The effect of stratospheric sudden warming (SSW) and vortex intensification (VI) on the tropospheric climate is examined through composite analysis of the observational data. Specifically examined in the present study is the Eulerian meridional circulations associated with SSW and VI. It is found that prominent signal in the troposphere tends to appear associated with the occurrence of SSW and VI. The patterns created are very similar between SSW and VI except for the polarity. In the high latitude region, the pattern similar to the Arctic Oscillation (AO) is created before and after the occurrence of SSW and VI with changing polarities. In the tropics, convection tends to enhance in the Southern Hemisphere (Northern Hemisphere) tropics after the occurrence of SSW (VI). These signals are created through three prominent cells of the anomalous Eulerian meridional circulation that extends from polar cap to the tropical Southern Hemisphere. The mechanism for the formation of the cells associated with SSW and VI is also discussed.
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 Stratospheric sudden warming (SSW) is one of the most spectacular phenomena in the atmosphere [e.g., Labitzke and van Loon, 1999]. It is characterized by a very rapid increase (about 40 K in a week) of the stratospheric polar cap temperature at about 10-hPa level. As it occurs in the stratosphere, the influence on the tropospheric climate is not well organized; however, recent advanced studies on the troposphere-stratosphere coupling have revealed that it significantly influences the tropospheric climate [e.g., Baldwin and Dunkerton, 2001; Limpasuvan et al., 2004]. In fact, Baldwin and Dunkerton  demonstrated that the effect of SSW propagates down to the surface and lasts more than two month after the occurrence of SSW, and that the surface pressure signal shifts more toward a negative pattern of the Arctic Oscillation (AO) [Thompson and Wallace, 1998]. Limpasuvan et al.  also examined the life cycle of SSW, including the troposphere and surface, and noted its similarity of the AO.
 Interestingly, an inverse phenomenon of SSW exists as well, although the variation is not so violent as SSW. It is characterized by a cooling of the polar cap temperature. Limpasuvan et al.  called this phenomenon as the vortex intensification (VI) because the polar vortex is intensified with the cooling of the polar cap temperature. They found that SSW and VI have many similar aspects except for the polarity, although there are some significant differences as well.
 Recently, Kodera  and Eguchi and Kodera  noted the possibility that SSW can also change the convective activity of the tropical troposphere. In fact, Kodera  found that, associated with the Northern Hemisphere (NH) SSW, convective activity center is shifted to the Southern Hemisphere (SH). Eguchi and Kodera  also noted the southward shift of the tropical convection associated with the SH SSW in 2002.
 In the previous studies, we examined time evolution of the surface pressure change associated with the stratospheric variability called the Polar-night Jet Oscillation (PJO) and the AO [Kuroda and Kodera, 2004; Kuroda, 2005]. It should be noted that the time evolution of the PJO includes SSW and VI as parts of their stages [Kodera et al., 2000]. However, previous studies involved analysis for slower variability as 30-d averaged fields. Thus for the analysis of shorter timescale, especially with SSW or VI events, previous analysis is insufficient. Previous studies, however, do indicate that Eulerian diagnosis is a convenient tool for examining the dynamical linkage among the forcing, meridional circulation, and the surface signal.
 In the troposphere, changes in the meridional circulation are closely related to changes in the climate. Thus in this study we directly examined the Eulerian mass stream function. By extending previous studies, we also used Eulerian diagnosis to examine the dynamical linkage between the eddy and nonconservative forcings and meridional circulations. Limpasuvan et al. [2004, 2005] selected SSWs and VIs from the zonal wind signal in the lower stratosphere. Such a key signal in the lower stratosphere is suitable for capturing the troposphere-stratosphere coupling, but it does not capture the typical signal with SSW or VI in the troposphere. In the present study, we adopted a key signal from the polar temperature in the middle stratosphere to capture the typical stratospheric signal with SSWs and VIs more directly.
 We used daily 43-year data to achieve larger statistical significance in the present study. However, it is still not large enough to capture signals with highly statistical significance. To compensate, we compare extracted signals associated with SSW and VI. If the anomalous tropospheric responses to SSW and VI are very similar except for the sign, the signal could be considered as true because anomalous effects of SSW and VI on the troposphere should be the same except for the sign if SSW and VI can be treated as near linear variations on the climate. In fact, results of Limpasuvan et al.  and the linear analysis in the present study support such a hypothesis. Such a comparison will greatly help our understanding of SSW and VI on the tropospheric climate.
 This paper is organized as follows. The data set and the principal method of analysis are described in section 2. Section 3 provides the results of the analysis. After a discussion in section 4, conclusion and remarks are offered in section 5.
2. Data and Method of Analysis
 We used daily reanalysis data from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) [Kalnay et al., 1996; Kistler et al., 2001]. The period we analyzed was from 1 January 1958 to 31 December 2000. We did not include data after 2001 because the tropical lower stratosphere changed significantly after 2001 [Randel et al., 2006], and such change will greatly modify the effect of SSW and VI on the tropics.
 First, we compiled daily temperature climate and anomalous data based on the area average poleward of 80°N. Anomalous data are 3-d running averaged for smoothing. We then conducted the Empirical Orthogonal Function (EOF) analysis for the vertical level from 30 hPa to 10 hPa for daily anomalous temperature of 180 d from 2 November to 30 April. Areal as well as height weighting has been considered for the EOF analysis. The first mode (EOF1) explained 88% of the total variance and revealed a homogeneous monopole structure that slightly amplifies with height. We next performed a composite analysis based on the first principal component (PC1) associated with the EOF1.
 For the analysis of SSW or VI, we had selected the peak day of PC1 as the key day for the composite. For the criterion to select SSW, we chose PC1 greater than 3. Also to avoid analyzing different peaks of the same SSW, we made a different criterion that the peak should be separated more than 50 d. Using these criterions, we selected 28 SSWs. For VI, we used the same criterions except for the threshold for PC1 to be taken smaller than −1.5. In this way, we selected 27 VIs. Composite analysis of SSWs or VIs was then performed for various meteorological fields based on the key day.
 Climatologically daily data are defined as the average of the calendar days from 1 January 1958 to 31 December 2000. Anomalous meteorological data are then defined from the departure from climatology. All anomalous data are 3-d running averaged for smoothing. Composite analysis is performed for these anomalous data based on the key day of the PC1. Statistical significance is evaluated based on the Student's-t statistics. For composites of sequential daily data, however, we should consider their statistical dependence as well. Though decorrelation timescales actually depend both on elements and areas or levels, we will estimate independent number of samples as a quarter of number of days used to evaluate the Student's-t for the composite of sequential daily data in the present study.
 Vertical velocity is present only up to 100-hPa level in the present data set. Thus Eulerian mass stream function χ is calculated every day from daily mean meteorological data by integrating the following equation:
where z0 corresponds geopotential height for 100-hPa, ϕ is the latitude, a is the radius of the Earth, ρs is the reference density, overbar denotes the zonal-mean, and other notations follow the usual convention [e.g., Andrews et al., 1987].
 Data of nonconservative quantities such as frictional forcing and diabatic heating is created from the residuals of the dynamical and thermal equations from 6 hourly three-dimensional meteorological data as used by Kuroda and Kodera .
are eddy mechanical and thermal forcings, G and S are frictional forcing and diabatic heating, ϕ is the latitude, ω is the vertical pressure velocity, Γ = −∂T0/∂p + κT0/p is the stability of the basic atmosphere, Ω is the angular velocity of the Earth, a is the radius of the Earth, field variables with primes denote departure from zonal mean, overbar denotes zonal averaging, and other symbols follow the usual convention [e.g., see Andrews et al., 1987]. See Appendix of Kuroda and Kodera  for more detail.
Figure 1 compares some key quantities associated with SSW (left) and VI (right). They are the zonal-mean temperature averaged for 80° to 90°N (1st row), zonal wind for 50° to 70°N (2nd row), vertical component of the E-P flux for 50° to 70°N (3rd row), meridional wind for 40° to 80°N (4th row), zonal wind (5th row) and meridional wind (6th row) at the surface. Heavy (light) shading is applied for the region of greater than 95% (85%) significance by the Student's-t criterion. Bold lines are applied for periods of greater than 95% significance.
 For the time evolution of SSW, the anomalous temperature is cooler before day −20, but it begin to increase especially from day −7 and reaches 30 K at the 10 hPa level on day 0. After the peak day, the temperature begins to cool but it remains warmer especially in the lower stratosphere until around 40 d. From day 20, the temperature at 10 hPa becomes cooler and it propagates downward. Overall temperature change well captures the quasiperiodic time evolution of the Polar-night Jet Oscillation (PJO), as reported by Kodera et al. . Associated with the temperature change, zonal wind exhibits similar quasiperiodic behavior through the thermal-wind relationship; zonal wind at 60°N is stronger until around day −15, weaken very quickly from day −7, and have a peak value of −21 m/s on day 0 at 10-hPa; however, it remains negative until around day 40. Such changes in temperature and zonal wind should be closely related with the wave propagation from below. In fact, anomalous vertical E-P flux in the stratosphere is strongly positive with peaks on day −5 and turns negative after the key day with a peak on day 20. Although not as prominent as the zonal wind, the meridional wind also indicates some downward propagation starting on the key day, on which polarity completely changed. More interesting feature can be seen in the lowermost surface; southerly anomaly appears from day −20 to day 0, and northerly anomaly is observed from day 20 to day 50. This feature can be regarded as a counter flow against the wind in the upper stratosphere [Limpasuvan et al., 2004, 2005]. It is noted that signals in the troposphere, except for the lowermost area, are statistically very weak. Zonal wind around 60°N at the surface exhibits an AO-like structure; it is positive before day 5, but turns negative afterward and lasts until day 50. It is noteworthy that time evolutions of the meridional and zonal winds at the surface are very similar.
 Time evolution of VI is very similar to that of SSW, except for the polarity. However, it is clear that the time evolution of VI is more gradual than that of SSW, as can be seen for the time evolution of the temperature at 10-hPa on key days. The maximum values reaches about −15 K at 10-hPa on the key day. Although the time evolution of the temperature also indicates some quasiperiodic structure as SSW, the signal is vaguer. The temperature and zonal wind signals indicates prominent downward propagation, like those of SSW. However, the duration of the downward propagation is shorter; it breaks around day 30 in the troposphere. Such variation should be closely related with the wave propagation from below. In fact, anomalous vertical E-P flux in the stratosphere is strongly negative with peaks on day −5 and it turns positive after the key day, with a peak on day 20. For the meridional wind, the behavior is similar to that of SSW except for the polarity, and greater values appear in the upper stratosphere and upper troposphere, although statistical significance of the signal in the upper stratosphere is very weak. The magnitude of the meridional wind at the upper troposphere is almost the same as that for SSW. The appearance of the counter flow in the lowermost troposphere is also similar but is associated with a shorter duration of the downward propagation; anomalous southerly wind at the surface lasts only until day 30. From the zonal wind at the surface, a negative AO-like structure appears before day 5 but turns positive afterward and lasts until day 30. Similarities between the time evolution of the meridional and zonal winds at the surface is observed in this case also.
 To demonstrate the global change of the circulation around the key day for SSW, Figure 2 presents the time evolution of the zonal wind with the E-P flux (top), Eulerian mass stream function (middle), and sea level pressure (bottom) for day −10 to day 30, with 10-d intervals. Here each panel is calculated not from a composite of only 1 d but averaged from 11 d centered for each day. Here statistical significance is calculated from independent number of days of 28 × 11 × 1/4.
 Vertical propagation of the E-P flux around 60°N is very strong on day around −5, with largely decelerated zonal wind at the upper stratosphere. Upward propagation of the E-P flux becomes weaker than climatology on day 0, and anomalous E-P flux turns downward (i.e., weaker than climatology) and peaks around day 20, and lasts until day around 50. It should be noted that associated with the vertical propagation of the E-P flux, horizontal propagation of the E-P flux from the subtropics to tropics on the tropopause is prominent. For example, anomalous equatorward propagation of the E-P flux centered at around 20°N and 200 hPa is prominent on day −10. Such wave propagation produces anomalous wave forcings and meridional circulation. Here, the time evolution of the Eulerian mass stream function rather than that of the Transformed Eulerian Mean (TEM) is shown (middle), because effect on the troposphere is more effectively shown by Eulerian circulation [Kuroda and Kodera, 2004]. The main cell associated with SSW is the one in the polar cap area. It is anticlockwise from day −10 to day 0, but becomes clockwise from day 10 and after. It is also interesting to note that aside from the main polar cell with SSW, smaller cells, mostly trapped in the troposphere, extends to the SH. Anomalous sea level pressure (SLP) corresponds well with the Eulerian meridional circulation in the troposphere (bottom). In fact, anomalous polar cap SLP appears with a negative signal from day −10 to day 0, but becomes a prominent positive signal from day 20 and after. It is interesting that the polar pattern from day −10 to day 0 is very similar to the positive pattern of the Arctic Oscillation (AO) [Thompson and Wallace, 1998], and that from day from 20 and after is similar to the negative AO.
Figure 3 presents the time evolution for VI. The overall feature of the time evolution is very similar to that of SSW except for the sign. The propagation of the E-P flux to the stratosphere is weaker than climatology with a peak on day −5, but becomes stronger and has a peak value around day 20 (top). Associated with the change of the vertical propagation of the E-P flux, an area with stronger zonal wind propagates downward and reaches the surface on day around 10. Horizontal propagation of the E-P flux to the tropics exhibits behavior similar to that of SSW as the vertical propagation of the E-P flux around 60°N; anomalous poleward propagation around 10°N and 200 hPa is prominent on day −10, but it becomes equatorward propagation around 20°N and 200 hPa from day 10 to day 20. For the Eulerian meridional circulation (middle), the main polar cell is clockwise from day −10 but becomes counterclockwise on day 10 and after. It is interesting to note that two strong cells in the tropical to subtropical troposphere persists from day 0 to day 30. One is counterclockwise on the equator, and the other is clockwise at around 20°N. SLP on the polar cap is positive from day −10 to day 0, but is negative on day 10 and after (bottom). Like that of SSW, the polar pattern on day −10 is very similar to the negative AO; that from day 10 and after is very similar to the positive AO. The overall time evolution of the SLP is very similar to that of SSW, except for its polarity.
 To determine the typical mean circulation and eddy forcings after the occurrence of SSW and VI, we calculated the Eulerian mass stream function and eddy forcings (Figure 4). The mean times we had used are from day 20 to day 45 for SSW and from day 10 to day 30 for VI. These mean times are adopted from the appearance of prominent surface zonal and meridional winds in Figure 1. It can be seen that the mean meridional circulation includes four cells extending to the subtropical SH both for SSW and VI, and their features are very similar except for the polarity (left). The polar-most side cells (called the polar cells) extend to the stratosphere and directly corresponds to stratospheric change. However, there are two other prominent cells in the troposphere; one is in the upper troposphere on the equator (called the tropical cell), the other is in the lower troposphere at around 20°N (called the subtropical cell). Examination of the eddy forcings suggests that the polar cells are created by the eddy forcings (middle and right). In fact, as positive (negative) mechanical forcing acts to create equatorward (poleward) flow, and positive (negative) thermal forcing acts to create upward (downward) flow, polar cells are thought to be created by the activity of these forcings.
 The left of Figure 5 compares the SLP signal associated with the mean circulation after the occurrence of SSW and VI. It can be seen that the SLP signal is very similar to the AO both for SSW and VI, although polar-cap signal is smaller than that of the typical AO [Kuroda, 2005]. In the case of SSW, the polar center has higher pressure peaked at 3 hPa at the Arctic pole, which is surrounded by a lower pressure belt at the middle latitude, centered in England with a peak of −2 hPa. For VI, the polar center has lower pressure peaked at −3 hPa at the Arctic pole, which is surrounded by a higher pressure belt at the middle latitude, centered in England with the peaked value of 2 hPa and in the North Pacific with a peak of 3 hPa. The overall feature of SSW and VI are very similar, except that the signal over the North Pacific is very prominent for VI but is almost absent for SSW. The middle compares the meridional wind at the surface. For SSW, equatorward wind is very strong around Iceland, and other polar cap area also has a weaker significant equatorward signal. A similar signal for the meridional wind is observed for VI except for the polarity, although signals on the North Pacific are rather different. When geostrophic winds were calculated from SLP signals, observed meridional winds were found to be very similar to the geostrophic winds for both SSW and VI. However, it should be noted that if observed meridional winds are explained completely by the geostrophic wind, the zonal mean should vanish and no signal should appear on the surface (Figure 1). Therefore ageostrophic-wind components are essential for zonal mean meridional circulation. Calculation reveals that a negative or positive ageostrophic meridional wind signal extends rather homogeneously around the pole with peaks over the Rocky Mountains, Labrador, Scandinavia, and northern Central Siberia for both SSW and VI (not shown). Thus zonal mean meridional flow on the surface is created in some geographically specific areas. The right compares the vertical wind at the 500-hPa level. The signals are very similar to corresponding meridional winds at the surface in the polar area, although vertical winds appear busier. This phenomenon could be partially explained as follows. Higher surface pressure areas are associated with downward flow, and lower surface pressure areas are associated with upward flow in the troposphere. Surface meridional winds develop through the continuity of these winds. As a result, when the annular mode appears, upward flow in the polar cap area corresponds to northward surface flow, and downward flow corresponds to southward surface flow.
 It is interesting to note that the meridional circulations associated with SSW and VI are extended toward 20°S of the SH. A tropical cell exists on the equator, as can be seen in the left of Figure 4. Thus the convective activity in the tropics is also significantly influenced by the occurrence of SSW and VI. To illustrate this phenomenon directly from the vertical velocity in the tropics, Figure 6 compares the vertical section of the vertical winds for the NH subtropical area averaging from 5° to 15°N and SH subtropical area averaging from 15° to 5°S with SSW and VI. For SSW, the enhanced convective area tends to shift from the NH to the SH, and the suppressed area shifts from the SH to the NH with the occurrence of SSW, although small significance areas appear after the key day. For VI, convection becomes stronger on day −10 and lasts until day 30 in the NH, but becomes weaker in the SH at the same time. Convective change occurs a little prior to the key day and the transition is as clear as with SSW. Comparison of SSW and VI reveals that the polarity of the anomalous vertical velocity becomes completely opposite after the key day, but the significance is stronger for VI than for SSW, corresponding with the stronger cells on the equator (left of Figure 4).
Figure 7 compares the vertical wind at the 300-hPa level in the tropics. The composite is calculated from day 5 to day 30 for SSW, and from day −5 to day 20 for VI. The days of composite are taken from the period of prominent signal seen in Figure 6. It can be seen that for SSW enhanced convection in the tropics take place almost exclusively in the SH Pacific, but suppression occurs in northern tropical Africa, the North Indian Ocean, the Maritime Continent, and the Northern Pacific. On the other hand, for VI, enhanced convection in the tropics take place in northern tropical Africa, the North Indian Ocean, and the Maritime Continent, but convection is suppressed in the South Indian Ocean, the SH West Pacific, the tropical East Pacific, and the South America. Convection in the area from northern tropical Africa to the Maritime Continent indicates a prominent opposite response, but the meridional dipole signal in the Central Pacific is clear for only SSW. Opposite polarity of the wave train from west coast of South America to the NH North Pacific and the signal in the Atlantic are also prominent.
 It is interesting to examine how the observed AO-like structure and the tropical convection are sustained. This phenomenon could be understood in terms of the structure of the meridional circulation, because higher (lower) pressure area will be produced on the Eulerian downward (upward) flow in the troposphere. Eulerian meridional circulation is driven by the eddy forcings as well as the frictional forcing and the diabatic heating. Thus we calculated the composite of the eddy forcings, frictional forcing, and the diabatic heating in these periods for SSW and VI. In Figure 8, mechanical and thermal forcings in Figure 4 is presented again for comparison with the frictional forcing and diabatic heating. Frictional forcing is very significant only in the lower troposphere both for SSW and VI. These forcings are created as a passive reaction for the meridional dipole structure of the zonal wind with the node at around 40°N in this period (Figures 2 and 3). Diabatic heating indicates tripole structures centered at 10°S, 10°N, and 35°N, with high values in the troposphere. Also it is interesting to note that the structures are very similar between SSW and VI, except for the polarity. Comparison between the frictional and mechanical forcings reveals that the mechanical forcing is more dominant in the subtropical upper troposphere. Also, comparison between thermal forcing and diabatic heating indicates that diabatic heating is far greater in the tropics.
 To examine how these forcings contribute to the formation of observed meridional circulation, we calculated the meridional circulation by applying these forcings with the use of the quasi-geostrophic model on the sphere. Winter mean stability is used for the calculation. Figure 9 presents the results from all the forcings. The overall feature is reproduced well by this model for both SSW and VI, although polar and tropical cells are reproduced a little weaker. Applying respective forcing reveals that the polar cell is produced mainly by eddy forcings, whereas the tropical cell is driven by diabatic heating. The greatest contribution to the formation of the subtropical cell is found to come from the frictional forcing from the surface. However, the mechanical forcing and diabatic heating also contributed significantly. The results suggest that the AO-like structure is created by the meridional circulation driven by eddy forcings in the high-latitude troposphere to the stratosphere, whereas the subtropical cell is created through frictional effect of the surface against lower-latitude side of the zonal wind with the AO-like structure. The tropical cell is driven by the diabatic heating from the convection.
 Analysis of eddy and nonconservative forcings reveals that polar and subtropical cells are created through direct and indirect activity of eddy forcings. However, the tropical cell is created mainly by the diabatic heating, and no linkage with the eddy forcing is found. So it is not clear how the creation of the tropical cell is linked with the dynamical evolution of SSW or VI. It will be clear, however, that once convection takes place in some latitude by some external trigger, meridional circulation will function to maintain the same meridional circulation and diabatic heating. It will be then necessary to identify such external trigger forcing in the time evolution of SSW or VI. Figures 2 and 3 indicate that tropical cells evolve first on day around 10 for SSW, and on day 0 for VI. Therefore we examined the time evolution of eddy and nonconservative forcings for SSW and VI from day −10 to day 10. Potential meridional circulations were also evaluated using a quasi-geostrophic model on the sphere and applying respective forcing. Figure 10 depicts the time evolution of the mechanical forcing and diabatic heating. Here we present only dominant forcings in the tropical upper troposphere as representative. It can be seen that prominent wavy structure for the mechanical forcing appear around the tropopause in the NH from day −10 to day 10 for both SSW and VI, which should be associated with the horizontal propagation of the E-P flux depicted in Figures 2 and 3. The effect of potential meridional circulation induced by these waves is therefore a possible source of convective activity in the tropics. The bottom panels in Figure 10 depict mass stream functions calculated from all eddy and nonconservative forcings. It can be seen that overall observed meridional circulations (middle of Figures 2 and 3) are well simulated by the model. To examine the role of eddy forcings in the tropics on the formation of the tropical cell, we compared potential vertical winds from waves and diabatic heating in the tropics.
Figure 11 compares the time evolutions of potential vertical winds of two regions (5°N to 15°N and 15°S to 5°S) from eddy forcings and diabatic heating at the 300 hPa level for SSW (left) and VI (right). Winds at 300 hPa and diabatic heating averaged from 850 hPa to 200 hPa from reanalysis data are also presented for comparison. Here, potential vertical winds are calculated from 3-d running averaged forcings. It is observed that the time evolution of the diabatic heating is well-controlled by the potential vertical wind from eddy forcings for both SSW and VI for the region of 5°N to 15°N. In fact, potential vertical velocity from waves declines and becomes negative on day 0 for SSW. In association, diabatic heating also becomes smaller starting on day −4, becomes negative on day 0, and continues to decrease until day 8. Potential vertical velocity associated with diabatic heating indicates a similar variation, although decreasing begins to accelerate on day −2. Similarly, for VI, increased diabatic heating and potential vertical velocity from diabatic heating from day −12 corresponds with the increased potential vertical velocity from eddy forcings from day −12. For the region of 15°S to 5°S, potential vertical velocity from the eddy corresponds well with the diabatic heating for SSW, but not for VI. Comparison of SH and NH regions suggests that convective activity in the SH is much more influenced by that of its NH counterpart, and it is directly shown by the model (not shown). This will be because waves associated with SSW or VI propagate from NH and their influence becomes weaker in the SH. Potential vertical velocity is generally estimated to be smaller than that in the reanalysis, but the time evolutions are qualitatively well estimated. The present analysis supports the hypothesis that eddy forcings from a horizontally propagating wave trigger the creation of the tropical cell.
 The present analysis indicates that SSW and VI have significant effects on the tropospheric climate from the Arctic pole to the tropical SH. The polar SLP signal changes from a positive to a negative AO-like pattern with the occurrence of SSW, and from a negative to a positive AO-like pattern with VI. In particular, 10 to 20 d after the occurrence of SSW or VI, a stable AO-like signal appears at the surface and lasts 20 to 30 d, accompanying the meridional flow at the surface with the barotropic vertical flow in the troposphere. They are very similar between SSW and VI except for the sign. The creation of such a surface signal is associated with the formation of the Eulerian meridional circulation driven by the eddy forcings, frictional forcing, and diabatic heating. In the tropics, the meridional circulation is found to be formed through diabatic heating from convective activities. Such meridional circulation and diabatic heating are suggested to be triggered by waves that propagate in the tropopause from the high latitude associated with SSW and VI.
 Analysis reveals that an AO-like pattern after the occurrence of SSW and VI is sustained by the eddy forcings in the polar troposphere and stratosphere. It is clear that the eddy forcings corresponds well with the reduced (enhanced) upward propagation of the E-P flux after the occurrence of SSW (VI). The reduced upward propagation of the E-P flux after SSW should correspond with the downward propagation of the anomalous easterly wind to the surface, which should reduce interaction with the surface and generate waves with small amplitude at the surface. Note that downward propagation of the zonal wind in the stratosphere is created by the wave-mean flow interaction, but in the troposphere it is created through meridional circulation that extends to the surface [Kuroda and Kodera, 2004].
 Evaluation of the potential vertical velocity of eddy forcings in the tropics confirms that they come mostly from the troposphere. In fact, eddy forcings below 150 hPa reproduces the result well. Both mechanical and thermal forcings contribute to the effects, though the contribution from mechanical forcing was generally a little larger. This result contrasts with the conjecture of Kodera  that vertical motion in the stratosphere have an important role.
 The analysis suggests that the effect of SSW and VI on the tropical troposphere comes from the wave propagation to the equatorial tropopause. SSW and VI in the stratosphere is produced by enhanced and reduced upward wave propagation into the stratosphere. However, the upward propagating planetary wave has a tendency to separate from the wave that propagates to the equator around the subtropical jet. So if wave generation at high latitude is enhanced, equatorward propagation of planetary wave will also be enhanced and work as a trigger for the formation of the tropical cell. This phenomenon was confirmed by dividing waves into planetary and synoptic waves. Analysis of a shorter timescale reveals that enhanced/reduced horizontal propagation of the E-P flux occurs about 5 to 10 d prior to the vertical enhanced/reduced propagation both for SSW and VI. Such a time lag is important for explaining the shift time of tropical cells for VI, although the reason why that of SSW takes place so late is not clear. Wave forcings from such a wave produce a tropical cell of reversed polarity compared with the one that is created after the key day for SSW, but they produce a tropical cell of the same polarity for VI. The reason of such difference should be resolved in a future study.
 Eulerian mechanical and thermal forcings are proportional to the latitudinal gradient of meridional and vertical components of the E-P flux. Therefore if the E-P flux does not change for propagation in the meridional direction in the tropical area, no wavy structure of the mechanical and thermal forcings, which would be triggered to produce the tropical cell, would be created. Comparison of Figures 2 and 3 suggests that the interaction between the zonal winds is one important source to modulate such wave propagation. More study is needed to understand the origin of the tropical eddy forcings.
 Detailed wave analysis indicates that enhanced or reduced vertical propagation of the E-P flux for SSW or VI has a smaller peak prior to the main peak. In fact, a smaller peak exists 12 d prior to the main peak for SSW, and 22 d prior for VI. For SSW, such an enhancement of the wave propagation is related to the “preconditioning” [e.g., Labitzke, 1981]. For VI, it indicates an analogous phenomenon with the preconditioning, although the time lag is greater in the case. Thus symmetrical relationship exists between SSW and VI in this respect, too.
 We used a quasi-geostrophic model on the sphere to diagnose the meridional circulation forced by the eddy and nonconservative forcings. The use of such a model around the equator may be problematic because it assumes geostrophic balance for the meridional direction. To assess the appropriateness of such an assumption, we evaluated the left-hand-side of the second equation of (2) from reanalysis data and computed meridional circulations originating from such quantities. The result reveals that effects from violation of the balance-wind relation were very small even on the equator. In fact, a comparison of Figures 4 and 9 or Figures 2, 3, and 10, leads to the conclusion that the use of this model for the present diagnosis captures some truth even in the tropics. The difference between the present diagnosis and reanalysis will come mainly from nonlinear terms. Diagnosis with the use of a more precise model should be the subject of future work.
 We have mainly analyzed meridional circulations and vertical winds in the present study. However, such quantities, especially in the tropics, may include many model-driven quantities and thus may not represent the truth. To check this, we used NOAA-interpolated daily Outgoing Long-wave Radiation (OLR) data [Liebmann and Smith, 1996] as direct observational data. As the data became available only after June 1974, we compared the data for the same SSWs and VIs as were analyzed in the present study. Nineteen SSWs and twelve VIs were available. The time evolution of zonal mean vertical winds is very similar to that depicted in Figure 6, and it corresponds well with the OLR (not shown). Figure 12 compares the OLR anomalies and anomalous vertical winds at the 300-hPa level that corresponds with SSW and VI. The composite was calculated in the same way as in Figure 7. It should be noted that OLR is a radiative energy mainly from the cloud top, and anomalous negative OLR corresponds to higher convectivity and then larger upward velocities in the troposphere. It should also be noted that OLR tends to have negatively larger values in the Indian Ocean to the western tropical Pacific, due to higher convective activities. Comparison of OLR and vertical velocities indicated that their overall features are very similar. In fact, positive areas correspond well to the area of negative vertical velocities, and negative OLR areas correspond to the area of positive vertical velocities. It should also be noted that the overall tropical responses between SSW and VI are very similar except for the sign. The analyzed meridional circulations and vertical winds used in the present study thus have sufficiently good quality. Also, overall distributions of the vertical velocities are very similar to those obtained in Figure 7; therefore, the response of the tropics with SSW or with VI is not significantly dependent on the period used for the analysis. However, some potential discontinuities were observed in the NCEP/NCAR reanalyses of the late 1970s, when copious satellite data became available. It is thus possible that some of the highly derived fields, including the mass stream function before that period, did not have sufficiently high accuracy [Kistler et al., 2001].
 We examined the tropical reactions to SSW and VI but did not consider equatorial conditions to create SSW or VI in the present study. However, Limpasuvan et al.  noted that SSWs tend to occur more frequently in the El Niño winters, whereas VIs tend to occur in the La Niña winters. Such effects will be inevitably included in the tropics of our analysis. In fact, Figures 7 and 12 indicate that convective activity in the central to eastern equatorial Pacific was more active as the El Niño when SSW occurred, but less active as the La Niña when VI occurred. To remove the effect of this basic condition of El Niño or La Niña winters, we performed the same composite, except removing seasonal averages of anomalies from day −30 to day 60. The results for the time evolution of zonal mean vertical winds are very similar to those indicated in Figure 6 for both SSW and VI, except that significance becomes weaker for VI. Figure 13 illustrates anomalous vertical winds at 300 hPa calculated from 1974 to 2000, the same as those presented in Figure 12, except for the composite of departures from seasonal averages. Though signals of the central to eastern equatorial Pacific become weaker by this operation, prominent signals are still present for both SSW and VI, and they are similar to those in Figure 7 except for central to eastern equatorial Pacific. Similar results were obtained for the data from 1958 to 2000.
 We used all SSW and VI in the present analysis. However, there are many types of SSWs (e.g., vortex separation and vortex shift types). Different types of SSWs may have different effect on the troposphere. In fact, Nakagawa and Yamazaki  found that SSWs with vortex separation have more influence on the troposphere. Analysis based on characteristics of SSW or VI is left to future work.
 Climatologically, the convective activity attains its peak around 5°N and 10°S in winter. However, convection is more active in the SH during January and February, and in the NH until December and after March. It is hoped that the activity of SSW and VI on tropical convection will be affected by such climatology. Seasonal dependence of' the active latitude as well as its longitude for the convection should be examined in a future study.
5. Conclusion and Remarks
 The effect of stratospheric SSW and VI on the tropospheric climate is examined through the composite analysis of the observed daily data. It is found that the tropospheric climate is significantly changed from the polar area to the tropical area in association with SSW and VI. In the polar area, the effect appears for the formation of the AO-like pattern on the surface. The transition corresponds from the positive to the negative phase of the AO for SSW, and from the negative to the positive phase for VI. Such a structure is found to be sustained by the formation of the Eulerian meridional circulation forced by the eddy forcings in the polar troposphere and stratosphere. The effect extends to the tropical SH as well. In particular, the effect on the tropics is significant. It is found that tropical convection tends to be enhanced in the SH for SSW, and in the NH for VI after these events. Analysis indicates that the polar and subtropical effect is created through direct and indirect activity of the upward propagation of the planetary wave associated with SSW or VI. However, the effect on the tropics is caused by nonuniform meridional propagation of the planetary wave around the tropopause associated with the upward propagation of the planetary wave to the stratosphere. Once the wave triggers the meridional circulation in the tropics near the time of the key day, positive feedback between the convection and meridional circulation takes place and creates tropical circulation.
 Analyses also reveal that the effect of SSW and VI on the troposphere is almost the same except for the polarity. This result indicates that though SSW and VI are violent variation in the stratosphere, they can be regarded as relatively small perturbations on the mean tropospheric climate, and nonlinear processes that violated the symmetry are relatively small. In fact, diagnosis using the quasi-geostrophic model indicates that the effect of both SSW and VI on the troposphere is well described by this linear model.
 The author is grateful to J. M. Wallace and K. Kodera for their useful comments. He is also grateful to anonymous reviewers for critical comments. This work was supported in part by a Grant-in-Aid (16340144, 18204043, 19340135) for Science Research of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.