.
5. Conclusions and discussion
In this study, we investigated the multiple time scale variations in the winter WACE pattern from the perspective of the Siberian storm track by using the NCEP–NCAR global atmospheric reanalysis dataset. Specifically, we studied the interaction between the WACE pattern and the Siberian storm track on the interannual time scale and explored the underlying physical mechanism on the intraseasonal time scale. The main conclusions are as follows.
The winter WACE pattern is prominently negatively correlated with the Siberian storm track on the interannual time scale. A winter with a noticeable WACE pattern tends to be accompanied by a weakened Siberian storm track. Their significant out-of-phase relationship is robust regardless of the choice of eddy metrics and filter methods. The intensified WACE pattern exerts a significant influence on the Siberian storm track by reducing the lower-tropospheric atmospheric baroclinicity over midlatitude Eurasia. The atmospheric circulation anomalies related to the WACE pattern are similar to those related to the Ural blocking but with reversed signs, and the Siberian storm track is also negatively correlated with the Ural blocking. The attenuated Siberian storm track can strengthen the WACE pattern by increasing high-frequency transient eddy-induced geopotential height tendencies over the Barents and Kara Seas.
The feedback forcing from synoptic-scale eddies associated with the Siberian storm track is important to the formation and development of the Ural blocking. The significantly negative anomalies of high-frequency transient eddy-induced geopotential height tendencies over the vicinity of Ural Mountains attain maximum intensity on the peak day of the Siberian storm track activity and maintain that intensity on the following day. The Ural cyclonic circulation associated with the Siberian storm track can also basically persist its maximum intensity for one day after the peak of the Siberian storm track activity, which contributes to a strong cold Arctic–warm Eurasia pattern 2–4 days after the peak of the Siberian storm track activity. The cold Arctic–warm Eurasia pattern preceded by the intensified Siberian storm track attenuates the winter WACE pattern. Therefore, the Siberian storm track can weaken the WACE pattern by suppressing the Ural blocking.
Instead of the Lagrangian definition manifested as tracking of cyclones (Hoskins and Hodges 2002), it should be emphasized that the present study focuses on the storm track activity by the Eulerian definition. Previous studies often used the Eulerian definition to investigate interannual and longer time scales or climatology (e.g., Hoskins and Hodges 2019; Ma et al. 2020; Yang et al. 2021c). To the authors’ knowledge, this is the first time it has been used to study the daily time scale. According to the physical interpretation of the Eulerian definition, the time-filtered eddy metric reflects both cyclonic and anticyclonic activities. Because anticyclones tend to move at a slower pace and possess weaker pressure anomalies than do cyclones, it is highly probable that the fluctuations will be predominantly influenced by cyclones.
When we emphasize understanding variations in the WACE pattern from the perspective of the Siberian storm track, we also note that upstream blocking is significantly related to the Siberian storm track on the interannual time scale (Fig. 6). Previous studies (Luo et al. 2012) reported that there is a close connection between upstream blocking and the North Atlantic Oscillation (NAO). The phase transition of NAO may result in the variability of the Siberian storm track. It is likely that the WACE pattern and the Siberian storm track are jointly influenced by the NAO. Therefore, our future work will focus on the impact of upstream signals on the Siberian storm track to further advance the understanding of variations in the WACE pattern.
Acknowledgments.
The authors thank anonymous reviewers and the editor Dr. Isla Ruth Simpson for their helpful and crucial comments, which improved the paper substantially. This research was supported by the National Natural Science Foundation of China (Grants 42205046, 42105066, and 42205045), Hunan Provincial Natural Science Foundation of China (Grants 2023JJ30628 and 2022JJ30660), the Research Project of the National University of Defense Technology (projects ZK22-29 and ZK20-45), the China Postdoctoral Science Foundation (2021M701754), and the Postdoctoral Research Funding of Jiangsu Province (2021K052A).
Data availability statement.
The NCEP–NCAR reanalysis dataset was obtained online (https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html). The HadISST dataset was also obtained online (https://www.metoffice.gov.uk/hadobs/hadisst/data/download.html).
APPENDIX
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