Recovery processes after a major stratospheric sudden warming (SSW) with the formation of an elevated stratopause and a strong polar-night jet are investigated using a gravity-wave-resolving GCM. The major SSW that occurred in the GCM bears a strong resemblance to observations in January 2006 and January 2009. The recovery phase of the SSW in the GCM is divided into two stages. In the first stage during about five days just after the SSW, a large positive Eliassen-Palm (E-P) flux divergence associated with the growth of planetary waves contributes to the quick recovery of eastward wind above 2 hPa (about 42 km), which is likely due to baroclinic and/or barotropic instabilities. In the second stage over the next three weeks, a prolonged westward wind in the lower stratosphere blocked upward propagation of gravity waves with westward intrinsic phase velocities. It reduces the deceleration of eastward wind in the upper mesosphere and raises the breaking height of gravity waves. Since the height of westward gravity wave forcing also rises, the polar stratopause created by the gravity-wave-driven meridional circulation is formed at an elevated height (about 75 km) compared to that before the SSW (55–65 km). In addition, the weaker westward gravity-wave forcing in the upper mesosphere drives weaker downwelling around 1 hPa and forms a cold layer. Consequently, the strong polar-night jet forms at a higher altitude than before the SSW as a result of adjustment toward the thermal wind balance. This indicates that these two stages provide eastward acceleration in different ways.
 Major stratospheric sudden warming (SSW) is the most drastic event in the middle atmosphere, which is characterized by a reversal of zonal wind direction and meridional temperature gradient in the winter polar stratosphere [Andrews et al., 1987]. A major SSW has occurred almost every year in the last decade [Tomikawa, 2010]. A recent development of satellite measurements enabled us to observe the spatial structure of the SSW from the ground up to the lower thermosphere and its time evolution (e.g., TIMED/SABER [Remsberg et al., 2003], Aura/MLS [Schwartz et al., 2008], ODIN/SMR [Urban et al., 2007]). These observations captured an unprecedented elevation of the winter polar stratopause up to an altitude of 75–80 km after the major SSWs that occurred in January 2004, January 2006, and January 2009 [Hoppel et al., 2008; Manney et al., 2008, 2009; Orsolini et al., 2010].
 Mechanisms for the stratopause elevation after the major SSW have been examined using several models with a model top higher than 80 km. Limpasuvan et al. showed the evolution of the whole polar atmosphere before, during, and after the major SSW including the stratopause elevation, which was simulated by the National Center for Atmospheric Research Whole Atmosphere Community Climate Model (WACCM) with a model top around 145 km. They demonstrated that the strong downwelling induced by the planetary wave forcing in the upper mesosphere played a primary role in the formation of elevated stratopause after the major SSW and also that the gravity waves played a key role afterwards in bringing the stratopause down to its climatological position. On the other hand, several studies using high-top models indicated that the gravity wave forcing in the mesosphere was altered by the SSW and contributed to the formation of elevated stratopause [Chandran et al., 2011; Marsh, 2011; Ren et al., 2008; Siskind et al., 2007, 2010; Yamashita et al., 2010]. They suggested the importance of gravity wave filtering by the prolonged westward wind in the lower stratosphere after the major SSW. Recent satellite measurements also suggested changes of the gravity wave activity and momentum flux in the stratosphere and mesosphere due to the gravity wave filtering by the westward wind in the lower stratosphere during the SSW [Wang and Alexander, 2009; Wright et al., 2010].
 The formation of an elevated stratopause after the major SSWs observed in 2006 and 2009 was associated with the formation of the stronger polar-night jet at a higher altitude than before the major SSW [Manney et al., 2008, 2009]. If the formation of elevated stratopause results from the polar descent induced by a certain wave forcing, it is likely to be a westward forcing considering the downward control principle [Haynes et al., 1991; Garcia and Boville, 1994]. Thus, the reformation of eastward winds at 60–80 km after the SSW in 2006 and 2009 is not likely to be wave-driven. In the stratosphere below 50 km, it is reported that an amplification/generation of planetary waves in the westward wind during some SSWs provides a large eastward acceleration and brings about a quick recovery of the eastward wind [Jung et al., 2001; Tomikawa, 2010]. However, their impacts on the height region above 50 km have not been examined because of the limitations of available data sets.
 These previous studies clearly indicated that both planetary and gravity waves played an essential role in the recovery phase after the major SSW. On the other hand, the relative roles of the planetary and gravity waves are variable among models and possibly between the SSW events. Since the pioneering work of Liu and Roble , the previous studies using high-top models in which the major SSWs were spontaneously generated adopted some kind of gravity wave drag parameterization in the model. It is also of interest to us whether the role of gravity waves during the recovery phase of the major SSW depends on the representation of the gravity wave drag in the model (i.e., parameterization or explicitly resolving). In addition, the representation of a full spectrum of gravity waves is still impossible both in models and observations [Alexander, 1998; Alexander et al., 2010]. For further understanding of the recovery processes after the major SSW, we need to accumulate the knowledge obtained from studying many SSW events using various models and observations especially with a high resolution.
 In this study, a major SSW event which occurred spontaneously in the high-resolution GCM with a model top at 85 km is examined in detail. The simulated major SSW shows a realistic time evolution including the formation of an elevated stratopause and a strong polar-night jet in its recovery phase. A distinct feature of the GCM used in this study is absence of gravity wave drag parameterization in the model [Watanabe et al., 2008]. Gravity waves in the GCM are spontaneously generated, and three-dimensionally transport and deposit momentum. The high vertical resolution of this GCM (i.e., 300 m) makes it possible to represent realistic propagation and dissipation of gravity waves in the middle atmosphere [Sato et al., 2009]. A purpose of this study is to demonstrate the relative roles of planetary and gravity waves in the recovery phase of the major SSW and to clarify a mechanism for the formation of elevated stratopause and strong polar-night jet after the major SSW using the gravity-wave-resolving GCM.
 The rest of this paper is organized as follows. Details of the GCM used in this study and the transformed Eulerian-mean (TEM) diagnostics are given insection 2. Section 3 presents the time evolution of zonal wind and temperature during and after the major SSW. In addition, a relative contribution of each wave component is evaluated using the TEM diagnostics. Section 4describes mechanisms for the formation of elevated stratopause and strong polar-night jet after the SSW. A relationship between the large positive Eliassen-Palm flux divergence and the growth of planetary waves is also discussed.Section 5 concludes this study.
2. Data and Methods
2.1. Model Description
 The high-resolution middle atmosphere GCM developed for the KANTO project [seeWatanabe et al., 2008] is used in this study. The GCM has a horizontal resolution of T213 spectral truncation (i.e., approximately equivalent to 0.5625° longitude-latitude grid) and 256 vertical levels from the ground up to an altitude of 85 km with a vertical spacing of about 300 m from the upper troposphere through the mesosphere. The GCM was integrated over three model years from initial conditions on January 1 obtained after a spin-up for three months. A sponge layer is implemented at top six levels above 0.01 hPa (i.e., about 80 km) in the GCM. The analysis results only below 0.01 hPa are shown to avoid the effect of the sponge layer. More details of the experimental setup of the GCM are described byWatanabe et al. . Meteorological fields are output every 1 h.
 No gravity wave drag parameterization is adopted in the model. Gravity waves in the GCM are spontaneously generated by topography, jet-front systems, convection, and so on [Watanabe et al., 2008; Sato et al., 2009, 2012]. Nonetheless, this GCM cannot represent a full spectrum of gravity waves in the real atmosphere. Especially small-scale gravity waves with horizontal wavelengths shorter than 188 km are not resolved. On the other hand, this model successfully reproduces seasonal and interannual variations of the middle atmosphere [Watanabe et al., 2008], seasonal variation of gravity wave momentum fluxes [Sato et al., 2009], the equatorial quasi-biennial oscillation [Kawatani et al., 2010a, 2010b], the semiannual oscillation [Tomikawa et al., 2008], mesospheric wave dynamics [Watanabe et al., 2009], and the fine vertical structure at the extratropical tropopause [Miyazaki et al., 2010a, 2010b]. These previous studies imply that the meteorological field in this model is sufficiently realistic for this study, including the effect of gravity waves on the mean flow.
 The major SSW which satisfies its criterion [Charlton and Polvani, 2007; Tomikawa, 2010] occurred twice during three model years in the GCM. This study focuses on one of them in which an elevation of the winter polar stratopause in its recovery phase similar to the observations was observed.
2.2. Transformed Eulerian-Mean (TEM) Diagnostics
 The transformed Eulerian-mean (TEM) zonal momentum equation is written as follows:
where and represent the residual meridional and vertical velocities, respectively, ūis the zonal-mean zonal wind, andFis the Eliassen-Palm (E-P) flux [cf.Andrews et al., 1987]. includes horizontal and vertical diffusions and truncation errors in the GCM. The rest of the notations follow the usual convention.
 In order to evaluate the effects of different kinds of waves on the mean flow, the E-P flux is divided into three groups. The first group is planetary waves (PWs) with zonal wave number (s) 1–3. The second group is medium-scale waves (MWs) with total horizontal wave number (n) 1–21, excluding s = 1–3. The MWs represent waves with horizontal wavelengths longer than 1900 km. The third group, with n > 21 and s > 3, includes most of the gravity waves (GWs), whose wavelengths are shorter than 1900 km [Sato et al., 2009].
3.1. Time Evolution During and After the Major SSW
Figures 1a and 1bshow time-pressure sections of zonal-mean zonal wind at 50°N–70°N and temperature at 70°N–80°N, respectively, during the first 90 days of the first model year. Since the zonal wind and temperature mostly satisfies the thermal wind balance throughout the period and the temperature change in the northern hemisphere midlatitudes is smaller than that in the polar region, the zonal wind at 50°N–70°N representing the polar-night jet and the temperature at 70°N–80°N representing the Arctic temperature are shown in this paper. Before day 5, the eastward wind of the polar-night jet is maximized at 0.3 hPa (i.e., about 55 km) and the stratopause is located around 0.3–0.1 hPa (i.e., 55–65 km). These heights are similar to those in January of the second and third model years (not shown) and that observed before the major SSW in January 2009 [Manney et al., 2009]. The westward wind appears for a wide height range above 5 hPa (i.e., about 35 km) on day 5, and descends into 10 hPa (i.e., about 30 km) on day 8. At the same time, the polar atmosphere becomes warm between 20 and 0.3 hPa and cool above 0.3 hPa, which lowers the stratopause down to 5 hPa. Two definitions of a major SSW (i.e., changes of zonal wind direction and meridional temperature gradient at 60°N and 10 hPa) were fulfilled on day 8, which is called the central date of the major SSW [Charlton and Polvani, 2007; Tomikawa, 2010].
 After the central date, the westward wind gradually descends into the lower stratosphere and exists for 26 days at 60°N and 10 hPa. On the other hand, the eastward wind reappears above 2 hPa (i.e., about 42 km) on day 13 and gets stronger until about day 45. The reformed polar-night jet has a maximum wind speed faster than 90 m s−1at 0.2 hPa (i.e., about 60 km), which is located higher than the polar-night jet (i.e., about 55 km) in the other Arctic winters in this GCM. The temperature rises above about 0.3 hPa and drops below that level from the central date until about day 60, which forms warm and cold layers above and below 0.3 hPa, respectively. As a result, the stratopause height rises from 5 hPa (i.e., about 35 km) on day 11 up to 0.02 hPa (i.e., about 75 km) on day 23, and then gradually goes down to the usual winter position at 0.3–0.1 hPa. The peak height of the polar-night jet is 5–10 km lower than the stratopause height and descends together with the stratopause. The evolutions of zonal wind and temperature are quite similar to those in the observed major SSWs of January 2006 and January 2009 except that it takes a longer time for the reformed stratopause and polar-night jet to go back to the climatological position than the observations [Manney et al., 2008, 2009; Orsolini et al., 2010].
 Time evolutions of the residual meridional and vertical velocities at 50°N–70°N and 70°N–80°N during the major SSW in the GCM are shown in Figures 1c and 1d, respectively. Just before the central date, strong upwelling and downwelling are observed above and below 1 hPa (i.e., about 48 km) at 70°N–80°N, respectively. At the same time, strong equatorward and poleward flows centered at 0.01 and 1 hPa, respectively, are observed at 50°N–70°N. These flows compose a two-cell residual circulation in the northern hemisphere middle atmosphere, which is a typical feature of the SSW [Matsuno, 1971; Holton, 1983].
 On day 9–13 just after the central date, an opposite two-cell residual circulation appears in which the residual vertical flow is upward below 1 hPa and downward above 1 hPa at 70°N–80°N. After day 14, the whole height range above 100 hPa at 70°N–80°N is mostly covered by a downwelling, but the downwelling below 0.1 hPa is weaker than that in the other Arctic winters in this GCM as shown insection 4.1. The peak height of the downwelling is located above 0.01 hPa before day 45, and then gradually descends with time. The stratopause is located around the bottom of the strong downwelling (i.e., about −20 mm s−1), which is a feature common to the other Arctic winters in this GCM [cf. Hitchman et al., 1989]. It should be noted that the poleward and downward flow above 0.1 hPa is relatively weak on day 14–35 compared to the later period. During this weak residual circulation period, the lower stratosphere was covered by the westward wind.
3.2. TEM Analysis During and After the Major SSW
 In order to clarify processes responsible for the zonal wind tendency during and after the major SSW, each term in the TEM equation for the zonal wind is evaluated following equation (1). Figure 2shows time-pressure sections of zonal wind tendency, zonal wind acceleration due to the E-P flux divergence, and zonal momentum advection due to residual meridional and vertical velocities at 50°N–70°N. The E-P flux is computed using all the resolved waves such as planetary and gravity waves. The E-P flux divergence and the meridional advection are dominant and tend to cancel each other throughout the period. As a result, the zonal wind tendency is roughly given as a small residual between these two terms. Contributions of vertical advection and in equation (1) computed as a residual of the other terms are relatively small except in the sponge layer above 0.01 hPa.
 Large negative and positive E-P flux divergences are observed below and above 0.1 hPa, respectively, just before the central date. They are mostly canceled by the meridional momentum advection, which indicates that the two-cell residual circulation was driven through the wave-mean flow interaction. The zonal wind tendency follows the sign of the E-P flux divergence in most of the height range. However, the zonal wind tendency is negative up to 0.03 hPa, while the E-P flux divergence is negative up to 0.1 hPa only. This feature is also seen in previous SSW studies [Dunkerton et al., 1981; Limpasuvan et al., 2012]. Just after the central date, a large positive E-P flux divergence appears between 10 and 0.05 hPa (i.e., 30–70 km), which significantly contributes to the eastward acceleration of the zonal wind above 10 hPa [cf.Tomikawa, 2010]. A mechanism inducing such a large positive E-P flux divergence is discussed in the subsequent section.
 A large negative E-P flux divergence is observed above 0.3 hPa from day 14 until day 90, and nearly canceled by the meridional momentum advection. The zonal wind tendency during this period does not always follow the sign of the E-P flux divergence unlike the behavior before day 14. Especially until day 45, the meridional advection is slightly larger than the negative E-P flux divergence at 0.2 hPa, and contributes to the strengthening of the polar-night jet. This large negative E-P flux divergence after day 14 is observed at an altitude higher than that in the other Arctic winters in the GCM (not shown). Another point to be noted is that the negative E-P flux divergence above 0.1 hPa during day 14–35 is smaller than that in the later period. How this small negative E-P flux divergence contributes to the formation of the elevated stratopause is discussed insection 4.1.
 Contributions of different kinds of waves to the E-P flux divergence are examined through the zonal and total horizontal wave number decomposition of the E-P flux.Figure 3shows time-pressure sections of E-P flux divergence due to all the waves, planetary waves (PWs), medium-scale waves (MWs), and gravity waves (GWs) at 50°N–70°N. Before day 5, the total E-P flux is convergent in the whole stratosphere and mesosphere, which is mostly due to the PWs below 0.1 hPa and due to the GWs above 0.1 hPa. The negative E-P flux divergence due to the GWs during this period is maximized at 0.05 hPa.
 The positive/negative E-P flux divergence between day 5 and 14 is dominated by the PWs for the whole height range above 100 hPa. Both the large negative and positive E-P flux divergences before and after the central date, respectively, between 10 and 0.1 hPa are mostly due to s = 1 planetary waves as shown later. On the other hand, the GWs show a large positive E-P flux divergence above 0.1 hPa between day 6 and 12, during which the stratosphere and mesosphere are covered by the westward wind. Although the GWs partly contribute to the total E-P flux divergence before day 8 above 0.1 hPa, the positive E-P flux divergence due to the GWs is overwhelmed by the negative E-P flux divergence due to the PWs after day 8.
 The negative E-P flux divergence above 0.1 hPa is primarily due to the GWs after day 14, and partly due to the MWs between day 20 and 50. The negative E-P flux divergence due to the GWs above 0.1 hPa gradually becomes larger after day 14. Its peak height is seen above 0.01 hPa until day 50, and then gradually descends into 0.02 hPa corresponding to the usual winter position in this GCM. Below 0.1 hPa, both of the PWs and GWs contribute to the positive/negative E-P flux divergence after day 14. While the positive/negative E-P flux divergence due to the PWs is intermittent, the GWs show the positive E-P flux divergence descending with the westerly shear of the zonal wind. It indicates that the critical level filtering of the GWs with eastward intrinsic phase velocities contributes to the recovery of eastward wind (in other words, descent of westerly shear) in the recovery phase of the major SSW.
3.3. Planetary Waves During and After the Major SSW
Figure 4 shows polar stereographic maps of geopotential height at 10, 2, and 0.5 hPa on day 4, 8, and 12. The Aleutian anticyclone centered at 150°W and 65°N at 10 hPa is significantly amplified on day 4, and the polar vortex is displaced off the pole toward 40°E and 70°N. The polar vortex moves slightly westward and loses its strength by the central date (i.e., day 8). Although the polar vortex shows a little tendency to split on day 12, this SSW can be regarded as a vortex displacement type associated with the amplification of the Aleutian anticyclone [Charlton and Polvani, 2007]. Since the phase of the s = 1 planetary wave (PW) causing this SSW has a westward tilt with height, the center of the polar vortex on day 4 and 8 is shifted westward at 2 and 0.5 hPa compared to that at 10 hPa.
 Contributions of the s = 1 PWs to the total E-P flux and its divergence just before and after the central date are shown inFigure 5. The s = 1 PWs propagating from below (i.e., troposphere) account for the most part of the negative E-P flux divergence between 10 and 0.1 hPa on day 5–7. On the other hand, the s = 1 PWs account for a large fraction of the positive E-P flux divergence between 10 and 0.5 hPa on day 10–12. During this period, the E-P flux due to the s = 1 PWs is directed upward above 2 hPa and downward below 2 hPa, so that it is vertically divergent. In addition, it is worth noting that this large positive E-P flux divergence is observed only in the westward wind region.
 In order to capture a time evolution of s = 1 PW at each pressure level, Hovmöller diagrams of s = 1 geopotential height disturbances at 10, 2, and 0.5 hPa along 60°N are presented in Figure 6. The amplitude of s = 1 PWs at 10 hPa is maximized on day 3–4, and then becomes smaller with time until day 30. The s = 1 PWs at 10 hPa show a quasi-stationary feature throughout this period. On the other hand, the s = 1 PWs at 2 and 0.5 hPa are different from that at 10 hPa. They are quasi-stationary and have large amplitudes before the central date, but rapidly decay after the central date. Then another s = 1 PW with a westward phase velocity of 30–40 m s−1(i.e., a ground-based period is 6–7 days) starts to grow on day 10 at 2 and 0.5 hPa. The amplitudes of the westward-propagating s = 1 PWs are maximized on day 12, and rapidly decay by day 16.
Figure 7shows longitude-pressure sections of s = 1 geopotential height disturbances along 60°N at 1200 UT on day 4, 8, and 12. The phase of s = 1 PWs shows a westward tilt with height up to 0.05 hPa on day 4 and 8. The westward-propagating s = 1 PWs on day 12 also shows a westward tilt with height above 2 hPa. On the other hand, there can be seen a phase jump around 5 hPa on day 12. A relationship between the spatial structure of s = 1 PWs and their E-P flux will be discussed in the next section.
4.1. Mechanism for Formation of Elevated Stratopause and Strong Polar-Night Jet
 While the Earth's stratopause is usually located around 50 km primarily as a result of absorption of the solar ultraviolent radiation due to ozone, the height of winter polar stratopause is controlled by adiabatic heating due to the downwelling of the mesospheric meridional circulation [Hitchman et al., 1989]. The mesospheric meridional circulation which consists of summer-to-winter meridional flow and descent (ascent) motion around the winter (summer) pole is primarily driven by momentum deposition due to gravity waves [Holton, 1983; Garcia and Solomon, 1985]. A significant role of the GWs in driving the meridional circulation above 0.1 hPa is commonly observed both before and after the SSW in this GCM. In addition, the winter polar stratopause is located just below the strong downwelling of the mesospheric meridional circulation during these periods in this GCM. Thus it is considered that the formation of the elevated stratopause after the SSW depends on the vertical distribution and strength of the wave forcing driving the meridional circulation.
 The negative E-P flux divergence due to the GWs above 0.1 hPa during day 14–35 was smaller than after this period, and its peak was located above 0.01 hPa. During this period, the zonal wind in the lower stratosphere was westward. After the westward wind in the lower stratosphere disappeared, the magnitude and peak height of the negative E-P flux divergence due to the GWs gradually went back to the usual winter situation in this GCM. In order to examine the effect of the westward wind in the lower stratosphere on the E-P flux due to the GWs, vertical profiles of the vertical component (Fz) of the E-P flux due to the GWs during days 21–30 and 51–60 are shown inFigure 8. Since the energy flux of the GWs is always upward in this height and latitude region (not shown), positive and negative Fz represent upward propagation of the GWs with westward and eastward intrinsic phase velocities (i.e., phase velocity relative to the background wind), respectively. In addition, the positive E-P flux divergence shown inFigure 8 is mostly due to the vertical divergence.
 One common feature observed in the vertical profiles of Fz during these two periods is that Fz is nearly constant with height where the zonal wind (ū) having westerly shear (more eastward at higher altitudes) is stronger than about 50 m s−1(i.e., in the height regions of 0.5–0.1 hPa for day 21–30 and of 2–0.1 hPa for day 51–60). This implies that the GWs with eastward ground-based phase speeds greater than 50 m s−1propagating from below are too weak to cause large positive E-P flux divergence by critical level filtering. Instead, a significant negative E-P flux divergence corresponding to westward wind acceleration is observed above 0.1 hPa. This is likely due to the breaking of the GWs having westward intrinsic phase speeds which do not suffer from critical level filtering but have large amplitudes because of exponential decrease of the atmospheric density with height.
 A significant difference between the two periods is that the magnitude of the nearly constant Fz above the level where ū = 50 m s−1 is much larger on day 51–60 than on day 21–30. This difference is likely related to the fact that there are levels where ū < 0 m s−1in the stratosphere on day 21–30 (i.e., 3–30 hPa) and not on day 51–60. This means that any GWs with ground-based phase velocities small enough to encounter critical levels (i.e., orographic GWs) are filtered out before reaching the mesosphere on day 21–30 and not on day 51–60. Thus, smaller Fz around 0.1 hPa and smaller negative E-P flux divergence above 0.1 hPa on day 21–30 can be attributable to the absence of GWs with small ground-based phase velocities there.
 In addition, it should be noted that the eastward zonal wind around 0.01 hPa is stronger on day 21–30 than on day 51–60. Since the deceleration of the eastward wind above the core of the polar-night jet is mainly due to the GWs [Lindzen, 1981; Watanabe et al., 2008], the smaller Fz around 0.1 hPa can lead to the weaker gravity wave breaking and the stronger eastward wind around 0.01 hPa on day 21–30. The stronger eastward wind around 0.01 hPa prevents the gravity wave breaking, which raises the peak height of the negative E-P flux divergence due to the GWs. These facts suggest that the prolonged westward wind in the lower stratosphere plays a key role for the formation of elevated stratopause after the major SSW through the filtering of the GWs with a westward intrinsic phase velocity (mainly orographic GWs) [cf.Chandran et al., 2011].
 The TEM analysis in the previous section showed that the zonal wind tendency during the reformation of strong polar-night jet did not always follow the sign of the E-P flux divergence and was determined by a small residual between the E-P flux divergence and the momentum advection due to the residual meridional velocity. On the other hand, the thermal wind balance was almost maintained (not shown). The cold layer formed around 1 hPa enhances negative meridional temperature gradients (i.e., ) and raises the height of zero meridional temperature gradients around 60°N (not shown). Consequently, the strong polar-night jet which satisfies the thermal wind balance was reformed at a higher altitude than before the SSW [Chandran et al., 2011].
 In order to examine which waves contribute to the formation of the cold layer around 1 hPa, the contribution of each wave to the residual vertical velocity at 70°N–80°N is computed from the E-P flux divergence using the downward control principle [Haynes et al., 1991]. The residual vertical velocity estimated by the downward control principle is given as follows: [cf. Randel et al., 2002]
Figure 9shows vertical profiles of the residual vertical velocities computed directly based on its definition and using the downward control principle during day 21–30 of the first and second model years. The polar-night jet is located at 0.3 hPa with a maximum wind speed of about 70 m s−1 and the stratopause is at 0.2 hPa during day 21–30 of the second model year. This is a typical condition in the Arctic winter without the major SSW. In the first model year with the major SSW, it is found that the residual vertical velocity around 1 hPa is quite small and not contributed to by any kind of waves. On the other hand, Figure 9bclearly demonstrates that the downwelling around 1 hPa is much stronger than that of the first model year and mostly explained by the E-P flux divergence due to the GWs. Thus it is deduced that the weaker meridional circulation driven by the weaker GW forcing in the recovery phase of the major SSW deformed the temperature structure and the zonal wind field was adjusted to satisfy the thermal wind balance with the temperature distribution.
Limpasuvan et al. suggested that a large negative E-P flux divergence due to the PWs above 80 km drove the strong polar descent and contributed to the formation of elevated stratopause before the westward gravity wave forcing in the mesosphere was reinstated in their WACCM simulation. Similarly, a large negative E-P flux divergence due to the PWs is observed between 0.1 and 0.01 hPa around day 10 in this GCM (Figure 3b) and drives the strong polar descent down to 1 hPa (Figure 1d). It raises the polar temperature between 0.1 and 1 hPa and contributes to the elevation of the polar stratopause up to 0.2 hPa on day 14 (Figure 1b). On the other hand, the formation of elevated stratopause around day 23 is mostly attributable to the formation of warm and cold layers around 0.02 and 1 hPa, respectively. If the high temperature induced by the polar descent around day 10 was maintained until day 23, the formation of cold layer around 1 hPa on day 23 could not be achieved. Thus it is considered that the large negative E-P flux divergence due to the PWs above 0.1 hPa around day 10 do not contribute to the formation of elevated stratopause on day 23.
4.2. Positive E-P Flux Divergence Associated With Amplification of Westward-Propagating s = 1 Planetary Waves
 As shown in the previous section, the positive E-P flux divergence due to the s = 1 PWs made a large contribution to the quick recovery of the eastward wind above 10 hPa just after the SSW. At the same time, the polar downwelling above 1 hPa and upwelling below 1 hPa driven by a pair of the positive and negative E-P flux divergence above 5 hPa significantly contributed to the warming and cooling, respectively, between day 9 and 13. During this period, the quasi-stationary s = 1 PWs were seen at 10 hPa, whereas the westward-propagating s = 1 PWs grew at 2 and 0.5 hPa. The height and period of the large positive and negative E-P flux divergence showed a good agreement with those of the growth of westward-propagating s = 1 PWs. Since the westward-propagating s = 1 PWs have a phase velocity clearly different from the quasi-stationary s = 1 PWs, they are not due to upward propagation of the quasi-stationary s = 1 PWs.Smith proposed the excitation mechanism of PWs in the mesosphere due to the zonally asymmetric gravity wave forcing resulting from the filtering by planetary waves in the stratosphere. Since the gravity waves filtered by the quasi-stationary planetary waves in the stratosphere would create the anti-phase quasi-stationary planetary waves in the mesosphere, this mechanism cannot explain the excitation of the westward-propagating s = 1 PWs in the mesosphere. Thus a possibility of in situ (i.e., baroclinic and/or barotropic) instability is subsequently discussed.
 Following Palmer , the refractive index squared (Qs,c) is defined in the meridional plane:
where crrepresents the zonal phase velocity of the westward-propagating s = 1 PWs, and is the quasi-geostrophic potential vorticity gradient. Here the ground-based period of the westward-propagating s = 1 PWs is assumed to be seven days at all the latitude regions (seeFigure 6), so that cr is given by
The static stability (N2) dependent on latitude and height is computed using the monthly and zonal-mean temperature. Meridional and/or vertical propagation of the wave is allowed whereQs,c > 0, whereas the wave has an evanescent form in the region of Qs,c < 0.
Figure 10shows latitude-pressure sections ofQs,c, , and contributions of second and third terms of equation (6) to on day 10. Red contours represent the critical levels of westward-propagating s = 1 PWs whose phase velocity is given byequation (7). Negative is observed around the core of westward wind centered at 65°N and 2 hPa, and is primarily due to a meridional curvature of ū (i.e., the second term of equation (6)) and partly due to the vertical gradient of static stability (i.e., the third term of equation (6)). This situation satisfies the necessary condition for the baroclinic and/or barotropic instabilities. In addition, positive Qs,c is observed where and the zonal wind is westward relative to the zonal phase velocity (cr) of westward-propagating s = 1 PWs. A comparison ofFigures 5 and 10clearly demonstrates that the large positive E-P flux divergence occurs whereQs,c > 0 and . This result suggests that the in situ instability causes the growth of westward-propagating s = 1 PWs accompanying the large positive E-P flux divergence. Since the E-P flux is divergent mainly in the vertical at 60°N–70°N and converges above 0.5 hPa whereQs,c > 0 and , the baroclinic instability likely plays an important role. The westward-propagating s = 1 PWs has a westward phase tilt with height against the background wind shear above 2 hPa at 60°N (Figure 7c), which also supports the possibility of the baroclinic instability.
 In order to examine whether the s = 1 PWs can grow by the baroclinic instability in the observed background state at 60°N–70°N on day 10, we consider the quasi-geostrophic flow on a midlatitude beta plane. A linearized quasi-geostrophic potential vorticity equation in a background flow (ū) is given by
where ψ is a stream function of the disturbance. Looking for solutions of the form
where c ≡ cr + ici is a complex phase velocity, and k and l are dimensional zonal and meridional wave numbers, respectively, equation (8) reduces to
The eigenvalue problem is solved with boundary conditions which are taken to be zero vertical velocity at z = 0 km and z = 100 km [cf. Dickinson and Clare, 1973]. The dimensional meridional wave number (l) is π/L, where L is a meridional length scale which is taken to be 5000 km considering from Figure 4. The background state for the eigenvalue problem is given as follows:
with z0 = 45 km, z1 = 32 km, u0 = 55 m s−1, δ = 12 km, N02 = 3 × 10−4 s−2, N12 = 6 × 10−4 s−2, Λ1 = 10−5 km−1 s−2, and Λ2 = 2 × 10−5 km−1 s−2. Their vertical distributions shown by short-dashed lines inFigure 11 bear a strong resemblance to those at 60°N–70°N on day 10 shown by solid lines. The vertical distribution of computed from equations (11) and (12) does not exactly accord with that on day 10 as shown in Figure 11c because the meridional curvature of ū is not included. Values of f and β at 65°N are used for the computation of . In order to reproduce the distribution of similar to that on day 10, the term given by with B0 = − 5 × 10−11 m−1 s−1 is added on in 25 km < z < 55 km and shown by a long-dashed line inFigure 11c. Zonal phase velocities and growth rates are numerically obtained in the background states with and without the term B, and shown as a function of zonal wave number (s) in Table 1.
Table 1. Zonal Phase Velocities (Cr) and Growth Rates (k*Ci) as a Function of Zonal Wave Number (s) in the Background States Without and With the Term Ba
Zonal Wave Number
See the text for details.
Without Term B
Cr (m s−1)
With Term B
Cr (m s−1)
 In both background states, the growth rate is maximized for s = 2, but the unstable mode exists also for s = 1. While the growth rate of s = 2 unstable mode in the background state including the term B is 98% for three days (i.e., exp(0.228 × 3) = 1.98), that of s = 1 unstable mode is 37% (i.e., exp(0.106 × 3) = 1.37). Since, in case of the SSW due to the s = 1 PWs discussed in this paper, the amplitude of s = 1 PWs is already much larger than other waves before the growth, only the growth of s = 1 PWs would be observed. Figure 6showed that the s = 1 PWs in the GCM grew by about 100% at 2 hPa and by about 50% at 0.5 hPa during the period of day 10–12. Their growth rate in the GCM is larger than that (i.e., 37%) estimated by the one-dimensional model. On the other hand, the phase velocity of s = 1 unstable mode in the background state including the term B is close to that observed in the GCM. Although there are some differences between the GCM and the one-dimensional model, the result obtained by the one-dimensional model seems consistent with the growth of s = 1 PWs in the GCM. Their differences could be because the background state used for the calculation is not completely identical to the observed one and the problem is solved in one dimension.
 On the other hand, the positive and negative E-P flux divergences are latitudinally aligned equatorward of 60°N in the GCM, where the E-P flux directed equatorward and the s = 1 PWs have an eastward phase tilt with latitude against the background wind shear at 2 and 0.5 hPa (not shown). Thus the barotropic instability may also contribute to the growth of the s = 1 PWs. In order to confirm whether this kind of recovery processes after the SSW occur also in the real atmosphere, case studies based on the observational and objective analysis data are further needed.
5. Concluding Remarks
 The formation of an elevated stratopause and a strong polar night jet has been observed in a recovery phase of recent major stratospheric sudden warmings (SSW). However, why the stratopause was formed at an elevated height and what processes are responsible for the reformation of the strong polar-night jet are questions that remain to be answered. In order to examine these issues, a major SSW event which spontaneously occurred in a high-resolution middle atmosphere GCM was analyzed in detail.
 The major SSW in the GCM occurred on day 8 of the first model year and showed a signature of vortex displacement associated with the amplification of the Aleutian anticyclone. The westward wind in the lower stratosphere continued for about one month after the SSW, whereas the eastward wind quickly recovered above 2 hPa (i.e., about 42 km) and developed to be faster than 90 m s−1 at 0.2 hPa (i.e., about 60 km) on day 45. The stratosphere below 0.3 hPa (i.e., about 55 km) was heated before and during the early stages of the SSW, which lowered the stratopause down to 5 hPa (i.e., about 35 km) on day 11. Subsequently, the lowered stratopause disappeared and an elevated stratopause was formed at 0.02 hPa (i.e., about 75 km) on day 23. The time evolution of temperature and zonal wind after the SSW was quite similar to the major SSWs observed in January 2006 and January 2009 [e.g., Manney et al., 2008, 2009].
 The transformed Eulerian-mean analysis clearly demonstrated that planetary waves (PW) with zonal wave number 1 (s = 1) were responsible for a large positive Eliassen-Palm (E-P) flux divergence above 10 hPa (i.e., about 30 km) during day 9–13 and contributed to the quick recovery of eastward wind. During this period, westward-propagating s = 1 PWs developed between 2 and 0.5 hPa and showed clearly different features from the quasi-stationary s = 1 PWs causing the SSW. A relationship between the growth of westward-propagating s = 1 PWs and the region of negative quasi-geostrophic potential vorticity gradient and the result of one-dimensional stability analysis suggested that the baroclinic and/or barotropic instabilities contributed to their growth and the large positive E-P flux divergence.
 The gravity waves (GW) usually induce a negative E-P flux divergence and drive the poleward and downward flow in the winter polar mesosphere. However, they showed a large positive E-P flux divergence above 0.1 hPa between day 6 and 12 during which the SSW occurred in the GCM. After the eastward wind recovered above 2 hPa on day 13, the negative E-P flux divergence due to the GWs reappeared above 0.3 hPa. Since its peak was located above 0.01 hPa which is higher than before the SSW, the strong downwelling driven by the negative E-P flux divergence due to the GWs was also formed in a higher region. As a result, the polar stratopause controlled by adiabatic heating due to the strong downwelling also appeared at an elevated position (i.e., about 75 km) on day 23 [cf.Chandran et al., 2011]. During this period, a prolonged westward wind in the lower stratosphere blocked the upward propagation of the GWs with a westward intrinsic phase velocity such as orographic GWs, which leads to a small westward GW forcing above 0.1 hPa. Consequently, it is considered that the eastward wind above the core of the polar-night jet was not sufficiently decelerated and the height of GW breaking became higher.
 In addition, the decrease of westward GW forcing above 0.1 hPa after the SSW reduced the downwelling around 1 hPa compared to the usual Arctic winters. This produced a cold layer around 1 hPa and enhanced negative meridional temperature gradients. The radiative relaxation toward the thermal wind balance gives rise to a transient meridional circulation that accelerates the polar-night jet eastward via the Coriolis torque. As a result, the strong polar-night jet satisfying the thermal wind balance with the temperature distribution was formed at an altitude higher than before the SSW.
 Therefore, the recovery phase of the major SSW associated with the formation of an elevated stratopause and strong polar-night jet is divided into two periods (i.e., days 9–13 and 14–35). The most important difference between these two periods is that, while the PWs play a key role in the former one (i.e., day 9–13), the GWs do in the latter (i.e., day 14–35).
 Although the major SSW event generated in this GCM showed a strong resemblance to the observations, the descent of the elevated stratopause and reformed polar-night jet was slower than the observations. One possible cause is that the downward advection due to the meridional circulation in the GCM is slow. However, since the temperature around the elevated stratopause was close to the observations, the strength of the downwelling creating the stratopause is expected to be realistic. Another possibility is that the momentum deposition due to GW breaking occurs at a higher altitude than in the real atmosphere. Although this GCM has a finer vertical resolution (i.e., 300 m) than other GCMs, it is still not enough to represent turbulent processes associated with the gravity wave breaking. This would lead to the slower loss of momentum during the upward propagation of GWs and the momentum deposition at a higher altitude in the GCM. Thus it may be essential to represent the gravity wave breaking processes more exactly in the GCM for the reproduction of the SSW recovery phase.
 This study demonstrated the relative roles of PWs and GWs in a recovery phase of the major SSW associated with a formation of elevated stratopause and strong polar-night jet using the gravity-wave-resolving GCM. The role that the GWs played in the recovery phase of the major SSW in this GCM was similar to that inChandran et al. . On the other hand, smaller-scale GWs which are not resolved in this GCM may play some important role [cf.Limpasuvan et al., 2011]. Relative roles of orographic and non-orographic GWs in the change of GW forcing were also uncertain [cf.Limpasuvan et al., 2012; Ren et al., 2008; Siskind et al., 2007, 2010]. The change of GW propagation during the evolution of the SSW was discussed in this paper, whereas the change of GW source could have some impact on the GW forcing [cf. Limpasuvan et al., 2011]. Although the SSW occurred in this GCM was a vortex displacement type, the relative roles of PWs and GWs might change in the SSW of a vortex split type because of the interaction between PWs and GWs [Yamashita et al., 2010]. In addition, how the region above 80 km affects the SSW cannot be captured by this GCM. In order to resolve these issues, future work needs to analyze various SSW events using various models with a higher model top [e.g., Watanabe and Miyahara, 2009] and high-resolution observations in the mesosphere and lower thermosphere.
 This work is a contribution to the Innovative Program of Climate Change Projection for the 21st Century supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. This work was supported by a Grant-in Aid for Scientific Research (19204047) from MEXT, Japan, and an NIPR publication subsidy. Calculations were conducted using the Earth Simulator, and figures were prepared using the GFD-DENNOU library and GTOOL.