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 A middle atmosphere general circulation model is used to examine the effects of zonally asymmetric ozone (ZAO) on the Northern Hemisphere planetary waveguide (PWG) during winter (December–February). The morphology of the PWG is measured by a refractive index, Eliassen-Palm flux vectors, the latitude of the subtropical zero wind line, and the latitude of the subtropical jet. ZAO causes the PWG to contract meridionally in the upper stratosphere, expand meridionally in the lower stratosphere, and expand vertically in the upper stratosphere and lower mesosphere. The ZAO-induced changes in the PWG are the result of increased upward and poleward flux of planetary wave activity into the extratropical stratosphere and lower mesosphere. These changes cause an increase in the Eliassen-Palm flux convergence at high latitudes, which produces a warmer and weaker stratospheric polar vortex and an increase in the frequency of stratospheric sudden warmings. The ability of ZAO to alter the flux of planetary wave activity into the polar vortex has important implications for accurately modeling wave-modulated and wave-driven phenomena in the middle atmosphere, including the 11-year solar cycle, stratospheric sudden warmings, and the phase of the Northern Hemisphere annular mode.
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 The concept of a planetary waveguide (PWG) was first proposed by Dickinson  to describe the regions of the Northern Hemisphere (NH) winter stratosphere where the background zonal wind supports the upward propagation of planetary waves. Matsuno  expanded on Dickinson's PWG concept and derived a refractive index for planetary waves on a sphere and showed that planetary wave propagation is strongest in regions where the refractive index is large and positive. For a typical NH winter zonal wind distribution (Figure 1), large, positive values of the refractive index occur in the region bounded on the south by the zero wind line [Tung, 1979] and on the north by the southern edge of the polar vortex [Chapman and Miles, 1981].
 The zero wind line and the vortex edge do not, however, provide a complete description of planetary wave propagation within the PWG; indeed, there exist robust features of the background flow within the PWG that exert substantial control over how much planetary wave activity enters the PWG from the troposphere and where that wave activity propagates once inside the stratosphere. For example, the vertical shear of the zonal-mean wind near the tropopause exerts significant influence over the amount of planetary wave activity that propagates upwards from the troposphere into the lower stratosphere [Chen and Robinson, 1992]. And once planetary waves arrive in the lower stratosphere, the local minimum in the refractive index associated with the negative vertical and horizontal gradients of the zonal-mean wind (above and to the north of the subtropical jet) splits the PWG into two “channels” through which planetary wave activity may either propagate poleward and upward into the interior of the stratosphere or equatorward where the waves are confined to the lower stratosphere [Chapman and Miles, 1981; Huang and Gambo, 1982; Li et al., 2006]. For the planetary waves that propagate upward and poleward into the interior of the stratosphere, the height that planetary waves are able to propagate is largely controlled by the ratio of the meridional gradient of potential vorticity to the zonal-mean westerly wind [Charney and Drazin, 1961; Matsuno, 1970]. In addition, Nigam and Lindzen  showed that modest latitudinal shifts in the location of the subtropical jet greatly alter the amount of planetary wave activity that is refracted into the mid-latitude and polar stratosphere. These results show that the PWG is largely defined by its meridional width (measured by the location of the zero wind line), its vertical extent (measured by the refractive index), and the strength of wave propagation around the subtropical jet and within the waveguide (both measured by the refractive index).
 The structures of the zonal-mean wind and PWG are determined by a balance between radiative heating due to ozone, long-wave radiative cooling, and dynamical heating due to planetary waves. Any physical process that alters this three-way balance will in turn modulate the PWG. One such process involves the feedbacks between planetary wave activity and stratospheric ozone. Specifically, as planetary waves propagate from the troposphere into the stratosphere during NH winter, they produce large zonal asymmetries (waves) in wind, temperature, and ozone [Gabriel et al., 2007]. Observations show that zonally asymmetric ozone (ZAO) constitutes a significant fraction of the total stratospheric ozone field [e.g., Wang et al., 2005; Gabriel et al., 2007; Crook et al., 2008]. That fraction reaches 10% during boreal winter (based on decadal averages) [Crook et al., 2008], 15% in the lower stratosphere near ~70°N and ~65°S [Gillett et al., 2009], 50% during the Antarctic stratospheric sudden warming of 2002 [Wang et al., 2005], and 50% during the breakup of the Antarctic ozone hole [Crook et al., 2008]. The phasing between the wind, temperature, and ozone waves produce fluxes that modulate both the spatial-temporal damping of the wave fields and the driving of the zonal-mean circulation [Nathan and Li, 1991; Nathan and Cordero, 2007; Albers and Nathan, 2012].
 General circulation modeling studies have also shown that ZAO has a large effect on the zonal-mean temperature and wind structure of the wintertime middle atmosphere in both hemispheres [Kirchner and Peters, 2003; Sassi et al., 2005; Gabriel et al., 2007; Brand et al., 2008; Crook et al., 2008; Waugh et al., 2009; Gillett et al., 2009; McCormack et al. 2011]. For example, Crook et al.  examined the effect of ZAO on the high latitude Southern Hemisphere and found that including ZAO produces lower stratospheric cooling that is comparable in magnitude to the cooling produced by the springtime Antarctic ozone hole. In a study that focused on the Northern Hemisphere, McCormack et al.  carried out an ensemble of GCM simulations over the December–March period and found that ZAO produces a warmer and more disturbed stratospheric polar vortex and an increased incidence of stratospheric sudden warmings (SSWs). Although McCormack et al. showed that ZAO changes temperatures and winds in the polar stratosphere, the mechanisms involved in the changes were not fully investigated; yet, understanding the connections between ZAO and the polar stratosphere is vital to producing reliable assessments of human-caused impacts on key features of the climate system, including the upward flux of planetary wave activity, the frequency of SSWs, and the phase of the Northern Hemisphere annular mode. Here we investigate how the physics associated with ZAO changes the morphology of the PWG. The results that we obtain underscore the importance of accurately accounting for ZAO in global climate models.
 In the following section, we introduce the model and diagnostics that we use to measure changes in the morphology of the PWG. In section 3, we present our results, and in section 4, we discuss the implications of our results for global climate modeling.
2 Model Description and Diagnostics
 We investigate the effects of ZAO on planetary wave propagation during NH winter using the NOGAPS-ALPHA global spectral general circulation model [see, for example, Eckermann et al., 2009; McCormack et al., 2011, and references therein]. NOGAPS-ALPHA extends from the surface to ~90 km in height and utilizes 68 hybrid (σ-p) vertical levels with triangular truncation at wave number 79. The model includes prognostic equations for O3 and H2O, which are calculated using the photochemical parameterizations of McCormack et al. [2006, 2008]. Shortwave heating and long-wave cooling rates are computed using prognostic O3 and H2O fields and a fixed profile of CO2. Sea surface temperatures and ice distributions are specified at the model lower boundary using 12-hourly observations from operational global analyses.
 We analyze 15 pairs of model simulations spanning early December to late March (121 days). Each pair of simulations was initialized using identical profiles of wind, temperature, and chemical constituents acquired from the NOGAPS-ALPHA data assimilation system [Eckermann et al., 2009]. The initialization dates were staggered in time in order to generate an ensemble of 15 independent pairs of model simulations [for details, see McCormack et al., 2011]. For each pair of simulations, one used fully prognostic ozone in the radiative heating and cooling calculations (designated 3DO3), and the other used zonal-mean values of the instantaneous prognostic ozone field to evaluate the radiative heating and cooling rates (designated ZMO3). We isolate the effect of ZAO on the circulation by taking the difference between 3DO3 and ZMO3 simulations for any given variable. When calculated in this way, the difference between the 3DO3 and ZMO3 simulations isolates the effect of ZAO-heating but not the effect of changes in zonal-mean ozone heating due to wave-ozone transports. Consistent with Albers and Nathan , however, the heating due to the wave-ozone transports is of secondary importance compared to the ZAO-heating. This means that the zonal-mean ozone distribution is similar for the 3DO3 and ZMO3 simulations.
 Statistical significance of the differences between ensemble means of model variables is assessed using a Student's t-test at the 95% confidence level. As stated in McCormack et al. , the 3DO3 model runs produced four SSWs, while the ZMO3 runs produced only one SSW. Statistical significance calculations were also carried out with all of the runs containing SSWs removed. Doing so did not change the qualitative nature of our results.
 We evaluate the morphology of the PWG in terms of two properties: (i) its shape, measured by its vertical extent and meridional width, and (ii) by the strength and direction of wave propagation within the waveguide itself. To measure these properties, we use a refractive index, Eliassen-Palm flux vectors, the latitude of the subtropical zero wind line, and the latitude of the subtropical jet.
 To diagnose the shape of the PWG and to distinguish regions of wave propagation versus evanescence, we employ the spherical form of the quasi-geostrophic refractive index squared [Andrews et al., 1987]:
is the zonal-mean potential vorticity gradient, ū is the zonal-mean wind, ϕ is latitude, z is height, s is the spherical integer zonal wave number, N(z) is the buoyancy frequency, f is the Coriolis parameter, H is the mean scale height [=7 km], ρ [= ρ0exp(−z/H)] is the standard density in log-pressure coordinates, ρ0 is the sea-level reference density, a is the radius of the Earth, Ω is the Earth's rotation frequency, and subscripts denote derivatives with respect to the given variable.
 Planetary waves propagate in regions where and are evanescent in regions where . Thus, the vertical extent of the PWG is measured by the height where . The meridional width of the PWG is determined by its northern and southern boundaries. We measure the northern boundary of the PWG by the latitude where becomes negative. The southern boundary of the PWG, however, cannot be measured directly by . This is because as ū → 0, so that interpretation of near the subtropical zero wind line becomes problematic. What is important here is that near the zero wind line the sign of ū largely controls the sign of . We therefore use the location of the zero wind line as a measure of the southern boundary of the PWG, consistent with previous studies [e.g., Holton and Tan, 1982]. In addition, we also use the location of the subtropical jet as a diagnostic to measure wave propagation within the PWG. This diagnostic is motivated by Nigam and Lindzen  who showed that small shifts (<3° in latitude) in the location of the subtropical jet can greatly alter the guiding of planetary waves from the troposphere into the extratropical stratosphere.
 When measuring changes in , we examine the relative importance of the strength, shear, and curvature of the zonal-mean wind. Equation ((1)) shows that the strength of wave propagation within the PWG depends on the ratio of the potential vorticity gradient to the zonal-mean wind, where the potential vorticity gradient (2) depends on the shear and curvature of the wind. Equation ((1)) also shows that as the planetary-wave wave number s increases, decreases; this explains why the propagation of planetary waves into the stratosphere is largely confined to planetary wave numbers s = 1–3 [Charney and Drazin, 1961].
 We measure the strength and direction of planetary wave propagation within the PWG by using two related diagnostics: the Eliassen-Palm flux (EP-flux) and . For steady, slowly varying plane waves, the planetary wave group velocity is locally parallel to the EP-flux vector [Edmon et al., 1980]. In addition, the EP-flux vector is curved up the gradient of ns and, in particular, is guided along ridges of ns [Palmer, 1981; Palmer, 1982; Karoly and Hoskins, 1982]. The magnitude of the EP-flux vector is related to by [Palmer, 1981; Palmer, 1982]:
where is defined in (4) and (5) below; ψs is the amplitude of a steady, conservative, linear wave with zonal wave number s. Regions of larger are associated with larger EP-flux vectors, and the trajectories of the EP-flux vectors are refracted up the gradient of . Thus, the EP-flux vector and provide a useful way of visualizing the propagation pattern of planetary waves in the latitude-height plane. Under quasi-geostrophic conditions, the EP-flux vector  and its divergence are defined in log-pressure coordinates as [Andrews et al., 1987]
where u and v are the zonal and meridional winds and θ is the potential temperature; the overbars and primes denote zonal-mean and perturbation quantities, respectively; and the subscripts in (5) denote partial differentiation. In accordance with (4) and (5), an upward directed EP-flux vector corresponds to a poleward heat flux; an equatorward directed EP-flux vector corresponds to a poleward momentum flux. The divergence of the EP-flux (6) measures the net planetary wave driving of the zonal-mean wind. Specifically, negative values of the EP-flux divergence (i.e., convergence) exert a westward drag on the mean wind that weakens the winter stratospheric westerly winds. When plotting the EP-flux vectors and divergence, we adopt the scaling procedure of Butchart et al. , which ensures that the relative size of the EP-flux vector components is preserved when plotted in Cartesian coordinates. For this scaling, the vector components (4) and (5) are multiplied by 2πa cosϕ and (4) is additionally multiplied by c = 0.0091; the units of the rescaled EP-flux divergence are kg s−2.
 The relationship between and the direction and magnitude of the EP-flux has been successfully used to describe a variety of stratospheric phenomenon including stratospheric sudden warmings [Butchart et al., 1982; Palmer, 1981], decadal temperature and circulation trends [Hu et al., 2005], annular mode variability [Lorenz and Hartmann, 2002], and the propagation of planetary waves between the troposphere and stratosphere [Chen and Robinson, 1992]. However, and its connection to the EP-flux are built on several simplifying assumptions that may not be valid under some circumstances.
 For example, Harnik and Lindzen  have shown that when the middle stratosphere contains a reflecting surface, the traditional (1) may be an unreliable measure of the boundaries of the PWG. This is because (1) is a bulk quantity that does not distinguish between propagation in the meridional and vertical directions. In fact, vertical propagation may be squelched, while remains positive. This can occur when meridional propagation is sufficiently strong. This point was underscored by Harnik and Lindzen who defined a wave number diagnostic, which, together with a linear model, provided boundaries for meridional and vertical wave propagation. Using the diagnostic for specific cases during Southern Hemisphere winter, they found that when a reflecting surface formed in the upper stratosphere, it was about 10 km lower than that produced by the traditional .
 Because the differences between the Harnik and Lindzen  wave number diagnostic and the traditional diagnostic appear to be largest when reflecting surfaces form in the upper stratosphere, we calculated a reflection index following Perlwitz and Harnik  for all of our 3DO3 and ZMO3 model simulations. We found that for the 3DO3 ensemble simulations, 6 out of 15 Januarys had reflective surfaces in the upper stratosphere. For the ZMO3 simulations, only 3 out of 15 winters had reflective surfaces (one in December and two in January). For the February simulations, there were no reflective surfaces in the upper stratosphere. For this reason, and since February is also the time when our simulations show that ZAO has its strongest effect on the model circulation (see section 3), we can expect to be a representative measure of the morphology of the planetary waveguide.
 Another potential concern regarding the diagnosis of wave propagation using (1)–(6) is that the mathematical relationship between the EP-flux and formally holds for slowly varying plane waves and for sufficiently small wave damping. These conditions may not be met in the real atmosphere due to wave reflection, tunneling, or damping, which may complicate the interpretation of the and EP-flux relationship or invalidate it altogether [Harnik, 2002].
 The above caveats notwithstanding, our results will show that the relationship between the EP-flux divergence and explains a significant portion of the wind and PWG variability observed in the model simulations that include ZAO.
 We compare the morphology of the PWG for the ZMO3 and 3DO3 cases for the winter months of December, January, and February (DJF). We follow with a discussion describing how ZAO causes the morphology of the PWG to evolve differently during January and February.
3.1 Mean Winter Results (December–January–February)
 Figures 1 and 2 show, respectively, the ZMO3 and 3DO3 ensemble mean zonal-mean wind and for stationary planetary wave s = 1 averaged over DJF; similar results were obtained for planetary wave s = 2 (not shown). Figures 1 and 2 show features of that are common to previous studies of NH planetary wave propagation [Chapman and Miles, 1981; Chen and Robinson, 1992]. These features include a local minimum in in the middle latitude lower stratosphere (~42°N latitude at 20 km) and a local maximum in between 50° and 60°N latitude and between 25 and 30 km. The local minimum in is due to the large negative gradient in potential vorticity (2). The large potential vorticity gradient results from the negative vertical and meridional gradients in zonal-mean wind located just above and to the north of the subtropical jet (Figure 1a). For waves originating in the extratropical troposphere, the local minimum in in the lower stratosphere splits the vertical propagation of planetary waves along two “channels” [Chapman and Miles, 1981; Huang and Gambo, 1982; Li et al., 2006]. The splitting of wave propagation along two wave channels is a common feature of the NH PWG during the midwinter to late winter (the time period of interest in this study) but may be less common during the early winter months of November–December [compare Shaw et al., 2010, Figure 9 bottom left and bottom right]. We shall refer to the two channels as the southern and northern wave channels.
 Along the southern channel of the PWG, the planetary waves are confined to the lower to middle stratosphere where they are refracted equatorward, eventually dissipating before they reach the upper stratosphere. Along the northern channel, the waves propagate through the local maximum in associated with the weak westerly winds located slightly north of the region between the subtropical and polar night jets. The region between the jets is centered at ~56°N latitude and 25 km in Figure 1a. From the local maximum in , waves tend to propagate upwards along the southern edge of the vertical axis of the polar night jet, where wave propagation is enhanced due to the combination of positive vertical and meridional shear of the zonal-mean wind. Waves that emanate from the sub-polar and polar regions tend to merge into the guide formed by the northern channel. The EP-flux vectors shown in Figures 1b and 2b clearly show planetary wave propagation along these two channels.
 Planetary wave activity within the PWG is generally strongest during midwinter to late winter, when the polar vortex is generally weaker. This is consistent with Charney and Drazin  who showed that planetary wave propagation from the troposphere into the stratosphere is favored in westerly flows that are not too strong. Because NH zonal asymmetries in ozone are predominantly generated by planetary wave activity, we also expect the ZAO field to be largest in late winter [Peters and Entzian, 1999; Peters et al., 2008]. As winter wanes, the solar zenith angle decreases and the ozone heating becomes stronger. Thus, we can anticipate that the effects of ZAO, particularly with regard to the PWG, will be strongest in midwinter to late winter. This is indeed the case, and in the discussion that follows, we focus our attention on January and February.
McCormack et al. , in a preliminary study examining the effects of ZAO on the NH wintertime circulation, found that ZAO has the largest affect on the dynamics of the NH polar winter stratosphere during January and February. Figures 3a and 3b show the difference in the ensemble mean zonal-mean wind (3DO3 minus ZMO3) for January and February. Wind differences that are statistically significant above the 95% confidence level are shaded. Overall, the effects of ZAO produce weaker westerly flow. During January (Figure 3a), the largest ensemble mean differences (~10 m/s) are located throughout the tropical stratopause region. During February (Figure 3b), the zonal wind differences extend poleward and downward with the largest differences (~17 m/s) located in the polar region between 40 and 50 km. Although the largest change in the wind speed occurs in February in the NH, changes in and the EP-flux divergence begin in January and grow as the winter season proceeds. By February, there is a large change in wind speed in the extratropical stratosphere. We next consider January and February in more detail.
3.2 January Results
 Figures 4a and 4b show the 3DO3 EP-flux divergence and EP-flux difference (3DO3 minus ZMO3) contours for January. Also shown are the corresponding EP-flux vectors. Figure 4b shows two important changes in the EP-flux due to ZAO. First, between 10 and 15 km and between ~10° and 50°N latitude, the EP-flux difference vectors are directed poleward. This corresponds to an increase in equatorward momentum flux, which is associated with the weakened extratropical upper tropospheric and lower stratospheric westerly flow. Second, between 10 and 30 km and between ~50° and 80°N latitude, the EP-flux difference vectors are directed upwards. This represents an increase in both vertical wave propagation and the meridional heat flux, which is associated with the weakening of the westerly flow. The change in the momentum flux in January continues to grow as the winter proceeds and will be important for explaining the equatorward shift in the subtropical jet seen later in February (Figure 3b). The effect of the increased meridional heat flux on the PWG, however, becomes readily apparent by the end of January.
 ZAO affects the zonal-mean wind, and by extension , via two pathways [Albers and Nathan, 2012]. Along one pathway, ozone-flux convergences due to ZAO modify the zonal-mean ozone field. The change to the zonal-mean ozone field produces changes in the zonal-mean radiative heating rate and thus the zonal-mean temperature. To maintain thermal wind balance, the changes to the zonal-mean temperature result in changes to the zonal-mean wind. Along the other pathway, ZAO-heating affects the EP-flux divergence, which in turn also modulates the zonal-mean wind. However, the difference between the 3DO3 and ZMO3 zonal-mean ozone fields is small between December and mid-February, which means that the first pathway plays a minor role in driving the changes to in the 3DO3 simulations. As a result, any changes in the zonal-mean wind and during this time period must be due to changes in the EP-flux divergence associated with ZAO-heating.
 Figure 4b shows that the increase in the EP-flux divergence within the northern channel of the PWG is primarily due to an increase in the vertical component of the EP-flux vector (this is confirmed by the near verticality of the EP-flux difference vectors in this region). To confirm that changes in the meridional heat flux precede changes in within the northern channel of the PWG, we next compare the time evolution of the meridional heat flux and .
 Figure 5 shows the time series of the ensemble mean and area-weighted average of the meridional heat flux and . The time series spans December 1 to February 28, and the area-weighted average is between 50° and 75°N at ~27 km in height. This height and latitude band lies roughly in the center of the northern channel of the PWG. During the time period considered, the heat flux and exhibit qualitatively different behaviors before and after 5 January.
 Prior to 5 January, the difference between the 3DO3 and ZMO3 heat fluxes (Figure 5a) does not produce a significance difference in the respective values of (Figure 5b). In contrast, after 5 January, the heat flux of 3DO3 remains larger than the heat flux of ZMO3 (the exception is a small 2-day period just after 10 January). As a result, for the 3DO3 ensembles also become larger than for the ZMO3 ensembles during mid to late January. Yet, there are two important differences between the temporal evolution of the versus the heat flux. First, the increase in the 3DO3 lags the increase in the 3DO3 heat flux by ~5 days. Second, the increase in the 3DO3 remains rather small until the final 5–10 days of January. The time lag between the change in the heat flux and the change in is not unexpected because it takes time for the ZAO-induced changes in the planetary waves to be manifest as changes in the zonal-mean wind. Once the ZAO-heating triggers the initial increase in the meridional heat flux, however, a positive feedback cycle is initiated that ultimately affects the PWG and any subsequent planetary wave activity. In short, the initial increase in the EP-flux convergence due to ZAO-heating causes changes in the strength of the extratropical westerly flow and the meridional potential vorticity gradient that combine to increase . The increase in , in turn, causes a further increase in vertical wave propagation that reinforces the initial increase in the EP-flux convergence. To gain further insight into the increase in vertical wave propagation, we next consider the spatial evolution of the vertical component of the EP-flux (F(z)) and the PWG.
 Figure 6a shows contours of the January ensemble mean difference (3DO3 minus ZMO3) in F(z) (5). The increase in F(z) is primarily concentrated in two plumes located within the northern and southern wave channels. The primary plume originates in the sub-polar and polar latitudes centered at ~60°N latitude, while the second, smaller plume is centered at ~30°N latitude. The two plumes and the gap between them are representative of three features of the PWG discussed in section 3.1; that is, the plumes represent an increase in vertical wave propagation along both the northern and southern planetary wave channels, while the gap between the plumes of F(z) is likely due to the local minimum in seen in Figures 1b and 2b at ~42°N latitude and 20 km.
 To examine the connection between the increase in F(z) along each of the planetary wave channels and changes in the morphology of the PWG, we computed the change in (3DO3 minus ZMO3) for two periods during January. Guided by the time series in Figure 5, we calculated the change in between 1 and 25 January and between 25 and 31 January. Between 1 and 25 January, there is very little change in (not shown); this result is consistent with the relatively small change in the January monthly mean zonal-mean wind shown in Figure 3a and the time series shown in Figure 5b. The final 5 days of January, however, show changes in that match very well with the increase in vertical wave propagation. In particular, the two plumes in F(z) shown in Figure 6a are collocated with notable increases in along both planetary wave channels (Figure 6b).
 We next examine how the ZAO-related changes in the PWG that first appear in late January expand and amplify to produce the large change in the zonal wind in February.
3.3 February Results
 Figure 3b shows that ZAO produces statistically significant decreases in the zonal-mean westerly flow of 5–11 m s−1 in the equatorial upper stratosphere and middle mesosphere, as well as decreases of 3–18 m s−1 throughout the NH extratropical stratosphere and mesosphere during February. A third, smaller region of statistically significant wind difference is located near the location of the subtropical jet at ~30°N in the upper troposphere and lower stratosphere (UTLS); the wind change at this location represents an increase of ~1–3 m s−1. The differences in the NH zonal-mean wind show three notable results. First, the decrease in the wind speed in the tropical upper stratosphere and lower mesosphere causes a northward migration of the tropical easterlies and a northward shift of the zero wind line. As Figure 7 shows, the northward shift in the zero wind line varies from about 1° to 8° latitude between about 30 km and 65 km in height. Second, the decrease in wind speed within the extratropics and polar region represents a weaker polar vortex and a warmer stratosphere (see also McCormack et al. [2011, Figure 2]. Third, the increased wind speed in the subtropical UTLS shifts the subtropical jet equatorward by about 3°. The zonal wind differences in Figures 3 and 7 qualitatively agree with recent studies suggesting a connection between northward shifts in the upper stratospheric zero wind line and an increase in the frequency of SSWs. For example, Gray  found that similar to the so-called “Holton-Tan” mechanism in the lower stratosphere [Holton and Tan, 1982], a northward shift in the upper stratospheric zero wind line produces a narrower PWG that directs more planetary wave activity poleward. The increase in planetary wave activity induces more wave drag on the zonal-mean circulation and creates a warmer extratropical and polar stratosphere and an increased incidence of SSWs. Indeed, as our EP-flux diagnostics will show, the combination of a narrower PWG and an increase in wave propagation combine to produce an increase in wave drag, the weaker polar vortex shown in Figures 1a and 2a, and an increased incidence of major SSWs (four in the 3DO3 ensembles versus one in the ZMO3 ensembles).
 Figures 8a and 8b compare values of the February ensemble mean (1) for ZMO3 and 3DO3 for stationary planetary wave s = 1. The scale varies from red to blue, which corresponds with large to small , respectively. Regions where planetary waves are evanescent (<0) are denoted by white space. In addition to showing , Figures 8a and 8b are overlaid with a qualitative outline of the PWG where values at either extreme of the scale are excluded and shaded by the transparent light gray color; the solid black line that outlines the PWG traces the 15 and 65 contours on the poleward and equatorward side of the PWG, respectively. Outlining the PWG this way greatly aids in visualizing changes to ; moreover, excluding the extreme values of is a physically reasonable approximation for two reasons. First, approaching the subtropical zero wind line, → ∞ as ū → 0. In this limit, becomes an unreliable measure of wave propagation. Second, because planetary waves tend to propagate towards and through large values of , changes in within the region of very small on the poleward side of the PWG play a minor role in determining where planetary waves propagate. Regardless, choosing different extreme values to exclude from the PWG outline does not change the qualitative nature of our results.
 Figure 8 shows that ZAO increases planetary wave propagation in three important ways. First, the vertical extent of the PWG increases, which allows the waves to propagate 10 to 15 km higher within the mesosphere between 45° and 70°N. Second, ZAO causes an increase in the magnitude of throughout the entire stratosphere and, in particular, an increase in wave propagation along both the southern and northern wave channels. The increase in along the southern wave channel is significant beginning at the surface and extending upwards to ~35 km between 30° and 40°N. The increase in within the northern wave channel extends upwards from ~20 km all the way to into the mesosphere near ~75 km. And third, ZAO also causes a significant increase in in the polar UTLS between ~60° and 80°N. The increases in wave propagation described above are each due to different structural changes in the wind and are embodied by competing terms in (1), namely, the strength of the zonal-mean wind versus the meridional potential vorticity gradient.
 According to the first term on the right-hand side (RHS) of (1), weaker westerly winds and increases in the meridional potential vorticity gradient together increase . Ozone-induced changes in the potential vorticity gradient, in turn, are due to changes in the meridional and vertical shear terms of the zonal-mean wind [the second and third terms on the RHS of (2)]. We compared each of the terms in (2) for the 3DO3 and ZMO3 sets of ensembles and found that nearly all of the changes in due to changes in the potential vorticity gradient are due to the third term on the RHS of (2). Further details can then be exposed by expanding the third term on the RHS of (2), which yields
 The first term on the RHS of (7) is proportional to the vertical shear of the mean wind, while the second term is proportional to the vertical curvature of the mean wind. Thus, an increase in positive vertical wind shear (or a decrease in negative vertical wind shear) increases the meridional potential vorticity gradient (2) and increases (1). Based on a numerical comparison of the two terms on the RHS of (7), we found that the vertical shear term is the dominant term and largely accounts for changes between the 3DO3 and ZMO3 ensembles. Thus, the changes in shown in Figure 8 can be explained by the ratio ūz/ū.
 With the exception of the UTLS region along the southern wave channel, the entire extratropical stratosphere and lower mesosphere is characterized by weakened westerly winds (Figure 3b), consistent with an increase in within the PWG shown in Figure 8. The weakened polar vortex in the 3DO3 simulations, however, also affects the vertical wind shear. Figure 2a shows that the location of the maximum wind speed in the vortex core extends from ~60 km at ~40°N to ~40 km at ~60°N, so that much of the region above ~40–50 km is characterized by negative vertical wind shear, while the region below ~40 km is largely characterized by positive vertical wind shear. These features are clearly seen in Figure 9a, which depicts the change in the vertical wind shear between the 3DO3 and ZMO3 ensembles. As a consequence of the weaker polar vortex in the 3DO3 simulations, the vertical wind shear along the upper portion of the northern wave channel (between 40° and 70°N and above ~40 km) and along the southern wave channel (between 30° 40°N in the UTLS) becomes weaker (less negative); this contributes positively to the increase in . In contrast, the region along the lower portion of the northern wave channel (between ~55° and 85°N and between 10 and 40 km) is characterized by a decrease in positive vertical wind shear that contributes negatively to ; thus, the increase in in the this region is due solely to the weakened westerly winds in the 3DO3 simulations. Each of the changes in the magnitude and vertical shear of the zonal-mean wind just described will prove to be important for explaining the increases in the February EP-flux convergence as discussed in the next section.
 We have shown that ZAO-heating causes an increase in the EP-flux beginning in early to mid January. This initial increase in the EP-flux produces changes in the zonal-mean wind that are manifest as changes in the PWG. The changes in the PWG occur via variations in the location of the subtropical jet, shifts in the latitude of the subtropical zero wind line, and the strength of wave propagation within the extratropical stratosphere. These changes in the EP-flux and PWG represent a positive feedback, where the initial ZAO-induced changes in wave amplification/damping trigger changes in the PWG that affect subsequent planetary wave activity entering the stratosphere. As the winter season progresses, the ZAO-induced changes in the PWG become increasingly important.
 To better understand how ZAO affects the PWG during late January and February, we consider how the ZAO-weakened lower stratospheric zonal winds combine with the equatorward shift in the subtropical jet. First, we present some background.
 Using a primitive equation model, Nigam and Lindzen  found that small perturbations (<5 m s−1) to the zonal-mean wind could produce equatorward shifts in the location of the subtropical jet. Although small, these shifts could nonetheless substantially enhance the guiding of planetary waves from their primary source region (the Himalayas at ~27°N) into the polar stratosphere. Similarly, Hu and Tung  showed that the low index phase of the Northern Hemispheric annular mode (which is characterized by an equatorward shift in the NH zonal jet) is associated with weakened zonal-mean winds and increased in the UTLS region between 60° and 80°N. In addition to changes in , Limpasuvan and Hartmann  showed that the low index phase of the Northern annular mode is also characterized by anomalous increases in poleward directed EP-flux vectors; the resulting increase in equatorward momentum fluxes are associated with a weakened stratospheric westerly winds. Our results suggest that ZAO modulates and the EP-flux in a similar fashion to each of the phenomenon described by Nigam and Lindzen, Hu and Tung, and Limpasuvan and Hartmann. Indeed, the equatorward shift in the subtropical jet in the 3DO3 simulations is accompanied by an anomalous increase in upward directed EP-flux vectors into the stratosphere and an anomalous increase in poleward directed EP-flux vectors in the UTLS between ~30° and 75°N (Figure 9b), weakened westerly winds (Figure 3b), and increased values (Figure 8b) throughout the extratropical UTLS. The increase in the anomalous poleward and upward directed EP-flux vectors observed in February reinforce the positive feedback cycle between the EP-flux convergence and first established in late January; the net result is an increase in wave propagation throughout both channels of the PWG. To better understand the implications of the expansion of the PWG in the vertical and the increase in wave propagation within the PWG, we next consider the EP-flux convergence.
 Figures 10a shows contours of the difference (3DO3 minus ZMO3) of the EP-flux convergence in February. In a continuation of the EP-flux convergence differences that first appeared in January, the February difference clearly shows two plumes of increased convergence along both the northern and southern wave channels. There is a 30–50% increase in the EP-flux convergence along the northern wave channel between 15 and 20 km, and a 15–100% increase along the southern wave channel at the same heights. As in January, the two plumes of increased EP-flux convergence correspond with significant increases in vertical wave propagation; this can be verified by examining the increased EP-flux vectors in Figure 9b and, more specifically, the increase in F(z) shown in Figure 10b. In addition to an increase in magnitude, the ZAO-induced increase in F(z) during February also extends ~10–15 km higher than was observed during January (compare Figures 6a and 10b); this is consistent with the 10–15 km increase in height of the February PWG depicted in Figure 8.
 The increases in vertical wave propagation along the northern and southern wave channels, however, correspond to the qualitatively different changes in wind structure described in section 3.3. The increase in vertical wave propagation along the southern wave channel (~30°–40°N) in the UTLS is due to a combination of changes in the vertical shear, meridional shear, and curvature of the zonal-mean wind rather than changes in the magnitude of the wind. This is verified in Figure 3b, which shows that the UTLS is characterized by an increase in the mean wind that contributes negatively to the magnitude of . The dominant contribution to the increase in and the increased vertical propagation along the southern wave channel is due to the increase in positive vertical wind shear depicted in Figure 9a between ~30° and 40°N. The meridional shear and curvature terms (not shown) also contribute to the increase in , but their contribution is secondary to that of the vertical shear term. The importance of vertical wind shear along the tropopause is perhaps not surprising in light of the study by Chen and Robinson  who showed that even small changes in vertical wind shear near the tropopause may produce significant changes (20–40%) in and EP-flux convergence in the UTLS. In contrast to the changes along the southern wave channel, the increase in vertical wave propagation along the northern wave channel are due to increases in associated solely with the weakened westerly winds; this is verified by noting the decrease in positive vertical wind shear (Figure 9a) that contributes negatively to .
 Despite the similarities between the distributions in the January and February EP-flux convergences (compare Figures 4b and 10a), there are two notable changes between the two months. First, the local minimum in the EP-flux convergence along the northern wave channel (centered at ~60°N and 18 km) has increased slightly from −36 to −32 kg s−2, while the local minimum along the southern wave channel (centered at ~32°N and 16 km) has decreased by ~60% from −27 to −43 kg s−2. This indicates that the local increase in and the equatorward shift in the subtropical jet have combined to significantly increase the poleward and vertical propagation of planetary waves (Figures 9b and 10b), which results in the large increase in the EP-flux convergence along the southern wave channel. Second, while the increased EP-flux convergence due to ZAO extended all the way from the middle stratosphere down to the surface between 50° and 70°N during January (Figure 4b), there is no increase in convergence between ~10 and 15 km and between 30° and 70°N during February (Figure 10a); this difference cannot be explained by the changes in described earlier. There are several possible explanations for this apparent discrepancy between the increase in the EP-flux convergence and .
 One possible explanation for the increase in the EP-flux convergence in the UTLS is associated with the ability of ZAO to alter the EP-flux convergence through wave amplification/damping. Indeed, it is ZAO-heating that triggers the initial increase in the EP-flux convergence and the PWG in mid to late January described in section 3.2. The ozone-modified refractive index derived in Nathan and Cordero  describes how ZAO and zonal-mean ozone combine to alter both planetary wave propagation and wave damping. Albers and Nathan  subsequently used the ozone-modified refractive index to show how changes in wave propagation and damping due to ZAO act together or in opposition to produce small or large changes in the EP-flux in the lower stratosphere. Although the current experimental setup does not make it possible to separate ZAO-related effects due to wave propagation and wave damping, it is indeed possible that the apparent discrepancy between the increase in seen in Figure 8 and decrease in the EP-flux convergence seen between ~5 and 15 km and between 30° and 70°N in Figure 10 could be related to ZAO-induced changes in wave damping and wave propagation that are not taken into account by the inviscid form of (1) employed in this study. This issue will be the subject of future modeling and observational studies.
 A second possible explanation for the apparent discrepancy between the increase in the EP-flux convergence and was discussed in section 2. That is, wave tunneling or wave reflection, separately or in combination, may invalidate the relationship between the EP-flux and employed here [Harnik, 2002]. Yet, a third possibility is that the ZAO-induced changes in the stratospheric circulation have caused changes in the troposphere that increase the generation of planetary wave activity. Indeed, our results show that ZAO affects the circulation of the troposphere (e.g., Figures 3 and 10a). Thus, it is possible that some of the increase in the EP-flux convergence in the UTLS is due to an increase in planetary wave generation in the troposphere.
4 Summary and Conclusions
 Using a middle atmosphere general circulation model, we have shown that zonally asymmetric ozone (ZAO) alters the morphology of the PWG in three distinct ways. First, the PWG contracts meridionally and expands vertically within the upper stratosphere and lower mesosphere. Second, the magnitude of wave propagation increases throughout the interior of the stratospheric waveguide between ~30° and 75°N. And third, the subtropical jet shifts equatorward. In combination, the changes in the shape and strength of the PWG are associated with increased deceleration of the zonal-mean westerly flow, resulting in a weaker and warmer stratospheric polar vortex. These changes correlate well with the increased incidence of SSW's in the presence of ZAO reported by McCormack et al. .
 Changes in the PWG have important implications for modeling SSWs, variations in stratospheric dynamics associated with the 11-year solar cycle, and the Northern Hemisphere annular mode (NAM). For example, Charlton et al.  investigated the ability of a series of GCMs—which did not consider the effects of ZAO on the PWG—to generate an accurate number of SSWs. The results showed that most GCMs failed to produce enough SSWs when compared to observations. In the current GCM study—where we explicitly consider the effects of ZAO on the PWG—the model runs with ZAO had a noticeably larger EP-flux emanating from the upper troposophere and lower stratosphere and produced a larger number of SSWs compared to similar runs without ZAO. This increase in the EP-flux correlates well with the increase in in the lower stratosphere, indicating that changes in the PWG associated with ZAO may play an important role in modulating the flux of wave activity entering the stratosphere from the troposphere, which is known to drive SSWs.
 SSWs have also been correlated with a northward shift of tropical easterlies and the zero wind line within the upper stratosphere and lower mesosphere [Gray, 2003; Vineeth et al., 2010]. Gray  hypothesized that because vertically propagating planetary waves have vertical wavelengths comparable to the distance between the tropopause and the upper stratosphere during midwinter to late winter, it is possible that shifts of the zero wind line in the upper stratosphere help guide waves poleward in much the same manner as the traditional Holton-Tan mechanism in the lower stratosphere. Although our experiments were not designed to test Gray et al.'s hypothesis, it is nonetheless interesting to note the correlation between the northward shift in the zero wind line and the increase in frequency of SSWs in our model runs that include ZAO.
 In addition to SSWs, two aspects of the PWG discussed in this study—the width and strength—may provide a means for ZAO to communicate and amplify the 11-year solar cycle signal. The relationship between the width of the PWG and solar-modulated ZAO has been shown by Cordero and Nathan  to be an important pathway for communicating the solar signal to the quasi-biennial oscillation (see their Figure 1). Because our results show that ZAO plays a role in modulating the upper stratospheric tropical easterlies, it is therefore likely that in a similar manner to the Cordero and Nathan solar-quasi-biennial oscillation mechanism, ZAO may also play a role in modulating the semi-annual oscillation in the tropical upper stratosphere. Because the semi-annual oscillation plays a dominant role in the location and timing of shifts in the upper stratospheric zero wind line, modulation of the semi-annual oscillation by ZAO may provide an important pathway for solar modulation of the width of the PWG. Indeed, this is a topic that deserves further attention given the parallel timing of the peak in wind modulation from ZAO in our results and the robust solar signal observed during midwinter to late winter in the tropical upper stratosphere [e.g., Labitzke and van Loon, 1988; Naito and Hirota, 1997]. In addition to solar modulation of the width of the waveguide, ZAO also provides a way to change the strength of wave propagation within the waveguide itself. This scenario is supported by work demonstrating the link between the 11-year solar cycle and changes in wave propagation and planetary wave drag in the extratropical stratosphere [Nathan et al., 2011; Gabriel et al., 2011].
 Finally, we note that the analysis in this paper has examined the effects of ZAO from a “bottom-up” perspective. From this perspective, ZAO enhances the amount of planetary wave activity that is refracted into the interior of the stratosphere from the troposphere below. This phenomenon can be understood as a positive feedback cycle where increases in the EP-flux convergence cause wind changes that increase within the PWG; the increase in within the PWG in turn leads to further increases in the vertical propagation of planetary waves with subsequent increases in the EP-flux convergence. However, changes in the upward flux of planetary wave activity and consequent variations in local wave-mean flow interaction in the stratosphere can also drive downward propagating zonal-mean wind anomalies [Plumb and Semeniuk, 2003], a “top-down” effect. Such downward propagating wind anomalies have been shown to be important for stratosphere-troposphere communication [Kodera and Kuroda, 2000; Christiansen, 2001; Polvani and Waugh, 2004; Perlwitz and Harnik, 2004] and NAM variability [e.g., Baldwin and Dunkerton, 1999; Limpasuvan and Hartmann, 2000]. The model simulations examined in this paper provide evidence that ZAO affects both the downward propagation of wind anomalies and the phase of the NAM. The downward propagation of the wind anomalies is seen in the space-time evolution of the ZAO-induced wind anomalies depicted in Figure 3 and in McCormack et al. [2011, Figures 4a–4d]. The effect of ZAO-heating on the phase of the NAM is seen in the equatorward shift in the subtropical jet and a weakened polar vortex (compare Figures 3 and 7), which are both common features of the low index phase of the NAM. The equatorward shift in the subtropical jet shown in our results is consistent with the work of Brand et al.  who found that including ZAO produces a shift in the NAM towards its low index phase; this indicates that the relationship between ZAO and shifts in the phase of the NAM is likely a robust result. We are currently investigating the effects of ZAO on downward signal propagation and annular mode variability.
 We thank Dr. Nili Harnik and two anonymous reviewers for providing helpful comments on the manuscript. JRA and TRN were supported in part by NSF grant ATM-0733698 and by NASA/NRL grant NNH08AI67I. JPM was supported in part by the Office of Naval Research and in part by NASA Heliophysics Living with a Star TR&T Program award NNH08AI67I.