A reflection of stratospheric planetary waves and its impact on the troposphere during a stratospheric sudden warming of March 2007 are investigated. Zonal propagation and reflection of the planetary waves is clearly seen in the longitude-height sections of the eddy geopotential height and the vertical and zonal component of the three-dimensional wave activity flux. A wave packet propagating upward and eastward from Eurasian continent was reflected by a negative wind shear in the upper stratospheric westerly jet caused by stratospheric warming. Waves then propagated downward to the American-Atlantic sector of the troposphere, which led to the formation of a deep trough over the Atlantic and brought cold weather to the northeastern part of the American continent.
 A reflection of stratospheric planetary waves had been proposed as a possible mechanism of the stratosphere-troposphere coupling [e.g., Hines, 1974, Geller and Alpert, 1980; Bates, 1981]. However, the impact of the wave reflection from the upper stratosphere is usually considered to be negligible in the troposphere because of the difference of the air density. Recently, measurable tropospheric impact of the reflection of the planetary waves from the upper stratosphere was statistically demonstrated by Perlwitz and Harnik  using a lagged correlation analysis. They demonstrated that the change in the zonal wavenumber 1 (wave 1) component of the 500 hPa geopotential height lagged six days behind that of 10 hPa when the reflection occurred in the upper stratosphere. However, from this analysis it is difficult to see how the change in the wave propagation occurs in the stratosphere and how the waves are reflected back to the troposphere.
Coughlin and Tung  reported that the deceleration of zonal winds due to a stratospheric major warming made a reflection of planetary wave in the stratosphere, which leads to a change in wave 1 structure in the troposphere. It is still difficult to clearly separate the impact of reflected planetary waves from a tropospheric variation itself because the planetary waves are generally generated in the troposphere. Here we found a special case during a stratospheric warming of March 2007 in which the wave propagated upward and eastward from Eurasia and was reflected back to the North American-Atlantic sector. Because the upward- and downward-propagating regions are different we can easily follow the evolution of wave field and clearly identify the impact of reflected waves.
Figure 1a depicts the variation of the north polar temperature at 30 hPa during January–March 2007. For this study we used the JCDAS/JRA-25 reanalysis datasets of the Japan Meteorological Agency (JMA) [Onogi et al., 2007]. A major stratospheric sudden warming occurred at the end of February 2007. Zonal winds at 10 hPa became easterly north of 60°N on February 25. This major warming was very short lived, and the westerly jet was re-established already on March 1. Planetary waves then again propagated upward along the stratospheric westerly jet, and the second warming restarted. Figure 1b presents meridional sections of the zonal-mean zonal winds and Eliassen-Palm (E-P) flux during March 2 to 5, 2007 (indicated by vertical lines in Figure 1a). The E-P flux is parallel to the local group velocity of the wave, and its convergence indicates deceleration of the zonal flow due to wave forcing. Strong upward propagation of the planetary waves occurred on March 2 and 3, which leads to a weakening of the upper stratospheric polar night jet. On March 4, planetary waves propagated downward as indicated by the downward direction of the E-P flux vector north of 65°N, although upward propagation still persists in lower latitudes. The downward propagation further develops on March 5 in the lower stratosphere and lasts until March 7.
 The above is the usual view of the two-dimensional propagation of planetary waves. However, planetary waves can also propagate zonally [Hayashi, 1981]. Plumb  has extended the E-P flux to three-dimensional (3-D) propagation. To investigate planetary-scale wave activity, 3-D Plumb flux for zonal-wave component of waves 1 to 3 is calculated. Figure 2 shows horizontal distribution of Plumb flux at 100 hPa for March 2 and 4. It can be seen that upward- and downward propagation occur in different sectors. A strong upward and eastward propagation occurs over Siberia on March 2. On March 4, upward propagation becomes weaker but the downward propagation develops over the American sector.
 In order to investigate evolution of the longitudinal propagation in more detail, longitude-height sections of the vertical and zonal components of the Plumb flux averaged over 60°N to 70°N latitudes are depicted in Figure 3 together with the eddy geopotential height field of the four days from March 2 to 5. Here the eddy field is defined as a departure from the zonal mean. Same as the Plumb flux, the eddy geopotential height field is also for the zonal-wave 1 to 3. The daily mean 500 hPa geopotential height for the zonal-wave 0 to 3 is displayed for the 40°N to 70°N latitudinal band under each longitude-height wave activity flux section to illustrate the tropospheric aspect of the variation.
 In the lower stratosphere, a trough is located over Siberia at around 90°E on March 2. The trough shifts westward with increasing altitudes, and at 10 hPa it is found around 40°E. A westward tilt of the trough line means upward propagation of the Rossby wave. Upward propagation is obviously seen as upward wave activity flux over Siberia consistent with Figure 2. Waves propagate upward and eastward in the stratosphere. Wave activity in the stratosphere is confined mainly in the eastern hemisphere, and the wave amplitudes are smaller in the western hemisphere. Downward and eastward propagation of tropospheric waves from Siberia is found over the Pacific region. Inspection of the 500 hPa geopotential height field reveals that this wave activity is mainly due to the wave 3 component.
 The amplitude of the upper stratospheric eddy geopotential height increases in the western hemisphere on March 3. In order to follow the eastward shift of wave activity, figures display 360° longitudes from the longitude where the upward propagation starts in the stratosphere. The ridge at 10 hPa shifts eastward and is located at 140°W, 180° away from the trough at 40°E, which exhibits a zonal wave 1 structure. In the lower stratosphere, the ridge in the eastern Pacific sector increases slightly in association with a downward propagation of waves there.
 Downward propagation of stratospheric waves increases and extends more eastward over the Atlantic sector while the upward propagation in the stratosphere over the Eurasian sector decreases on March 4. As a consequence, zonally averaged wave activity flux becomes downward consistent with the downward propagation of E-P flux north of 65°N in Figure 1. Downward propagation over the North American-Atlantic sector manifests itself as eastward tilt of the trough with increasing altitudes. Development of a trough at 500 hPa around 90°W is thus associated with downward-propagating planetary waves originating from Eurasia.
 On March 5, downward propagation of waves further intensifies and extends eastward over eastern Atlantic-Europe. Accordingly, the trough over the Atlantic and the ridge over Europe develop further. Note that the geopotential height near the surface decreases over the Atlantic Ocean. The wave activity near the surface also increases from March 4. The major contribution of the vertical component of the wave activity flux comes from the eddy heat flux term. The increase of the wave activity near the surface thus means increased thermal advection near the surface. Figure 4 illustrates the 850 hPa air temperature change over the American-Atlantic sector from March 4 to 6. Cold polar air was advected southeastward over the North American continent, and it brought very cold weather to the northeast coast of the North American continent.
3. Discussions and Concluding Remarks
 Due to a strong upward propagation of the planetary waves on March 2 and 3, 2007, upper stratospheric zonal-mean zonal wind is substantially weakened, while the lower stratospheric jet remains stronger (Figure 1). This creates a negative vertical wind shear in the upper stratosphere from March 3 to 4, which provides a favorable condition for a reflection of upward-propagating planetary waves. Perlwitz and Harnik  use, in fact, the difference of the zonal wind velocity between 2 and 10 hPa as an index of the reflection condition. In Figure 1 the reflection of waves are clearly seen as downward E-P flux vectors. It should be noted that here displayed is not an anomalous but a total E-P flux.
 We can see in Figure 2 that the planetary waves are propagating up in the stratosphere from a relatively small region over Siberia. Smaller scale waves being trapped in the troposphere, only wave 1 and 2 components can propagate into the stratosphere along the westerly jet. However, wave 2 cannot propagate in a strong westerly jet, so only wave 1 can reach the upper stratosphere [Charney and Drazin, 1961].
 The longitude-height section of the eddy geopotential height of March 4 or 5 in Figure 3 exhibits an apparent wave 1 pattern with one ridge in the upper stratosphere, and presents a wave 2 pattern with two ridges in the lower stratosphere and the troposphere. This wave-2-like structure in the lower stratosphere should not be interpreted as upward propagation of wave 2 from the troposphere because the Eurasian trough tilts westward while the Atlantic one tilts eastward with height, which means upward propagation from Eurasia and downward propagation over the American sector as clearly illustrated in Figure 2.
 Therefore, the evolution of the eddy geopotential height pattern like unfurling a folding-fan from March 2 to 5 should be understood as a stratospheric bridge due to a reflection of a zonally propagating wave packet similar to that found for smaller-scale Rossby waves by Nishii and Nakamura . Note, however, that in their study waves are defined as departure from a time mean field which generally includes upward propagating planetary waves. So that anomalous downward wave flux does not necessarily means a downward propagation but a less upward propagation of waves. Whereas, in the present study the waves are defined as departure from the zonal mean field, so that the downward wave flux really means a downward propagation of waves.
 The problem of the reflection of the planetary waves has so far been studied primarily by decomposing waves into a single wave number. It is therefore difficult to distinguish the reflected wave component from that generated in the troposphere. However, in the present study, upward and downward propagation occurs in different sectors, providing clear evidence that the planetary wave reflected from the upper stratosphere. The evolution of the eddy geopotential height field occurs consistently with the change of the propagation direction indicated by the Plumb flux.
Perlwitz and Harnik  noted that major sudden warmings are not related to wave reflection. However an occurrence of the wave reflection during the major warming of February–March 1999 was suggested by Coughlin and Tung . Also our preliminary analysis indicates that the wave reflection took place after the major warming of February 2008. More works are needed to clarify the condition under which produces the wave reflection in the stratosphere, and the impact on the troposphere by the reflection.
 We thank Y. Harada, H. Nakamikawa, and T. Ujiie for useful discussions. JRA-25 reanalysis data were provided by JMA. This study was supported in part by a Grant-in-Aid for Scientific Research of the Japanese Ministry of Education, Culture, Sports, Science, and Technology (19340135) and SELIS COE program of Nagoya University.