Possible Associations between the Number of Cold Days over East Asia and Arctic Oscillation and Arctic Warming

: Based on the NECP/NCAR reanalysis dataset, the associations between the number of cold days (NCD) over East Asia (100–150 ◦ E, 25–55 ◦ N) and Arctic Oscillation (AO)/Arctic warming during 1956–2015 are explored. The results show the NCD was closely associated with AO during 1956–1990 and Arctic warming during 1991–2015. It reveals NCD over East Asia showed a downward trend and a signiﬁcantly negative correlation with AO in the previous stage, while it presented an upward trend and notably positive association with Arctic warming in the later period. Meanwhile the increase in the earlier-stage AO will often be accompanied by the weakness of the Siberian high (SH), the Ural Mountains Blocking high (UBH), and the East Asian trough (EAT), and a “positive– negative–positive” wave band exist in the upper troposphere, which is linked with weakened northerly wind over East Asia. All these anomalies are unfavorable for the southward transportation of cold air, eventually leading to the decrease in NCD over East Asia. Additionally, when the near-surface temperature over the Arctic rises in the later period, on the one hand, SH reinforces and further results in more NCD over East Asia; on the other hand, the 1000–500 hPa thickness ﬁeld displays a “north positive–south negative” pattern, which is conducive to the deceleration of the westerlies at mid-latitudes over Eurasia, and further bring about the enhancement of EAT and UBH, favoring the southward intrusion of cold air, ﬁnally, more NCD are generated.


Introduction
Cold surges are the most profound climate feature in boreal winter impacting East Asian countries, such as China, Japan, and Korea [1], and variability of winter temperature over East Asia and its causes have been investigated extensively [2][3][4][5][6]. East Asia exhibits a warming trend in winter; however, in recent decades, cold days have struck East Asia more frequently [7], which have profound influences on people's livelihoods, transportation, energy supply, electricity transmission, economy, and agriculture production [8]. Additionally, East Asia is located in the "heart" of the East Asian winter monsoon (EAWM), between the Aleutian low and Siberian high (SH) and underneath the southern part of East Asian trough (EAT) with northerly winds, a region closely related to the main components of the EAWM circulation systems. Moreover, densely populated East Asia is home to a large number of modern industries. Therefore, understanding the causes for the variability of the number of cold days (NCD) over East Asia in winter is of great importance.
One of the main factors contributing to winter NCD anomalies over East Asia is the EAWM, interestingly, the Arctic Oscillation (AO), as the leading mode of extratropical climate variation in the north hemisphere during the boreal winter in which the sea level pressure anomalies over the Arctic have an opposite sigh to the anomalies at mid-latitudes [9,10], could influence NCD indirectly through its impact on the EAWM. Gong et al. [11] found a significant out-of-phase relationship between the AO and EAWM

Data and Method
The primary data used in this study include (1) monthly sea level pressure (SLP), geopotential height at 500 hPa (Z500), and zonal wind at 300 hPa (U300) with a horizontal resolution of 2.5 • × 2.5 • [20]; 2-m air temperature (T2m) and daily minimum 2-m air temperature (Tmin_2m) at 192 × 94 T62 gaussian grids during the period 1956-2016 from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR Reanalysis 1); (2) monthly AO indices from the Beijing Normal University (BNU) (http://ljp.gcess.cn/dct/page/65607, accessed on 10 June 2021), which was compared with AO indices from the National Oceanic and Atmospheric Administration Climate Prediction Center (NOAA-CPC, https://www.esrl.noaa.gov/psd/data/ correlation/ao.data, accessed on 10 June 2021) [21], the results showed that they are highly correlated with each other. In this study, winter refers to December, January and February in the following year (DJF). In order to remove intraseasonal scale variations, parameters were averaged seasonally [22]. East Asia refers to 100-150 • E,  • N region in the present study.
The statistical methods applied in the study consist of correlation and regression analysis. The significance of the correlation and regression coefficients were determined by Student's t-test.
Previous studies have developed some indices to quantify NCD. For example, the 'Day-count' index employs constant thresholds, which are unsuited for East Asia as it shows large spatial variations [23]; moreover, a given temperature threshold which is good for representing cold days at mid-latitudes may only indicate a mild winter day at higherlatitudes. However, indices based on the count of days crossing percentile thresholds can provide useful local information. For instance, Gong et al. [24] counted the number of days when daily temperature anomaly is negative, and the absolute value is less than twice the Atmosphere 2021, 12, 842 3 of 13 temperature standard deviation of the winter day as NCD index. Jiao et al. [25] defined the index of cold days as the number of days with daily maximum temperature below 10th percentile of daily maximum temperature, while the index of cold nights indicated the number of days with daily minimum temperature below 10th percentile of daily minimum temperature, and the indices are conducive to study its association with Arctic Sea ice reduction. Some other NCD indices were defined by the daily difference between mean temperature and a base temperature [26].
In the present study, the threshold utilized to define NCD was the 10th percentile of daily Tmin_2m at each grid instead of a fixed threshold. First, the Tmin_2m from low to high in each day during the winter of 1956-2015 at each grid over East Asia were ranked, then the 10th percentile value was taken as the threshold. When Tmin_2m was below the threshold, it was counted as a cold day. We also used the 15th and 20th percentile to conduct statistical analysis. Figure 1 shows the threshold values for winter, the threshold values did not manifest big changes from December to February: the area-average 10th percentile thresholds over the entire East Asia were −12.8 • C for December, −15.4 • C for January, and −14.3 • C for February. The 15th percentile results were −11.7 • C, −14.3 • C, and −13.0 • C, respectively, meanwhile, −10.9 • C, −13.4 • C, and −12.1 • C for the 20th percentile. Spatially, the thresholds generally increased from northwest to southeast over East Asia. The 0 • C line mainly extended northeastwardly from the eastern costal China, through the Sea of Japan, to the east of Japan.
Atmosphere 2021, 12, x FOR PEER REVIEW 3 of 14 number of days when daily temperature anomaly is negative, and the absolute value is less than twice the temperature standard deviation of the winter day as NCD index. Jiao et al. [25] defined the index of cold days as the number of days with daily maximum temperature below 10th percentile of daily maximum temperature, while the index of cold nights indicated the number of days with daily minimum temperature below 10th percentile of daily minimum temperature, and the indices are conducive to study its association with Arctic Sea ice reduction. Some other NCD indices were defined by the daily difference between mean temperature and a base temperature [26].
In the present study, the threshold utilized to define NCD was the 10th percentile of daily Tmin_2m at each grid instead of a fixed threshold. First, the Tmin_2m from low to high in each day during the winter of 1956-2015 at each grid over East Asia were ranked, then the 10th percentile value was taken as the threshold. When Tmin_2m was below the threshold, it was counted as a cold day. We also used the 15th and 20th percentile to conduct statistical analysis. Figure 1 shows the threshold values for winter, the threshold values did not manifest big changes from December to February: the area-average 10th percentile thresholds over the entire East Asia were −12.8 °C for December, −15.4 °C for January, and −14.3 °C for February. The 15th percentile results were −11.7 °C, −14.3 °C, and −13.0 °C, respectively, meanwhile, −10.9 °C, −13.4 °C, and −12.1 °C for the 20th percentile. Spatially, the thresholds generally increased from northwest to southeast over East Asia. The 0 °C line mainly extended northeastwardly from the eastern costal China, through the Sea of Japan, to the east of Japan. Threshold values (°C) defined NCD over East Asia, which were 10th percentile of Tmin_2m within the month of (a) December, (b) January, and (c) February. The contour interval (CI) was 5 °C. (d-f) and (g-i) the same as (a-c), but for the 15th and 20th, respectively.
We also performed EOF analysis for NCD based on the three percentiles, the first leading mode depicted a generally homogeneous pattern over East Asia, and they severally explained 27.06%, 19.80%, and 31.84% of the total NCD variance. The first principal component was highly associated with NCD index. Meanwhile, the second leading mode showed a pattern of opposite change between the northern and southern part of East Asia, Figure 1. Definition of NCD. Threshold values ( • C) defined NCD over East Asia, which were 10th percentile of Tmin_2m within the month of (a) December, (b) January, and (c) February. The contour interval (CI) was 5 • C. (d-f) and (g-i) the same as (a-c), but for the 15th and 20th, respectively.
We also performed EOF analysis for NCD based on the three percentiles, the first leading mode depicted a generally homogeneous pattern over East Asia, and they severally explained 27.06%, 19.80%, and 31.84% of the total NCD variance. The first principal component was highly associated with NCD index. Meanwhile, the second leading mode showed a pattern of opposite change between the northern and southern part of East Asia, accounting for 17.36%, 17.62%, and 17.75%, respectively (Figure 2, 15% and 20% threshold not shown). The first two leading modes were distinguished from each other according to the rule put forward by North et al. [27]. However, as it is intended to analyze the NCD over the entire East Asia, we did not have to cope with the accumulated NCD at each grid. Instead, the area-average NCD index over East Asia was defined. Figure 3 shows the time series of NCD index based on 10th, 15th, and 20th percentile during 1956-2015. They were highly correlated with each other. The trend was −0.47 day·decade −1 , −0.62 day·decade −1 , and −0.75 day·decade −1 during 1956-2015. Thus, the statistics results of NCD in winter over East Asia are robust and not sensitive to the selection of different threshold. Therefore, NCD index based on the 10th percentile can be used to describe the climate changes in winter over East Asia, and the rest of the sections are on this basis. There was a downward trend (−0.386 day·decade −1 ) before 1990 and an upward trend (1.645 day·decade −1 ) after 1990 ( Figure 4a). Stronger cold anomalies have struck East Asia more frequently in recent decades [7,28], and it is consistent with the upward trend of NCD after 1990. How the NCD index represents local information at each grid is demonstrated in Figure 4b, the index commendably represents the number of cold days over the most of grids except in the northeast corner of East Asia. Therefore, NCD index is meaningful for the majority of the grid points over East Asia. accounting for 17.36%, 17.62%, and 17.75%, respectively (Figure 2, 15% and 20% threshold not shown). The first two leading modes were distinguished from each other according to the rule put forward by North et al. [27]. However, as it is intended to analyze the NCD over the entire East Asia, we did not have to cope with the accumulated NCD at each grid. Instead, the area-average NCD index over East Asia was defined. Figure 3 shows the time series of NCD index based on 10th, 15th, and 20th percentile during 1956-2015 They were highly correlated with each other. The trend was −0.47 day·decade −1 , −0.62 day·decade −1 , and −0.75 day·decade −1 during 1956-2015. Thus, the statistics results of NCD in winter over East Asia are robust and not sensitive to the selection of different threshold Therefore, NCD index based on the 10th percentile can be used to describe the climate changes in winter over East Asia, and the rest of the sections are on this basis. There was a downward trend (−0.386 day·decade −1 ) before 1990 and an upward trend (1.645 day·dec ade −1 ) after 1990 ( Figure 4a). Stronger cold anomalies have struck East Asia more fre quently in recent decades [7,28], and it is consistent with the upward trend of NCD after 1990. How the NCD index represents local information at each grid is demon strated in Figure 4b, the index commendably represents the number of cold days over the most of grids except in the northeast corner of East Asia. Therefore, NCD index is meaningful for the majority of the grid points over East Asia.   accounting for 17.36%, 17.62%, and 17.75%, respectively (Figure 2, 15% and 20% threshold not shown). The first two leading modes were distinguished from each other according to the rule put forward by North et al. [27]. However, as it is intended to analyze the NCD over the entire East Asia, we did not have to cope with the accumulated NCD at each grid. Instead, the area-average NCD index over East Asia was defined. Figure 3 shows the time series of NCD index based on 10th, 15th, and 20th percentile during 1956-2015.
They were highly correlated with each other. The trend was −0.47 day·decade −1 , −0.62 day·decade −1 , and −0.75 day·decade −1 during 1956-2015. Thus, the statistics results of NCD in winter over East Asia are robust and not sensitive to the selection of different threshold. Therefore, NCD index based on the 10th percentile can be used to describe the climate changes in winter over East Asia, and the rest of the sections are on this basis. There was a downward trend (−0.386 day·decade −1 ) before 1990 and an upward trend (1.645 day·decade −1 ) after 1990 ( Figure 4a). Stronger cold anomalies have struck East Asia more frequently in recent decades [7,28], and it is consistent with the upward trend of NCD after 1990. How the NCD index represents local information at each grid is demonstrated in Figure 4b, the index commendably represents the number of cold days over the most of grids except in the northeast corner of East Asia. Therefore, NCD index is meaningful for the majority of the grid points over East Asia.

Atmospheric Circulation Anomalies Associated with NCD
To further figure out what the circulation anomalies are when more NCD occu East Asia, correlative patterns of SLP, Z500, U300, and T2m with NCD index ar demonstrated in Figure 5. The more NCD appeared over East Asia, and the more p nently positive SLP anomalies prevailed in the northern Ural Mountains (Figure indicated a northwestward shift and enhancement of the SH, at the same time, a dom large-scale seesaw existence between mid-latitudes and the Arctic, which is similar negative phase of AO. Correspondingly, the above circulation anomalies are favorab the occurrence of northerly wind over the northern part of the Eurasian continent, m the transport of cold air from high-latitudes to East Asia easier. The negative Z500 a alies lay over northeast China and eastern Mongolia (Figure 5b), suggesting the stre ening of the EAT when there were more NCD over East Asia; positive Z500 anom over Ural Mountains indicated the enhancement of the UBH when NCD increased distribution of Z500 anomalies implies a pronounced wave train which provides a per-level dynamical condition favorable for the intrusion of cold air into East Asi 31]. Associated with the rise in the NCD index, U300 accelerated at about 30° N an celerated at mid-high-latitudes over Eurasia ( Figure 5c). Previous studies have p that the deceleration of the mid-latitudes westerlies over Eurasia is beneficial to the e exchange between the Arctic and lower-latitudes [14,32], including the delivery of co to East Asia. It is noteworthy that these circulation anomalies are similar to the 'Nor mode' of the EAWM [3], and NCD are remarkably associated with EAWM [33-3 response to the variations of the above circulation systems, cold winter appeared a most of Eurasian continent (Figure 5d).

Atmospheric Circulation Anomalies Associated with NCD
To further figure out what the circulation anomalies are when more NCD occur over East Asia, correlative patterns of SLP, Z500, U300, and T2m with NCD index are first demonstrated in Figure 5. The more NCD appeared over East Asia, and the more prominently positive SLP anomalies prevailed in the northern Ural Mountains (Figure 5a). It indicated a northwestward shift and enhancement of the SH, at the same time, a dominant large-scale seesaw existence between mid-latitudes and the Arctic, which is similar to the negative phase of AO. Correspondingly, the above circulation anomalies are favorable for the occurrence of northerly wind over the northern part of the Eurasian continent, making the transport of cold air from high-latitudes to East Asia easier. The negative Z500 anomalies lay over northeast China and eastern Mongolia (Figure 5b), suggesting the strengthening of the EAT when there were more NCD over East Asia; positive Z500 anomalies over Ural Mountains indicated the enhancement of the UBH when NCD increased. The distribution of Z500 anomalies implies a pronounced wave train which provides an upper-level dynamical condition favorable for the intrusion of cold air into East Asia [29][30][31]. Associated with the rise in the NCD index, U300 accelerated at about 30 • N and decelerated at midhigh-latitudes over Eurasia (Figure 5c). Previous studies have proven that the deceleration of the mid-latitudes westerlies over Eurasia is beneficial to the energy exchange between the Arctic and lower-latitudes [14,32], including the delivery of cold air to East Asia. It is noteworthy that these circulation anomalies are similar to the 'Northern mode' of the EAWM [3], and NCD are remarkably associated with EAWM [33][34][35][36]. In response to the variations of the above circulation systems, cold winter appeared among most of Eurasian continent (Figure 5d).
Some studies pointed out that the East Asian temperature at the interannual timescale is significantly related to the T2m over the Arctic [37,38]. As shown in Figure 5d, NCD was closely associated with T2m over East Asia, so NCD may also be linked with T2m over the Arctic, but no obvious T2m anomalies existed over the Arctic with respect to the rise in NCD (Figure 6a). However, it does not indicate there is no relationship between them. Average wintertime temperatures have decreased over Eurasia since the late 1980s, a sustained cooling that bucks the global warming trend. Moreover, Arctic T2m has dramatically increased since 1990 (Figure not shown); simultaneously, NCD has greatly risen since 1990 (Figure 4a). For 1956-1990, NCD was positively correlated with T2m over the Arctic, but not significantly (Figure 6b). Notable changes were detected for 1991-2015 (Figure 6c), i.e., significantly positive correlations emerged over the Arctic, especially to the north of the Barents-Kara Sea (0-80 • E, 73-84 • N). Therefore, there existed a close relationship between NCD and T2m over the Arctic for the period 1991-2015, i.e., the increased NCD after 1990 was closely linked with Arctic warming. Some studies pointed out that the East Asian temperature at the interannual timescale is significantly related to the T2m over the Arctic [37,38]. As shown in Figure 5d, NCD was closely associated with T2m over East Asia, so NCD may also be linked with T2m over the Arctic, but no obvious T2m anomalies existed over the Arctic with respect to the rise in NCD (Figure 6a). However, it does not indicate there is no relationship between them. Average wintertime temperatures have decreased over Eurasia since the late 1980s, a sustained cooling that bucks the global warming trend. Moreover, Arctic T2m has dramatically increased since 1990 (Figure not shown); simultaneously, NCD has greatly risen since 1990 (Figure 4a). For 1956-1990, NCD was positively correlated with T2m over the Arctic, but not significantly (Figure 6b). Notable changes were detected for 1991-2015 (Figure 6c), i.e., significantly positive correlations emerged over the Arctic, especially to the north of the Barents-Kara Sea (0-80° E, 73-84° N). Therefore, there existed a close relationship between NCD and T2m over the Arctic for the period 1991-2015, i.e., the increased NCD after 1990 was closely linked with Arctic warming. As mentioned above, NCD was linked with AO pattern during 1956-2015 ( Figure  5a). Moreover, there was an upward trend for AO index before 1991 (Figure 7a), and the correlation coefficient between AO and NCD reached −0.64 during , indicating that about 41% of the total variance of NCD could be explained by AO, while that between  Some studies pointed out that the East Asian temperature at the interannual timescale is significantly related to the T2m over the Arctic [37,38]. As shown in Figure 5d, NCD was closely associated with T2m over East Asia, so NCD may also be linked with T2m over the Arctic, but no obvious T2m anomalies existed over the Arctic with respect to the rise in NCD (Figure 6a). However, it does not indicate there is no relationship between them. Average wintertime temperatures have decreased over Eurasia since the late 1980s, a sustained cooling that bucks the global warming trend. Moreover, Arctic T2m has dramatically increased since 1990 (Figure not shown); simultaneously, NCD has greatly risen since 1990 (Figure 4a). For 1956-1990, NCD was positively correlated with T2m over the Arctic, but not significantly (Figure 6b). Notable changes were detected for 1991-2015 (Figure 6c), i.e., significantly positive correlations emerged over the Arctic, especially to the north of the Barents-Kara Sea (0-80° E, 73-84° N). Therefore, there existed a close relationship between NCD and T2m over the Arctic for the period 1991-2015, i.e., the increased NCD after 1990 was closely linked with Arctic warming. As mentioned above, NCD was linked with AO pattern during 1956-2015 ( Figure  5a). Moreover, there was an upward trend for AO index before 1991 (Figure 7a), and the correlation coefficient between AO and NCD reached −0.64 during 1956-1990, indicating that about 41% of the total variance of NCD could be explained by AO, while that between As mentioned above, NCD was linked with AO pattern during 1956-2015 ( Figure 5a). Moreover, there was an upward trend for AO index before 1991 (Figure 7a), and the correlation coefficient between AO and NCD reached −0.64 during , indicating that about 41% of the total variance of NCD could be explained by AO, while that between detrended NCD and AO was −0.67, both exceeding 99% confidence level based on Student's t-test. Additionally, the correlation coefficient between AO and NCD over East Asia is demonstrated in Figure 7b, and a significantly negative correlation prevailed over the majority of East Asia. This implies NCD was associated with AO during 1956-1990 and the decreased NCD can be explained by the ascendant AO. However, during 1991-2015, the correlation coefficient between AO and NCD decreased. Thus, the following will explore the associations between Arctic warming (1991-2015)/AO  and NCD in different epochs, respectively. In order to analyze influence pathways and mechanisms of Arctic warming/AO on NCD, atmospheric circulation anomalies caused by Arctic warming/AO should be discussed first. majority of East Asia. This implies NCD was associated with AO during 1956-1990 and the decreased NCD can be explained by the ascendant AO. However, during 1991-2015, the correlation coefficient between AO and NCD decreased. Thus, the following will explore the associations between Arctic warming (1991-2015)/AO  and NCD in different epochs, respectively. In order to analyze influence pathways and mechanisms of Arctic warming/AO on NCD, atmospheric circulation anomalies caused by Arctic warming/AO should be discussed first.    Previously, we found NCD was linked with AO/Arctic warming during 1956-1990/1991-2015. To better understand how AO/Arctic warming influenced NCD over East Asia during 1956-1990/1991-2015, maps of regressed circulation anomalies, which are related to EAWM, against AO/Arctic warming are provided. Figure 9 illustrates regressed SLP, Z500, U300, and T2m against AO during 1956-1990. In the lower troposphere, in response to the increasing AO index, significantly negative SLP anomalies formed over the Arctic and at middle-high-latitudes over Eurasia (Figure 9a), indicating the weakening of SH. In the middle troposphere, when AO index   Figure 9 illustrates regressed SLP, Z500, U300, and T2m against AO during 1956-1990. In the lower troposphere, in response to the increasing AO index, significantly negative SLP anomalies formed over the Arctic and at middle-high-latitudes over Eurasia (Figure 9a), indicating the weakening of SH. In the middle troposphere, when AO index rose, negative Z500 anomalies existed over the Ural Mountains, and positive Z500 anomalies emerged over East Asia (Figure 9b), suggesting the weakening of UBH and EAT which is unfavorable for the southward transportation of cold air from high-latitudes. In the upper troposphere, significant 'positive-negative-positive' U300 anomalies existed over the Pacific Ocean. This three-band structure was closely connected to the weakening of low-level meridional northerly wind over East Asia; in addition, positive U300 anomalies existed at mid-highlatitudes over Eurasia (Figure 9c), which is not conducive to the cold air outbreaks [32]. Additionally, when AO index increased, positive T2m anomalies were located over Eurasia (Figure 9d), implying the decrease in NCD over East Asia. In this sense, during 1956-1990, AO exerted considerable influences on NCD over East Asia through its direct control of the EAWM-related circulations. In the previous section, we found NCD was significantly correlated with T2m to the north of the Barents-Kara Sea (0-80° E, 73-84° N), and the average T2m over this region was defined as Arc-index. Song et al. [39] pointed out the area and location of SH are not fixed, and variations in intensity, area and location will cause significant changes in East Asian temperatures; when Siberian high central intensity enhances (weakens), its coverage expands (shrinks), its eastern boundary extends eastward (retreats westward), and the temperature over East Asia decreases (increases). Figure 10a demonstrates the regressed SLP against the Arc-index. When Arc-index increased, the Siberian high central intensity enhanced, the Siberian high area enlarged, and the Siberian high east boundary extended eastward, thus leading to lower temperatures over East Asia; when Arc-index decreased, the situation tended to be opposite. This indicates the Siberian high is a bridge linking the Arctic and East Asian climate to some extent, i.e., the Arctic warming → Siberian high central intensity enhances, Siberian high area expands, and Siberian high east boundary extends eastward → East Asia become colder → more NCD occur over East Asia.

Atmospheric Circulation Anomalies Associated with AO/Arctic Warming
Additionally, when Arc-index rose, a positive SLP anomalous center emerged on the northwest side of the Baikal Lake (Figure 10a), extending southeast to East Asia, simultaneously, there was an unusually strong northerly wind near costal East Asia, conducive to the transportation of cold air from high-latitudes to East Asia, i.e., the enhanced SH favors more occurrences of NCD over East Asia. Regressed Z500 anomalies against the Arc-index (Figure 10b) implied that associated with Arctic warming, positive Z500 anomalies appeared at middle-high-latitudes over Eurasia, indicating the reinforcement of UBH and the Baikal Lake Blockings, especially UBH. It can be seen from the vertical distribution In the previous section, we found NCD was significantly correlated with T2m to the north of the Barents-Kara Sea (0-80 • E, 73-84 • N), and the average T2m over this region was defined as Arc-index. Song et al. [39] pointed out the area and location of SH are not fixed, and variations in intensity, area and location will cause significant changes in East Asian temperatures; when Siberian high central intensity enhances (weakens), its coverage expands (shrinks), its eastern boundary extends eastward (retreats westward), and the temperature over East Asia decreases (increases). Figure 10a demonstrates the regressed SLP against the Arc-index. When Arc-index increased, the Siberian high central intensity enhanced, the Siberian high area enlarged, and the Siberian high east boundary extended eastward, thus leading to lower temperatures over East Asia; when Arc-index decreased, the situation tended to be opposite. This indicates the Siberian high is a bridge linking the Arctic and East Asian climate to some extent, i.e., the Arctic warming → Siberian high central intensity enhances, Siberian high area expands, and Siberian high east boundary extends eastward → East Asia become colder → more NCD occur over East Asia.

Summary and Discussions
In this study, we preliminarily inquired into the variations of NCD over East Asia, and its possible relationships with AO and Arctic warming were further discussed. The results are as follows:  Additionally, when Arc-index rose, a positive SLP anomalous center emerged on the northwest side of the Baikal Lake (Figure 10a), extending southeast to East Asia, simultaneously, there was an unusually strong northerly wind near costal East Asia, conducive to the transportation of cold air from high-latitudes to East Asia, i.e., the enhanced SH favors more occurrences of NCD over East Asia. Regressed Z500 anomalies against the Arcindex (Figure 10b) implied that associated with Arctic warming, positive Z500 anomalies appeared at middle-high-latitudes over Eurasia, indicating the reinforcement of UBH and the Baikal Lake Blockings, especially UBH. It can be seen from the vertical distribution of the correlation coefficient between SH index (defined as the average SLP among 80-120 • E, 40-60 • N) and geopotential height ( Figure 11) that the "negative-positive-negative" wave train from the west to the east was linked with the enhancement of SH; the positive anomalies were more pronounced over the Ural Mountains and the positive anomaly signals traveled downward and eastward to the Siberian plateau, eventually leading to the enhancement of SH. It suggests that when the Arc-index rises (decreases), it is favorable (unfavorable) for the establishment and development of UBH, further strengthening (weakening) SH, resulting in cold (warm) East Asia, finally, more (fewer) NCD emerge over East Asia. Numerical simulation results also suggest that the reduction in Arctic Sea ice (increase in near-surface temperature) has a stimulating effect on the formation of UBH [40], and Wang et al. [3] pointed out that at the interannual timescale, UBH activities have a good relationship with SH and East Asian winter climate. These in turn reflect that SH is an important bridge connecting the Arctic and East Asian climate, i.e., Arctic warming→ Eurasian blockings develop → SH reinforce → East Asian temperature decrease → more NCD occur over East Asia.
When the Arctic Sea ice reduces in summer, the thickness of the atmosphere increases at high-latitudes in autumn and winter due to the heating effect of the lower troposphere [41], which makes the thickness gradient between middle and high latitudes smaller. The thickness gradient, as one of the driving forces of the zonal wind, satisfies the thermal wind relationship with zonal wind [42], and the decrease in it will cause the zonal wind to weaken. The zonal wind can significantly influence the propagation velocity and amplitude of the Rossby wave. The wave velocity formula (1) suggests that when zonal wind weakens, the large-scale Rossby wave propagates to the east at a slower speed, usually accompanied by an increase in wave amplitude, where u is the zonal wind speed; β = ∂f ∂y , f is Coriolis force parameter, y is the north direction of the local cartesian coordinate system, β is smaller at middle-high-latitudes, and is considered constant at the latitude range of the wave amplitude; L is the wavelength, deepening of the trough and elongation of the ridge [43], and this circulation situation is conducive to an increase in the meridional pressure gradient at middle-high-latitudes, thus cold air at high-latitudes is more easily to be transported southward, resulting in more cold events [14]. It is well known that the average atmospheric thickness of 1000-500 hPa is thick at low-latitudes and thin at high-latitudes. The regressed 1000-500 hPa thickness anomalies against Arc-index (Figure 10c) showed that when Arc-index increased, positive thickness anomalies existed to the north of 60 • N, and the positive center was located near the Barents-Kara Sea, and significant negative thickness anomalies were found to the south of the Baikal Lake. The pattern of the thickness variation reduced the gradient of the thickness between middle-latitudes and high-latitudes in the northern hemisphere, resulting in deceleration of zonal wind at middle-latitudes over the Eurasia. As demonstrated in Figure 10d, when Arctic warming happened, a "positive-negative-positive" pattern of U500 from the subtropical to the Arctic emerged, i.e., a positive "northeast-southwest" direction anomalous wind speed belt prevailed from the southern part of Japan to JiangHuai River Basin. Meanwhile, a negative "east-west" direction wind speed belt existed at 50-70 • N over the Eurasian continent; a positive wind speed belt also located over the Arctic. The deceleration of zonal wind at middle-latitudes over Eurasia was conducive to the invasion of cold air from high-latitudes to the south, resulting in cold in East Asia. In order to prove the relationship between the deceleration of zonal wind and UBH and EAT, a zonal wind index was defined-average U500 among 60-135 • E, 50-70 • N. Z500 anomalies were regressed against this index. When the zonal wind over Eurasia decelerated, the positive Z500 anomalies were observed from the Barents-Kara Sea to the Baikal Lake, and negative Z500 anomalies prevailed in East Asia (Figure not shown) implying the reinforcement of UBH and EAT. To conclude, when Arc-index rises, the anomalous thickness of the "north positive-south negative" makes the meridional gradient between middle-latitudes and high-latitudes decrease, and the reduced thickness gradient leads to the deceleration of zonal wind at middle-latitudes over Eurasia, further strengthens UBH and EAT, and these can increase the meridional pressure gradient of the Eurasian middle-high-latitudes circulations, causing cold air to be transported southward, resulting in a colder East Asia, and eventually, more NCD occur over East Asia correspondingly. The situation tends to be opposite when Arc-index decreases.

Summary and Discussions
In this study, we preliminarily inquired into the variations of NCD over East Asia, and its possible relationships with AO and Arctic warming were further discussed. The results are as follows: Figure 11. The longitude-height cross-section of correlation coefficients between SH index and geopotential height averaged over 40-60 • N in the winter during 1991-2015. Shaded values are significant, exceeding 95% confidence level based on Student's t-test.

Summary and Discussions
In this study, we preliminarily inquired into the variations of NCD over East Asia, and its possible relationships with AO and Arctic warming were further discussed. The results are as follows: 1.
NCD over East Asia had a downtrend (−0.386 day·decade −1 ) during 1956-1990 and an uptrend (1.645 day·decade −1 ) during 1991-2015. Additionally, increasing NCD was associated with the enhancement of SH in the lower troposphere, strengthening of EAT and UBH in the middle troposphere and deceleration of the westerlies at midhigh-latitudes over Eurasia, and the variations of the above systems were conducive to the intrusion of cold air into East Asia.

3.
During 1956-1990, the trends of SLP, Z500 and U300 indicated the weakening of SH, Eurasian Blockings and EAT, acceleration of mid-high-latitudes westerlies, and they explained why NCD decreased over East Asia. During 1991-2015, the situation tended to be the opposite, and this was why NCD increased over East Asia.

4.
When AO index increased during 1956-1990, the SLP field showed significantly negative anomalies at mid-high-latitudes over Eurasia and over the Arctic, indicating an obvious weakening of SH. Meanwhile, significant negative Z500 anomalies existed over the Ural Mountains and positive Z500 anomalies emerged over East Asia, implying the weakening of UBH and EAT. In addition, U300 displayed a "positive-negative-positive" anomalous band from low-latitudes, mid-latitudes to high-latitudes over East Asia-North Pacific region; this three-band structure was linked with the weakening of northerly wind over East Asia. These were favorable conditions for a weaker-than-normal EAWM, and T2m over East Asia increased, suggesting decreased NCD over East Asia. When AO index decreased, the situation tended to be opposite.

5.
When Arc-index increased during 1991-2015, on the one hand, SH reinforced and further led to more NCD over East Asia; on the other hand, the 1000-500 hPa thickness field demonstrated a "north positive-south negative" pattern, resulting in a thickness meridional gradient decrease between mid-latitudes and high-latitudes in the northern hemisphere, and the reduced thickness meridional gradient led to the decelerated westerlies at mid-latitudes over Eurasia, further bring about the enhancement of EAT and UBH, i.e., the meridional pressure gradient of the Eurasian mid-high-latitudes circulation increased, which was conducive to the southward transportation of cold air, eventually causing a colder East Asia, i.e., more NCD emerged over East Asia. When Arc-index decreased, the situation tends to be opposite.
Recent studies show that the Arctic sea-ice-air coupled system has a close connection with the extreme weather and climate events across Eurasian continent during winter. Simultaneously, the key processes and physical mechanisms involved in this connection is far from being fully understood. Therefore, more observational analyses, dynamical diagnoses and numerical simulation experiments should be carried out for thorough understanding of Arctic's impacts on East Asian winter climate.