1. Introduction
The most prominent feature of the winter stratosphere is the polar vortex: the cyclonic westerly winds that circumnavigate the pole, playing an important role in the dynamical circulation and the distribution of trace gases (e.g., Plumb 2002). The polar vortex can initiate tropospheric changes, including the transfer of tropical variations to midlatitudes, an altering of the storm tracks, and a modulation of near-surface weather patterns (e.g., Baldwin and Dunkerton 2001; Thompson et al. 2002; Bell et al. 2009), via a downward migration of zonal-mean zonal wind and temperature anomalies. Thus, understanding the physical mechanisms that cause variations of the polar vortex is vital to studying climate variability.
The quasi-biennial oscillation (QBO), an oscillation of easterly and westerly jets in the tropical stratosphere that descends from 3 to 70 hPa over a period of approximately 28 months, is one of the major factors that affect interannual variability of the polar vortex (Baldwin et al. 2001). One intriguing feature of the Northern Hemisphere (NH) winter is a phenomenon known as the Holton–Tan effect (HTE; Holton and Tan 1980), whereby a stronger polar vortex exists when the QBO in the lower stratosphere (~50 hPa) is in its westerly phase (QBOw), and, conversely, a weaker polar vortex exists when the QBO is in its easterly phase (QBOe; Holton and Tan 1980). The HTE also holds when the QBO is defined by the vertical wind shear between 50 and 70 hPa, but it tends to be weaker for the QBO defined at other levels (Hitchman and Huesmann 2009, hereafter HH09). The HTE has been confirmed by observational studies (e.g., Dunkerton and Baldwin 1991; Naito and Hirota 1997; Lu et al. 2008, 2014) as well as by both mechanistic (e.g., O’Sullivan and Young 1992; Naito and Yoden 2006; Pascoe et al. 2006) and complex general circulation models (e.g., Calvo et al. 2009; Marshall and Scaife 2009). However, the mechanism behind the HTE is still under debate (e.g., Naoe and Shibata 2010; Yamashita et al. 2011; Garfinkel et al. 2012; Lu et al. 2014).
The polar vortex is most sensitive to planetary-scale Rossby waves propagating upward from the troposphere (e.g., McIntyre 1982). In extreme cases, these wave disturbances can cause rapid breakdowns of the vortex and rising temperatures in the polar stratosphere, a phenomenon known as a stratospheric sudden warming (SSW; Labitzke 1982). It has been found that SSWs tend to occur more frequently under QBOe than under QBOw conditions (e.g., Dunkerton and Baldwin 1991; Naito and Hirota 1997; Lu et al. 2008); thus, it is natural to suspect that a QBO modulation of planetary waves is responsible for the changes in the frequency of SSWs and the overall polar vortex strength (Holton and Tan 1980; Calvo et al. 2009).
A number of mechanisms have been proposed for the HTE, the most well-known of which was proposed by Holton and Tan (1980). It involves changes in the width of the extratropical waveguide and, consequently, the propagation of quasi-stationary planetary waves as a result of a latitudinal shift in the subtropical critical line (Holton and Tan 1980). Under QBOe conditions, the critical line in the lower stratosphere is located farther poleward in the NH, resulting in a narrower extratropical waveguide and, hence, a confinement of upward planetary wave fluxes from the troposphere to the stratosphere, to high latitudes. Furthermore, waves with small enough amplitude are reflected poleward by the critical line, causing a more disturbed polar vortex (Tung 1979). Conversely, under QBOw, the critical line is located in the summer hemisphere, resulting in a latitudinally wider extratropical waveguide and allowing for more wave propagation away from the polar vortex. This leads to a less-disturbed, stronger, and colder vortex. This mechanism is referred to as the HT mechanism herein.
Efforts to verify the HT mechanism have not been very successful. For instance, Holton and Tan (1982) examined the Eliassen–Palm (EP) fluxes and EP flux divergence but could not establish statistically significant differences between different QBO phases. Dunkerton and Baldwin (1991) found that the QBO modulation of the EP flux was consistent with the observed wind anomaly but that there were only marginal differences in planetary wave amplitudes and the number of planetary wave events between the two QBO phases. Modeling studies have suggested that the QBO does cause changes in planetary wave amplitude in addition to changes in the EP flux and EP flux divergence (e.g., Holton and Austin 1991; Naito and Yoden 2006; Calvo et al. 2009; Watson and Gray 2014), although exactly how the QBO induces these wave changes remains unclear (Anstey and Shepherd 2014).
There have been a number of recent studies that have suggested that the changes in EP fluxes between QBOe and QBOw may be caused by something other than a change of waveguide in the lower stratosphere (e.g., Naoe and Shibata 2010; Yamashita et al. 2011; Garfinkel et al. 2012; Lu et al. 2014). For instance, Naoe and Shibata (2010) found quite the opposite to the HT mechanism; planetary waves tend to propagate more equatorward and upward in the midlatitude lower stratosphere under QBOe than under QBOw. By imposing easterly wind anomalies at different altitudes throughout the tropical stratosphere, Gray et al. (2001, 2004) found that the polar winds and temperatures are most sensitive to wind changes in the tropical and subtropical upper stratosphere, with easterly anomalies in the tropical upper stratosphere leading to an earlier onset of SSWs in comparison to their control simulations. These authors suggested that planetary waves of deep vertical structure are modulated by the subtropical upper-stratospheric wind anomalies associated with the QBO modulation of the critical line in the upper stratosphere.
Another mechanism, related to the QBO-induced secondary meridional circulation and the effect it has on wave propagation in the middle-to-upper stratosphere, has been suggested by Ruzmaikin et al. (2005) and recently supported by Garfinkel et al. (2012) and Lu et al. (2014). In this mechanism, an anomalously strong meridional circulation under QBOe creates a barrier for equatorward wave propagation in the middle-to-upper stratosphere, hence encouraging poleward planetary wave propagation and resulting in enhanced EP flux convergence at high latitudes. Such modulation is not consistent with the HT mechanism, whereby, along with an overall poleward shift of upward-propagating wave activity, vertically alternating poleward, equatorward, and poleward wave propagation in the lower, middle, and upper stratosphere, respectively, is expected. However, a modeling study by Gray et al. (2003) found that a disturbed polar vortex can also be generated when a vertically deep easterly wind anomaly is imposed in the tropics. They consequently suggested that the QBO-induced meridional circulation, which is associated with a vertical wind shear in the tropics, is not required to produce the HTE and that instead the change in waveguide throughout the depth of the stratosphere associated with a critical-line shift is needed.
In studying the HTE, the most frequently used measures of wave activity are the EP fluxes and EP flux divergence, which give an indication of the net direction of wave propagation and wave drag imposed on the mean flow, and the refractive index, which identifies regions where wave propagation, wave absorption, and wave attenuation occur (e.g., Naoe and Shibata 2010; Garfinkel et al. 2012; Lu et al. 2014). An alternative way of measuring the wave–mean flow interaction involves potential vorticity (PV). In the absence of diabatic heating and friction, PV is conserved and advected along isentropic (i.e., potential temperature) surfaces so that there is no cross-isentropic movement of air (Haynes and McIntyre 1987). These properties make PV an ideal quantity to describe Rossby wave propagation in terms of meridionally displaced air parcels. Also, the meridional gradient of PV is an important parameter determining the refractive index (Matsuno 1970). Positive gradients, such as those associated with a positive wind shear, favor wave propagation, whereas negative gradients imply wave breaking (McIntyre and Palmer 1983).
PV-based metrics have been used to diagnose wave breaking both in the troposphere (e.g., Martius et al. 2007; Kunz et al. 2009) and the stratosphere (e.g., Baldwin and Holton 1988; Abatzoglou and Magnusdottir 2007; Hitchman and Huesmann 2007, HH09). For instance, Baldwin and Holton (1988) studied the climatology of planetary wave breaking at 850 K in the NH winter by defining wave breaking as a reversal in the meridional PV gradient. Studies have also utilized eddy fluxes of PV along isentropic surfaces to examine the diffusive properties of wave forcing (e.g., Butler et al. 2011; Birner et al. 2013). Birner et al. (2013) used the up-/down-PV-gradient eddy PV fluxes to investigate Rossby wave decay/growth in the vicinity of the tropospheric subtropical jet. However, there has been limited work that studies the HTE using PV on isentropic levels. One exception is HH09 who calculated a series of PV-based measures to determine the QBO modulation of Rossby wave propagation and breaking, finding a significant HTE during 1979–2002 in the reanalysis datasets they used.
The main objectives of this study are threefold: 1) to provide a comprehensive description of the climatology and QBO modulation of wave–mean flow interactions in the lower to middle stratosphere using an isentropic coordinate framework; 2) to extend the work of HH09 using a longer (1979–2012) and higher-resolution reanalysis dataset; and 3) to identify/corroborate a plausible mechanism that can explain why the HTE is strongly associated with the lower-stratospheric QBO in NH winter. To complete these objectives, we examine both the December–February (DJF)-mean climatology and composite differences of a series of PV-based measures developed by HH09, EP flux diagnostics, and eddy fluxes of PV. The majority of our analyses are based on the zonal-mean momentum budget and the wave-activity conservation law in the small-amplitude limit. For the third objective, we shall, in particular, explore the extent to which the QBO signatures of wave propagation, growth, and breaking support or conflict with the HT mechanism.
2. Theoretical framework
a. Potential vorticity in isentropic coordinates
In the NH winter stratosphere, the meridional PV gradient 
b. Zonal-mean momentum equation
Equation (2) states that the zonal-mean-flow tendency 
c. Wave-activity conservation law
The zonal-mean momentum budget expressed by Eqs. (2)–(4) allows us to examine the effect of waves on the zonal-mean circulation by evaluating the wave forcing in terms of the EP flux divergence term 
3. Data and methods
Here, we use daily averages estimated from 6-hourly ERA-Interim data, with a horizontal resolution of 0.7° from the European Centre for Medium-Range Weather Forecasts (ECMWF; Dee et al. 2011; see www.ecmwf.int) for the period of 1979–2012. From this dataset, we use PV data on nine isentropic levels from 350 to 850 K (~150–10 hPa or 10–33 km). Additionally, we use the horizontal wind field u and υ, temperature T, and geopotential height Z, which have been interpolated from the archived 37 pressure levels to the same nine isentropic levels as the PV data using a piecewise cubic Hermite interpolating polynomial. Of the 37 pressure levels, approximately 10 are spanned by the 350- and 850-K isentropic levels. We focus on the NH middle winter (DJF), during which the HTE bears its strongest signal and the stratospheric polar vortex is most variable (Dunkerton and Baldwin 1991). For brevity, the year associated with each DJF period is defined by the year in which December falls (e.g., the year labeled as 1986 indicates the winter period from December 1986 to February 1987).
Three PV-based measures developed by HH09 are adopted here to examine wave propagation, wave breaking, and wave activity. They are as follows: (i) the zonal-mean meridional PV gradient 
Terms present in the zonal-mean momentum budget [Eqs. (2)–(4)] and the wave-activity conservation law [Eqs. (5) and (6)] are estimated based on daily PV and interpolated daily data of u, υ, T, and Z in isentropic coordinates. See sections 2b and 2c for more details.
To define the QBO phase for each DJF period, we utilize the definition given in Huesmann and Hitchman (2001), which is also used by HH09, and calculate the vertical difference between the 50- and 70-hPa pressure surfaces (approximately 530- and 475-K isentropic surfaces, respectively) of the DJF-averaged zonal-wind anomalies averaged between 5°S and 5°N. The sign and magnitude of this difference then determines the phase of the QBO, with a positive difference (≥2 m s−1) indicating QBOw and a negative difference (≤−2 m s−1) indicating QBOe. All other DJF winters that do not satisfy either criterion are classified as neutral. We note that Huesmann and Hitchman (2001) used a different threshold of 1.5 m s−1, although we find that this does not change any of our conclusions qualitatively. Here, we refer to our QBO definition as QBO50–70hPa or QBO for simplicity. The result of our definition for each DJF winter from 1979 to 2011 is shown in Fig. 1, with 16 QBOw, 11 QBOe, and 6 neutral winters overall. Composite differences between QBOe and QBOw (QBOe − QBOw) are calculated for all of the aforementioned quantities. The confidence levels for these differences are determined at the 90% and 95% levels using two-sided Student’s t tests. For certain statistically significant regions (to be defined in the relevant sections), linear correlations between the relevant quantity and the QBO are performed, with the results shown as time series plots, to provide an appreciation of the temporal effect of the QBO. Also, we note that qualitatively similar results can be obtained if the QBO is defined as the wind anomalies at 50 hPa, because the QBO wind anomalies at 50 hPa are approximately twice as large as those at 70 hPa, and these two levels are usually in phase with one another (not shown).
Time series of DJF anomalies of the zonal-mean wind difference between the 50- and 70-hPa pressure surfaces, QBO50–70hPa, averaged between 5°S and 5°N. Note that the year corresponds to the year in which December falls (e.g., the year labeled 1986 indicates the winter period from December 1986 to February 1987). Black star markers denote QBOw years, and black circle markers denote QBOe years. Gray square markers denote those years affected by two major volcanic eruptions. In total, excluding those four years affected by volcanoes, there are 14 QBOw and 10 QBOe winters.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
To account for the possible contamination of the QBO signal by the two major volcanic eruptions (El Chichón, March 1982, and Mount Pinatubo, June 1991), which released large quantities of volcanic aerosols into the stratosphere and caused anomalous warming of the stratosphere for two years after the eruption, we exclude the four winters that fell into the periods of March 1982–February 1984 and June 1991–May 1993 (shown in Fig. 1 as gray square markers) from our composite analysis. This results in 14 QBOw and 10 QBOe winters overall. Sensitivity tests nevertheless suggest that similar results can be obtained if those four winters are included in our composite analysis.
4. Results
a. The Holton–Tan effect in wind and temperature
In this section, the zonal-mean zonal wind 
The DJF-mean climatology of 
(a) Climatology and (b) QBO composite difference (QBOe − QBOw) of the DJF-averaged zonal-mean zonal wind 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
Figure 2c shows that the DJF-mean 
Figures 3a and 3b examine the temporal evolution of the high-latitude winds and temperature in relation to the QBO. It shows that the zonal-mean zonal wind anomalies, area weighted and averaged over 55°–75°N, 700–850 K, correlates positively with the QBO (r = 0.44, p = 0.01), while the zonal-mean temperature anomaly, area weighted and averaged over 65°–85°N, 430–600 K, is negatively correlated with the QBO (r = −0.37, p = 0.035). Together, they indicate that a significantly weaker, warmer polar vortex is associated with QBOe, agreeing with Figs. 2b and 2d and with previous studies based on pressure coordinates (e.g., Lu et al. 2014).
(a) Time series of the DJF mean of 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
b. Effect on PV-based measures
In this section, we analyze a series of PV-based measures developed by HH09 (see section 3 for definition) in order to examine the climatology and the QBO modulation of wave activity and its preference to either propagate or break.
The zonal-mean meridional PV gradient 
(a),(b) As in Figs. 2a and 2b, but for the zonal-mean meridional PV gradient 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
The QBO composite difference of 
Negative PV gradients are associated with wave breaking. Hence, the occurrence frequency of zonal-mean negative gradients 
Figure 4d shows the QBO composite difference of the DJF occurrence of 
The standard deviation of the daily meridional PV gradient 
(a),(b) As in Figs. 2a and 2b, but for 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
The 
An alternative measure of wave activity, as defined in section 2c, is 
c. Effect on the zonal-mean momentum budget
In this section, the zonal-mean momentum budget [Eq. (2)] is used to determine the effect of the net wave forcing, in terms of the EP flux divergence term 
Figure 6a shows the DJF climatology of the EP flux vectors 
(a) DJF climatology and (b) DJF composite differences of the EP flux F and the EP flux divergence term 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
The QBO composite differences of the DJF-mean 
The relative contributions to the momentum budget of the upward change in form drag 
The climatological 
In a seasonal mean, as we analyze here, the net wave forcing 
As in Figs. 2a and 2b, but for the residual mean meridional circulation term 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
Figure 7b shows the QBO composite difference of the DJF-mean Θ. The Θ anomalies are broadly in balance and anticorrelated with the 
An alternative way to determine the net wave forcing of the zonal-mean circulation is to calculate the eddy PV flux term 
(a),(b) As in Figs. 2a and 2b, but for 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
The QBO composite difference of 
The difference between the eddy PV flux term 
The QBO composite difference of D in Fig. 8d shows negative anomalies in the midlatitude lower stratosphere (45°–60°N, 450–525 K) indicating that small-scale gravity waves, nonconservative effects, and/or nonlinear processes may also play a role in the region where the fountain-like feature appears in the EP flux anomalies (Fig. 6b). Further, the lack of signal in the extratropical middle stratosphere implies that the QBO modulation of wave forcing in this region is mainly due to resolved waves. The vertical dipole structure in the subtropics, with negative D anomalies in the lower stratosphere and positive D anomalies in the middle stratosphere, shares the same sign as those associated with the EP flux divergence term 
The temporal behavior of the QBO modulation of the DJF-mean 
(a) Time series of DJF mean of 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
d. Effect on the wave-activity conservation law
In this section, the wave-activity conservation law [Eq. (5)] is used to identify the regions of wave decay/growth in response to the interactions between waves and the mean flow, given by the up-/downgradient eddy PV fluxes Γ. We analyze the climatology and quantify the first-order (i.e., linear) effect of the QBO on wave decay/growth in the 350–850-K isentropic layer averaged over the winter months of DJF.
Figure 10a shows the DJF climatology of the up-/downgradient eddy PV flux term 
(a),(b) As in Figs. 2a and 2b, but for the up-/downgradient eddy PV fluxes 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
The associated QBO composite difference is shown in Fig. 10b. In general, the subtropical anomalies correspond broadly to 
The wave decay/growth of the resolved waves is approximated by 
The QBO composite difference of 
Figure 11 shows the temporal behavior of the QBO modulation of the DJF-mean 
As in Fig. 3, but showing 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-14-0358.1
5. Conclusions and discussion
For the first time, a systematic examination of the zonal-mean momentum budget and up-/downgradient eddy potential vorticity fluxes, together with three PV-based measures developed by HH09, is utilized to provide a comprehensive description of the climatology and QBO modulation of wave–mean flow interactions in the Northern Hemisphere winter lower-to-middle stratosphere.
Based on the ERA-Interim dataset, we find that the classical Holton–Tan effect (HTE) can be robustly observed during December–February when the relevant variables are mapped to isentropic coordinates. Our analysis of the three PV-based measures provides clear evidence that the QBO modulates wave propagation, wave breaking, and wave activity. At high latitudes, there is enhanced wave breaking, contributing to the weaker polar vortex under QBOe. This is associated with an overall decreased meridional PV gradient and reduced wave activity. In the lower stratosphere, the pattern of PV gradients appears to favor wave activity at midlatitudes and in the vicinity of the QBO-induced critical line.
Our analysis of the QBO modulation of the Eliassen–Palm fluxes and EP flux divergence provide supporting information to the PV-based measures on how the QBO affects wave propagation and the wave forcing of the mean flow. The EP flux anomalies indicate that the enhanced PV gradient in the midlatitude lower stratosphere is associated with increased upward wave propagation. This enhanced upward propagation at 40°–55°N is accompanied by meridional wave divergence, leading to anomalous horizontal wave convergence both at ~15°–45°N, 450–600 K and at high latitudes. In the middle stratosphere, the horizontal EP flux convergence induced by enhanced poleward wave propagation at high latitudes acts to weaken the polar vortex. The overall enhanced stratospheric EP flux convergence drives a stronger poleward meridional circulation, contributing to the warmer high-latitude lower stratosphere under QBOe. Our analysis also suggests that these wave-forcing anomalies are predominantly associated with a change of planetary waves. Overall, these EP flux diagnostics are dynamically agreeable to the HTE.
Analysis of the eddy PV fluxes further supports the general picture that has been obtained from the PV-based measures and the EP flux diagnostics. Under QBOe, enhanced downgradient eddy PV fluxes (indicating wave growth) occur in the lower stratosphere, between the QBO-induced critical line and midlatitudes, in agreement with the equatorward eddy PV fluxes in this region. At 25°–30°N, 350–400 K and 50°–65°N, 350–450 K, there are anomalous upgradient eddy PV fluxes (indicating wave decay). This pattern of up-/downgradient eddy PV fluxes in the upper troposphere–lower stratosphere suggests that the enhanced wave growth at midlatitudes is accompanied by wave decay on the equatorward flank of the subtropical jet and at high latitudes. This pattern seems to form a “valve” for upward wave propagation from the troposphere (Chen and Robinson 1992), in agreement with the enhanced upward wave propagation at midlatitudes, as shown by the EP fluxes. Downgradient eddy PV fluxes are found in the high-latitude middle stratosphere, indicating planetary wave growth inside the polar vortex; this is in dynamical agreement with the HTE.
Our results show clear and consistent patterns of the QBO modulation of wave activity and wave–mean flow interactions in the extratropics. Nevertheless, they only provide partial support for the classic Holton–Tan (HT) mechanism, whereby a poleward shift in wave propagation and wave activity is expected under QBOe. The QBO signature in the wave-activity measures, however, indicates enhanced wave activity in the midlatitude lower stratosphere and decreased wave activity poleward of 55°N. There is an enhanced upward flux of wave activity into the lower stratosphere at ~40°–55°N, which forms a fountain-like feature that diverges horizontally, both equatorward toward the critical line and poleward toward the polar vortex. The poleward EP flux anomalies are associated with an EP flux convergence and increased wave breaking inside the polar vortex, in agreement with the HT mechanism. However, the presence of the equatorward EP flux anomalies in the subtropical-to-midlatitude lower stratosphere and the decrease of wave activity within the polar vortex do not suggest an overall poleward shift of wave forcing under QBOe, as expected by the HT mechanism. Additionally, the enhanced wave growth at midlatitudes with regions of wave decay on the equatorward flank of the subtropical jet and at high latitudes is not explainable by the HT mechanism. These observations are in agreement with recent studies (e.g., Naoe and Shibata 2010; Yamashita et al. 2011; Garfinkel et al. 2012; Lu et al. 2014) that suggest the HT mechanism is not the dominant mechanism governing the HTE. Nevertheless, caution must be taken with the interpretation of our results, which are based on seasonal averages from December to February. These seasonal averages do not allow us to distinguish the response from the cause and therefore to draw a firm conclusion on the ability of the HT mechanism to explain the observed HTE.
Our comprehensive diagnostics suggest that the change in waveguide associated with the latitudinal shift of the tropospheric subtropical jet may play a role in explaining the HTE. Under QBOe, the QBO-induced meridional circulation appears to cause a poleward shift of the subtropical jet, which consequently encourages upward wave propagation at midlatitudes because of the increased baroclinicity (Lachmy and Harnik 2014). A similar shift of the jet was also found by Garfinkel and Hartmann (2011), though the effect they identified is only significant in early and late winter. An enhancement of baroclinicity in the midlatitude lower stratosphere is supported by our zonal-mean momentum budget analysis, whereby there are strengthened zonal-wind anomalies that arch down from the middle stratosphere to the upper troposphere, associated with enhanced wave activity. This is also indicative of a positive feedback, whereby the increased baroclinicity associated with the arching zonal-wind anomalies encourages upward wave propagation from the troposphere, which then diverges meridionally in the fountain-like feature, causing an eddy momentum-flux convergence at midlatitudes and a concurrent strengthening of the zonal-wind anomalies. This, in turn, encourages further upward wave propagation. Accompanying the change in wave forcing in the midlatitude lower stratosphere is a stronger poleward meridional circulation, which aids in the weakening of the polar vortex. Thus, the intensified shift of the subtropical jet under QBOe appears to play a role in the change in wave propagation, and hence wave forcing, and the associated changes in the meridional circulation in the extratropical lower stratosphere.
In light of the aforementioned evidence and drawing on the work of recent studies, we put forward a new, additional mechanism, which has the potential to account for the QBO-induced wave-forcing anomalies in the lower stratosphere during DJF. Under QBOe conditions, this new mechanism works as follows: The QBO-induced mean meridional circulation causes an intensified poleward shift of the subtropical jet in the upper troposphere. The upscaling of wave forcing in the vicinity of the subtropical jet, whereby an excitement of transient planetary waves on the poleward flank of the jet occurs at the expense of synoptic-wave decay (Birner et al. 2013), is also shifted poleward to midlatitudes. These newly generated planetary waves propagate upward, having a positive feedback with the arching zonal winds in the subtropics to midlatitudes and acting to drive an enhanced poleward meridional circulation in the lower stratosphere, thus contributing to the weaker and warmer polar vortex. The poleward shift of the subtropical jet also results in less baroclinic planetary wave activity at high latitudes, as a result of upward-propagating baroclinic waves favoring propagation toward regions of high baroclinicity (e.g., Lachmy and Harnik 2014). While our analysis does provide certain evidence for the HTE causality in terms of wave driving, we appreciate that our arguments are based on correlations drawn from reanalysis data. Further work, especially model simulations, must be undertaken to unambiguously determine the validity of this new mechanism.
Previous studies have suggested that the QBO-induced secondary meridional circulation in the middle-to-upper stratosphere may play a role in explaining the HTE (e.g., Ruzmaikin et al. 2005). Via changes in the background mean-flow geometry, the QBO alters the midlatitude waveguide by affecting the refractive index and causing more poleward wave propagation at 20–5 hPa (Garfinkel et al. 2012; Lu et al. 2014). Our results in the middle stratosphere are in agreement with those authors, whereby we find that the QBO-induced meridional circulation in the subtropics and the enhanced Brewer–Dobson circulation (BDC) at mid-to-high latitudes correspond to EP flux divergence patterns that are responsible for anomalous poleward wave propagation under QBOe. This reduced equatorward wave refraction above 700 K is dynamically agreeable to the weaker polar vortex. Additionally, this increased poleward wave propagation, in combination with the enhanced planetary wave growth at high latitudes, indicates in situ instability or an energy conversion process from the basic state. If this is the case, the QBO-induced meridional circulation plays very different, albeit complementary, roles in both the lower and middle stratosphere to cause the observed teleconnection between the QBO and the polar vortex via a modulation of planetary wave activity.
The HTE associated with the lower-stratospheric QBO is not necessarily the only layer where a teleconnection between the tropics and the polar vortex occurs. For instance, the QBO-induced subtropical wind anomalies in the upper stratosphere can also contribute to the QBO modulation of wave activity and hence to the HTE (e.g., Gray et al. 2001, 2004). Such an effect is not studied here because of the height range of the PV dataset we used. Furthermore, our results hint that other processes, such as gravity waves, nonconservative effects, and nonlinear processes may play a role in the vicinity of the QBO critical line, the mid-to-high-latitude lower stratosphere (Fig. 8d), and the high-latitude middle stratosphere (Figs. 10b,d). Investigation into such processes may help to improve our understanding of the QBO modulation of wave–mean flow interactions and possible wave–wave interactions in these regions. Finally, an analysis of the seasonal life cycle in terms of the growth and decay of finite-amplitude waves is needed to aid our understanding of the dynamical evolution of the HTE, to better separate the cause and response, and to differentiate the extent to which different mechanisms can play a role. Research regarding the seasonal evolution is currently being undertaken and will be published elsewhere.
Acknowledgments
This study is funded by the Natural Environment Research Council (NERC). We acknowledge the use of the ECMWF reanalysis datasets. We would also like to thank the two anonymous reviewers whose constructive comments have helped to improve the manuscript. IW is funded by NERC Ph.D. studentship NE/K50094X/1.
REFERENCES
Abatzoglou, J. T., and G. Magnusdottir, 2007: Wave breaking along the stratospheric polar vortex as seen in ERA-40 data. Geophys. Res. Lett., 34, L08812, doi:10.1029/2007GL029509.
Andrews, D. G., 1983: A finite-amplitude Eliassen–Palm theorem in isentropic coordinates. J. Atmos. Sci., 40, 1877–1883, doi:10.1175/1520-0469(1983)040<1877:AFAEPT>2.0.CO;2.
Andrews, D. G., 1987: On the interpretation of the Eliassen–Palm flux divergence. Quart. J. Roy. Meteor. Soc., 113, 323–338, doi:10.1002/qj.49711347518.
Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics.International Geophysics Series, Vol. 40, Academic Press, 489 pp.
Anstey, J. A., and T. G. Shepherd, 2014: High-latitude influence of the quasi-biennial oscillation. Quart. J. Roy. Meteor. Soc., 140, 1–21, doi:10.1002/qj.2132.
Baldwin, M. P., and J. R. Holton, 1988: Climatology of the stratospheric polar vortex and planetary wave breaking. J. Atmos. Sci., 45, 1123–1142, doi:10.1175/1520-0469(1988)045<1123:COTSPV>2.0.CO;2.
Baldwin, M. P., and T. J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294, 581–584, doi:10.1126/science.1063315.
Baldwin, M. P., and Coauthors, 2001: The quasi-biennial oscillation. Rev. Geophys., 39, 179–229, doi:10.1029/1999RG000073.
Bell, C. J., L. J. Gray, A. J. Charlton-Perez, M. M. Joshi, and A. A. Scaife, 2009: Stratospheric communication of El Niño teleconnections to European winter. J. Climate, 22, 4083–4096, doi:10.1175/2009JCLI2717.1.
Birner, T., D. W. J. Thompson, and T. G. Shepherd, 2013: Up-gradient eddy fluxes of potential vorticity near the subtropical jet. Geophys. Res. Lett., 40, 5988–5993, doi:10.1002/2013GL057728.
Butler, A. H., D. W. J. Thompson, and T. Birner, 2011: Isentropic slopes, downgradient eddy fluxes, and the extratropical atmospheric circulation response to tropical tropospheric heating. J. Atmos. Sci., 68, 2292–2305, doi:10.1175/JAS-D-10-05025.1.
Calvo, N., M. A. Giorgetta, R. Garcia-Herrera, and E. Manzini, 2009: Nonlinearity of the combined warm ENSO and QBO effects on the Northern Hemisphere polar vortex in MAECHAM5 simulations. J. Geophys. Res., 114, D13109, doi:10.1029/2008JD011445.
Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83–109, doi:10.1029/JZ066i001p00083.
Chen, P., and W. A. Robinson, 1992: Propagation of planetary waves between the troposphere and stratosphere. J. Atmos. Sci., 49, 2533–2545, doi:10.1175/1520-0469(1992)049<2533:POPWBT>2.0.CO;2.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828.
Dunkerton, T. J., and M. P. Baldwin, 1991: Quasi-biennial modulation of planetary-wave fluxes in the Northern Hemisphere winter. J. Atmos. Sci., 48, 1043–1061, doi:10.1175/1520-0469(1991)048<1043:QBMOPW>2.0.CO;2.
Edouard, S., R. Vautard, and G. Brunet, 1997: On the maintenance of potential vorticity in isentropic coordinates. Quart. J. Roy. Meteor. Soc., 123, 2069–2094, doi:10.1002/qj.49712354314.
Garfinkel, C. I., and D. L. Hartmann, 2011: The influence of the quasi-biennial oscillation on the troposphere in winter in a hierarchy of models. Part I: Simplified dry GCMs. J. Atmos. Sci., 68, 1273–1289, doi:10.1175/2011JAS3665.1.
Garfinkel, C. I., T. A. Shaw, D. L. Hartmann, and D. W. Waugh, 2012: Does the Holton–Tan mechanism explain how the quasi-biennial oscillation modulates the Arctic polar vortex? J. Atmos. Sci., 69, 1713–1733, doi:10.1175/JAS-D-11-0209.1.
Gray, L. J., S. J. Phipps, T. J. Dunkerton, M. P. Baldwin, E. F. Drysdale, and M. R. Allen, 2001: A data study of the influence of the equatorial upper stratosphere on northern-hemisphere stratospheric sudden warmings. Quart. J. Roy. Meteor. Soc., 127, 1985–2003, doi:10.1002/qj.49712757607.
Gray, L. J., S. Sparrow, M. Juckes, A. O’Neill, and D. G. Andrews, 2003: Flow regimes in the winter stratosphere of the northern hemisphere. Quart. J. Roy. Meteor. Soc., 129, 925–945, doi:10.1256/qj.02.82.
Gray, L. J., S. Crooks, C. Pascoe, S. Sparrow, and M. Palmer, 2004: Solar and QBO influences on the timing of stratospheric sudden warmings. J. Atmos. Sci., 61, 2777–2796, doi:10.1175/JAS-3297.1.
Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional or other forces. J. Atmos. Sci., 44, 828–841, doi:10.1175/1520-0469(1987)044<0828:OTEOVA>2.0.CO;2.
Hitchman, M. H., and A. S. Huesmann, 2007: A seasonal climatology of Rossby wave breaking in the 330–2000-K layer. J. Atmos. Sci., 64, 1922–1940, doi:10.1175/JAS3927.1.
Hitchman, M. H., and A. S. Huesmann, 2009: Seasonal influence of the quasi-biennial oscillation on stratospheric jets and Rossby wave breaking. J. Atmos. Sci., 66, 935–946, doi:10.1175/2008JAS2631.1.
Holton, J. R., 1983: The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. Atmos. Sci., 40, 2497–2507, doi:10.1175/1520-0469(1983)040<2497:TIOGWB>2.0.CO;2.
Holton, J. R., and C. H. Tan, 1980: The influence of the equatorial quasi-biennial oscillation on the global circulation at 50 mb. J. Atmos. Sci., 37, 2200–2208, doi:10.1175/1520-0469(1980)037<2200:TIOTEQ>2.0.CO;2.
Holton, J. R., and C. H. Tan, 1982: The quasi-biennial oscillation in the Northern Hemisphere lower stratosphere. J. Meteor. Soc. Japan, 60, 140–148.
Holton, J. R., and J. Austin, 1991: The influence of the equatorial QBO on sudden stratospheric warmings. J. Atmos. Sci., 48, 607–618, doi:10.1175/1520-0469(1991)048<0607:TIOTEQ>2.0.CO;2.
Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877–946, doi:10.1002/qj.49711147002.
Huesmann, A. S., and M. H. Hitchman, 2001: The stratospheric quasi-biennial oscillation in the NCEP reanalyses: Climatological structures. J. Geophys. Res., 106, 11 859–11 874, doi:10.1029/2001JD900031.
Jones, D. B. A., H. R. Schneider, and M. B. McElroy, 1998: Effects of the quasi-biennial oscillation on the zonally averaged transport of tracers. J. Geophys. Res., 103, 11 235–11 249, doi:10.1029/98JD00682.
Kinnersley, J. S., 1999: Seasonal asymmetry of the low- and middle-latitude QBO circulation anomaly. J. Atmos. Sci., 56, 1140–1153, doi:10.1175/1520-0469(1999)056<1140:SAOTLA>2.0.CO;2.
Kunz, T., K. Fraedrich, and F. Lunkeit, 2009: Impact of synoptic-scale wave breaking on the NAO and its connection with the stratosphere in ERA-40. J. Climate, 22, 5464–5480, doi:10.1175/2009JCLI2750.1.
Labitzke, K., 1982: On the interannual variability of the middle stratosphere during the northern winters. J. Meteor. Soc. Japan, 60, 124–139.
Lachmy, O., and N. Harnik, 2014: The transition to a subtropical jet regime and its maintenance. J. Atmos. Sci., 71, 1389–1409, doi:10.1175/JAS-D-13-0125.1.
Lait, L. R., 1994: An alternative form for potential vorticity. J. Atmos. Sci., 51, 1754–1759, doi:10.1175/1520-0469(1994)051<1754:AAFFPV>2.0.CO;2.
Lu, H., M. P. Baldwin, L. J. Gray, and M. J. Jarvis, 2008: Decadal-scale changes in the effect of the QBO on the northern stratospheric polar vortex. J. Geophys. Res., 113, D10114, doi:10.1029/2007JD009647.
Lu, H., T. J. Bracegirdle, T. Phillips, A. Bushell, and L. J. Gray, 2014: Mechanisms for the Holton–Tan relationship and its decadal variation. J. Geophys. Res. Atmos., 119, 2811–2830, doi:10.1002/2013JD021352.
Marshall, A. G., and A. A. Scaife, 2009: Impact of the QBO on surface winter climate. J. Geophys. Res., 114, D18110, doi:10.1029/2009JD011737.
Martius, O., C. Schwarz, and H. C. Davies, 2007: Breaking waves at the tropopause in the wintertime Northern Hemisphere: Climatological analyses of the orientation and the theoretical LC1/2 classification. J. Atmos. Sci., 64, 2576–2592, doi:10.1175/JAS3977.1.
Matsuno, T., 1970: Vertical propagation of stationary planetary waves in the winter Northern Hemisphere. J. Atmos. Sci., 27, 871–883, doi:10.1175/1520-0469(1970)027<0871:VPOSPW>2.0.CO;2.
McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 1775–1800, doi:10.1175/1520-0469(1987)044<1775:TEOOEG>2.0.CO;2.
McIntyre, M. E., 1982: How well do we understand the dynamics of stratospheric warmings? J. Meteor. Soc. Japan, 60, 37–65.
McIntyre, M. E., and T. N. Palmer, 1983: Breaking planetary waves in the stratosphere. Nature, 305, 593–600, doi:10.1038/305593a0.
Naito, Y., and I. Hirota, 1997: Interannual variability of the Northern winter stratospheric circulation related to the QBO and the solar cycle. J. Meteor. Soc. Japan, 75, 925–937.
Naito, Y., and S. Yoden, 2006: Behavior of planetary waves before and after stratospheric sudden warming events in several phases of the equatorial QBO. J. Atmos. Sci., 63, 1637–1649, doi:10.1175/JAS3702.1.
Naoe, H., and K. Shibata, 2010: Equatorial quasi-biennial oscillation influence on northern winter extratropical circulation. J. Geophys. Res., 115, D19102, doi:10.1029/2009JD012952.
Newman, P. A., E. R. Nash, and J. E. Rosenfield, 2001: What controls the temperature of the Arctic stratosphere during the spring? J. Geophys. Res., 106, 19 999–20 010, doi:10.1029/2000JD000061.
O’Sullivan, D., and R. E. Young, 1992: Modeling the quasi-biennial oscillation’s effect on the winter stratospheric circulation. J. Atmos. Sci., 49, 2437–2448, doi:10.1175/1520-0469(1992)049<2437:MTQBOE>2.0.CO;2.
O’Sullivan, D., and T. J. Dunkerton, 1995: Generation of inertia–gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci., 52, 3695–3716, doi:10.1175/1520-0469(1995)052<3695:GOIWIA>2.0.CO;2.
Pascoe, C. L., L. J. Gray, and A. A. Scaife, 2006: A GCM study of the influence of equatorial winds on the timing of sudden stratospheric warmings. Geophys. Res. Lett., 33, L06825, doi:10.1029/2005GL024715.
Plumb, R. A., 2002: Stratospheric transport. J. Meteor. Soc. Japan, 80, 793–801, doi:10.2151/jmsj.80.793.
Plumb, R. A., and R. C. Bell, 1982: A model of the quasi-biennial oscillation on an equatorial beta-plane. Quart. J. Roy. Meteor. Soc., 108, 335–352, doi:10.1002/qj.49710845604.
Rhines, P. B., and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid Mech., 122, 347–367, doi:10.1017/S0022112082002250.
Ruzmaikin, A., J. Feynman, X. Jiang, and Y. L. Yung, 2005: Extratropical signature of the quasi-biennial oscillation. J. Geophys. Res., 110, D11111, doi:10.1029/2004JD005382.
Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414–432, doi:10.1175/1520-0469(1978)035<0414:TLCOSN>2.0.CO;2.
Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15, 1421–1428, doi:10.1175/1520-0442(2002)015<1421:SCTNHW>2.0.CO;2.
Tung, K. K., 1979: A theory of stationary long waves. Part III: Quasi-normal modes in a singular waveguide. Mon. Wea. Rev., 107, 751–774, doi:10.1175/1520-0493(1979)107<0751:ATOSLW>2.0.CO;2.
Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.
Watson, P. A. G., and L. J. Gray, 2014: How does the quasi-biennial oscillation affect the stratospheric polar vortex? J. Atmos. Sci., 71, 391–409, doi:10.1175/JAS-D-13-096.1.
Yamashita, Y., H. Akiyoshi, and M. Takahashi, 2011: Dynamical response in the Northern Hemisphere midlatitude and high-latitude winter to the QBO simulated by CCSR/NIES CCM. J. Geophys. Res., 116, D06118, doi:10.1029/2010JD015016.
