a. North Polar latitudes

Figure 1 shows the time series over four 11-yr solar cycles (1959–2001) of January–February (J–F) averaged NP temperature anomaly at 30 hPa from the ERA-40 dataset together with the equatorial wind anomaly at 44 hPa in December–January (D–J) of the same winter. This figure may be compared with the corresponding figure from the Berlin stratospheric analyses and equatorial rocketsonde dataset shown in Fig. 2a of G2001b. Both time series show semiregular ∼2-yr variations of alternating sign. There are occasional years in which the variation “skips” a year and the anomaly remains the same sign for two or more consecutive years, for example, 1964–65. The two signals are anticorrelated for several periods of time, for example, 1960–68, 1971–79, 1984–88, 1991–96, and 1999–2001 but are either unrelated or positively correlated during the intervening periods.

As noted by LvL88, Naito and Hirota (1997), and G2001b, the periods of anticorrelation tend to coincide with periods of solar minimum. This is confirmed by comparison of Fig. 1a with Fig. 1b, which shows the time series of 10.7-cm solar radio flux. This relationship is also highlighted in Figs. 1c and 1d, which show the same polar temperature data separated into QBO/E and QBO/W years and are plotted in a similar manner to LvL88 (see also G2001b, their Fig. 4). Generally, when only the QBO/W years are plotted, there is a positive correlation with the 11-yr variation in solar flux and vice versa in QBO/E years. However, Figs. 1c and 1d show that this is by no means always the case. The 11-yr SC and QBO influences are only two of several factors that influence the variability of SSWs. Other possible influences include planetary wave variations associated with ENSO and the inherent nonlinearity of the atmospheric flow. In addition, we note that using J–F-averaged polar temperatures is not necessarily the ideal indicator of SSWs since there is often a period following the warming when the vortex is reestablished and is anomalously cold, so averaging over several months can mask the real signal.

A standard Pearson's correlation of the two time series in Figs. 1c and 1d gave correlations of +0.34 in the QBO/W phase and −0.52 in the QBO/E phase. In order to compare with the correlations shown in Labitzke and van Loon (2000, their Fig. 7) the calculations were repeated for the period 1959–97 using February data only (instead of J–F). The correlation amplitudes increased to +0.59 and −0.51, respectively. Labitzke and van Loon (2000) show maps of correlations with values of the order of +0.7 and −0.1 for the QBO/W and QBO/E phase respectively. Their corresponding values for geopotential fields are +0.7 and −0.4, respectively. Hence, our results agree very well with Labitzke and van Loon (2000) both in terms of the sign of the correlations in each QBO phase and the comparable amplitudes of the correlations. Interestingly, our QBO/W correlations increased slightly, if a small time lag was introduced, so that the 10.7-cm solar flux led the polar temperatures by 4 months, for example, the February correlations then become +0.64 and −0.4, respectively.

b. QBO composites

Figure 2 shows composites of monthly averaged latitude–height cross sections of zonally averaged zonal wind anomalies from the 1979–2001 mean for the months October through April. We use only the data since 1979 because of the improvements to the upper atmosphere representation after that date due to satellite data assimilation. The years have been composited into QBO/E (7 yr) and QBO/W (9 yr) using the D–J-averaged equatorial winds at 44 hPa (approximately 24 km). Years when the amplitude was less than ±5 m s⁻¹ were excluded (see Fig. 1a). The QBO/E minus QBO/W differences are also shown (right-hand column) with shading indicating the 95% and 99% confidence levels. As expected, the equatorial regions are dominated by the QBO, with an anomaly maximum centred at 20–30 km and a second anomaly of opposite sign directly above it centred at 30–40 km. These anomalies descend slowly throughout the period as the phase of the QBO descends.

There is also a third anomaly directly above this, centred at 40–55 km. It has the same sign as the lower-stratospheric anomaly at 20–30 km and thus forms a region of three heightwise layers of alternating signs between 20 and 55 km (see also Pascoe et al. 2004). The amplitude of the third anomaly above 40 km is of the order ±5–10 m s⁻¹ and is significant at the 95% level. This threefold QBO structure can be explained in the following way. Height–time series of zonal winds at the equator indicates that the QBO signal extends upward to at least 50–60 km and the rate of descent of the QBO is slow enough that the next incoming phase is usually present at ∼50 km while an earlier phase of the same sign is still present at 20–30 km, thus forming a threefold structure in height (G2001b). Previous assumptions that the QBO had only a twofold structure over this height region (e.g., Baldwin et al. 2001) were based on analyses that were less accurate than the rocketsonde measurements examined by G2001b or the ERA-40 data shown in Fig. 2. We also note here that this third, upper-level anomaly is unlikely to be caused by anomalous horizontal advection of summer easterlies by the mean circulation associated with SSWs since it is already present in autumn/early winter before the SSWs develop.

At high latitudes, the anomalies in Fig. 2 are as expected from the Holton–Tan relationship. The QBO/E composite (left column) shows an easterly anomaly at high NH latitudes already present by November that gradually increases in magnitude through January. However, the differences between QBO/E and QBO/W composites (right column) are barely significant at the 75% confidence level except in early winter (November). Increasing the number of years of data by using the whole dataset (not shown) does not improve the statistical significance in this region.

c. Eleven-year solar cycle composites

Figure 3 shows monthly averaged latitude–height cross sections of zonally averaged zonal wind anomalies from the 1979–2001 mean for the months October through April. The years have been composited into S_max (11 yr) and S_min (9 yr) phases using the D–J-averaged 10.7-cm radio flux. Years in which the value fell within the range 105–145 (× 10⁻²²) W m⁻² Hz⁻¹ were defined as transition years and are excluded from the composites (see Fig. 1b). The S_min composite (left column) has an easterly anomaly above 50 km at the equator in October that moves poleward and downward reaching a maximum amplitude in January. This is evidence of a disturbed vortex in early to midwinter. The S_max composite has a similar anomaly but of the opposite sign. Hence, the S_max minus S_min difference plot (right column) has a strong positive region that moves poleward and downward with time, indicating a colder more stable vortex in S_max years. The confidence levels in December and January for this feature are greater than 95%. These results are very similar to those reported by Kodera et al. (2000).

In February and March, however, this situation is reversed. The S_min composite has a westerly anomaly at high latitudes, evidence of a strong stable vortex, while the S_max composite has an easterly anomaly. The pattern viewed as a whole throughout the winter suggests that S_min winters are characterized by early to midwinter warmings, while S_max winters are characterized by late-winter warmings.

a. Equatorial forcing

The aim of the first set of experiments was to test the sensitivity of the modeled NP temperature evolution to imposed equatorial easterlies at different heights. The control for this experiment was taken from Gray et al. (2003) in which the equatorial winds were relaxed toward 0 m s⁻¹ at all heights in the range 16–60 km. The evolution of the area-weighted temperature north of 62.5°N at 32 km of this control is shown in Fig. 4a. Since the initial conditions were from typical August distributions, the initial NH zonal flow was easterly. There is a rapid readjustment to the imposed perpetual January radiative conditions in the first 30–40 days with strong polar cooling and the onset of a westerly vortex. A large disturbance is apparent in all ensemble members between days 50 and 90, as evident from the rise and fall of polar temperatures during this period. After day 90 approximately half of the ensemble members proceed to develop a stratospheric warming, peaking at various times between days 170 and 230, while half continue to cool and remain relatively undisturbed throughout the rest of the integration. Thus there is a large degree of variability in this control experiment.

Five sensitivity experiments were then carried out, prompted by the pancakelike structure of the QBO composite anomalies in Fig. 2. The target equatorial wind height profile was modified so that the target equatorial winds were −20 m s⁻¹ in a specified 10-km height region while the remainder of the target profile was kept at 0 m s⁻¹. The transition between −20 and 0 m s⁻¹ at the top and bottom of the 10-km region was carried out smoothly over several grid boxes so that the height region of easterlies actually extends to ∼14 km. The specified 10-km height regions for the five experiments were 20–30, 25–35, 30–40, 35–45, and 40–50 km. We denote these as E20–30, E25–35, E30–40, E35–45, and E40– 50, respectively. This experiment is similar in nature to the experiment described by Gray (2003) in which the equatorial atmosphere was divided rather more crudely into a lower stratosphere (20–40 km) and an upper stratosphere (40–60 km).

Figures 4b–f show the resulting NP temperature evolution from each of the experiments. It is immediately apparent that an imposed easterly band at any height serves to make the winter evolution more disturbed since every ensemble member of every experiment now displays a warming at some stage during the integration, compared with the control experiment in which only about half were disturbed. This result is in good agreement with the theory proposed by Holton and Tan (1982) that equatorial easterlies confine the propagation of planetary waves to high latitudes and result in a more disturbed vortex.

b. Lower versus middle stratosphere

We now consider in more detail the results of each separate experiment. With imposed equatorial easterlies at 20–30 km (E20–30) all of the ensemble members are disturbed, with some peaking earlier than in the control run, at around day 130, while others peak at the same time as in the control, at around day 170–200. When the imposed band of easterlies is raised to 25–35 km (E25–35), the SSWs tend to occur even earlier, with most members now achieving a warming by day 130 and the variability between ensemble members is reduced. As a measure of comparison between the experiments, we note that, in E20–30, 7 of the 20 ensemblers members peaked by day 130 while, in E25–35, 13 of the 20 peaked by day 130.

When the imposed band of easterlies is moved up to 30–40 km (E30–40), two interesting features are apparent. First, the variability is reduced substantially, with almost all of the members following a very similar evolution for at least 200 days. Second, the SSWs occur consistently later than in the previous two experiments, peaking at around day 170. Because of this delay, none of the E30–40 ensemble members peak by day 130.

To further explore this interesting behavior, we show in Fig. 5 a comparison of the Eliassen–Palm (E–P) diagnostics from E25–35 and E30–40 at selected times during the experiment. Because of the relatively small variability between ensemble members in these two experiments, the E–P flux diagnostics are presented as ensemble averages so that an estimate of statistical significance can be achieved. The zero-wind line is also shown as an aid to interpretation. The patterns of the E–P flux divergences from the two experiments are very similar until around day 60–70 when significant differences of a few meters per square second are evident, centered around 45°N, 50 km. By days 90–100 and 100– 110, just preceding the SSWs at day 130 in E25–35, these differences are accentuated.

Finally, at days 120–130 at the peak of the SSWs in E25–35 the zero-wind line in the Tropics extends toward midlatitudes and a zero-wind line is also present at upper levels over the pole in E25–35, as the winter vortex reverses in sign and becomes easterly. This latter zero-wind line penetrates downward over the next 10–20 days as the warming reaches its mature stage. In contrast, E30– 40 shows a similar evolution but delayed by 30–40 days. We note that, while the position of the zero-wind line in the tropical region clearly shows the different imposed equatorial distributions, these differences are really rather small, especially in the subtropics, and neither the E–P flux diagnostics nor the position of the zero-wind line in the lower equatorial/subtropical winter stratosphere provides an obvious explanation for the 30–40-day delay in evolution of the SSWs in E30–40.

In Fig. 6 the evolutions of the polar temperatures at different heights are shown for E25–35 and E30–40. For this comparison, we show results from a single typical ensemble member from each experiment. At 50 km the evolution is similar in the two experiments with rising temperatures from around day 15 when the flow has become sufficiently westerly for the first planetary waves to propagate. This rise in temperature is also seen at the lower levels but at a later time. There are many similarities in the detailed behavior of the two experiments during the lead up to the first warming event except that the events in E30–40 occur slightly later and then evolve, more slowly. One very interesting feature is that although the SSWs in E30–40 take longer to evolve, the actual temperatures achieved at 24 km are 7°–8° warmer at the peak of the warming (223 K at day 175) compared with E25–35 (215 K at day 140). This difference, which is an indication of the extent to which the lower-level vortex has been disrupted, may have important implications for stratospheric influence on the tropospheric circulation below.

In Fig. 7, we further explore the temperature evolution at 44 km by showing the evolution at all latitudes between the equator and the pole. Again, while the overall evolution is rather similar in the two experiments, there are interesting differences. At the equator/subtropics the temperature gradient in E30–40 is greater, an indication that the region of imposed equatorial easterly winds is just below the 44-km level and this level is in a region of positive vertical wind shear as the equatorial wind profile changes from −20 m s⁻¹ at 40 km to 0 m s⁻¹ by around 48 km (see position of the zero-wind line in Fig. 5). In contrast, E25–35 has virtually no temperature gradient between the equator and 20°N since the region of imposed easterlies is well below 44 km in this experiment and there is no equatorial vertical wind shear present. At higher latitudes there are a number of fairly regular small-scale fluctuations, especially in E30–40 between 30° and 80°N from around day 90 to 100. These disturbances were noted by Scaife and James (2000) and Gray et al. (2003) to be an indication of the presence of small anticyclones resulting from the incursion of a tongue of equatorial [low potential vorticity (PV)] air into the subtropics that are then advected around the edge of the vortex and merge with the Aleutian high [see also earlier studies of these anticyclones by O'Neill and Pope (1988) and Harvey et al. (1999)]. These fluctuations are also present in E25– 35 except that at around day 100 there is one large fluctuation that leads to much higher temperatures, forming the start of the warming.

In summary, the earlier onset of the warming in E25– 35 appears to be a result of a single effective event at around day 100, while E30–40 exhibits three to four smaller events between days 95 and 115 before it, too, achieves a dramatic rise in temperatures to form the warming. Examination of the corresponding latitudinal temperature evolutions at lower heights (not shown) also indicates that a similar behavior occurs there, with E30– 40 exhibiting small-scale fluctuations for a longer time before the sudden warming eventually occurs.

c. Lower versus upper stratosphere

As the region of imposed easterlies is moved higher from E30–40 through E35–45 to E40–50 (Fig. 4), the timing of the SSWs becomes more variable and they occur earlier. Indeed, the same proportion of the ensemble achieves a warming by day 130 in E40–50 as in E25–35 and several of the SSWs in E40–50 peak as much as 30 days earlier than in E25–35. This result is consistent with the study of Gray (2003) and related earlier work that found a marked sensitivity of the timing of sudden SSWs to the equatorial winds in the upper stratosphere.

Rather than proceed immediately to a full analysis and comparison of these latter results, which would necessitate the analysis of just a single ensemble member because of the variability in timing of the SSWs in E40– 50, we choose to proceed to the next set of (subtropical) experiments since they are very similar in nature and allow improved estimates of statistical significance.

d. Summary of equatorial forcing experiments

In summary, we have shown that the presence of easterlies at the equator at any height will result in a more disturbed vortex. However, the timing of the resulting SSWs is sensitive to the height of those easterlies. Easterlies in the lower equatorial stratosphere (20–30 km, 25–35 km) tend to speed up the onset of SSWs. Easterlies in the mid equatorial stratosphere (30– 40 km) tend to slow down the onset of SSWs. Easterlies in the upper equatorial stratosphere (35–45 km, 40–50 km) tend to speed up the onset of SSWs. It is not clear how such a small difference in the height range of imposed easterlies at the equator influences the timing of the warming. A full PV budget study of the developing SSWs might help to identify the mechanism of this influence, but is beyond the scope of this study.

e. Subtropical forcing

Leading on from the apparent sensitivity of the polar flow to imposed easterlies in the upper equatorial stratosphere, a similar experiment was conducted but this time relaxing toward 20 m s⁻¹ easterlies in the NH subtropical upper stratosphere instead of the equatorial upper stratosphere. This “subtropical forcing” experiment was prompted by Fig. 3 and previous work, for example, by Kodera et al. (2000), in which an easterly anomaly in S_min is observed to develop in the northern subtropics near the stratospause level in early winter (see November/December, left column in Fig. 3), which then moves poleward and downward as the Aleutian high develops and forces a polar warming event.

In this experiment, which we denote S40–50, an identical zonal-wind relaxation method toward a target wind profile was employed except that the central latitude of the relaxation forcing was at 12.5°N instead of the equator. The easterly forcing therefore extended over the approximate latitude range 0°–30°N. The relaxation was applied only in the height region 40–50 km, and the target winds were −20 m s⁻¹. This forcing was applied only for the first 60 days of the integration to ensure that the forcing did not interfere with the evolution of the sudden warming. Once the warming commences and the vortex evolves toward the characteristic “comma” shape, a substantial tongue of westerlies extends out into the subtropics and any easterly forcing at this stage would therefore interfere with the evolution of the warming itself.

As a “control” for this experiment we used a 20-member ensemble of integrations in which no imposed forcing has been applied anywhere. The zonally averaged zonal-wind fields at day 10 are shown in Fig. 8 from a typical ensemble member from the control and S40–50 experiment to illustrate the effect of the imposed subtropical forcing in S40–50. As with all models with no artificial forcing at the equator (e.g., via our equatorial relaxation method or via a gravity wave drag parameterization scheme), the equatorial regions in the control experiment are easterly everywhere, apart from a small region in the very lowest stratosphere where it takes slightly longer to move away from the initial westerly conditions because the radiative relaxation time is long there. The main effect of the imposed subtropical easterly forcing (see Fig. 8a) is above 40 km: the developing westerly NH polar jet is confined poleward of 30°N instead of spreading across the subtropics into equatorial latitudes. We note that the S40–50 vortex is similar to the “preconditioned” state, long identified as being a precursor to stratospheric warmings, in which the core of the jet becomes more upright and strengthens slightly.

The polar temperature evolution at 32 km of S40–50 and its control experiment is shown in Fig. 9. The control ensemble displays substantial variability, although all members achieve a warming event by day 200, as one would expect knowing that the equatorial winds are weakly easterly at nearly all heights. The S40–50 distribution is quite different. It shows remarkably little variability, with a very early SSW in all ensemble members, peaking by day 100 and in some cases by day 85. If this is compared with the similar equatorial forcing experiment in Fig. 4f, it may be seen that easterly forcing in the subtropics of the upper stratosphere is even more effective at forcing a consistently early SSW than when the easterly forcing is at the equator. This early establishment of the SSWs in S40–50 is seen in Fig. 10, which shows the 1650 K PV distributions at day 50 from a typical S40–50 ensemble member, compared with the corresponding control integration. The S40–50 distribution shows a very well established Aleutian high by day 50 whereas the corresponding control integration has only a weak feature. It is not difficult to understand these differences since the easterly forcing at 0°–30°N in S40–50 is in precisely the latitudinal region to reinforce the anticyclonicity of the Aleutian high and also the travelling anticyclones that are advected around the edge of the vortex and merge with the Aleutian high (see Fig. 10a).

In Fig. 11 we show the E–P flux diagnostics from S40–50 at various stages leading up to the warming. (Note that the scaling of the E–P flux vectors at days 20–30 and 30–40 has been increased for clarity). The main feature at days 20–30 and 30–40 is the dipole structure in E–P flux divergence centred around 25°– 45°N, 50 km. This region coincides with strong horizontal shear in the zonal wind field (see Fig. 8) and indicates horizontal shear instability. Examination of the PV (q) distribution in S40–50 at day 50 in Fig. 10 suggests the presence of a region of negative q_y in the vicinity of 30°N and this is confirmed in Fig. 12, which shows the PV cross sections (scaled as in Polvani and Saravanan 2000) on day 20, corresponding to approximately the same time as the E–P flux diagnostics in Fig. 11 (top). Note the minimum in q near 40°N and hence negative q_y in the latitude range 25°–40°N and positive q_y poleward of this. The dipole structure in the S40–50 E–P flux divergence in Fig. 11 at days 20–40 reflects this change in q_y. We note also that the zero-wind line is embedded within the region of negative q_y.

The region of EP flux divergence near 30°N, 50 km indicates that wave activity is being focused (overreflected) back into higher latitudes. This is an almost identical situation to that discussed by O'Neill and Pope (1988, their Fig. 5). More wave activity returns to high latitudes than leaves it [for further discussion of this behavior see Lindzen and Tung (1978), Killworth and McIntyre (1985), Haynes (1985), and Robinson (1986)]. In our experiment, the critical layer in the region of 30°–40°N appears to act as a reflector in the early stages of the integration (days 20–40). From around day 40, it becomes more strongly absorbing and the evolution of the E–P flux diagnostics leading up to the warming event become more typical. These diagnostics show that the easterly forcing in the subtropics in the early stages of this experiment has helped to speed up the evolution of the SSWs.

a. ERA-40 analysis: Solar cycle/QBO composites

We may check the predictions in Table 1 using the ERA-40 dataset. Figure 13 shows composites of monthly averaged latitude–height cross sections of zonally averaged zonal-wind anomalies from the 1958/59– 2000/01 mean for the months October through April. The composites have been compiled on the basis of both the 11-yr solar cycle phase and the QBO phase, giving four plots: S_min/E (7 yr), S_min/W (8 yr), S_max/E (8 yr), S_max/W (8 yr). The criteria employed for defining the QBO and SC phase were as described in section 2. We have used data from all the available years in order to maximize the number of years in each composite. This means that distributions below 10 hPa (∼32 km) are reliable, but above this level there were very few assimilated observations pre-1979 and these must therefore be treated with caution.

The equatorial/subtropical NH anomalies above 40 km in Fig. 13 show a distinct pattern that partially agrees with the predictions summarized in Table 1. In S_min/E and S_max/W there are indeed easterly and westerly anomalies, respectively, in this region and most are statistically significant at the 75% level or higher. However, there is little evidence that they are larger in amplitude than in the S_min/W or S_max/E years, so we do not see a clear signature of the signals reinforcing or canceling out. This is perhaps not surprising, given the paucity of observations that have contributed to the dataset above 32 km. An examination of the corresponding composites using only data since 1979 (not shown), when more satellite data became available, supports the predicted reinforcement/cancelation of anomalies more convincingly, but there are so few years in each composite (average of only 3 yr in each) that the statistical significance of the results is very low.

At NH polar latitudes there are substantial variations in Fig. 13 between the composites. The timing of the NH warmings, indicated by an easterly anomaly at high NH latitudes, is described in this section and the results are summarized in Table 2. In the S_min/E composite (first column) an easterly anomaly builds up at high latitudes in December, reaching maximum amplitude in January, and then moves downwards and weakens in February. In the S_max/E composite (third column) there is an easterly anomaly at high latitudes in December, similar to the anomaly in the S_min/E composite, but this is not perpetuated into the following months. Thus, in both QBO/E composites the early winter is relatively disturbed. This can be compared with, for example, December in the two QBO/W composites (second and fourth columns), both of which have a westerly anomaly at the NP, indicating a stronger, less-disturbed vortex than average. This difference in the early winter behavior between the QBO/E and QBO/W composites is in good agreement with the Holton–Tan relationship. However, this east–west difference is only present in early winter (November/December) and does not continue into midwinter, suggesting that the influence of the QBO is greatest in early winter. Using the same model, Gray (2003) found similar results, that the direction of the equatorial wind in the lower stratosphere influenced the early winter evolution but the equatorial upper stratosphere was more influential in mid- to late winter, in agreement with previous studies (e.g., Labitzke 1987; LvL88; Dunkerton and Baldwin 1992; Naito and Hirota 1997). There are two to three protracted migration events per year for the subtropical westerly jet. Poleward/downward migration by wave–mean flow interaction takes a fairly long time, consistent with the idea that the first event may be more affected by certain regions while the second or third, later in the winter, may be affected more by other regions and circumstances. There is also an increase in tropospheric wave forcing as the winter proceeds, which may be another influencing factor.

In the S_min/W composite (fourth column), the NH vortex is anomalously strong throughout the whole winter and an easterly anomaly does not appear until April, the time of the final warming. The S_max/W composite (second column) has a rather different pattern, however. Although the early winter is similarly quiet, in accordance with the Holton–Tan relationship since both are in westerly QBO phases, an easterly anomaly develops in February and moves poleward and downward by March, indicating midwinter warming events in S_max/W years despite the lack of a strong waveguide in the equatorial lower stratosphere. Thus, if one compares all of the December distributions, we see that the polar easterly anomalies are in S_min/E and S_max/E, as expected from the Holton–Tan relationship, but in February they are found in S_min/E and S_max/W. Hence a comparison of the two S_max composites in February shows a reversal of the Holton–Tan relationship. It is this feature of the SC– QBO interaction that has been most puzzling. However, we note that this feature is barely statistically significant at the 75% level. It may therefore be more accurate to say that the Holton–Tan relationship has been disrupted rather than reversed, at least until more data are available to improve statistical significance.

In Fig. 14 we show the daily time series of NP temperature at 50 hPa for each NH winter, again grouped into SC–QBO composites as described above. These plots not only show the day-to-day variations that are masked by the monthly averages but also provide information on the variability within each of the composites. The major features already noted in the monthly averaged plots of Fig. 13 are confirmed in Fig. 14 (see Table 2). In early winter (November–December), the most disturbed, and most variable, composites are the two QBO/E phase composites. In midwinter however (January–March), the two composites showing most disturbances in midwinter are the S_min/E and S_max/W composites. The disturbed nature of the S_max/W composite thus supports earlier evidence that the Holton– Tan relationship is disrupted in S_max years.

b. A speculative mechanism

We propose that the development of SSWs is sensitive to relatively small wind anomalies near the equatorial/ subtropical stratopause region, especially in mid- to late winter when the flow is highly nonlinear. We note that this altitude sensitivity near the tropical stratopause occurs where a meridional jet exists from inertial instability, as part of the semiannual oscillation (Hitchman and Leovy 1986), and the trajectory of planetary wave activity in latitude/altitude is such that the waves tend to focus on the tropical stratopause region [see Gray et al. (2003) and references therein]. Specifically, we propose that an easterly anomaly in this region helps to establish the Aleutian high, which then speeds up the onset of the SSW, while a westerly anomaly slows it down. In this way, the superposition of easterly anomalies associated with S_min conditions and QBO/E conditions results in SSWs in S_min/E years that are consistently earlier than average. Similarly, westerly anomalies associated with S_max conditions and QBO/W years superpose in S_max/W years and result in SSWs that are consistently later than average. In the other combinations that is, S_min/W and S_max/E the anomalies associated with the SC and QBO are of opposite sign and partially cancel, so there is no consistent speeding up or slowing down of the SSW in those years and hence no signal of SC–QBO interaction emerges.

Our results and those from earlier model experiments (Gray 2003) suggest that in early winter the influence of the lower-stratospheric equatorial winds proposed by Holton and Tan (1980, 1982) is strongest so that the polar vortex in early winter is more disturbed in QBO/E phase years. This is reflected in Table 2 with peak easterly anomalies in December of the QBO/E years, indicating a weakened vortex, and no corresponding signature in the QBO/W years. Later in the winter, however, when the flow is more highly nonlinear, the results suggest a greater influence from the equatorial and subtropical upper stratosphere, the region where both QBO and the 11-yr SC have zonal wind anomalies. In S_min/E both QBO and SC influences produce an easterly anomaly in that region and they will combine to produce a relatively strong easterly anomaly (see Table 1). The model results suggest that this will tend to speed up the onset of the SSWs. This is confirmed by the observations (Table 2) that indicate a consistently disturbed vortex in January. Similarly, in S_max/W years both QBO and SC influences produce a westerly anomaly in the upper equatorial stratosphere and these will reinforce each other and slow down the evolution of the SSWs. This is confirmed in Table 2, which indicates a consistently disturbed vortex in February, approximately 1 month later than in the S_min/E years. We note here that just because the onset of the SSWs is slowed down, this does not mean that the SSWs will not occur, provided there is time before the end of winter. Thus, in S_min/E and S_max/W years there will be a consistent pattern of early and late SSWs, respectively.

However, in S_min/W and S_max/E years the SC and QBO anomalies above 40 km are likely to partially cancel each other. Thus, there will be only a very weak influence on the SSW evolution from the upper equatorial stratosphere. In those years, with no strong guide from that region, the timing of the SSWs will not reflect any particular tendency toward either early or late SSWs; the SSWs will occur at any time throughout the winter and, when averaged together to form the composites, there will be no consistent pattern emerging, that is, no strong anomalies in any particular month. This again is confirmed in Table 2, since the main anomaly in both of those composites is in March/April at the time of the final warming.

Further research is required in order to fully test this proposed mechanism for SC–QBO influence on the NH polar vortex. One of the main problems is the short period of available data. This is crucial when compositing both on the basis of the 11-yr SC and the QBO. Statistical significance is therefore not high, and it may be many years before this is achieved. Nevertheless, we believe that a working hypothesis such as this may still be helpful. We also note the idealized nature of the model experiments, in terms of the model employed, the nature of the imposed forcing, and the lack of seasonality in the model runs. Although the recent GCM simulations of the SC–QBO interaction of Matthes et al. (2004) are encouraging and suggest that this mechanism is active, further GCM experiments would be useful.