Case studies are used to elucidate the relationship between stratospheric planetary wave reflection and blocking formation in the troposphere. The enhanced upward propagation of a planetary-scale wave packet from the Eurasian sector, involving a Euro-Atlantic blocking, leads to a stratospheric sudden warming (SSW). Following the weakening of the stratospheric westerly jet due to polar warming, the stratospheric planetary wave packet then propagates downward over the American sector, inducing a ridge over the North Pacific as well as a trough over eastern Canada in the upper troposphere. The ridge promotes the formation of a Pacific blocking. This result explains why Pacific blockings tend to form after SSW, and why they are associated with suppressed upward propagation of planetary waves.
 The association of the tropospheric blocking phenomenon with stratospheric sudden warming (SSW) had been noticed before the mechanism of the SSW was identified [Labitzke, 1965]. Matsuno  demonstrated that SSWs are generated by an enhanced vertical propagation of planetary waves from the troposphere. Amplification of a planetary wave is generally thought to be produced by a blocking phenomenon in the troposphere [Tung and Lindzen, 1979]. However, it is also possible that the amplification of the planetary waves leads to a formation of blocking [Austin, 1980].
 Regarding the tropospheric influence, stratosphere seems to be more sensitive to a variation of certain regions of the troposphere. For example, a strong correlation between the stratospheric polar vortex and tropospheric variation over the North Pacific and Eastern Europe is explained by amplitude modulation of the wintertime tropospheric stationary waves [Garfinkel et al., 2010]. In a case study of the SSW of January 2006, an important role of the amplification of tropospheric ridge over the North Atlantic is pointed out [Coy et al., 2009]. Moreover, numerical forecast experiments of Mukougawa et al. [2005, 2007], in which Atlantic blocking-like anomalies are introduced in the initial conditions, demonstrated well that the Atlantic blocking promotes the occurrence of a SSW.
 Conversely, stratospheric change can also create regional or local impacts in the troposphere. For instance, reflection of planetary waves in the upper stratosphere can modify tropospheric planetary wave structure [Perlwitz and Harnik, 2003]. In a numerical model study of SSWs, Taguchi  showed a possibility of strengthening of tropospheric planetary waves through interaction with tropospheric synoptic-scale waves. In a case study, Colucci  showed a significant contribution of the stratospheric circulation on the positive height tendency in the troposphere during a blocking formation over the Euro-Atlantic sector. A contribution of the stratospheric polar vortex on simultaneous occurrence of high-latitude blockings in the Atlantic and the Pacific sectors was also noted [Woollings and Hoskins, 2008].
 Recent statistical analyses confirm a significant relationship between the blocking events in the troposphere and the occurrence of SSWs [e.g., Martius et al., 2009; Castanheira and Barriopedro, 2010; Woollings et al., 2010; Bancalá et al., 2012]. However, the causal relationship between blockings and SSWs is not completely clear yet [Taguchi, 2008], because some blockings occur after SSWs [Labitzke, 1965; Austin, 1980; Quiroz, 1986; Kodera and Chiba, 1995]. In particular, Pacific blocking tends to form after SSW.
 A tropospheric blocking usually produces an enhancement of stratospheric planetary wave activity. Nishii et al. , however, found that northwestern Pacific blockings reduce planetary wave activity in the stratosphere. Nishii et al. [2010, 2011], Castanheira and Barriopedro , and Woolings et al.  explained this unexpected relationship by a change in the interference between the climatological planetary wave and a Rossby wave associated with the blocking location. However, it is also possible that stratospheric circulation change affects the occurrence of the tropospheric blocking.
 The numerical experiments of Shaw and Perlwitz  suggest that the blocking occurrence frequency is modified due to changes in planetary wave propagation conditions in the stratosphere. In the present study, we examine changes in the structure of planetary waves (i.e., amplitude and geographical location of ridges and troughs) associated with a modification of the vertical and zonal propagation of stratospheric planetary waves and their effects on subsequent blocking formation. More specifically, the relationship between the occurrence of Pacific blockings and downward propagation of stratospheric planetary wave packet is investigated by using case studies. To get insight into an involved physics, we selected the following different circulation situations in which downward propagation of planetary waves and blocking formation are observed: a weak polar night jet case related with a stratospheric warming in the Northern Hemisphere (NH), a stronger polar night jet case accompanied by a stratospheric vacillation in the NH, and a weak climatological planetary wave case in the Southern Hemisphere (SH).
 The article is organized as follows. The data used for analysis are explained in section 2. An example of the reflection of stationary planetary wave packets is discussed in section 3. The results of four case studies of the blocking formation are presented in section 4. Finally, discussions and concluding remarks are given in section 5.
 For this study, we use reanalysis data sets produced by the Japan Meteorological Agency (JMA), namely, the JMA Climate Data Assimilation System and the Japanese 25 year Reanalysis data sets [Onogi et al., 2007]. The climatology is defined as a 28 year mean from 1979 to 2006.
 Here, we make use of a blocking index based on the meridional gradient of geopotential height (Z) at 500 hPa [Tibaldi and Molteni, 1990] as follows: First, geopotential height gradients at higher latitude (GHGH) and lower latitude (GHGL) are computed at each longitude:
with Δ = − 5°, 0°, 5°.
 A given longitude is then defined as blocked at a specific instant in time if the following conditions are both satisfied for at least one value of Δ:
 The intensity of the blocking is evaluated using the blocking strength defined by GHGL of equation (1), according to the National Oceanic and Atmospheric Administration Climate Prediction Center.
3 Vertical and Zonal Propagation of Stationary Planetary Wave Packet
 Reflection of planetary waves in the stratosphere and their impact on the troposphere is studied by Perlwitz and Harnik . It should be noted, however, that the reflection of planetary waves treated in their study is a special case for transient planetary waves having only one zonal wave number component. In contrast, we are dealing with the reflection of planetary wave packet composed of several zonal wave number components in this study. In this section, we, therefore, first show an example of the reflection of zonally propagating planetary wave packet.
 Planetary waves usually propagate as a wave packet from the troposphere to the stratosphere, although wave number 1 component becomes dominant in the upper stratosphere [Hayashi, 1981]. Quasi-stationary planetary wave structure becomes prominent in monthly mean fields because smaller-scale transient waves are attenuated by time averaging. Figures 1a and 1b show monthly mean geopotential height in December 2008. Clear wave number 2 pattern is found in the troposphere at 500 hPa, while wave number 1 pattern is prominent in the middle stratosphere at 10 hPa. It is difficult to explain why wave number 1 pattern prevails in the stratosphere, whereas wave number 2 pattern is dominant in the troposphere in the framework of the wave number decomposition.
 Height-longitude section of zonal asymmetric component of geopotential height averaged over 60°N–70°N is depicted in Figure 1c. The ridge over Europe does not extend into the stratosphere, while that over the Pacific sector expands into the stratosphere. A tropospheric trough over Siberia is connected with that in the stratosphere, whose phase shifts westward with height, while a trough over Canada tilts eastward with height. Two troughs merge into one in the upper stratosphere. These eastward and westward tilt of trough lines with height indicates upward and downward propagation of planetary waves, respectively, as indicated by three-dimensional wave activity flux by Plumb . This structure also indicates that a wave packet propagating upward from the eastern hemisphere to the stratosphere reflects back to the troposphere in the western hemisphere. Therefore, the tropospheric wave number 2 pattern with an enhanced ridge over Aleutian and trough over Canada can be attributed to a trapping of the stationary waves in the polar stratosphere and troposphere.
 Difference in the vertical propagation property according to the difference in the horizontal scale of the wave can be understood according to the work of Charney and Drazin . However, if we extract only zonal wave number 1 component as Perlwitz and Harnik , downward propagation is not apparent (Figure 1d), although a nodal structure in amplitude near the tropopause indicates an interference of upward and downward propagating waves [Sato, 1974]. Wave number 2 component exhibits an evanescent character of almost constant amplitude in spite of the decrease of the air density with height (Figure 1e).
 In the case of two dimensional E-P flux, cross-terms between different zonal wave number components are not important, because they will vanish when zonally averaged. However, in the case of the three-dimensional wave activity flux, these cross-terms play an important role. Respective upward and downward propagation over Eurasian and American sectors in Figure 1c are, in fact, due to the presence of cross-terms. Such regional propagation property cannot be reproduced by summing up the results of single wave number analysis as in Figures 1d and 1e. Hence, it is important to investigate planetary wave propagation as a wave packet without zonal wave number decomposition to detect the influence of the stratosphere on the regional tropospheric circulation.
4 Planetary Waves and Blocking
Kodera et al.  reported on the impact of reflected stratospheric planetary waves on the Canadian trough. Although not discussed in that article, this accompanies the development of Pacific ridge which leads to a formation of blocking. We first analyze this March 2007 event to explore a possible relationship between the stratospheric planetary wave reflection and the Pacific blocking. Next, we study how a planetary wave reflection contributes to a typical Pacific blocking event in March 2003 that was analyzed by Yamazaki and Itoh . It is also of interest to study the relationship not only for a particular event but also a stratospheric vacillation cycle throughout a winter period. For this purpose, we select the 2010-2011 winter season. As a typical example of blocking producing a decrease of planetary wave activity in the stratosphere, we investigate a northwestern Pacific blocking event in November 1995, which was examined by Nishii et al. . Since the climatological planetary wave of the SH is very different from that in the NH, we also examine a blocking event in the SH in June 2010.
4.1 March 2007 Event
 The impacts of the reflection of planetary waves from the stratosphere were investigated in Kodera et al. . In that study, only planetary-scale (with zonal wave components of wave numbers 1 to 3) eddies were examined. Hence, blockings were ignored in that study. In the present analysis, we retain all wave number components without any truncation.
 To study how the blocking formation is connected with the propagation of stratospheric planetary waves, the time evolution of the March 2007 event is investigated. The zonal-mean zonal wind at 10 hPa, averaged over 60°N–70°N, and the vertical component of the Eliassen-Palm (E-P) flux at 100 hPa, averaged over 45°N–75°N, are shown in Figures 2a and 2b, respectively. A longitude-time section of the NH blocking strength is shown in Figure 2c. The stratospheric westerlies weaken as planetary wave propagates upward. The criterion for a major SSW, i.e., zonal-mean zonal wind at 60°N and 10 hPa changing to easterly, is satisfied on 24 February 2007. Planetary wave activity then soon decreases and zonal wind recovers around 28 February. The Pacific blocking occurs over the date line following the SSW around 3 March (Figure 2c). The vertical component of the E-P flux continuously decreases and becomes negative around 5 March.
 The evolution of the wave structure is depicted in Figure 2d with longitude-height sections of three-day mean eddy geopotential height averaged over 60°N–70°N at 5 day intervals. Here, the wave is defined as a departure from the zonal mean. The vertical and zonal propagation of the planetary wave is visualized using the 3-D wave activity flux defined by Plumb  associated with zonal wave number components from 1 to 3. The planetary wave packet propagates eastward and upward over the Eurasian continent and then reflects downward from the stratosphere. The enhanced upward propagation of planetary waves over the Eurasian sector is also seen as a westward tilt of ridge and trough lines with height on 23 February, while a downward propagation over the American sector is consistent with an eastward tilt of those lines with increasing altitude on 5 March.
 The evolution of the tropospheric circulation during this event is shown in the 500 hPa height maps in Figure 2e. On 23 February, a ridge is located over the Atlantic sector near Greenland, while no apparent ridge is found in the Pacific sector except for the subtropics. On 28 February, the stratospheric ridge over the North Pacific extends downward in association with a suppression of the upward propagation of planetary waves in the western hemisphere. This manifests itself in the troposphere through the development of the ridge in the Pacific sector. A dipole-type blocking builds up from this ridge at the beginning of March. Interaction with high frequency transient eddies is particularly important for blocking formation in the Pacific sector [Nakamura et al., 1997]. Note that the blocking anticyclone near the date line is connected with the Aleutian high in the stratosphere (Figure 2d), which forms as a result of the propagation of a planetary wave packet (wave numbers 1–3) from the troposphere over Eurasia [Hayashi, 1981]. Thus, we propose a working hypothesis that the Pacific blocking is formed through the interaction between a tropospheric ridge amplified due to downward propagating planetary waves and transient eddies. This will be examined in the next subsection.
4.2 March 2003 Event
 Here, we investigate a typical Pacific blocking event from March 2003 examined by Yamazaki and Itoh  demonstrating a new blocking maintenance mechanism called the Selective Absorption Mechanism in which the blocking maintains itself by selectively attracting and absorbing anticyclonic synoptic transient eddies. Figure 3 illustrates the evolution of this event using the same presentation as in Figure 2.
 A major warming event during the March 2002 winter occurs on 17 January. After the polar vortex recovers, the stratospheric westerly jet decreases again following an increase in the upward propagation of planetary waves at the end of February. Strong blocking over the Pacific begins in March when the upward propagation of planetary waves decreases.
 An evolution similar to the 2007 case is also seen in height-longitude sections of eddy geopotential height (Figure 3d). An increased upward propagation of waves from the Eurasian sector occurs around 28 February leading to an easterly wind in the polar stratosphere slightly higher than 60°N at the beginning of March. After this minor SSW, planetary waves are trapped in the lower stratosphere and troposphere. Planetary waves propagating upward from the Eurasian sector propagate eastward and downward over the American sector from 5 to 10 March (Figure 3d). Finally, the reflected wave component becomes dominant and the vertical component of the E-P flux becomes negative in the lower stratosphere on 11 March (Figure 3b). Similar to the 2007 case, the development and downward extension of the Pacific ridge occur in conjunction with the development of a trough over North America. However, the planetary waves are trapped in a region of somewhat lower altitude compared with the previous case. The blocking (Figure 3e), once formed, is maintained through the interaction with transient synoptic eddies.
4.3 2010-2011 Winter
 In contrast with the two winters discussed above, no major SSW occurred during the 2010-2011 winter. In spite of a strong westerly jet, planetary waves propagate along the jet core and stratospheric vacillation occurs throughout the winter due to the interaction between the zonal wind and planetary waves [Holton and Mass, 1976]. Figure 4 shows (a) the vertical shear of zonal wind in the upper stratosphere averaged over 60°N–70°N, (b) the vertical component of the E-P flux at 100 hPa averaged over 45°N–75°N, (c) the zonally asymmetric component of 500 hPa geopotential height averaged over 60°N–70°N, (d) the daily blocking strength, and (e) the transient synoptic eddy heat flux at 850 hPa averaged over the northwestern Pacific (130°E–150°E, 30°N–45°N) from 1 November 2010 to 31 March 2011. Here, the synoptic eddies are defined by an 8 day high-pass filtered component, and a 16 day low-pass filter is applied to obtain the heat flux associated with the synoptic eddies, in order to represent its activity (Figure 4e).
 The vertical shear of zonal wind between 2 and 10 hPa was introduced by Perlwitz and Harnik  as an index to represent the state of planetary wave reflection in the upper stratosphere. This choice of index is based on the fact that a negative wind shear above the westerly jet core usually produces a negative refractive index favorable for wave reflection. Vertical lines in Figure 4 indicate minima of the vertical shear index. Minima of this index occur around maxima of the E-P flux at 100 hPa as shown in Figure 4b. We define five stratospheric vacillation cycles according to the minimum of the shear index (numbered as i to v in Figure 4a).
 The concurrent evolution of the tropospheric wave structure is shown by the time-longitude cross section of the 500 hPa eddy (i.e., the departure from the zonal mean) geopotential height averaged over 60°N–70°N (Figure 4c). The longitudinal location of the trough (T) and ridge (R) evolves with the vacillation cycle. Inspection reveals that the deepening of a trough over Canada (80°W) precedes the development of an Atlantic ridge (20°W) in one region. In another region, the deepening of a trough over eastern Siberia (130°E) precedes the development of a ridge over the Pacific around the date line. Thus, the position of the ridge changes from the Atlantic to the Pacific sector in association with the decrease in the vertical component of E-P flux, after the minimum in the vertical shear index during the stratospheric vacillation cycle. Inspection of Figure 4d reveals that the blocked regions over the Atlantic and the Pacific coincide well with the ridges of the planetary-scale waves (Rs in Figure 4c). Therefore, the transition of blocked regions from the Atlantic to the Pacific sector occurs with the vacillation cycle in the 2010/2011 winter.
 The blocking strength is, however, not proportional to the magnitude of the preexisting planetary-scale ridge. For example, the Pacific ridge during vacillation cycle iv around 1 February is prominent, but it produces only a small blocking. Thus, a well-developed quasi-stationary ridge is not a sufficient condition to produce a blocking, but another agent such as synoptic-scale eddies has to play an important role in the formation of the blockings [Shutts, 1983; Yamazaki and Itoh, 2009]. In fact, around the end of January when the blocking strength is weak (Figure 4d), the activity of synoptic eddies over the Pacific is comparatively weak (Figure 4e) in spite of the existence of the enhanced planetary-scale ridge over the Pacific (Figure 4c).
 In order to extract a mean feature associated with the vacillation cycle, composite means are calculated by using five minima of the vertical shear index in Figure 4a as the key date (= day 0). Figure 5 shows composite three-daily mean (a) zonally-averaged zonal wind and E-P flux, (b) zonally asymmetric component of geopotential height averaged over 60°N–70°N and planetary wave (wave numbers 1 to 3) activity flux defined by Plumb , and (c) 500 hPa geopotential height for days −8, −4, 0, 4, and 8.
 A blocking ridge is found over the North Atlantic on day −8 (Figure 5c). An upward propagating wave packet occurs east of the blocked region (30°W) (Figure 5b). The Aleutian high develops in the stratosphere, and the lower-stratospheric Siberian trough extends toward the northwestern Pacific on day −4. The Aleutian high starts to extend downward into the troposphere on day 0 in association with a westward shift of the Siberian trough. This means that planetary waves propagate in the upper troposphere more in the horizontal rather than the vertical direction from the Eurasian to the American sector. Upper stratospheric zonal winds weaken substantially from day −8 to day 0 (Figure 5a), due to an enhanced upward propagation of planetary waves. On day 4, the upward propagation of planetary waves in the lower stratosphere apparently weakens. This can also be seen by a slight eastward tilt of the Pacific ridge with altitude in the lower levels (Figure 5b). Less upward propagation of planetary waves is consistent with the increase of zonal wind in the upper stratosphere on day 8. Waves trapped in the lower stratosphere propagate downward over the American sector, creating a trough over eastern Canada, while the Siberian trough retreats. A blocking over the Aleutian Islands develops following a growth of the Pacific ridge. These composite mean features associated with the vacillation cycle are quite similar to those associated with particular events following the SSWs (Figures 2 and 3).
4.4 West Pacific (WP) Blocking of 1995
Nishii et al.  argued that West Pacific (WP) blockings cool the polar stratosphere by weakening stratospheric planetary waves because of the destructive interference between the climatological planetary wave and the Rossby wave packet originating from the WP blocking. A WP blocking event in November 1995 was described as a typical example. Here, we examine this event from the present context of stratospheric planetary wave reflection. Figure 6 shows (a) the zonal-mean zonal winds at 10 hPa, (b) the vertical component of E-P flux at 100 hPa, and (c) the daily longitude-time section of the blocking strength from 10 November to 5 December 1995. The gradual enhancement of the upward propagation of planetary waves around 15 November is associated with the occurrence of the Atlantic blocking. Following the weakening of the upward propagation of planetary waves around 25 November, the polar night jet strengthens. The negative vertical component of E-P flux at the end of November indicates the occurrence of planetary wave reflection, which coincides with the formation of blocking over the North Pacific around the date line. Then, the blocking retrogrades and intensifies over the northwestern Pacific. We also identify a concurrent transition of the blocked region from the Atlantic to the Pacific sector, which is associated with the suppression of the upward propagation of planetary waves; this is similar to the example in the 2010-2011 winter.
 The relationship between the planetary wave reflection and the occurrence of the blocking over the North Pacific is also confirmed from Figure 7. The Atlantic blocking is seen in the 500 hPa geopotential height field over the North Atlantic around 15 November (Figure 7b). This blocking produces the upward propagating wave packet from the Euro-Atlantic sector (Figure 7a). The main region of upward propagation shifts over Siberia around 20 November. Then, a change in the direction of vertical propagation is detected as the vertical tilt of the trough and ridge lines changes from westward to eastward with height over the western hemisphere from 25 to 30 November in the lower stratosphere (Figure 7a). The downward extension of the Pacific ridge from the stratosphere is connected with a development of the blocking over the date line. The blocking retrogrades toward Siberia following the evolution of the planetary wave structure. We therefore reconfirm that the blocking is produced in association with the reflection and subsequent trapping of planetary waves, as in the previous examples.
4.5 SH Blocking
 Figure 8 shows planetary waves and blocking activity in June 2010 in the SH. The upward propagation of planetary waves increases starting in mid-June, and the planetary waves reflect back into the troposphere around 25 June in association with the strengthening of zonal-mean zonal winds in the upper stratosphere (Figure 8a). This reflection occurs after the vertical component of E-P flux in the lower stratosphere reaches a maximum around 19 June (Figure 8b). A longitude-height cross section of eddy geopotential height averaged over 60°S–70°S (Figure 8d) shows that planetary waves are still weak on 15 June. Wave number 1 structure becomes apparent with a ridge near the Antarctic Peninsula (80°W) and a trough around 90°E on 20 June. The upward propagation of planetary waves is clearly recognized by the westward tilt of trough and ridge lines with altitude. The stratospheric ridge extends vertically into the troposphere, and a trough develops east of the ridge when the waves are reflected back from the stratosphere on 25 June. A blocking ridge is formed in the troposphere at the tip of stratospheric ridge over the south of New Zealand around 170°E (Figure 8e). It should also be noted that a deepening of a trough downstream of the blocking around 60°W (Figures 8d and 8e) is similar to that of the Canadian trough in the NH case.
5 Discussions and Concluding Remarks
 The results of the case studies show that the occurrence of the Pacific blocking is preconditioned by a development of a planetary-scale ridge, of which formation is related with a change in the direction of the vertical propagation of the stratospheric planetary waves from upward to downward.
 The relationship between planetary wave reflection/trapping and blocking formation suggested by our study is summarized as follows.
 The enhanced upward propagation of the planetary wave packet from the Eurasian sector is initiated by an enhanced ridge over the Euro-Atlantic region in association with a blocking. The enhanced upward propagation of planetary waves involves the development of the trough over Siberia and the Aleutian high in the stratosphere.
 Increased stratospheric planetary wave activity modifies the zonal wind field in the stratosphere, which in turn suppresses upward propagation of planetary waves. In particular, zonal wave number 2 and 3 components tend to be trapped in the lower stratosphere and the troposphere. The suppressed vertical propagation requires less westward tilt of trough and ridge lines with altitude, which is realized by the descent of the Aleutian high and the retrogression of the Siberian trough. Since the ridge that developed over the Pacific provides conditions favorable for the occurrence of the blocking, the Pacific blocking subsequently develops through interaction with synoptic transient eddies.
 The propagating direction of the planetary wave packet then changes its direction from zonal to downward, especially over the American sector. This appears as the development of the Canadian trough and the slight westward shift of the Pacific ridge associated with a retreat of the Siberian trough.
 If the polar stratosphere cools down due to the precedent suppression of the upward propagation of planetary waves, planetary waves can propagate again into the stratosphere through the reestablished westerly jet. Then, the above sequence can be repeated as a stratospheric vacillation.
 The above sequence from (i) to (iii) for the evolution of the relationship between the propagation of planetary waves in the stratosphere and the tropospheric blocking is schematically illustrated in Figure 9.
 Recent studies [Nishii et al., 2010, 2011; Castanheira and Barriopedro, 2010; Woollings et al., 2010] revealed that the relationship between blocking and stratospheric planetary wave activity differs according to the longitudinal location of the blocking in the NH. Stratospheric planetary wave activity increases following the formation of the blocking in the Euro-Atlantic sector, as usually expected, whereas the wave activity decreases in association with the formation of the blocking in the Pacific sector. This conflicting relationship has been explained by a destructive interference between the climatological planetary wave and the Rossby wave packet emanating from the blocking, using an anomaly field defined as a deviation from the climatology [Nishii et al., 2010, 2011; Woollings et al., 2010].
 However, the following aspects of the Pacific blocking event are difficult to understand from the viewpoint of the interference. The first aspect is the time evolution of the anomaly field. Figure 7c shows the anomaly field defined from the climatology for the Pacific blocking event in November 1995. When the blocking is located over the Euro-Atlantic sector (15 November), the anomaly field has a similar structure to the climatological wave field but with a smaller amplitude. At the end of November, when the blocking has formed over the North Pacific and retrogrades to the western Pacific, the anomaly has a structure quite different from the climatology, and its positive center descends from the stratosphere to the troposphere (Figure 7c, open circles). In contrast, the phase of the blocking ridge tilts westward with increasing altitude (30 November), which suggests the upward propagation of the anomaly. Hence, the apparent descent of the anomalous ridge is very hard to understand.
 The second aspect is the negative vertical component of the E-P flux observed at the end of November. Change in planetary wave propagation from upward to downward around 27 November 1995 is clearly seen in the E-P flux meridional section (Figure 6d). The conventional framework of the interference between the two upward propagating wave components of the climatological planetary wave and the anomaly field consisting of Rossby wave packet generated by the blocking cannot explain the negative heat flux or downward propagation from the stratosphere.
 The development of the Canadian trough is additional evidence for the downward propagation of the stratospheric planetary waves due to the reflection. Thus, the concept of the reflection and trapping of planetary waves in the stratosphere is more relevant for understanding the occurrence of the Pacific blocking after the warming of the polar stratosphere.
 The present study shows that the blocking does not always force the SSW, but forms due to the downward propagation of stratospheric planetary waves to the troposphere, because of the wave reflection which sometimes occurs just after the SSW. Thus, it is no wonder if no statistically significant relation is found between the occurrence of the blocking and the SSW [Taguchi, 2008]. Our newly obtained findings on the relevance of the downward propagation of planetary waves to the formation of the Pacific blocking give plausible grounds to explain why the Pacific blocking tends to occur after the SSW [Martius et al., 2009; Woollings, 2010; Bancalá et al., 2012].
 It should be noted that the reflection of planetary wave can occur under different zonal wind configurations in the upper stratosphere. The reflection described by Perlwitz and Harnik  is a specific case. Therefore, we focus in the present study on tropospheric effect of reflected waves leaving a question of how the reflection of planetary waves takes place in the stratosphere for a future study.
 The authors thank the Climate Information section of the Japan Meteorological Agency (JMA) for providing the meteorological reanalysis data. The “Interactive Tool for Analysis of the Climate System” developed by JMA was used for the preparation of this study. This work was supported in part by the Ministry of Education, Science, Sports, and Culture via Grants-in-Aid for Scientific Research (S)24224011 and (B)23340141.