1. Introduction
The stratospheric polar vortex is subject to strong vacillations during the Northern Hemisphere (NH) winter. This variability of the polar vortex is observed to be linked to the tropospheric circulation (Baldwin and Dunkerton 1999), suggesting a dynamical connection between the two layers. The coupling between the stratospheric and tropospheric circulations is readily observed in events of extreme stratospheric variability, such as stratospheric sudden warming (SSW) and final warming events (Baldwin and Dunkerton 2001; Black et al. 2006). After the onset of such events, a weakening of the high-latitude zonal wind is often observed in the troposphere for up to two months (Baldwin and Dunkerton 2001). This deceleration of zonal winds, both in the stratosphere and troposphere, projects well onto the negative phase of the northern annular mode (NAM) (Thompson and Wallace 2000), the dominant mode of variability in the NH extratropics.
Although there is a general consensus that the source of stratospheric circulation changes during weak polar vortex events comes from tropospheric planetary-scale waves that propagate into the stratosphere (Polvani and Waugh 2004), there is less agreement concerning the dynamical mechanisms of the tropospheric changes in response to extreme stratospheric variability. Considering balanced dynamics, such as potential vorticity (PV) inversion, stratospheric circulation anomalies are bound to have an impact on tropospheric circulation. Black and McDaniel (2004) and McDaniel and Black (2005) have shown through a piecewise PV inversion technique that the balanced tropospheric response to a weakened polar vortex (or negative PV anomaly) is characterized by negative zonal wind anomalies in the polar troposphere. However, the resulting tropospheric anomalies are generally much weaker than the observed ones unless eddy forcing is taken into account (e.g., McDaniel and Black 2005). More importantly, when considering the temporal evolution, it is unclear what processes are responsible for maintaining a balanced state.
Several mechanisms have been proposed to explain the transient coupling between the stratosphere and troposphere. These include 1) the effects of large-scale meridional circulation resulting from stratospheric wave driving, so-called “downward control” (Haynes et al. 1991; Thompson et al. 2006), 2) modification of wave breaking or reflection either by background flow change (Matsuno 1971; Zhou et al. 2002; Perlwitz and Harnik 2003; Limpasuvan et al. 2004; Simpson et al. 2009; Shaw and Perlwitz 2013) or wave property change (Chen and Held 2007), and last, 3) combination of the previous two (Song and Robinson 2004; Kushner and Polvani 2004). While all of these are based on wave–mean flow interaction, recent studies have also proposed the importance of nonlinear processes. In particular, it has been suggested that change in the type of wave breaking (e.g., cyclonic vs anticyclonic wave breaking) in response to vertical wind shear change in the lower stratosphere could drive different tropospheric anomalies (Wittman et al. 2007; Rivière 2011).
The above-mentioned dynamical mechanisms assume that stratospheric disturbances drive tropospheric anomalies. This is true if one considers the extended tropospheric response to weak polar vortex events for weeks to months (e.g., Baldwin and Dunkerton 2001; Limpasuvan et al. 2004). However, a recent study by Martineau and Son (2013) showed that downward coupling, usually observed as a downward propagation of circulation anomalies, does not always occur during the onset of polar vortex weakening events. Large variability is observed in the timing of tropospheric zonal wind change relative to the weakening of the stratospheric polar vortex. For example, some events show the onset of tropospheric and stratospheric circulation anomalies occurring at the same time, whereas others show tropospheric onset after or even before the weakening of the polar vortex. In the cases examined in Martineau and Son (2013), such variability is largely a consequence of anomalous upward and poleward propagation of planetary-scale waves, with an additional contribution of synoptic-scale waves.
The tropospheric anomalies during weak polar vortex events have been explained by different scales of waves in the literature. Limpasuvan et al. (2004) have demonstrated that the deceleration of tropospheric wind during the onset of weak polar vortex events is associated with meridional Eliassen–Palm (EP) flux. They found that while about half of tropospheric EP flux can be explained by wavenumber 4 or greater, the remainder is shared mostly by planetary-scale waves of wavenumber 1 (wave-1) and 3. But no robust tropospheric forcing is observed at zonal wavenumber 2 (wave-2). In contrast, McDaniel and Black (2005) documented that the events of pronounced zonal wind deceleration in the lowermost stratosphere and troposphere are caused by the enhanced upward and poleward EP fluxes of planetary-scale waves, including the wave-2 component. Nakagawa and Yamazaki (2006) also showed that weak polar vortex events that accompany stronger tropospheric anomalies are characterized by the enhanced vertical propagation of wave-2. Similarly, Martineau and Son (2013) found that wave-2 disturbances are often responsible for the fast deceleration of tropospheric zonal wind during the onset of the weak polar vortex events, but mostly because of the poleward propagation of those waves in the upper troposphere rather than vertical propagation. These results indicate that the tropospheric response (or forcing), which is related to planetary-scale waves, is not well quantified during weak polar vortex events.
Although there are some discrepancies, the above-described results suggest that stratosphere–troposphere coupling during the onset of weak polar vortex events is likely caused by planetary-scale waves and differs from the processes responsible for the maintenance of the tropospheric anomalies over weeks or months after the onset, which may heavily rely on synoptic-scale waves (e.g., Domeisen et al. 2013). The enhanced planetary-scale wave activity during weak polar vortex events has been partly explained by linear wave interference argument. Nishii et al. (2011) and Smith and Kushner (2012) showed that the alignment of transient and stationary waves can enhance the vertical propagation of planetary-scale waves. Such interference was shown to be especially important in displacement vortex events, as identified by Charlton and Polvani (2007).
The purpose of the present study is to examine the detailed evolution of zonal-mean circulation anomalies during polar vortex weakening events in the NH extratropics. An emphasis is placed on short-term coupling during the onset of such events with possible implications for the short-term weather forecast. Unlike previous studies, which have been primarily focused on the breakdown of the polar vortex, such as SSW events, polar vortex deceleration events under both strong and weak vortex conditions are considered as in McDaniel and Black (2005). By computing daily tendency from long-term reanalysis data, we detect the events that display pronounced deceleration of the polar vortex, hereafter referred to as stratospheric vortex weakening (SVW) events. Here, the term SVW is used to distinguish the transient characteristic of the event “weakening” from the absolute state “weak.” As such, SVW events include both the events ending up with a reversal of zonal-mean zonal wind at 60°N at 10 hPa (i.e., major SSW) and those starting from strong vortex and ending up with no wind reversal.
By classifying SVW events based on dominant wave driving and stratospheric mean state, the time scale of vortex weakening and recovery, and the associated vertical coupling, are evaluated. A particular focus is to clarify the time scale of vertical coupling: whether tropospheric anomalies occur after, before, or simultaneous to the stratospheric vortex weakening. Such diagnostics are important to establish a causal relationship. Extending the work of Limpasuvan et al. (2004), Nakagawa and Yamazaki (2006), and Martineau and Son (2013), the role of planetary-scale waves in short-term vertical coupling is highlighted.
The dynamical processes that are responsible for the vertical coupling are evaluated by using the transformed Eulerian-mean (TEM) diagnostics of zonal-mean momentum in sections 3a and 3b. By comparing individual terms of the TEM equation to the observed wind tendency, the contribution of the residual circulation and local wave forcing to the tropospheric response are quantified. The results are then compared with the tendency of wave activity density (Solomon 2014), and the role of nonconservative sources or sinks of wave activity in the evolution of SVW events is estimated. In section 3c, differences between the evolution of SVW events resulting from wave-1 or wave-2 disturbances, which may have different tropospheric impacts (Mitchell et al. 2013), are also discussed. Following this, the structure of tropospheric and stratospheric disturbances leading to wave-1 and wave-2 events are examined with composite geopotential height anomalies. In section 3d, the sensitivity of the tropospheric response to the stratospheric background state is evaluated by comparing SVW events that occur under strong and weak polar vortex conditions. The SVW events occurring under weak polar vortex conditions, are also compared with SSW-like extreme events in section 4. Key results are then summarized in section 5.
2. Data and methodology
a. Data
This study is based on the 6-hourly European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) data (ECMWF 2009; Dee et al. 2011) from 1979 to 2012. Wind, temperature, and geopotential height are used on a grid of 1.5° latitude by 1.5° longitude and 37 pressure levels from 1000 to 0.1 hPa. An anomaly is defined as the 6-hourly value minus the seasonally varying climatology of 33 yr on which a 60-day low-pass filter is applied (e.g., Baldwin and Dunkerton 2001; Harada et al. 2010). Although all quantities, such as EP flux, are computed using 6-hourly data, they are presented as daily averages on which a 1–2–1 filter is applied to remove spurious noise. When variables are averaged over a latitude band, cosine weighting is applied so as not to overemphasize polar regions. Statistical significance is reported at the 95% confidence level with the null hypothesis being that the mean is equal to zero. We use a two-sided Wilcoxon nonparametric test, which holds no assumption on the distribution of sample and is therefore more appropriate for a small sample size. Such a test yields similar results to the standard Student’s t test for large samples.
To quantify variability in the troposphere and the stratosphere, we use the simplified NAM index, which is based on polar cap geopotential height anomalies. The NAM index is computed as the negative of geopotential height anomalies averaged over the area north of 65°N, then independently normalized by one standard deviation (σ) at each level. This method is a simple and robust alternative to EOF-based methods since the two are known to be well correlated at all pressure levels (Baldwin and Thompson 2009). In terms of zonal circulation, the positive phase of the NAM corresponds to a meridional dipole of zonal wind anomalies with anomalous westerlies at 60°N and easterlies at 30°N, representing a poleward displacement of the tropospheric westerly jet and an intensification of the stratospheric polar vortex (see Fig. 1 in Thompson and Wallace 2000).
b. Detection of SVW events
The SVW events are detected using the time derivative of the NAM index at 50 hPa. Although a similar approach was taken by McDaniel and Black (2005), they used the NAM index tendency at 150 hPa, which does not necessarily represent polar vortex variability. The criterion for defining SVW events consists of a decrease of 1σ of the NAM index at 50 hPa in a period of 5 days, ensuring a rapid and strong deceleration of the polar vortex. Here, the NAM index at 50 hPa is used, as it effectively represents lower-stratospheric variability and is reasonably well coupled with tropospheric variability. The sensitivity to the choice of vertical level (e.g., 10 hPa) is discussed in the appendix. To ensure the independence of the selected events, SVW events need to be spaced a minimum of 30 days apart (Nakagawa and Yamazaki 2006; Charlton and Polvani 2007). When more than one event is found within that period, only the strongest one is kept. This simple definition yields a total of 33 SVW events, as listed in Table 1 and illustrated in the appendix. Here it is important to note that SVW events do not necessarily result in a weak vortex anomaly or wind reversal in the stratosphere, as seen in SSW events (e.g., Charlton and Polvani 2007). Some SVW events involve the weakening of an unusually strong vortex to a state close to climatology and therefore do not result in negative NAM anomalies in the stratosphere or reversal of zonal-mean wind [this is similar to the declining phase of the positive NAM index event in McDaniel and Black (2005)]. Nonetheless, our results suggest that such events also present an impact on the troposphere for several weeks. It is not our intent here to devise a new definition of SSW: SVW events are instead designed to capture events of strong deceleration, regardless of the background stratospheric circulation.
Onset dates of extreme stratospheric events according to different definitions: wind reversal, threshold, midpoint, minimum, and SVW events. Wave-1 and wave-2 SVW events are indicated by w1 and w2, respectively. The symbols + and − are used for +NAM and −NAM SVW events, respectively.
To better characterize SVW events, the detected events are classified whether they are dominated by wave-1 or wave-2 disturbances (see Table 1). This classification is made using the vertical component of EP flux at 50 hPa integrated over 45°–90°N in the same 5-day period of event detection. The SVW events that show large upward EP fluxes by wave-1 (top 50%) and unusually small fluxes by wave-2 (bottom 50%) are classified as wave-1 events. Opposite criteria are required for wave-2 events. This approach, which is similar to that of Shaw and Perlwitz (2014) and Dunn-Sigouin and Shaw (2015), who identified extreme stratosphere events using anomalous heat fluxes, is in contrast to that of Charlton and Polvani (2007) or Mitchell et al. (2013), who classified weak polar vortex events according to the visual appearance of the vortex and vortex moment, respectively.
To identify the sensitivity of SVW events to the background state, we further classify the events according to the background NAM index (e.g., McDaniel and Black 2005). The events that present NAM index above 
c. Transformed Eulerian-mean diagnostics
d. Finite-amplitude wave activity (FAWA)
While the TEM momentum budget has been extensively examined in the literature, wave activity density has been rarely analyzed. In this study, to better understand the nature of SVW events, a spatiotemporal evolution of wave activity density is examined by utilizing FAWA diagnostics (Nakamura and Zhu 2010; Nakamura and Solomon 2010; Solomon 2014).
After computing the 
3. Results
a. Dynamical evolution of SVW events
The composite evolution of SVW events is first shown using both the NAM index and zonal winds averaged over the polar region (Fig. 1). The NAM index initially shows positive anomalies in both the troposphere and stratosphere around lag −5 and then negative anomalies around lag 5. The transition from a strong to weak NAM index is approximately centered on lag 0, the onset date, and occurs in both layers. A second episode of a negative NAM index in the troposphere is observed around lag 20, suggesting a persistence of tropospheric anomalies after SVW events for up to three weeks (Fig. 1a). A similar temporal evolution is also observed in zonal-mean zonal wind anomalies averaged from 50° to 90°N, indicating that high-latitude wind is a good measure of NAM variability (Fig. 1c). It is evident from Fig. 1 that NAM index and zonal wind anomalies show near-simultaneous weakening from the stratosphere to the troposphere around lag 0. This indicates that downward coupling from the stratosphere to the troposphere may not always occur during the onset of SVW events. As illustrated in Martineau and Son (2013), large variability exists in the timing of tropospheric onset relative to the deceleration of the stratospheric vortex. Averaging lag and lead events together likely produces the near-instantaneous response observed in the composite. During troposphere lead events, tropospheric deceleration often reaches its maximum about 1–2 days before the peak stratospheric deceleration, as hinted in Fig. 1d.
Composite evolution of SVW events as a function of pressure and time. (a) NAM index anomaly and (b) its tendency are shown with contours of 0.25σ and 0.1σ day−1, respectively. (c) The zonal wind anomaly (m s−1) and (d) its tendency (m s−1 day−1) integrated over 50°–90°N are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of SVW events as a function of pressure and time. (a) NAM index anomaly and (b) its tendency are shown with contours of 0.25σ and 0.1σ day−1, respectively. (c) The zonal wind anomaly (m s−1) and (d) its tendency (m s−1 day−1) integrated over 50°–90°N are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of SVW events as a function of pressure and time. (a) NAM index anomaly and (b) its tendency are shown with contours of 0.25σ and 0.1σ day−1, respectively. (c) The zonal wind anomaly (m s−1) and (d) its tendency (m s−1 day−1) integrated over 50°–90°N are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
It is interesting to note from Figs. 1c,d that, prior to the SVW, the stratosphere undergoes a weak but significant episode of vortex intensification around lags −10 to −5, consistent with Charlton and Polvani (2007). After the event, another period of vortex intensification, that is associated with a weak recovery of the polar vortex is observed around lags 5–10 (Fig. 1d). This acceleration–deceleration–acceleration pattern probably reflects the dominant time scale of stratospheric variability. A similar time scale is found in McDaniel and Black (2005). A weak hint of acceleration is also observed in the troposphere after the onset of the event. However, it is much weaker than the intense deceleration episode from lag −3 to 1, therefore not completely reverting tropospheric zonal winds to their previous state. Consequently, the tropospheric anomalies that appeared during the onset are maintained for a while. This is in contrast to the stratospheric winds, which undergo partial recovery soon after the onset.
Figure 2 shows the composite evolution of high-latitude zonal wind during the events as well as the zonal momentum budget of the TEM equation. Here, Fig. 2a is identical to Fig. 1d, but covers a shorter period. The sum of all terms of the TEM equation, except 
TEM diagnostics of composite SVW events. All quantities are averaged over 50°–90°N and shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The vertical component of EP flux is shown with vertical lines on the 300-, 100-, and 50-hPa levels, with the distance from 300 to 100 hPa equivalent to 3.5 
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
TEM diagnostics of composite SVW events. All quantities are averaged over 50°–90°N and shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The vertical component of EP flux is shown with vertical lines on the 300-, 100-, and 50-hPa levels, with the distance from 300 to 100 hPa equivalent to 3.5
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
TEM diagnostics of composite SVW events. All quantities are averaged over 50°–90°N and shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The vertical component of EP flux is shown with vertical lines on the 300-, 100-, and 50-hPa levels, with the distance from 300 to 100 hPa equivalent to 3.5
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Decomposition of the EP fluxes into the contributions from different zonal wavenumbers (Figs. 2e,f,g) further reveals that the deceleration of the polar vortex results primarily from wave-1 and wave-2, both of which are characterized by enhanced upward EP fluxes in the lower stratosphere, resulting in anomalous EP flux convergence aloft (see also Nakagawa and Yamazaki 2006). This result contrasts with that of Limpasuvan et al. (2004), who showed a weak wave-2 but a pronounced wave-1 forcing driving SSW events. This discrepancy partly results from the fact that SVW events examined in Fig. 2 take into account both minor and major stratospheric warming events, while those in Limpasuvan et al. (2004) are solely based on major warming events. As discussed later, SVW events occurring under a weak polar vortex (i.e., −NAM SVW events), which are comparable to major warming events, are predominantly driven by wave-1 forcing, as in Limpasuvan et al. (2004). In the troposphere, EP flux convergence before lag 0 is dominated by wave-2, which shows highly anomalous upward EP fluxes across the tropopause. This contrasts with the tropospheric recovery period around lags 4–10, which is mostly explained by an anomalous EP flux divergence at all scales. These features are discussed in more detail in the next section.
Diagnostics of FAWA show that SVW events are characterized by an increase in wave activity in both the upper troposphere and stratosphere around the onset (Fig. 3a). Accordingly, FAWA tendency shows significantly positive values around the onset of the SVW events. This intensification of FAWA closely matches the magnitude and structure of EP flux convergence in the stratosphere (cf. Figs. 2c and 3b), suggesting that SVW dynamics are largely in the conservative limit [Eq. (5); see also Solomon (2014)]. In fact, nonconservative sink or source of wave activity, which is estimated from the residual of Eq. (5), is less than a quarter of EP flux convergence during the onset (cf. Figs. 2c and 3d). However, it still plays an important role in FAWA, especially during the vortex recovery period. In the stratosphere, a wave-activity sink is maintained for a while, resulting in a relatively slow decrease of FAWA.
FAWA diagnostics of composite SVW events. All quantities are averaged over 50°–90°N. (a) Wave activity density is shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1). (b),(c),(d) Tendency terms are shown with the same contours but have different units (m s−1 day−1). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
FAWA diagnostics of composite SVW events. All quantities are averaged over 50°–90°N. (a) Wave activity density is shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1). (b),(c),(d) Tendency terms are shown with the same contours but have different units (m s−1 day−1). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
FAWA diagnostics of composite SVW events. All quantities are averaged over 50°–90°N. (a) Wave activity density is shown with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1). (b),(c),(d) Tendency terms are shown with the same contours but have different units (m s−1 day−1). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
The nature of sinks of wave activity, however, cannot be evaluated in this study because this term is estimated from the residual. In a future study, more quantitative analysis needs to be conducted by using a numerical model. Figure 3 exhibits very noisy FAWA in the troposphere, showing only weak vertical coupling across the tropopause. The separation of FAWA across the tropopause also needs to be addressed in a future study.
b. Latitudinal structure
Returning to TEM diagnostics, Fig. 4 illustrates the meridional structure of zonal wind tendency averaged over lags −3 to 1, the period corresponding to the maximum stratospheric and tropospheric deceleration at high latitudes. We choose this period to focus on significant forcing for zonal wind deceleration as diagnosed by the TEM (Fig. 2b). Although not shown, cross sections examined for a longer period, lag −5 to 2 for example, show quantitatively similar results. The zonal wind tendency presents a dipole structure in the stratosphere with acceleration south of 50°N and deceleration north of 50°N (Fig. 4a). Unlike midlatitudes, the high-latitude deceleration extends all the way to the surface. A similar zonal wind tendency was also found in McDaniel and Black (2005; see their Fig. 6b). This zonal wind tendency is well reproduced by TEM diagnostics (Fig. 4b). Consistent with Fig. 2, EP flux convergence explains high-latitude wind changes remarkably well (Fig. 4c). While the residual circulation cancels roughly one-third of the wave forcing anomaly in the stratosphere, the cancellation is much stronger in the troposphere, nonetheless resulting in net deceleration (Fig. 4d). This result contrasts with stratospheric acceleration in midlatitudes, which is associated with the residual circulation alone (cf. Figs. 4b and 4d).
Cross section of composite zonal wind tendency and the (top) TEM forcing terms averaged from lag −3 to 1 and (middle) vertical and (bottom) meridional EP flux divergence. EP flux is illustrated as black arrows. For the EP flux divergences (first column) total fluxes are reported and then shown (second column)–(fourth column) for different contributing wavenumbers. The zonal wind tendency is illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The distance occupied by 10° latitude is equivalent to 1.7 
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Cross section of composite zonal wind tendency and the (top) TEM forcing terms averaged from lag −3 to 1 and (middle) vertical and (bottom) meridional EP flux divergence. EP flux is illustrated as black arrows. For the EP flux divergences (first column) total fluxes are reported and then shown (second column)–(fourth column) for different contributing wavenumbers. The zonal wind tendency is illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The distance occupied by 10° latitude is equivalent to 1.7
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Cross section of composite zonal wind tendency and the (top) TEM forcing terms averaged from lag −3 to 1 and (middle) vertical and (bottom) meridional EP flux divergence. EP flux is illustrated as black arrows. For the EP flux divergences (first column) total fluxes are reported and then shown (second column)–(fourth column) for different contributing wavenumbers. The zonal wind tendency is illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, … m s−1 day−1). Blue and red represent negative and positive values, respectively. The distance occupied by 10° latitude is equivalent to 1.7
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
A closer inspection of the EP flux anomalies that result in tropospheric EP flux convergence reveals enhanced upward and poleward fluxes in the troposphere (Figs. 4e,i), similar to the growth phase of SSW events examined in Limpasuvan et al. (2004). At first glance, the vertical component of EP flux divergence looks like the main contributor to the zonal wind deceleration in the troposphere from 50° to 80°N (Fig. 4e). However, this term is largely canceled by the residual circulation (cf. Figs. 4e and 4d). Similar observations were made by Pfeffer (1992), who suggested that while momentum flux convergence (i.e., meridional EP flux divergence) mainly acts to alter the zonal wind, heat fluxes mainly act to generate the residual circulation, therefore explaining why the vertical component of EP flux divergence and residual circulation are closely related. Pfeffer (1992) also argued that the effectiveness of the vertical component of EP flux divergence at driving zonal wind changes is largely a function of stability, being more effective in regions of high stability. This indicates that tropospheric deceleration is better explained by meridional EP flux divergence (i.e., the Eulerian-mean equation) than total EP flux divergence (i.e., the TEM equation). In fact, although not statistically significant, tropospheric deceleration north of 50°N in Fig. 4a is, to a large extent, explained by meridional EP flux convergence (Fig. 4i).
The EP flux is further decomposed into the contributions of different zonal scales of disturbances. Stratospheric vortex weakening is largely driven by the vertical component of planetary-scale EP flux (wave-1 and wave-2) with nonnegligible contribution by the meridional component of wave-1 EP flux. In the upper troposphere, EP flux divergence shows a dipole structure with a relatively weak divergence from 30° to 50°N at 200 hPa and strong convergence from 50° to 90°N at 300 hPa (Fig. 4c). This is caused by vertical EP fluxes (Fig. 4e). Specifically, the former is driven by zonal wavenumber 3 and higher (Fig. 4h), whereas the latter is dominated by wave-2 EP fluxes (Fig. 4g). However, as discussed above, this dipolar EP flux divergence in the upper troposphere is largely canceled by the residual circulation (Fig. 4d), and zonal wind tendency in the troposphere is better explained by meridional EP flux divergence alone (Fig. 4i). Figures 4j–l show that tropospheric deceleration north of 50°N is caused by all scales of waves with stronger contribution of planetary-scale waves (Fig. 4j,k) than synoptic-scale waves (Fig. 4l). This is clearly in contrast to stratospheric wind tendency.
The above results suggest that the onsets of SVW events are caused by anomalous upward and poleward propagation of wave-1 and wave-2 from the troposphere to the stratosphere. The associated zonal-wind changes in the stratosphere and troposphere occur within days of each other, promoting a coupling or synchronized evolution of the circulation in the two layers. In other words, tropospheric changes are not simply driven by the stratospheric disturbance. Instead, they are partly driven by the direct forcing resulting from the enhanced planetary-scale waves that propagate vertically into the stratosphere with a poleward component (McDaniel and Black 2005; Nakagawa and Yamazaki 2006; Martineau and Son 2013; Dunn-Sigouin and Shaw 2015).
The recovery phase (lags 5–10) is also investigated using EP flux cross sections (Fig. 5). The stratospheric recovery is characterized by planetary-scale EP flux divergence, dominated by anomalous equatorward propagation of wave-1 (Figs. 5i,j). This implies that anomalous upward and poleward propagation of wave-1 during the onset of SVW events (Figs. 4f,j) is followed by anomalous equatorward propagation (Fig. 5j). In other words, wave-1 is not completely dissipated in the stratosphere. This result is largely consistent with FAWA diagnostics that suggest SVW dynamics can be, to a first order, explained by conservative dynamics (Fig. 3). Smaller-scale waves also contribute to the polar vortex recovery through anomalous equatorward EP flux, which may result from a transfer of wave activity from larger to smaller scales in the course of the event (Figs. 5l). Although not significant, part of the vortex recovery is also caused by vertical EP flux divergence as upward fluxes in the stratosphere remain while incoming fluxes from the troposphere are suppressed (Fig. 5e). This suppression could possibly result from downward reflection of planetary-scale waves (Perlwitz and Harnik 2003; Shaw and Perlwitz 2013).
As in Fig. 4, but for lags 5–10.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 4, but for lags 5–10.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 4, but for lags 5–10.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
The zonal wind tendency in the troposphere is close to zero (Fig. 5a; see also Figs. 2a,b). Although statistically significant EP flux divergences are observed in the upper troposphere (Fig. 5c), they are, to a large extent, canceled by the residual circulation (Fig. 5d). Such EP flux divergences are explained by anomalous downward EP fluxes in the middle troposphere, which result in anomalous divergence aloft but convergence below (Fig. 5e). All wavenumbers contribute to anomalous vertical EP fluxes (Figs. 5f,g,h). Here, it is important to note that although planetary-scale EP flux anomalies point downward, absolute values of EP flux (anomaly + climatology) are directed upward (not shown). This suggests that a suppression of the vertical propagation occurs in the upper troposphere during the event but that net wave fluxes nonetheless remain upward. Unlike the vertical EP flux divergence, the meridional EP flux divergence is dominated by synoptic-scale waves (Fig. 5l).
c. Wave-1 versus wave-2 SVW events
Figure 2 clearly shows that the short-term coupling between the stratosphere and troposphere is highly dependent on the presence of wave-1 and wave-2 disturbances in the troposphere. However, not all events present the same levels of wave activity. The relative importance of wave-1 and wave-2 forcing in SVW events is examined in Fig. 6 in terms of composite evolution of wave-1 and wave-2 SVW events and in Fig. 7 in terms of spatial distribution of EP flux averaged over lag −3 to 1 days. A total of 11 events are used for both wave-1 and wave-2 SVW composites, as listed in Table 1. Both wave-1 and wave-2 SVW events show similar polar vortex deceleration around the onset date (middle-left column in Fig. 6). However, during wave-1 SVW events, zonal wind anomaly integrated over 50°–90°N is initially less positive but becomes more negative after the onset in comparison to wave-2 SVW events and shows extended persistence in the stratosphere (Figs. 6a,b). In contrast, wave-2 events are characterized by faster recovery both in the stratosphere and troposphere (Fig. 6f).
Composite evolution of (top) wave-1 and (bottom) wave-2 SVW events. (left)–(right) Zonal wind anomaly, its tendency, and EP flux divergence by wave-1 and wave-2 averaged over 50°–90°N are shown. The same graphical convention as in Fig. 2 is applied.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (top) wave-1 and (bottom) wave-2 SVW events. (left)–(right) Zonal wind anomaly, its tendency, and EP flux divergence by wave-1 and wave-2 averaged over 50°–90°N are shown. The same graphical convention as in Fig. 2 is applied.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (top) wave-1 and (bottom) wave-2 SVW events. (left)–(right) Zonal wind anomaly, its tendency, and EP flux divergence by wave-1 and wave-2 averaged over 50°–90°N are shown. The same graphical convention as in Fig. 2 is applied.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in the last two rows of Fig. 4, but for (top),(upper middle) wave-1 and (lower middle),(bottom) wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in the last two rows of Fig. 4, but for (top),(upper middle) wave-1 and (lower middle),(bottom) wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in the last two rows of Fig. 4, but for (top),(upper middle) wave-1 and (lower middle),(bottom) wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
The difference in vortex recovery tends to cause more persistent tropospheric anomalies after wave-1 SVW events than wave-2 SVW events, although they are not statistically significant because of a limited sample size. A weaker and slower vortex recovery during wave-1 SVW events essentially results from persistent vertical wave propagation: wave forcings are maintained over 10 days during wave-1 SVW events (see vertical lines in Fig. 6c). This clearly contrasts to wave-2 SVW events, for which wave forcings are focused around the onset day (Fig. 6h).
As expected, wave-1 SVW events are dominated by wave-1 EP flux convergence in the stratosphere (Figs. 6c and 7b,f). While polar vortex weakening is primarily caused by vertical convergence of wave-1 EP flux (Fig. 7b), it is also partly driven by meridional convergence of EP flux due to anomalous poleward wave propagation (Fig. 7f). In the troposphere, deceleration is not simply caused by planetary-scale waves. A significant EP flux convergence is also observed at wave-3+ scales around 50°N (Fig. 7h). The wave-2 SVW events are caused by vertical EP flux convergence of wave-2 in the extratropical stratosphere (Fig. 7k). The meridional EP fluxes also contribute to vortex weakening in the upper stratosphere (Fig. 7m). This is mainly caused by wave-1 instead of wave-2 (Figs. 7n,o). In other words, wave-2 SVW events are driven not only by anomalous upward propagation of wave-2 but also by anomalous poleward propagation of wave-1. This is in stark contrast with wave-1 SVW events, which are primarily caused by anomalous upward and poleward propagation of wave-1.
The above difference in wave evolution of wave-1 and wave-2 SVW events (e.g., Fig. 7) suggests that the spatial characteristics of the relevant waves may also differ greatly. Figures 8 and 9 present composite geopotential height anomalies over three periods that capture the short-lived nature of the anomalies in wave-1 and wave-2 SVW events. Those three periods represent the periods before (lag −12 to −6), during the onset (lag −4 to 2), and after the SVW events (lag 4 to 10). For reference, full fields at 50 and 500 hPa are also presented along with wave-1 and wave-2 components. Although TEM diagnostics show greater planetary-scale wave activities at 300 hPa compared to 500 hPa, we present only the 500-hPa level for a better comparison with previous studies. Overall, the structure of geopotential height anomalies is similar at these two levels (not shown).
Geopotential height anomalies of wave-1 SVW events at 50 and 500 hPa for the three periods: (left) lags −12 to −6, (middle) lags −4 to 2, and (right) lags 4 to 10. Shown are (top),(upper middle) the full field, (lower middle) the wave-1 component at 500 hPa, and (bottom) the wave-2 component at 500 hPa. Anomalies are shown in bright contours, while climatology is shown in pale contours with a contour interval of 20 m (50 m) at 500 hPa (50 hPa). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Geopotential height anomalies of wave-1 SVW events at 50 and 500 hPa for the three periods: (left) lags −12 to −6, (middle) lags −4 to 2, and (right) lags 4 to 10. Shown are (top),(upper middle) the full field, (lower middle) the wave-1 component at 500 hPa, and (bottom) the wave-2 component at 500 hPa. Anomalies are shown in bright contours, while climatology is shown in pale contours with a contour interval of 20 m (50 m) at 500 hPa (50 hPa). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Geopotential height anomalies of wave-1 SVW events at 50 and 500 hPa for the three periods: (left) lags −12 to −6, (middle) lags −4 to 2, and (right) lags 4 to 10. Shown are (top),(upper middle) the full field, (lower middle) the wave-1 component at 500 hPa, and (bottom) the wave-2 component at 500 hPa. Anomalies are shown in bright contours, while climatology is shown in pale contours with a contour interval of 20 m (50 m) at 500 hPa (50 hPa). Blue and red represent negative and positive values, respectively. Values that are statistically significant at the 95% confidence level are shown with gray shading.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 8, but for wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 8, but for wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 8, but for wave-2 SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
During wave-1 SVW events, 50-hPa geopotential height anomalies become prominent during the onset and project strongly onto the climatological wave-1 pattern (Fig. 8b). These anomalies are maintained for a while (Fig. 8c), consistent with a slow vortex recovery (Figs. 6a,b). In the troposphere, 500-hPa geopotential anomalies exhibit negative height anomalies over northern Russia and positive anomalies over northern Canada and the Atlantic, forming a wave-1 pattern in the polar region over 10 days (Figs. 8e,h). It is noteworthy that this tropospheric wave-1 pattern is not well matched to the SSW events of Limpasuvan et al. (2004) but is very similar to the upward wave events of Dunn-Sigouin and Shaw (2015). This may suggest that SVW events better detect the periods of large wave activity in the troposphere than midpoint SSW events, resulting in a more focused wave signal in composite fields. Note that the wave events of Dunn-Sigouin and Shaw (2015) are detected using poleward eddy heat fluxes, a quantity directly related to vertical fluxes of wave activity according to linear theory. It should also be stated that tropospheric anomalies are well connected by westward tilt to the stratospheric anomalies (cf. Figs. 8b to 8e). Such vertical arrangement of geopotential height anomalies is consistent with upward wave propagation, explaining the growth of wave disturbances in the stratosphere during the onset.
The wave-2 SVW events show a faster evolution of stratospheric anomalies (Figs. 9a–c). In the troposphere, a prominent wave-2 pattern is observed only during the onset of the events with strong positive anomalies over Alaska and eastern Europe and negative anomalies over the North Atlantic and northern Russia (Figs. 9e,k). This anomaly structure, which is again vertically tilted, matches reasonably well with the precursors of split SSW events (Martius et al. 2009; Cohen and Jones 2011; Mitchell et al. 2013) or structures that favor extreme upward EP fluxes by wave-2 (Garfinkel and Hartmann 2010).
It is important to note that tropospheric anomalies in both wave-1 and wave-2 events project positively onto the relevant climatological patterns (light contour in Figs. 8h, 9k), likely enhancing the vertical propagation of wave-1 and wave-2 through constructive linear interference. When transient waves align with the stationary waves, vertical wave propagation to the stratosphere is generally enhanced (Garfinkel and Hartmann 2010; Smith et al. 2010; Nishii et al. 2011; Smith and Kushner 2012). The role of linear wave interference in vertical wave propagation is quantified in this study following Smith and Kushner [2012; see their Eq. (2)]. The results are summarized in Fig. 10 in terms of 500-hPa heat flux. The heat flux associated with wave-1 SVW events is mainly explained by linear interference (cf. black and red lines in Fig. 10a). However, during wave-2 SVW events, less than two-thirds of total heat fluxes are explained by linear interference. This result again indicates that wave-2 SVW events are driven by more complicated dynamics than wave-1 SVW events, as hinted from Fig. 7.
Meridional heat fluxes averaged over 50°–90°N at 500 hPa during (a) wave-1 and (b) wave-2 SVW events. Only wavenumber-1 (2) fluxes are shown in wave-1 (wave-2) SVW events. The anomalous fluxes (black) are decomposed into their linear (LIN) and nonlinear (NONLIN) components according to Eq. (2) of Smith and Kushner (2012). The analysis period spans 1979–2012. Note that heat fluxes are associated with the vertical EP flux component [Eq. (3)]. Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Meridional heat fluxes averaged over 50°–90°N at 500 hPa during (a) wave-1 and (b) wave-2 SVW events. Only wavenumber-1 (2) fluxes are shown in wave-1 (wave-2) SVW events. The anomalous fluxes (black) are decomposed into their linear (LIN) and nonlinear (NONLIN) components according to Eq. (2) of Smith and Kushner (2012). The analysis period spans 1979–2012. Note that heat fluxes are associated with the vertical EP flux component [Eq. (3)]. Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Meridional heat fluxes averaged over 50°–90°N at 500 hPa during (a) wave-1 and (b) wave-2 SVW events. Only wavenumber-1 (2) fluxes are shown in wave-1 (wave-2) SVW events. The anomalous fluxes (black) are decomposed into their linear (LIN) and nonlinear (NONLIN) components according to Eq. (2) of Smith and Kushner (2012). The analysis period spans 1979–2012. Note that heat fluxes are associated with the vertical EP flux component [Eq. (3)]. Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
The time scale of linear interference is also different (Fig. 10). The wave-1 SVW events exhibit preexisting wave-1 fluxes up to several weeks before the onset, reflecting the presence of transient anomalies over a longer period. In contrast, linear interference is limited to several days before the onset of wave-2 SVW events. This result agrees partially with Smith and Kushner (2012), who found linear interference to be limited to wave-1 events. It is, however, clear that wave-2 events, as shown in Fig. 10b, are also influenced by linear wave interference. This discrepancy is possibly related to how event are aligned in composites. It is shown later that the evolution of weak polar vortex events is sensitive to the details of the definition.
d. +NAM versus −NAM SVW events
The evolution of SVW events presented above is not the same as the classical picture of SSW events, which exhibits persistent stratospheric anomalies and extended downward coupling in the troposphere (e.g., Baldwin and Dunkerton 2001; Limpasuvan et al. 2004). The difference may occur simply because the SVW events explored in this study are not constrained by the stratospheric mean state. As discussed earlier, no stratospheric background flow is imposed in defining SVW events: they can occur under both weak and strong stratospheric vortex conditions. To examine the sensitivity to the background state, Fig. 11 contrasts +NAM to −NAM SVW events. The latter events are comparable to major SSW events in the literature (Table 1). A total of 18 (12) events out of 34 SVW events are qualified to be −NAM (+NAM) events (Table 1; see also the appendix).
As in Fig. 6, but for (top) +NAM and (bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 6, but for (top) +NAM and (bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in Fig. 6, but for (top) +NAM and (bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As expected, −NAM SVW events show larger negative zonal wind anomalies in the stratosphere, with longer persistence compared to +NAM SVW events, which display only positive zonal wind anomalies (Figs. 11a,e). But in terms of tendency, both events show similar vertical coupling (Figs. 11b,f). This result suggests that a short-term vertical coupling occurs not only during weak vortex events, such as SSW events, but also during the weakening of an anomalously strong polar vortex (see also McDaniel and Black 2005).
Both −NAM and +NAM SVW events show a similar temporal evolution of zonal wind tendency and EP flux convergence around the onset, although the former has a generally longer time scale of vortex deceleration and recovery. An important difference is that time-lagged downward coupling is clearer in −NAM SVW events (Fig. 11f). Stratospheric deceleration starts to appear at lag −5, but statistically significant deceleration in the troposphere occurs only at lag −2. This downward propagation of zonal wind anomalies is also evident in EP flux divergence, at least in the stratosphere. However, no evidence of downward propagation of zonal-mean anomalies is found in +NAM SVW events (Fig. 11b). Tropospheric deceleration even appears earlier than maximum stratospheric deceleration. This result may suggest that downward coupling is sensitive to the stratospheric mean state. With respect to EP flux divergence, both types of events show a zonal wind deceleration associated with wave-1 and wave-2 on a similar time scale (see also Fig. 12). Wave-1 or wave-2 SVW events are therefore not limited to a specific stratospheric NAM state. However, there is a preference for wave-1 forcing in −NAM SVW events, where wave-1 EP flux divergence is about twice as strong as wave-2 divergence (note that the contour interval in Figs. 11g,h is logarithmic).
As in the last two rows of Fig. 4, but for (top),(upper middle) +NAM and (lower middle),(bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in the last two rows of Fig. 4, but for (top),(upper middle) +NAM and (lower middle),(bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
As in the last two rows of Fig. 4, but for (top),(upper middle) +NAM and (lower middle),(bottom) −NAM SVW events.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
The details of wave propagation during the onset of +NAM and −NAM SVW events are illustrated in Fig. 12. The +NAM SVW events are characterized by enhanced vertical EP flux convergence in the stratosphere (Fig. 12a) mainly due to wave-2 (Fig. 12c), consistent with Fig. 11d. The EP flux divergence in the meridional direction, however, is not well organized both in the stratosphere and troposphere.
The −NAM SVW events show vertical EP flux convergence that is qualitatively similar to +NAM SVW events (Fig. 12i). However, a significant difference is observed in meridional EP fluxes (cf. Figs. 12e and 12m). Unlike +NAM SVW events, anomalous planetary-scale waves propagate poleward, resulting in a significant zonal wind deceleration from the stratosphere to the troposphere. This vertically organized deceleration is similar to the all-SVW-event composite in Fig. 4i, indicating that tropospheric deceleration in the all-SVW-event composite is dominated by −NAM SVW events (cf. Fig. 4i with Figs. 12e,m). This result also indicates that, although zonal wind deceleration during +NAM and −NAM SVW events look qualitatively similar (Figs. 11b,f), their dynamical mechanisms are different.
It is also important to note that the stronger contribution of wave-1 than wave-2 in vortex deceleration during −NAM SVW events (Figs. 11g,h) is primarily due to the meridional EP flux convergence of wave-1 (Fig. 12n). In the troposphere, zonal wind deceleration north of 60°N is dominated by wave-2 (Fig. 12o), although wave-1 and wave-3 + also play a nonnegligible role. This result is consistent with McDaniel and Black (2005) and Nakagawa and Yamazaki (2006).
4. Comparison to other definitions
To further explore the nature of SVW events,−NAM SVW events are compared with SSW-like weak polar vortex events in the literature, as described in section 2b (Fig. 13). It is important to note that, while in principle the threshold, midpoint, minimum, and −NAM SVW definitions should detect similar events, the differences in the onset dates of events (Table 1) result in different spatiotemporal evolutions. For example, threshold and midpoint events show differences in the persistence of zonal wind anomalies in the lower stratosphere. While the threshold events show negative anomalies at 100 hPa from lag −5 to 35 (Fig. 13a), the midpoint events show long-lasting negative anomalies from lag −25 to 30 (Fig. 13d). The minimum events show a similar evolution to the midpoint events (Fig. 13g). As listed in Table 1, although the onset dates of midpoint and minimum events are not the same, they are close to each other (see also the appendix). Differences of 
Composite evolution of (left) the zonal wind anomalies, (middle) their time tendencies, and (right) EP flux divergence averaged over 50°–90°N for (top)–(bottom) the threshold, midpoint, minimum, and −NAM SVW events. The zonal wind (m s−1) and its tendency (m s−1 day−1) are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. The vertical component of EP flux is shown with the same graphical convention as in Fig. 2. Values that are statistically significant at the 95% confidence level are shown with gray shading. Significant EP fluxes are denoted with thick black lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (left) the zonal wind anomalies, (middle) their time tendencies, and (right) EP flux divergence averaged over 50°–90°N for (top)–(bottom) the threshold, midpoint, minimum, and −NAM SVW events. The zonal wind (m s−1) and its tendency (m s−1 day−1) are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. The vertical component of EP flux is shown with the same graphical convention as in Fig. 2. Values that are statistically significant at the 95% confidence level are shown with gray shading. Significant EP fluxes are denoted with thick black lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (left) the zonal wind anomalies, (middle) their time tendencies, and (right) EP flux divergence averaged over 50°–90°N for (top)–(bottom) the threshold, midpoint, minimum, and −NAM SVW events. The zonal wind (m s−1) and its tendency (m s−1 day−1) are illustrated with logarithmic contours (0.25, 0.5, 1, 2, 4, 8, …). Blue and red represent negative and positive values, respectively. The zero line is shown as a thin black line only for the tendency. The vertical component of EP flux is shown with the same graphical convention as in Fig. 2. Values that are statistically significant at the 95% confidence level are shown with gray shading. Significant EP fluxes are denoted with thick black lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
In Fig. 13, −NAM SVW events show a great resemblance to threshold events (cf. top and bottom rows). This result indicates that −NAM SVW events are essentially the same as classical SSW events with different temporal alignments in the composite analysis. However, tropospheric deceleration around lag 0 is much clearer in −NAM SVW events than others (Fig. 13k). The time scale of polar vortex deceleration is also shorter, indicating that wave driving is well focused in −NAM SVW events (Figs. 13l). These differences suggest that the weakening of the polar vortex, rather than its absolute state, may result in a better alignment of planetary-scale wave forcing in both the stratosphere and troposphere.
Figure 14 further highlights the sensitivity of the dynamical evolution of weak polar vortex events to their definitions, notably the forcing by synoptic- and planetary-scale waves in the stratosphere and troposphere. Most definitions show wave driving in the stratosphere (Fig. 14a) by both wave-1 and wave-2 (Figs. 14d,g). This feature is sharper and stronger in the −NAM SVW events, with the strongest contribution by wave-1 (Fig. 14d) in comparison to others. In contrast, the minimum and midpoint events show comparable roles of wave-1 and wave-2, while the threshold events are dominated by wave-2. This result indicates that, although EP flux divergence during the onset of weak vortex events is qualitatively similar in all definitions, the relative importance of wave-1 and wave-2 is slightly different. In most cases, wave-3 and higher plays a minimal role in vortex deceleration (Figs. 14j).
EP flux divergence averaged over 50°–90°N at (left) 50 hPa, (middle) 400 hPa, and (right) meridional component of EP flux divergence at 400 hPa decomposed according to (top)–(bottom) zonal wavenumber contribution (all units: m s−1 day−1). Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
EP flux divergence averaged over 50°–90°N at (left) 50 hPa, (middle) 400 hPa, and (right) meridional component of EP flux divergence at 400 hPa decomposed according to (top)–(bottom) zonal wavenumber contribution (all units: m s−1 day−1). Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
EP flux divergence averaged over 50°–90°N at (left) 50 hPa, (middle) 400 hPa, and (right) meridional component of EP flux divergence at 400 hPa decomposed according to (top)–(bottom) zonal wavenumber contribution (all units: m s−1 day−1). Values that are statistically significant at the 95% confidence level are shown with thick lines.
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
In the troposphere, large variability is observed among definitions when considering total EP flux convergence (Fig. 14b). In general, wave forcing is sporadic and statistically insignificant in the analysis period. When EP flux divergence is decomposed into individual wavenumbers, a significant value is found in wave-2 only in the threshold and −NAM SVW events (Fig. 14h).
Since tropospheric wind change is more sensitive to meridional EP flux divergence than total EP flux divergence (see section 3b), we also compare the meridional component of EP flux divergence between definitions (right column of Fig. 14). In all definitions, the meridional EP flux convergence of wave-3 and higher systematically increases during the onset (Fig. 14l). The relative importance of wave-1 and wave-2, however, differs substantially between the definitions. For example, the threshold events show no significant contribution of both wave-1 and wave-2 during the onset (blue in Figs. 14f,i), whereas the midpoint and minimum events exhibit significant wave-1 [light blue in Figs. 14f,i; see also Limpasuvan et al. (2004)]. The −NAM SVW events also show significant wave-1 and wave-2 contributions, but the latter is stronger than the former [red line in Figs. 14f,i; see also McDaniel and Black (2005) and Nakagawa and Yamazaki (2006)]. These differences suggest that the evolution of tropospheric eddy momentum flux in the course of the life cycle of SVW events is very sensitive to the definition of the event and may not be physically robust. To identify the source of this uncertainty, further analysis with a larger sample size is needed.
The above findings suggest that the details of stratosphere–troposphere coupling are somewhat sensitive to the definition of the events. However, in general, −NAM SVW events show more focused wave activity in the stratosphere. Although not shown, the same is true when composite analysis is performed with respect to strong poleward eddy heat flux events, which are shown to be well correlated with stratospheric NAM time tendency (Dunn-Sigouin and Shaw 2015). This may suggest that the detection of weak polar vortex events using wave forcing or flow response (i.e., tendency) is more advantageous than the detection of events based on anomalies.
5. Summary and conclusions
This study presents the dynamical evolution of stratospheric vortex weakening (SVW) events, which are episodes of fast and strong weakening of the stratospheric polar vortex in the Northern Hemisphere winter. A primary focus is placed on the short-term coupling between the stratosphere and troposphere around the onset of SVW events. Such events are detected using the time tendency of the NAM index rather than a specific value of the NAM (Baldwin and Dunkerton 2001) or stratospheric wind reversal, as in major stratospheric sudden warming (SSW) events (e.g., Charlton and Polvani 2007). This allows SVW events under both weak and strong polar vortices (McDaniel and Black 2005).
During the SVW events, the polar vortex is rapidly decelerated and then slowly recovers in a time scale of about two weeks. The initial weakening is mainly caused by an abrupt increase of wave activity density 
The SVW events are characterized by a near-simultaneous coupling between the troposphere and stratosphere (Limpasuvan et al. 2004). The coupling occurs on time scales of a few days, and both layers display deceleration of high-latitude zonal wind (50°N and poleward). This result is consistent with the findings of McDaniel and Black (2005), although they did not discuss the time lag between tropospheric and stratospheric changes. It is further found that the time-lagged tropospheric coupling occurs only in the SVW events under a weak vortex state (i.e., −NAM SVW events), which are comparable to major SSW events. No downward propagation of zonal-mean circulation anomalies is observed when SVW events occur under a strong polar vortex (i.e., +NAM SVW events).
The TEM diagnostics revealed that the short-term vertical coupling during SVW events is largely caused by interactions between planetary-scale waves and the zonal-mean wind (e.g., Limpasuvan et al. 2004; Polvani and Waugh 2004; McDaniel and Black 2005; Dunn-Sigouin and Shaw 2015). These waves (i.e., wave-1 and wave-2) are the dominant forcing responsible for the observed deceleration of zonal wind not only in the stratosphere, but also in the troposphere. In the troposphere, synoptic-scale waves also contribute to the deceleration.
Further classification of SVW events into the wave-1 and wave-2 SVW events shows a similar tropospheric zonal wind change. This result suggests that stratosphere–troposphere coupling during the onset of SVW events may not be sensitive to the details of stratospheric wave driving. However, the wave-1 SVW events generally show slower recovery than the wave-2 SVW events both in the stratosphere and troposphere. This causes more persistent circulation anomalies after the onset of wave-1 SVW events than wave-2 events. The dominant geopotential height anomalies in both events align well with climatological wave patterns, indicating that the weakening of the stratospheric vortex and the associated short-term coupling between the stratosphere and troposphere results from vertically propagating waves that linearly interfere with climatological waves (Smith et al. 2010; Nishii et al. 2011; Smith and Kushner 2012). Quantitatively, about 90% or 60% of troposphere heat fluxes during the onset of wave-1 or wave-2 SVW events respectively are explained by linear wave interference.
The robustness of the above results is tested by comparing −NAM SVW events with SSW-like events in the literature. For all definitions, stratospheric deceleration is explained by planetary-scale waves of wave-1 and wave-2. However, tropospheric deceleration is not simply explained by either planetary or synoptic-scale waves. The former is important in −NAM SVW events, whereas the latter is predominant in the midpoint and minimum events. Moreover, the relative importance of wave-1 and wave-2 varies between definitions. This result indicates that the momentum budget in the troposphere is sensitive to the choice of the onset date of weak polar vortex events, and great caution is needed in comparing different definitions. Here, we suggest that the differences in the evolution of stratospheric events from one definition to the other should not be necessarily taken as contradictory, but rather as different aspects of the evolution, which may be better highlighted with different methodologies. A larger sample size is needed to better understand the nature of those discrepancies and reduce the associated uncertainties.
While the role of planetary-scale waves is emphasized in the present study, other mechanisms, such as synoptic-scale wave feedback (Kushner and Polvani 2004; Simpson et al. 2009; Domeisen et al. 2013) and residual circulation extending to the surface (Haynes et al. 1991; Thompson et al. 2006) are not necessarily exclusive. They could be important especially for the slow downward coupling after the onset of extreme polar vortex events and the persistence of tropospheric anomalies over weeks or months (e.g., Baldwin and Dunkerton 2001).
Acknowledgments
We thank three anonymous reviewers for their helpful comments. This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMIPA 2015-2091-1.
APPENDIX
Onset Dates of Weak Polar Vortex Events
The onset dates of each extreme event are listed in Table 1. In this section, a graphical comparison of those dates is presented. Figure A1 clearly illustrates the differences between each definition. For example, for the record-breaking SSW event of 2009 (e.g., Martineau and Son 2013 and references therein), the onset date of the SVW event is found within a few days of threshold and wind-reversal events (26, 25, and 24 January, respectively), while the minimum event occurs on 3 February, and the midpoint event occurs latest on 12 February. The order of onset dates also varies from one event to the other (cf. the 1986/87 and 2008/09 events for example). This difference of onset dates for essentially the same extreme stratospheric events results in different dynamical evolution, as illustrated in Figs. 13 and 14. Note here that the minimum and midpoint events are not necessarily the same unless the time scales of vortex weakening and strengthening are the same. But they are located closely with each other.
Comparison of the onset dates across different definitions of weak polar vortex. The NAM index at 10 hPa (gray) and 50 hPa (black) is plotted as a function of time. Colored circles indicate the onset date according to the following definitions: threshold (red), midpoint (green), minimum (magenta), and SVW events (dark blue and pale blue for −NAM and +NAM SVW events, respectively). For reference, the onset dates of wind-reversal SSW events are indicated with vertical red lines. The red shading indicates periods of wind reversal at 10 hPa (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Comparison of the onset dates across different definitions of weak polar vortex. The NAM index at 10 hPa (gray) and 50 hPa (black) is plotted as a function of time. Colored circles indicate the onset date according to the following definitions: threshold (red), midpoint (green), minimum (magenta), and SVW events (dark blue and pale blue for −NAM and +NAM SVW events, respectively). For reference, the onset dates of wind-reversal SSW events are indicated with vertical red lines. The red shading indicates periods of wind reversal at 10 hPa (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Comparison of the onset dates across different definitions of weak polar vortex. The NAM index at 10 hPa (gray) and 50 hPa (black) is plotted as a function of time. Colored circles indicate the onset date according to the following definitions: threshold (red), midpoint (green), minimum (magenta), and SVW events (dark blue and pale blue for −NAM and +NAM SVW events, respectively). For reference, the onset dates of wind-reversal SSW events are indicated with vertical red lines. The red shading indicates periods of wind reversal at 10 hPa (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
To examine the sensitivity of vertical coupling to the reference level, major SSW events that accompany zonal-mean wind reversal at 10 hPa and 60°N are also identified (Table 1) and compared with SVW events evaluated using the 10-hPa NAM index (Fig. A2). Composite wind-reversal events are not quite significant in the troposphere in terms of zonal wind tendency (see also Cohen and Jones 2011). The SVW events detected with the NAM at 10 hPa also show weaker zonal wind response in the troposphere in comparison to those based on 50 hPa (cf. Figs. 1 and A2). This result may suggest that the lower stratosphere is better connected to the tropospheric circulation (Gerber et al. 2009). It is possible that the variability of upward-propagating planetary-scale waves from one event to the other blurs the tropospheric signal when identifying and aligning events in the higher stratosphere. Another possible source of discrepancy could include the response of the tropospheric residual circulation to the anomalous stratospheric wave drag. The latter could be enhanced when wave forcing is located lower in the stratosphere, resulting in a stronger Eliassen adjustment in the troposphere (Eliassen 1951). Although further analyses are needed, this result indicates that the tropospheric response to weak polar vortex events is somewhat sensitive to the choice of reference level.
Composite evolution of (top) major SSW events and (bottom) SVW events defined at 10 hPa instead of 50 hPa. A logarithmic contour interval is used (0.25, 0.5, 1, 2, 4, 8, …). Zonal wind anomaly is expressed in meters per second and tendency is in meters per second per day. Blue and red represent negative and positive values, respectively. Zonal wind reversal (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (top) major SSW events and (bottom) SVW events defined at 10 hPa instead of 50 hPa. A logarithmic contour interval is used (0.25, 0.5, 1, 2, 4, 8, …). Zonal wind anomaly is expressed in meters per second and tendency is in meters per second per day. Blue and red represent negative and positive values, respectively. Zonal wind reversal (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
Composite evolution of (top) major SSW events and (bottom) SVW events defined at 10 hPa instead of 50 hPa. A logarithmic contour interval is used (0.25, 0.5, 1, 2, 4, 8, …). Zonal wind anomaly is expressed in meters per second and tendency is in meters per second per day. Blue and red represent negative and positive values, respectively. Zonal wind reversal (
Citation: Journal of Climate 28, 18; 10.1175/JCLI-D-14-00478.1
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