Statistical Characteristics and Long-Term Variations of Major Sudden Stratospheric Warming Events

平流层强爆发性增温事件的统计特征及长期变化

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  • Corresponding author: Yuli ZHANG, zhangyuli@mail.iap.ac.cn
  • Funds:

    Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA17010105) and Key Laboratory of Middle Atmosphere and Global Environment Observation (LAGEO-2019-01)

  • doi: 10.1007/s13351-021-0166-3

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  • Using NCEP/NCAR reanalysis data, we investigate the statistical characteristics and the long-term variations of major sudden stratospheric warming (SSW) events in the Northern Hemisphere. We find that the strength and duration of major SSW events have increased from 1958 to 2019 because of the strengthening of winter planetary wave activity. The frequency of the SSW events related to displacement or split of the polar vortex differs between early, middle, and late winter. Early (middle) winter is dominated by displacement (split) SSW events, while late winter sees almost equal frequency of these two types of events. This is due to the differences in the relative strength of wavenumber-1 and wavenumber-2 planetary wave activity among the three winter periods. As a result of the increase in upward planetary wave activity and the decrease in westerly winds around the polar vortex in middle winter, more SSW events tend to occur in middle winter. In addition, we reveal the influence of the downward propagation of different types of SSW events on the surface temperature anomaly. Compared with earlydisplacement SSW events, middle split SSW events are followed by more surface cold centers in Russia, northern China, and North America.

    与以往大多数平流层爆发性增温SSW个例研究不同,本文基于长时段NCEP再分析数据,分析了强SSW事件的统计特征和长期变化。我们发现在1958–2019年间,SSW的强度有增强的趋势,其持续时间也有变长的趋势,这是由于上传行星波变得更活跃造成的。极涡偏心型SSW和极涡分裂型SSW在冬季的早、中期出现的频率不同,在早期出现的主要是偏心型SSW,中期主要出现的是分裂型SSW,这与行星1波和2波在不同时期的活跃程度有关。由于冬季中期上传行星波的加强和绕极西风环流的减弱,SSW更多地出现在了冬季中期。对比两种类型SSW信号的下传特征及其对地面天气的影响发现,与冬季早期极涡偏心型SSW相比,冬季中期分裂型SSW发生之后在俄罗斯、中国北部和北美地区出现了更多的地面冷中心。

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  • Fig. 1.  (a) Mean temperature anomalies, corresponding to lag days, in the polar region (60°–90°N) at 10 hPa for each SSW event (gray lines) and the average of all SSW events (black dashed line). Lag day 0 is the central day of SSW. (b) Interannual variation of the maximum of mean temperature anomalies (black dots) in the polar region at 10 hPa within 1 month (± 15 lag days) around the central day of each SSW event. The black line indicates the long-term trend.

    Fig. 2.  (a) Variation in the duration of SSW events in winter. (b) Interannual variation in the duration of SSW events (black dots) and its long-term trend (black line; passed the 95% confidence criterion).

    Fig. 3.  (a) Interannual variation of the mean eddy heat flux in 1 month (± 15 lag days) around the central day of SSW events within 45°–70°N at 100 hPa. (b) Interannual variation of the mean zonal-mean zonal wind in 1 month (± 15 lag days) around the central day of SSW events at 60°N, 10 hPa. The long-term trends are shown as black lines.

    Fig. 4.  Distributions of the polar vortex at 10 hPa (blue lines are geopotential height equal to 2980 dagpm), evolving with the lag day, for (a–e) displacement and (f–j) split SSW events.

    Fig. 5.  Distributions of vertical upward wave activity equal to 0.2 m2 s−2 at 100 hPa (red lines), evolving with the lag day, for (a–e) displacement and (f–j) split SSW events.

    Fig. 6.  The dates of all SSW events. Blue and red dots denote the central day of displacement and split SSW events, respectively. Blue and red solid lines are the averages of the central day of displacement and split SSW events, respectively. The whole winter period covering all SSW events is evenly divided into three periods (early, middle, and late winter) by the four black dashed lines.

    Fig. 7.  Latitude–height distributions of the mean E–P flux (colored arrow; kg s−2) and its divergence (black contour; kg m−1 s−2) within 1 month (± 15 lag days) around the central day of the two types of SSW events: (a) wavenumber-1 for displacement SSW events, (b) wavenumber-2 for displacement SSW events, (c) wavenumber-1 for split SSW events, and (d) wavenumber-2 for split SSW events.

    Fig. 8.  Evolution of the mean eddy heat flux within 50°–65°N at 100 hPa for (a) all wavenumbers and (b) wavenumber-1 (blue line) and wavenumber-2 (red line). The whole winter covering all SSW events is evenly divided into three periods (early, middle, and late winter) by the four black dashed lines. The horizontal solid lines represent the mean values during the three periods.

    Fig. 9.  Time–vertical sections of the northern annular mode (NAM) index (contour; blue for negative, red for positive) for (a) early displacement, (b) early split, (c) middle displacement, (d) middle split, (e) late displacement, and (f) late split SSW events. The color shading indicates statistical significance at the 95% confidence level based on a t-test.

    Fig. 10.  Distributions of the surface cold center for (a) early displacement, (b) middle displacement, (c) late displacement, (d) early split, (e) middle split, and (f) late split SSW events. Blue lines are the mean surface temperature anomalies equal to −4 K for the 30 days after the central day of the SSW events.

    Table 1.  The central dates and the types of SSW events identified in the NCEP/NCAR data

    Early
    (before 4 Jan)
    Middle (5 Jan–
    12 Feb)
    Late
    (after 13 Feb)
    Displacement30 Nov 195816 Jan 196022 Feb 2008
    8 Dec 196523 Jan 198713 Mar 1969
    27 Nov 19687 Jan 200420 Mar 1971
    2 Jan 197028 Jan 201729 Feb 1980
    4 Dec 198124 Feb 1984
    15 Dec 199820 Mar 2000
    16 Dec 200024 Feb 2007
    2 Jan 2002
    2 Jan 2019
    26 Feb 2017
    Split2 Jan 198530 Jan 195823 Mar 1965
    8 Dec 19878 Jan 196824 Feb 1966
    17 Jan 197122 Feb 1979
    2 Feb 197314 Mar 1988
    11 Feb 200122 Feb 1989
    18 Jan 200325 Feb 1999
    21 Jan 200614 Feb 2018
    24 Jan 2009
    9 Feb 2010
    10 Jan 2013
    Download: Download as CSV

    Table 2.  Long-term trends of mean eddy heat flux within 50°–65°N at 100 hPa and mean zonal wind at 60°N and 10 hPa in early, middle, and late winter. The trends with “*” passed the 95% confidence criterion

    Early winterMiddle winterLate winter
    Mean eddy heat flux
     (K m s−1 yr−1)
    0.05*0.08 0.01
    Mean zonal wind
     (m s−1 yr−1)
    0.11−0.08−0.01
    Download: Download as CSV
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Statistical Characteristics and Long-Term Variations of Major Sudden Stratospheric Warming Events

    Corresponding author: Yuli ZHANG, zhangyuli@mail.iap.ac.cn
  • 1. Carbon Neutrality Research Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
  • 2. University of Chinese Academy of Sciences, Beijing 100049
Funds: Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA17010105) and Key Laboratory of Middle Atmosphere and Global Environment Observation (LAGEO-2019-01)

Abstract: 

Using NCEP/NCAR reanalysis data, we investigate the statistical characteristics and the long-term variations of major sudden stratospheric warming (SSW) events in the Northern Hemisphere. We find that the strength and duration of major SSW events have increased from 1958 to 2019 because of the strengthening of winter planetary wave activity. The frequency of the SSW events related to displacement or split of the polar vortex differs between early, middle, and late winter. Early (middle) winter is dominated by displacement (split) SSW events, while late winter sees almost equal frequency of these two types of events. This is due to the differences in the relative strength of wavenumber-1 and wavenumber-2 planetary wave activity among the three winter periods. As a result of the increase in upward planetary wave activity and the decrease in westerly winds around the polar vortex in middle winter, more SSW events tend to occur in middle winter. In addition, we reveal the influence of the downward propagation of different types of SSW events on the surface temperature anomaly. Compared with earlydisplacement SSW events, middle split SSW events are followed by more surface cold centers in Russia, northern China, and North America.

平流层强爆发性增温事件的统计特征及长期变化

与以往大多数平流层爆发性增温SSW个例研究不同,本文基于长时段NCEP再分析数据,分析了强SSW事件的统计特征和长期变化。我们发现在1958–2019年间,SSW的强度有增强的趋势,其持续时间也有变长的趋势,这是由于上传行星波变得更活跃造成的。极涡偏心型SSW和极涡分裂型SSW在冬季的早、中期出现的频率不同,在早期出现的主要是偏心型SSW,中期主要出现的是分裂型SSW,这与行星1波和2波在不同时期的活跃程度有关。由于冬季中期上传行星波的加强和绕极西风环流的减弱,SSW更多地出现在了冬季中期。对比两种类型SSW信号的下传特征及其对地面天气的影响发现,与冬季早期极涡偏心型SSW相比,冬季中期分裂型SSW发生之后在俄罗斯、中国北部和北美地区出现了更多的地面冷中心。

1.   Introduction
  • Sudden stratospheric warming (SSW) has been known as the most dramatic disturbance in the stratosphere during winter since it was first found by Scherhag (1952). It is characterized by a rapid temperature increase in the stratospheric polar region (Andrews et al., 1987). It is important to reveal the characteristics and variations of SSW since it can modify stratospheric circulation, which in turn can affect tropospheric climate (Baldwin and Dunkerton, 2001; Xie et al., 2016, 2017). SSW events can be divided into major and minor events according to the definition of World Meteorological Organization (WMO; WMO CAS, 1978). Here we focus on the major SSW events in the Northern Hemisphere. During these events, not only an increase in temperature but also a reversal of circulation around the polar vortex is observed.

    The frequency, timing, duration, and strength of major SSW events are important metrics of polar stratospheric winter variability. Some modeling studies have predicted an increase in the frequency of major SSW events under future climate (McLandress and Shepherd, 2009; Bell et al., 2010; Butler et al., 2015); however, some studies have shown that the SSW frequency is model dependent (Mitchell et al., 2012b; Ayarzagüena et al., 2013). Domeisen (2019) suggested that the frequency of SSW events can be estimated from the surface conditions of the North Atlantic Oscillation (NAO). The minimum SSW frequency in the 1990s has been found to be coincident with the longest absence of an NAO event, which is defined as an increased persistence of the negative NAO phase and a change from a positive to a negative NAO. Mitchell et al. (2012a) found that there is no statistically significant change in SSW frequency over the twenty-first century, but the monthly distribution of SSW events has shifted toward February. Ayarzagüena et al. (2013) also predicted a shift in the timing of major SSW events toward midwinter in the future. Although some studies have suggested that the SSW frequency is similar during El Niño and La Niña events (Butler and Polvani, 2011; Garfinkel et al., 2012), Li and Tian (2017) found that the duration of major SSW events during the central Pacific El Niño is shorter than during the eastern Pacific El Niño. Zhang and Chen (2019) found a negative trend in the strength of both major and minor SSW events since 1979. They also showed that the maximum temperature centers are mainly located over Eurasia due to the shift in the polar vortex. By investigating all the major and minor SSW events from mid-November to mid-March, Maury et al. (2016) argued that the amplitude of SSW events shows a distinct seasonal distribution. They found that small-amplitude SSW events mainly occur in early and late winter and large-amplitude SSW events occur in midwinter.

    Other studies have shown that an SSW event is followed by a negative northern annular mode (NAM), which propagates from the upper stratosphere to the surface (Baldwin and Dunkerton, 2001; Charlton and Polvani, 2007). However, not all SSW events appear to influence the troposphere and the surface (Gerber et al., 2009). Nakagawa and Yamazaki (2006) found that SSW events with a larger wavenumber-2 flux were more likely to propagate into the troposphere than those with a reduced wavenumber-2 flux. Some studies have shown that different types (displacement and split) of SSW events have different impacts on the surface climate (Mitchell et al., 2013; Seviour et al., 2013; O’Callaghan et al., 2014). Mitchell et al. (2013) found that vortex split events are correlated with more significant surface weather anomalies. Seviour et al. (2013) showed that vortex split events are associated with a negative Arctic Oscillation pattern. O’Callaghan et al. (2014) found that the magnitude of the surface wind stress anomaly is larger for split SSW events in the 0–30-day period after the onset of an SSW event. However, other studies (Charlton and Polvani, 2007; Cohen and Jones, 2011) have argued that the influence of SSW events on the tropospheric state is found to be largely insensitive to the SSW type. Nevertheless, this stratosphere–troposphere coupling still provides opportunities to improve the intraseasonal predictability of surface weather anomalies in winter (e.g., Sigmond et al., 2013; Yu et al., 2015; Garfinkel et al., 2017; Karpechko et al., 2018; Rao et al., 2020).

    It can be seen that inconsistent and even controversial conclusions exist in previous studies about the characteristics and variations of SSW events, possibly due to different datasets, methods, and duration of study periods employed. In the present study, long enough (62-yr, 1958–2019) historical reanalysis data from NCEP/NCAR are to be used to further quantify climatological characteristics and long-term variations of major SSW events, in a consistent manner.

    The remainder of this paper is structured as follows. Section 2 describes the data and methods. Section 3 shows the long-term variations of SSW strength and duration. Section 4 provides a classification of SSW events according to the types of polar vortex and the time periods of winter. We analyze the variations in the planetary wave activity and westerly winds around the polar vortex that are responsible for the statistical characteristics and long-term variations of SSW events. Then, characteristics of the downward propagation and surface temperature response are shown in Section 5. Finally, Section 6 presents the conclusions and discussion of our findings.

2.   Data and methods
  • We use reanalysis data from the NCEP/NCAR (Kalnay et al., 1996) during the period of 1958–2019 to investigate all major SSW events in the Northern Hemisphere. The data are available at https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html. The daily mean temperature, wind velocity, and geopotential height at pressure levels, as well as the temperature at the surface, were used. On the basis of the definition of WMO CAS (1978), 40 major SSW events occurred in 62 winters during the period of 1958–2019. The details of SSW frequency can be found in the paper by Butler et al. (2015).

  • The strength of a major SSW event is defined as the maximum of the mean temperature anomaly in the polar region (mean temperature in 60°–90°N) within 31 days around the central day of the SSW event (central day ± 15 days) at 10 hPa. The central day of an SSW event is defined as the first day when the daily mean zonal-average zonal wind at 60°N and 10 hPa is easterly.

    During a major SSW event, the zonal-mean zonal wind at 60°N, 10 hPa reverses from westerly (positive) to easterly (negative). The duration of a major SSW event is defined as the time period around the day on which the minimum of the zonal-mean zonal wind at 60°N, 10 hPa is observed, and all the zonal-mean zonal wind velocities at 60°N, 10 hPa must be equal to or less than 0 m s−1 in this time period.

    For the classification of vortex displacement and split SSW events, we followed the definition of Charlton and Polvani (2007). According to this definition, there were 21 displacement and 19 split SSW events. The central date and the type of each event are shown in Table 1.

    Early
    (before 4 Jan)
    Middle (5 Jan–
    12 Feb)
    Late
    (after 13 Feb)
    Displacement30 Nov 195816 Jan 196022 Feb 2008
    8 Dec 196523 Jan 198713 Mar 1969
    27 Nov 19687 Jan 200420 Mar 1971
    2 Jan 197028 Jan 201729 Feb 1980
    4 Dec 198124 Feb 1984
    15 Dec 199820 Mar 2000
    16 Dec 200024 Feb 2007
    2 Jan 2002
    2 Jan 2019
    26 Feb 2017
    Split2 Jan 198530 Jan 195823 Mar 1965
    8 Dec 19878 Jan 196824 Feb 1966
    17 Jan 197122 Feb 1979
    2 Feb 197314 Mar 1988
    11 Feb 200122 Feb 1989
    18 Jan 200325 Feb 1999
    21 Jan 200614 Feb 2018
    24 Jan 2009
    9 Feb 2010
    10 Jan 2013

    Table 1.  The central dates and the types of SSW events identified in the NCEP/NCAR data

  • The Eliassen–Palm (E–P) flux and its divergence depict planetary wave activity and eddy forcing on the zonal mean flow (Eliassen and Palm, 1961; Edmon et al., 1980). Based on the daily NCEP/NCAR data, these two variables were examined to reveal the features of planetary wave activity during the SSW events. The E–P flux, ${{F}} \equiv \left({0,\;{F^{\left(\lambda \right)}},\;{F^{\left(z \right)}}} \right)$, is composed of meridional flux $ {F}^{\left(\lambda \right)} $ and vertical flux $ {F}^{\left(z\right)} $ components, which are defined as

    $$\hspace{-20pt} {{{F}}^{\left({{\lambda }} \right)}} \equiv {{{\rho }}_{\rm{0}}}{{a}}{\rm{cos\lambda }}\left({{{{{\bar u}}}_{{z}}}\overline {{{v'}}\varTheta '} /{{\bar \varTheta }_{{z}}} - \overline {{{v'u'}}} } \right),$$ (1)
    $$\hspace{-20pt} {{{F}}^{\left({{z}} \right)}} \equiv {{\rm{\rho }}_{\rm{0}}}{{a}}{\rm{cos\lambda }}\left\{ {\left[ {{{f - }}{{\left({{{a}}{\rm{cos\lambda }}} \right)}^{ - 1}}{{\left({{{\bar u}}{\rm{cos\lambda }}} \right)}_{\rm{\lambda }}}} \right]\overline {{{v'}}\varTheta '} - \overline {{{w}}'{{u}}'} } \right\},$$ (2)

    where Θ and $ \lambda $ refer to the potential temperature and latitude, respectively; $\overline {{{v}}'{{u}}'}$ refers to the eddy momentum flux; and $\overline {{{v}}'\varTheta '}$ refers to eddy heat flux. The divergence of the E–P flux is given by

    $$\hspace{-80pt} \nabla \cdot {{{{F}}}} \equiv {\left({{{a}}{\rm{cos\lambda }}} \right)^{ - 1}}\frac{\partial }{{\partial {\rm{\lambda }}}}\left({{{{F}}^{\left({\rm{\lambda }} \right)}}{\rm{cos\lambda }}} \right) + \frac{{\partial {{{F}}^{\left({{z}} \right)}}}}{{\partial {{z}}}}.$$ (3)

    We also use the three-dimensional E–P flux (Plumb, 1985) to show the horizontal distributions of upward wave activity on pressure levels,

    $${{{{{F}}}}_{3{\rm{D}}}} = \dfrac{{{p}}}{{{{{p}}_0}}}{\rm{cos\varphi }} \times \left[ {\begin{array}{*{20}{c}} {{{{v'}}^{2}} - \dfrac{1}{{2{{\varOmega a{\rm{sin}}}}2{\rm{\varphi }}}}\dfrac{{\partial \left({{{v'}}\varPhi '} \right)}}{{\partial {\rm{\lambda }}}}}\\ { - {{u'v'}} + \dfrac{1}{{2{{\varOmega a{\rm{sin}}}}2{\rm{\varphi }}}}\dfrac{{\partial \left({{{v'}}\varPhi '} \right)}}{{\partial {\rm{\lambda }}}}}\\ {\dfrac{{2{{\varOmega a{\rm{sin}}\varphi }}}}{{{S}}}\left[ {{{v'T'}} - \dfrac{1}{{2{{\varOmega a{\rm{sin}}}}2{\rm{\varphi }}}}\dfrac{{\partial \left({{{T'}}\varPhi '} \right)}}{{\partial {\rm{\lambda }}}}} \right]} \end{array}} \right],$$ (4)

    where φ, λ, and Ф are latitude, longitude, and geopotential height, respectively.

    The meridional eddy heat flux $\overline {{{v}}'{{T}}'}$ is proportional to the vertical component of the E–P flux (Polvani and Waugh, 2004). We also use the eddy heat flux at 100 hPa to quantify the upward-propagating planetary wave activity. The first two zonal wavenumber components (wavenumber-1 and wavenumber-2) are applied to the eddy heat flux to quantify the different wave activity during different types of SSW events (displacement and split, respectively).

3.   Long-term variations of SSW events
  • First, we calculated the daily temperature anomalies (daily temperature minus climatology). The mean value of the temperature anomalies in 60°–90°N for each SSW event is shown in Fig. 1a. SSW events are characterized by a rapid increase in polar stratospheric temperature, which reaches a maximum around the central day of the SSW event. On the basis of the definition of SSW strength in Section 2, Fig. 1b shows that the strength of SSW events has increased from 1958 to 2019. The maximum of the mean temperature anomaly in the stratospheric polar region (60°–90°N, 10 hPa) increased at a rate of 0.1 K yr−1.

    Figure 1.  (a) Mean temperature anomalies, corresponding to lag days, in the polar region (60°–90°N) at 10 hPa for each SSW event (gray lines) and the average of all SSW events (black dashed line). Lag day 0 is the central day of SSW. (b) Interannual variation of the maximum of mean temperature anomalies (black dots) in the polar region at 10 hPa within 1 month (± 15 lag days) around the central day of each SSW event. The black line indicates the long-term trend.

    SSW events with shorter durations occur in any period of winter; however, the events with longer durations tend to occur in midwinter (Fig. 2a). The long-term variation of SSW duration (Fig. 2b) shows that there are more SSW events with longer durations in the most recent two decades. Since 1998, 44% of the events last longer than 15 days, but only 11% of the events last longer than 15 days in 1979–1990. There are two SSW events longer than 30 days at the end of the 2000s. Although there are still SSW events with shorter durations in recent years, the duration generally increased at a rate of 0.21 day yr−1 from 1958 to 2019.

    Figure 2.  (a) Variation in the duration of SSW events in winter. (b) Interannual variation in the duration of SSW events (black dots) and its long-term trend (black line; passed the 95% confidence criterion).

    Driven by strong upward-propagating planetary wave activity (Matsuno, 1971; Polvani and Waugh, 2004; Coy et al., 2009), SSW events are known to occur under a relatively weak stratospheric polar vortex (Scott and Polvani, 2006; Horan and Reichler, 2017). Therefore, we further analyzed the long-term variations of the upward-propagating planetary wave activity and the strength of the stratospheric polar vortex during SSW events. The upward-propagating planetary wave activity can be represented by the 100-hPa mean eddy heat flux within 45°–70°N, where the strongest upward-propagating planetary wave activity is always observed. Figure 3a shows the long-term variation of the mean value of this eddy heat flux during the SSW events. The eddy heat flux shows an increasing trend (0.06 K m s−1 yr−1), indicating enhancement of the upward-propagating planetary wave activity during SSW from 1958 to 2019. The mean zonal-mean zonal wind at the edge of the stratospheric polar vortex (60°N, 10 hPa), which represents the strength of the vortex, shows a decreasing trend of −0.03 m s−1 yr−1 (Fig. 3b). The enhancement in upward-propagating wave activity and decrease in polar vortex strength might be responsible for the increasing strength and duration of SSW events.

    Figure 3.  (a) Interannual variation of the mean eddy heat flux in 1 month (± 15 lag days) around the central day of SSW events within 45°–70°N at 100 hPa. (b) Interannual variation of the mean zonal-mean zonal wind in 1 month (± 15 lag days) around the central day of SSW events at 60°N, 10 hPa. The long-term trends are shown as black lines.

4.   SSW classification and characteristics
  • According to the shape of the stratospheric polar vortex, SSW events can be divided into two types: vortex split SSW events, in which the polar vortex divides into two separate vortices; and vortex displacement SSW events, in which the polar vortex moves far away from the pole. On the basis of the definition of Charlton and Polvani (2007), we identified 21 displacement and 19 split SSW events during the period of 1958–2019.

    Figure 4 shows evolution of the polar vortex location at 10 hPa during the period of SSW central day ± 8 days for displacement (Figs. 4ae) and split (Figs. 4fj) SSW events. The polar vortex is characterized by low geopotential height at a given pressure level. Therefore, the polar vortex can be located by an area with geopotential height less than 2980 dagpm at 10 hPa (Fig. 4; blue circular line). The polar vortices for 21 displacement and 19 split SSW events were overlaid on a polar stereographic map. For displacement SSW events, the polar vortices are located over northern Europe and the North Atlantic Ocean before the central day (Figs. 4a, b). After the central day (Figs. 4ce), the polar vortices move farther from the pole (located south of 75°N) with much weaker strength (indicated by smaller areas). Compared with displacement SSW events, the polar vortices before split SSW events are located not only over northern Europe and the North Atlantic Ocean but also over North America before the central day (Figs. 4f, g). On the central day of split SSW events, the polar vortices are clearly split and located over two regions: northern Europe and North America (Fig. 4h). The polar vortices weaken quickly after the central day of split SSW events (Figs. 4i, j). On the basis of the three-dimensional E–P flux (Plumb, 1985), Fig. 5 compares the corresponding upward-propagating planetary wave activity between displacement and split SSW events. During displacement SSW events, strong upward-propagating planetary wave activities are observed over the north of Eurasia and North Pacific (Figs. 5ae). However, during split SSW events, the strong upward-propagating planetary wave activities cover almost all of the high latitudes of the Northern Hemisphere. Compared with displacement SSW events, there are stronger upward-propagating planetary wave activities over North America for split SSW events.

    Figure 4.  Distributions of the polar vortex at 10 hPa (blue lines are geopotential height equal to 2980 dagpm), evolving with the lag day, for (a–e) displacement and (f–j) split SSW events.

    Figure 5.  Distributions of vertical upward wave activity equal to 0.2 m2 s−2 at 100 hPa (red lines), evolving with the lag day, for (a–e) displacement and (f–j) split SSW events.

    Variations in the central date of the two types of SSW events are compared in Fig. 6. The mean dates of displacement (late January, shown by the blue solid line) and split (early February, shown by the red solid line) SSW events are close to each other. All SSW events have occurred within the period of late November–late March. The earliest one is the 1968–1969 SSW event with the central day on 27 November 1968, and the latest one is the 1964–1965 SSW event with the central day on 23 March 1965. Therefore, we evenly divided the period from 27 November to 23 March into three parts: early winter (from 27 November to 4 January), middle winter (from 5 January to 12 February), and late winter (from 13 February to 23 March). On the basis of this division, two characteristics can be found in Fig. 6.

    Figure 6.  The dates of all SSW events. Blue and red dots denote the central day of displacement and split SSW events, respectively. Blue and red solid lines are the averages of the central day of displacement and split SSW events, respectively. The whole winter period covering all SSW events is evenly divided into three periods (early, middle, and late winter) by the four black dashed lines.

    (1) The frequency of the two types of SSW events differs during the three winter periods. In early winter, there are nine displacement SSW events and only two split SSW events. However, in middle winter, there are 10 split SSW events and only 4 displacement SSW events. The number of displacement and split SSW events is almost equal (eight displacement and seven split SSW events) in late winter. Comparing early winter with middle winter, we found it interesting that displacement SSW events are dominant in early winter whereas split SSW events are dominant in middle winter.

    (2) There is a shift in the timing of SSW events toward middle winter. Most of the SSW events occur in middle winter in the most recent two decades instead of being evenly distributed throughout the winter period, as they were before the 1990s. Given the result that SSW events with a longer duration occur in middle winter (Fig. 2a), the shift of SSW timing further explains the increase in SSW duration (Fig. 2b). Using a coupled chemistry–climate model, Ayarzagüena et al. (2013) also predicted a shift in the timing of major SSW events toward midwinter in the future.

    To further explain the frequency differences, we first show the distribution of the mean E–P flux in one month around the central day of the two types of SSW events (Fig. 7). Since there are large differences in the magnitude of the E–P flux throughout the troposphere and stratosphere, to clearly show the E–P flux at all levels of the troposphere and stratosphere, the E–P flux calculated by Eq. (3) below 100 hPa is scaled by 1.0 and the flux between 100 and 10 hPa is scaled by 2.0 in Fig. 7. There is a strong upward wavenumber-1 E–P flux in both displacement and split SSW events. The upward wavenumber-2 E–P flux is much weaker than the upward wavenumber-1 E–P flux in displacement SSW events. However, in split SSW events, there is a strong upward wavenumber-2 E–P flux. Thus, the SSW event type depends more on wavenumber-2 rather than on wavenumber-1 planetary wave activity.

    Figure 7.  Latitude–height distributions of the mean E–P flux (colored arrow; kg s−2) and its divergence (black contour; kg m−1 s−2) within 1 month (± 15 lag days) around the central day of the two types of SSW events: (a) wavenumber-1 for displacement SSW events, (b) wavenumber-2 for displacement SSW events, (c) wavenumber-1 for split SSW events, and (d) wavenumber-2 for split SSW events.

    The mean eddy heat flux in 50°–65°N at 100 hPa can be used to quantify the upward-propagating planetary wave activity (Fig. 8). In general, the upward-propagating planetary wave activity involving all wavenumbers is strongest in middle winter and weakest in late winter (Fig. 8a). The upward-propagating wavenumber-1 planetary wave activity is strongest in early winter, and then gradually weakens in middle and late winter. The upward-propagating wavenumber-2 planetary wave activity is stronger (about 10 K m s−1) in middle winter than in early and late winter (about 5 K m s−1). The mean upward-propagating wavenumber-1 activity is much stronger than the mean upward-propagating wavenumber-2 activity in early winter, which leads to more displacement SSW events than split SSW events. However, the mean wavenumber-2 activity enhances and slightly exceeds the mean wavenumber-1 activity in middle winter, resulting in more split SSW events than displacement SSW events. In late winter, both wavenumber-1 and wavenumber-2 activities are weakened. The mean wavenumber-2 activity is weaker than the mean wavenumber-1 activity, but the difference between them (about 2.5 K m s−1) is not as large as in early winter (about 5 K m s−1). Therefore, the frequency of displacement and split SSW events is almost the same in late winter.

    Figure 8.  Evolution of the mean eddy heat flux within 50°–65°N at 100 hPa for (a) all wavenumbers and (b) wavenumber-1 (blue line) and wavenumber-2 (red line). The whole winter covering all SSW events is evenly divided into three periods (early, middle, and late winter) by the four black dashed lines. The horizontal solid lines represent the mean values during the three periods.

    For the shift in the SSW timing toward middle winter, we calculated the trends of mean eddy heat flux within 50°–65°N at 100 hPa and mean zonal-mean zonal wind around the polar vortex in the three winter periods (Table 2), as we did in Fig. 3. The most significant trends occur in middle winter, during which the mean eddy flux is increasing at a rate of 0.08 K m s−1 yr−1 and the mean zonal-mean zonal wind is decreasing at a rate of −0.08 m s−1 yr−1. This means that the planetary wave activity becomes more active and the westerly winds around the stratospheric polar vortex become weaker. In early winter, even though the mean eddy heat flux is increasing, the strengthening of the westerly winds around the polar vortex is still against the onset of SSW events. In late winter, there are small changes in the mean eddy heat flux and mean zonal wind. It becomes easier for the SSW events to occur under the condition of enhancing upward-propagating planetary wave activity and weakening westerly winds around the stratospheric polar vortex, leading to a shift in the SSW timing toward middle winter.

    Early winterMiddle winterLate winter
    Mean eddy heat flux
     (K m s−1 yr−1)
    0.05*0.08 0.01
    Mean zonal wind
     (m s−1 yr−1)
    0.11−0.08−0.01

    Table 2.  Long-term trends of mean eddy heat flux within 50°–65°N at 100 hPa and mean zonal wind at 60°N and 10 hPa in early, middle, and late winter. The trends with “*” passed the 95% confidence criterion

5.   Downward propagation and surface temperature anomalies
  • As the frequency and wave activity of displacement and split SSW events differ among the three winter periods, we further divided the SSW events into six types: early displacement, early split, middle displacement, middle split, late displacement, and late split SSW events. The NAM index for the six types of SSW events is compared (Fig. 9) to examine different characteristics in the downward propagation of the SSW events. The NAM index is calculated based on first empirical orthogonal function analysis of the daily mean geopotential height (Baldwin and Dunkerton, 1999). It should be noted that there are only two early split SSWs and four middle displacement SSW events, making the results for these two types of events less reliable than the results for the other four types. A strong negative NAM index occurs around the central day of both early displacement and middle split SSW events. The NAM index for these two types of events indicates downward propagation into the troposphere. Compared with the early displacement SSW events, a strong positive NAM index occurs about 40–80 days after the onset of middle split SSW events. The positive NAM index lasted about 40 days and propagated from 10 to 100 hPa, suggesting the recovery of the stratospheric polar vortex. The negative NAM indices of late displacement and split SSW events are much weaker and of shorter duration than that during the early displacement and middle split SSWs. It is difficult for these relatively weak stratospheric signals to propagate into the troposphere. Thus, the influence of the late SSW events on the troposphere is not as significant as the influence of the early displacement and middle split SSWs.

    Figure 9.  Time–vertical sections of the northern annular mode (NAM) index (contour; blue for negative, red for positive) for (a) early displacement, (b) early split, (c) middle displacement, (d) middle split, (e) late displacement, and (f) late split SSW events. The color shading indicates statistical significance at the 95% confidence level based on a t-test.

    To study the influence of different types of SSW events on surface weather, we compared the composites of mean surface temperature anomalies for the 30 days after the central day of six types of SSW events. The composites are not statistically significant (figure omitted); instead, we show the location of the surface cold center (Fig. 10), which is defined as the area where the mean surface temperature anomalies in the 30 days after the central day of an SSW event are less than or equal to a temperature threshold (−4 K in this paper). The surface temperature anomaly is defined as daily surface temperature minus the climatology. The middle displacement (Fig. 10b) and early split (Fig. 10d) SSW events can be ignored in the discussion here due to insufficient samples. Compared with late SSW events, there are more cold centers after the early displacement and middle split SSW events. The greatest difference between the early displacement and middle split SSW events is that there are more cold centers in Russia and the north of China after the onset of middle split SSW events (Fig. 10e). The other difference is that there are more cold centers in North America and fewer in Canada after the onset of middle split SSW events. The cold centers after the late displacement SSW events are mainly limited to high latitudes. Compared with late displacement SSW events, more cold centers occurred in northern Eurasia after the late split SSW events (Fig. 10f). The area of the surface cold center depends on the temperature threshold we choose, but even with a changed threshold, patterns of surface cold center are in general similar to those in Fig. 10. If we choose a threshold of −3 K, the cold centers extend to lower latitudes; when the temperature threshold is −5 K, the surface cold centers shift toward higher latitudes (figure omitted).

    Figure 10.  Distributions of the surface cold center for (a) early displacement, (b) middle displacement, (c) late displacement, (d) early split, (e) middle split, and (f) late split SSW events. Blue lines are the mean surface temperature anomalies equal to −4 K for the 30 days after the central day of the SSW events.

6.   Conclusions and discussion
  • Using the NCEP/NCAR reanalysis data, we have investigated the characteristics and long-term variations of major SSW events from 1958 to 2019 in this paper. We found that the strength and duration of the major SSW events have increased, which is manifested by an increase in the maximum temperature in the polar stratosphere and an increase in the duration of the easterly stratospheric winds around the polar vortex during the SSW events. As the upward-propagating planetary wave activity (Matsuno, 1971; Polvani and Waugh, 2004; Coy et al., 2009) and the zonal winds around the polar vortex (Scott and Polvani, 2006; Horan and Reichler, 2017) are known as the two conditions for the occurrence of SSW events, we also investigated the long-term variation of these two physical quantities. The variations of SSWs can be attributed to the enhancing planetary wave activity, which is shown by an increase in the upward eddy heat flux within 50°–65°N at 100 hPa, and a reduction in the westerly wind strength around the polar vortex.

    On the basis of the definition of SSW types by Charlton and Polvani (2007), 21 displacement and 19 split SSW events are identified from 1958 to 2019. During the displacement SSW events, the polar vortex is located over northern Europe and the North Atlantic Ocean with strong upward-propagating planetary wave activity over the north of Eurasia and North Pacific. Compared with displacement SSW events, the polar vortex during the split SSW events, which weakens quickly after the central day of SSW events, is located not only over northern Europe and the North Atlantic Ocean but also over North America due to the strong upward-propagating planetary wave activity over North America. We further distinguished all SSW events in early, middle, and late winter. Two interesting characteristics are found as follows.

    (1) The frequency of the two types of SSW events differs among the three winter periods. The E–P flux and eddy heat flux show that SSW events in early winter are almost always displacement SSW events due to the stronger upward wavenumber-1 activity. However, the wavenumber-2 activity is enhanced and almost equal to wavenumber-1 activity in middle winter, resulting in a greater number of split SSW events (10 events) than displacement SSW events (4 events) in this period. In late winter, the frequency of displacement and split SSW events is almost the same. The wavenumber-2 activity is weaker than the wavenumber-1 activity in late winter, but the difference between them is not as significant as in early winter.

    (2) There is a shift in the timing of SSW events toward middle winter. The most significant increase in the mean eddy flux and decrease in the mean zonal wind around the polar vortex are found in middle winter, indicating enhancing upward-propagating planetary wave activity and weakening westerly winds around the polar vortex. Under these conditions, it becomes easier for SSW events to occur in middle winter. Given that there are a greater number of split SSW events (10 events) than displacement SSW events (4 events) in middle winter, there might be more split SSW than displacement SSW events in the future if the SSW timing continues to shift toward middle winter. Mitchell et al. (2012a) argued that although most SSW events (1960–2000) occurred in February, climate model results showed that SSW events would become more evenly distributed throughout winter during the periods of 2010–2050 and 2060–2100. They predicted that there would be more displacement SSW events in the future due to an increase in wavenumber-1 activity. Therefore, whether there will be more split SSW events or displacement SSW events in the future is worth exploring.

    The downward propagation represented by the NAM index shows differences during the six types of SSW events: early displacement, early split, middle displacement, middle split, late displacement, and late split SSW events. The composites of mean surface temperature anomalies for the 30 days after the central day of the six types of SSW events are not as statistically significant as in Mitchell et al. (2013), because of the amplified uncertainty when subdividing displacement and split SSW events into early, middle, and late types. However, this does not mean that the tropospheric state is insensitive to the SSW type. We found that there are more surface cold centers in Russia and northern China after the onset of the middle split SSW events than early displacement SSW events. Also, there are more cold events in North America and fewer in Canada after the onset of middle split SSW events than early displacement SSW events. Compared with early and middle SSW events, the surface cold centers after the late SSW events are less significant. It should be noted that the influence of early split and middle displacement SSW events on the surface weather is still unknown due to the limited number of samples. If the SSW timing continues to shift toward middle winter and SSW strength and duration continue to increase in the future, we expect stronger and longer-lasting SSW events in the middle winter, during which the polar vortex split might occur more frequently than the polar vortex displacement. Under such a scenario, more attention should be paid to the surface response to middle split SSW events.

    Acknowledgments. We thank the NCEP/NCAR for providing the reanalysis data.

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