This study investigated the Holton-Tan relationship between the equatorial quasi-biennial oscillation (QBO) and the polar vortex as seen in the ERA-40 reanalysis and ERA-interim analysis (1980–2004, 25 years) data sets and in ensemble simulated data sets (five members covering the period 1980–2004, 125 years) by using the Meteorological Research Institute chemistry climate model (MRI-CCM) and focusing on the Northern Hemisphere winter. The primary tools employed were composite differences in zonal wind, temperature, and Eliassen-Palm (EP) fluxes. Although not many global circulation models can simulate the QBO realistically, the MRI-CCM, which includes the interaction between QBO dynamics and the ozone (hence heating) distribution, reproduces a self-generated QBO that is fairly realistic. In agreement with the finding of previous studies, our results revealed that the conventional Holton-Tan explanation that the equatorial winds in the lower stratosphere act as a waveguide for midlatitude planetary wave propagation cannot explain the winter circulation in either the ERA-40 data or the simulation. Although the composite differences in zonal wind and temperature show a slight yet statistically significant Holton-Tan effect, i.e., the stratospheric polar vortex is weaker and more disturbed under easterly QBO conditions, the EP flux diagnostics do not show more poleward propagation in the midlatitude stratosphere. Rather, planetary waves propagate more equatorward as well as more upward during the easterly phase of the QBO.
 The quasi-biennial oscillation (QBO), the alternating downward propagation of easterly and westerly winds with a variable period averaging 28 months, dominates the variability of the equatorial stratosphere (16 to 50 km) [e.g., Baldwin et al., 2001]. The QBO mechanism was first described by Lindzen and Holton , who showed that upward–propagating gravity waves can drive the QBO in zonal winds observed in the tropical stratosphere. Afterward, Holton and Lindzen  refined the work of Lindzen and Holton  and demonstrated that the QBO is driven by equatorial Kelvin waves and Rossby-gravity waves. More than 20 years later, it was demonstrated that Kelvin and Rossby-gravity wave momentum fluxes alone are not sufficient to account for the observed zonal accelerations of the QBO and that additional momentum flux must be supplied by a broad spectrum of gravity waves [Dunkerton, 1997; Sato and Dunkerton, 1997], similar to those initially postulated by Lindzen and Holton .
 Using observational data, Holton and Tan [1980, 1982] showed that when the equatorial QBO in the lower stratosphere is in its easterly phase, the stratospheric polar vortex is weaker, warmer, and more disturbed. They suggested that the QBO phase in the tropics modulates the strength of the effectiveness of the waveguide for the midlatitude planetary waves that propagate through the winter stratosphere. Such equatorial QBO influences on the extratropical atmosphere are commonly known as the Holton-Tan relationship, and these influences have been investigated by many statistical studies [e.g., Labitzke, 1982; Naito and Hirota, 1997; Lu et al., 2008]. For example, by using both the Berlin data and the National Meteorological Center data set in the 37 years between 1958 and 1994, Naito and Hirota  found that the Holton-Tan relationship is statistically significant only for the years 1962–1977. The relationship holds in general during 1958–2006 (47 years) in the ERA-40 and European Centre for Medium Range Weather Forecast operational combined data, but it was not stationary over that period, and the QBO signals were substantially weakened in the Northern Hemisphere (NH) stratosphere during 1977–1997 [Lu et al., 2008].
 Recently, Gray and coworkers [Gray et al., 2001a, 2001b; Gray, 2003; Gray et al., 2004] reported evidence that the equatorial upper stratosphere influences the NH winter stratospheric circulation. Indeed, they explicitly noted that planetary waves are very deep structures that encompass the whole depth of the stratosphere, so that it is unlikely that only the lower stratospheric QBO should be important. These effects involve extratropical planetary Rossby wave interaction with the QBO phase, causing different effects in different latitudinal ranges and at different altitudes. The extratropical stratosphere is also influenced by solar signals in the NH winter extratropics, but those signals are also QBO-phase dependent, moving poleward and downward as winter progresses [Lu et al., 2009].
 Part of the difficulty in identifying an extratropical QBO signal in the northern winter is that the QBO signal accounts for only a fraction of the variance. Various forcings (e.g., sea-surface temperature (SST) anomalies, the 11 year solar cycle, and volcanic eruptions) also appear to influence the variation in the extratropical stratosphere [Baldwin et al., 2001]. The QBO modulation of the polar stratosphere is weaker during El Niño events than during La Niña events [Wei et al., 2007]. Hence, the relation between the equatorial QBO and the extratropical circulation is not necessarily stable but depends on the time period.
 Modeling studies using general circulation models (GCMs) have attempted to simulate the QBO. Takahashi  first simulated QBO-like oscillations with a 1.5 year period by using a GCM with a spectral truncation of T21 and 60 vertical layers in which a vertical resolution in the upper troposphere and lower stratosphere is 500 m and the reduced horizontal diffusion is used there. A QBO-like oscillation with a period about half that of the QBO was also produced by Hamilton et al.  using 160-vertical-level Geophysical Fluid Dynamical Laboratory GCM with a vertical resolution of 400 m in the lower stratosphere. Watanabe et al.  studied atmospheric gravity waves with a T213 and 256-vertical-level GCM, to which gravity wave drag parameterizations were not supplied but were instead generated by convection, topography, instability, and adjustment processes. The model simulated a spontaneous QBO-like oscillation with a period of 15 months, much shorter than the observed period. These results suggest that even with high-resolution models, it is difficult to simulate a QBO realistically.
 Much of the required wave forcing for the QBO oscillation is generated by Kelvin waves, Rossby-gravity waves, and gravity waves. Because gravity waves are difficult to effectively resolve by a GCM, many GCMs have failed to reproduce the QBO. Thus, the interaction between the large-scale waves and the mean flow must be simulated explicitly for the resolved wave spectrum and implicitly by parameterization for the unresolved spectrum in order to simulate the QBO [Giorgetta et al., 2006]. When unresolved gravity waves are parameterized by employing a nonorographic gravity wave drag scheme, the simulations can be improved such that a realistic QBO with a two year to three year period in the lower stratosphere is generated [Scaife et al., 2000; Giorgetta et al., 2002; Shibata and Deushi, 2005a]. Parameterized gravity wave forcings produce a net force in the shear region, leading to a descent of wind maxima so that the modeled winds oscillate as alternate phases descend through the stratosphere.
 Only a few chemistry climate models (CCMs) based on such GCMs that can simulate a self-generated QBO realistically have been developed so far [Butchart et al., 2003; Shibata and Deushi, 2005a, 2005b; Schmidt et al., 2006]. Moreover, because these GCMs have not included the interaction between QBO dynamics and the ozone (hence heating) distribution, dynamics-ozone feedback may influence the relevance of the QBO simulation.
 In the present study, we aimed to identify the modulation of the extratropical circulation by the equatorial QBO (i.e., the Holton-Tan relationship) by using the Meteorological Research Institute CCM (MRI-CCM), which includes full stratospheric chemistries and employs the Hines nonorographic gravity wave drag scheme [Shibata and Deushi, 2005a, 2005b]. Naito and Yoden  analyzed the Holton-Tan relationship by using daily National Centers for Environment Prediction/National Center for Atmospheric Research reanalysis data and showed statistically significant differences between the westerly and easterly phases of the QBO, demonstrating that it is preferable to use daily data rather than monthly data to increase the sample size.
 In this study, we applied the analysis method of Naito and Yoden  to both an observational reanalysis data set (1980–2004, 25 years) and MRI-CCM data (1980–2004, 25 years by five members = 125 years) for the winter season in order to identify the Holton-Tan relationship, with the expectation that long-term simulated data would increase the confidence level of the results. Thus, we investigated the influence of the equatorial QBO on the extratropical circulation by using statistical methods and focusing on the NH winter.
Section 2 describes the reanalysis data and simulated data used in this study. Section 3 presents both the observation and simulation results for the equatorial QBO influence on NH winter circulation. Section 4 discusses the traditional Holton-Tan explanation. The final section presents our conclusions.
2.1. Observational Data
 The observational data sets used are based on daily and monthly ERA-40 reanalysis [Uppala et al., 2005] data for September 1957 to August 2002 and the ERA-interim reanalysis data (http://www.ecmwf.int/research/era/do/get/era-interim) for September 2002 to December 2004. The period analyzed in this study was the 25 years from 1980 through 2004, which is the same as the model-simulation period. The zonal-mean zonal wind U and the zonal-mean temperature T data were analyzed for the northern winter months (December, January, and February). Since the satellite observations began after 1979, the ERA-40 analyzed temperatures in the stratosphere may give unreliable estimates before the satellite era [Pascoe et al., 2005].
 We defined the QBO on the basis of the monthly mean zonal wind U at 50 hPa over the equator for each winter month, for consistency with Holton and Tan  and other studies [e.g., Lu et al., 2008]. In this study, we defined the westerly and easterly phases of the QBO as a monthly U ≥ 1 m s–1 and a monthly U ≤ –1 m s–1 at 50 hPa over the equator, respectively. As also reported by Lu et al. , we found that choosing other threshold values within the range ±0–3 m s–1 gave similar outcomes. Transitional periods when the absolute values of the QBO wind were smaller than 1 m s–1 were excluded from the analysis. For the period 1980–2004, 45 (26) months were classified as the westerly (easterly) phase of the QBO in the ERA-40 data set, and 204 (130) months were classified as the westerly (easterly) phase of the QBO in the five ensemble members of the simulation (125 years).
2.2. Basic Description of Model and Integration
 The dynamics module of the GCM includes the major physical processes (i.e., convection, radiation, planetary boundary layer, and ground hydrology with biosphere). The model has a T42 and 68-vertical-layer resolution in the eta-pressure coordinate with a lid at 0.01 hPa (∼80 km). The vertical resolution in the stratosphere is approximately 500 m between 100 and 10 hPa, above which the resolution gradually coarsens to 4 km at 0.5 hPa. Horizontal diffusion is weakened to become about one tenth of the standard value above 100 hPa but is left unchanged below 150 hPa in order to keep the effect of the horizontal diffusion on the QBO temporal and the spatial structure as low as possible; thus, the e-folding time of biharmonic diffusion is set at 100 h at a total wave number of 42.
 The nonorographic gravity wave drag scheme of Hines , which is introduced as nonresolved forcing, has crucial effects on the QBO simulation [Scaife et al., 2000; Giorgetta et al., 2002; Shibata and Deushi, 2005a]. Its source strength (root-mean-square wind perturbation) is enhanced symmetrically, with respect to latitude between 30°S and 30°N, by superimposing a Gaussian-function source (0.7 m s–1) on the isentropic source (2.3 m s−1) [Shibata and Deushi, 2005a]. The gravity wave spectrum is assumed to be isotropic, so the same spectrum is launched to eight equally spaced azimuths (e.g., north, northwest, west, etc.) at the lowest level with horizontal wave number k = 5.0 × 10−6 m−1. Vertical diffusion is not applied in the stratosphere in order to keep the sharp vertical shear in the QBO.
 The chemical module of the CCM contains the major stratospheric species (i.e., 34 long-lived and 15 short-lived species) with 79 gas-phase reactions, 34 photochemical reactions, six heterogeneous reactions on polar stratospheric clouds, and three heterogeneous reactions on sulfate aerosols. The transport process is based on a semi-Lagrangian scheme, which is of flux form in the vertical direction and is of ordinary form in the horizontal direction with quintic interpolation. The transport equation is solved to be compatible with the continuity equations; therefore, the mass of a chemical species is relatively well (although not perfectly) conserved [Shibata et al., 2005].
 The model is integrated under the REF1 scenario [Eyring et al., 2005], which was made for reference simulations of CCMs to improve our understanding of CCMs and their underlying GCMs through process-oriented evaluation. REF1 was designed to reproduce at least the core period of 25 years of the recent past (1980 through 2004), during which ozone depletion is well recorded. This transient simulation includes all anthropogenic and natural forcings based on changes in trace gases, the 11 year solar cycle, volcanic eruptions, and prescribed SSTs. Five members with slightly different initial conditions are integrated in the ensemble simulations. Thus, 125 years of the simulated data set (five members by 25 recent past years) are available and were used for investigating the equatorial QBO influence on extratropical circulation in the NH winter.
2.3. Analysis Methods for Isolating the QBO Phase Differences and Determining Their Statistical Significance
 In this study, the composite differences in zonal wind U and temperature T are defined as the westerly minus the easterly values, that is, [U] = UW - UE; [T] = TW - TE, where the subscripts W and E denote the westerly and easterly phases of the QBO, respectively.
 A statistically significant difference Z (nondimensional) in temperature between the two phases of the QBO was tested by the large sample method [Naito and Yoden, 2005], which means that the sampling distribution of any statistics of independent random variables is normal or nearly normal if the sample size is sufficiently large. Z is defined as
where the overbar denotes the average of zonal-mean temperature from the monthly mean data of the winter months during each phase of the QBO, σW and σE are the standard deviations of temperature, and NW and NE are the sample sizes. The significances of other variables (zonal wind and Eliassen-Palm (EP) -flux components) in monthly data or daily data were also tested in the same manner.
 The degrees of freedom ν for statistical significance are given by
 When we consider the independence of the sequential daily data, the sample sizes NW and NE are replaced by effective sample sizes NWeff ≡ NW t0 / teff and NEeff ≡ NE t0 / teff; hence, Z is replaced by the effective statistic Zeff [Naito and Yoden, 2005]:
where teff is the effective sampling time and t0 = 1 day in the present case. By using a lag correlation ρτ = exp(- τ / teff), where ρτ is the autocorrelation coefficient and τ is the lag, teff can be estimated. In this study, teff is defined as the shortest lag τ (day) for which ρτ falls below 1/e. The lag correlation ρτ at every grid point in the meridional plane was calculated using time series data after the climatological annual cycle was subtracted.
 We investigated the teff values of the meteorological variables that were used for estimating statistical significance. Figure 1 illustrates the effective sampling times teff evaluated for zonal winds U and temperatures T using daily data of ERA-40 and the simulation. The independence of the serial daily data was examined by calculating autocorrelation coefficients [Naito and Yoden, 2005]. In ERA-40 data, teff for U was shorter than 20 days in the troposphere and 20 to 40 days in the extratropical stratosphere, and it was longer than 100 days in the tropical stratosphere (Figure 1a); teff for T was shorter than 20 days in the extratropical troposphere and stratosphere, but it was longer than 100 days in the tropics (Figure 1b). The simulated teff values (Figures 1c and 1d) revealed a pattern similar to that of the observation data.
 However, teff exhibited large differences among variables. For example, typical e-folding times in the extratropical stratosphere were approximately calculated as 25 days for U and T but only 3 days for the meridional wind V, 3 days for the eddy momentum flux , and 4 days for the eddy heat flux . Exact estimations of effective sample sizes are beyond the scope of this study, but we expect that the effective sample time for U (or T) is not actually an order of magnitude longer than that for V. Therefore, as already stated, teff for U and T was defined as the e-folding time in the autocorrelation, but teff for V, , and was defined as twice the e-folding time (ρτ = exp(- 2τ / teff)). This assumption differs somewhat from that of Naito and Yoden , who used twice the e-folding time as teff for U and T. Thus, the statistical significance used in this study may vary in the range of ∣δ (Zeff) ∣ < 0.5, depending on the choice of teff.
3.1. Assessment of the Tropical QBO Simulation
 First, we demonstrated that the model (MRI-CCM) could reproduce the observed QBO. Figure 2 presents time–height sections of the monthly zonal-mean zonal wind at heights from 5 to 100 hPa, on the basis of the observational data set (ERA-40) and one member of the data set simulated under the REF1 scenario. The climatological seasonal cycle is removed to diminish the upper stratosphere semi-annual oscillation (SAO), which shows an almost fixed seasonal cycle. The time evolution of the zonal-mean zonal wind over the equator during the 25 years (1980 through 2004) demonstrates that the simulation could adequately reproduce the QBO in the stratosphere. It is apparent that downward propagating westerly and easterly regimes alternate, with a period varying from 24 to 30 months, in both the ERA-40 data and the simulation. Quantitatively, the amplitude of the zonal wind in the simulation is reduced to 15 m s−1 at 20 hPa, which is 70% of the observed amplitude [Shibata and Deushi, 2005a, 2008a].
 However, the QBO amplitude in the lowermost stratosphere is too small in the model simulation, although a similar defect is shared by many other models [e.g., Giorgetta et al., 2006]. Also, the asymmetry between easterly and westerly phases differs between the model and observations, with the model displaying very long easterly phases relative to the westerly phases (particularly above 20 hPa). Giorgetta et al.  indicated that one reason for this shortcoming is insufficient representation of resolved waves in the stratosphere by the simulation.
 The power spectra of the equatorial zonal-mean zonal wind at heights from 1 to 1000 hPa were averaged between 10°S and 10°N in the observation (ERA-40) data and the simulation (Figure 3). The simulation spectra were averaged over the five members. The observed SAO shows larger power values above 10 hPa in the upper stratosphere, with the power increasing with altitude and peaking near the stratopause. The annual components (12 months) also show a maximum at the stratopause, and certain power values increase with altitude. The simulation effectively captures both the SAO and the annual oscillation. In the average of the five members, the simulated QBO has a period of 27 months with a maximum at 20 hPa, which is very similar to the observed period (28 months). However, the simulated QBO power is underestimated (∼80 % of the observed power).
 Because the QBO may be somewhat synchronized to the annual cycle [e.g., Baldwin et al., 2001], we grouped the number of transitions (zero crossing) at 50 hPa by month during the years 1980–2004 in the observation data and the simulation and found that the number of easterly transitions was almost the same as the number of westerly transitions in both the observation data and the simulation. During these 25 years, the number of regime shift onsets during each season (from spring to winter) was 10, 2, 3, and 3, respectively, for the observation, and 6, 7, 6, and 2, respectively, for the simulation averaged over the five members. Because each ensemble member of the simulation used slightly different initial conditions, the model results somewhat differ from the observation results.
3.2. Influence of the Equatorial QBO on Extratropical Circulation and the Statistical Significance of QBO Phase Differences
Figure 4 shows the composite differences in zonal-mean zonal wind [U] and zonal-mean temperature [T], along with their statistical significance in the NH winter in the ERA-40 data and the simulation. In both the ERA-40 and simulation data sets, [U] (Figures 4a and 4c) was most significant at 50 hPa over the equator, where the phase of the QBO was defined. The positive [U] at 60°N in the stratosphere and upper troposphere was significant at the 90% confidence level. The area of statistical significances of the simulated [U] at the 90% confidence level extends into the lower troposphere because of the large-sample size (long-term simulation).
 In the ERA-40 data set, [T] (Figure 4b) was significant, not only in the equatorial QBO region, but also in the midlatitude and high-latitude stratosphere in the Northern Hemisphere. Its significance was particularly high (95% confidence level) in the lower stratosphere at high latitudes (Figure 4b). In the simulation, however, [T] (Figure 4d) showed relatively lower statistical significance (80%) in the high-latitude lower stratosphere. These results confirm that the simulated [U] effectively captured the observations in the extratropical stratosphere, but simulated [T] reflected some model bias, especially in the polar stratosphere.
 In the ERA-40 data set, [U] (Figure 4a) was positive and large at 50 hPa over the equator but, in this area, simulated [U] (Figure 4c) was underestimated (50% of observed [U]). Maximum [U] at the core of the polar night jet at 60°N had an amplitude at 10 hPa of 7 m s−1 in the ERA-40 data and 5 m s−1 in the simulation. A small-amplitude high-latitude positive anomaly and a small-amplitude midlatitude negative anomaly penetrate into the troposphere in both the ERA-40 data and the simulation.
 As already described in this subsection, a clear QBO signature could be seen in T with pronounced signals in both the tropics and the extratropics. The extratropical QBO signals arise from the secondary meridional circulation induced by the main equatorial QBO [e.g., Plumb and Bell, 1982]. The tropical temperature QBO has a thermal wind relationship with the vertical shear of U. In both the ERA-40 data and the simulation, [T] over the equator was positive (warm) in the westerly shear zone at 70 hPa and negative (cold) in the easterly shear zone at 20 hPa. The midlatitude QBO signals demonstrated a well-defined pattern of QBO-induced secondary circulation, which was connected by meridional and vertical positive/negative temperature anomaly cells [Lu et al., 2008]. Warming (2 to 3 K) occurred in the lower to midstratosphere, and weak cooling (0.3 K) occurred in the lowest stratosphere. The arctic lower stratosphere was colder by up to 3 K in the ERA-40 data and 2 K in the simulation.
Figure 5 presents latitude–height cross sections of U and the EP flux during the easterly phase of the QBO in the ERA-40 data set and the member of the ensemble simulation with the best fit to the observation (left panels). The right panels show the composite difference in U and the EP flux between the westerly and easterly QBOs. Positive wind differences (Figures 5b and 5d) were observed or simulated in the high-latitude stratosphere, implying a less disturbed polar vortex during the westerly QBO. A three-cell vertical structure of the QBO is evident in the tropics (Figures 5b and 5d) [Pascoe et al., 2005; Shibata and Deushi, 2008a, 2008b; Lu et al., 2008]. Positive anomalies are centered at 50 hPa over the equator, and above this anomaly, negative anomalies are present in the middle and upper stratosphere. Below the 50 hPa anomaly, a very weak easterly region is present in the lowest stratosphere. When all members of the ensemble simulation were included in the analysis, however, a discrepancy in the EP flux differences was found between the ERA-40 data and the simulation in the high-latitude upper stratosphere: the EP flux differences were directed downward in the ERA-40 data but upward in the simulation. This discrepancy probably resulted from the slightly different initial conditions used by each ensemble member.
 When the QBO is in its easterly phase (Figures 5a and 5c), planetary waves encounter a critical line (zero-wind line) on the winter side of the equator. Quasi-stationary waves cannot propagate in easterly winds, and the phase of the QBO in the tropics and subtropics thus alters the boundary between westerly and easterly zonal-mean winds and does the effective waveguide for these waves. According to the traditional Holton-Tan explanation or hypothesis [Holton and Tan, 1980; Baldwin et al., 2001], when there are easterly winds in the tropics, the effective waveguide for the planetary wave is narrower. This narrowed waveguide may be thought of as refracting the waves as they propagate out of the troposphere. However, the composite difference in EP flux is directed poleward as well as downward at the midlatitude in layers between 50 and 100 hPa (Figures 5b and 5d). Therefore, when the QBO is in its westerly phase, stationary planetary waves can propagate less equatorward as well as less upward. Thus, the conventional Holton-Tan hypothesis cannot explain this result in terms of the critical line and waveguide. The problem of the direction of the stationary planetary waves is presented in section 4.
 To investigate the polar stratospheric temperatures and EP flux differences in more detail, we analyzed their frequencies. Figure 6 shows the frequency distributions of polar temperature T at 50 hPa and the horizontal component of the EP flux EPy at 100 hPa and 40°N during the westerly (blue) and easterly (red) QBO phases in the ERA-40 data and the simulation. For reference, statistical quantities are also shown. Here, kurtosis krt is defined as the fourth moment μ4 around the mean divided by the fourth power of the standard deviation σ of the probability distribution minus 3:
For T, for both phases, frequencies of low values are higher, and high values are relatively fewer, so that the distribution is right skewed. Moreover, the distributions have relatively sharp peaks and long, fat tails: characteristics consistent with positive (high) kurtosis.
 In the ERA-40 data set, average T is 200.4 and 203.6 K in the westerly and easterly QBO, respectively, whereas in the simulation, average T is 200.6 and 202.6 K in the westerly and easterly QBO, respectively. Observed T during the easterly QBO shows a clear bimodal distribution (with warm and cold peaks). The cold peak is at 196 K and the warm one is at 218 K. This warm peak corresponds to observed warming events. Simulated T during the easterly QBO also has a bimodal distribution, but the warm mode, which peaks at 228 K, is less frequent. During the westerly QBO, on the other hand, in both the ERA-40 data and the simulation, T is unimodally distributed.
 In the ERA-40 data set, the difference in T between the westerly and easterly QBO phases is much larger at temperatures below 220 K, whereas it is smaller at those above 220 K. The frequency of large warming events (defined as T above 220 K) during the easterly QBO is almost the same as or less than that during the westerly QBO, whereas medium and small warming events (defined as T between 205 and 220 K) occur more frequently during the easterly QBO. In the simulation, however, the frequencies of medium and small warming events are almost the same during both QBO phases, whereas large warming events occur more often during the easterly QBO.
 The asymmetry in the frequency of warming events between ERA-40 and the simulation is related in part to the reduced amplitude of the QBO signals in the simulation. On closer inspection, we found that in the simulation, the Holton-Tan relationship tended to hold in January and February, whereas in the observation, it held in November and December [Lu et al., 2008]. This means that the weak QBO signal of the simulation may be responsible for the delayed Holton-Tan relationship.
Figures 6b and 6d depict frequency distributions of the horizontal component of EP flux (EPy) at 100 hPa and 40°N. The average EPy in the ERA-40 was –1.2 × 107 kg s−2 during the westerly QBO and –1.5 × 107 kg s−2 during the easterly QBO. The average EPy in the simulation is –1.7 × 107 kg s−2 during the westerly QBO and −1.8 × 107 kg s−2 during the easterly QBO. These results indicate that while most planetary waves in the midlatitude lower stratosphere are directed equatorward, more equatorward propagation of the planetary waves occurs during the easterly QBO than during the westerly in both the ERA-40 data and the simulation.
 Finally, we investigated upward EP fluxes of zonal wave numbers 1 and 2. Figure 7 shows composite differences in the eddy heat flux (, which is proportional to upward EP flux) carried by wave 1 and wave 2 during the westerly (blue curves) and easterly (red curves) QBOs at 30 hPa and 60°N in the ERA-40 data and the simulation. A 31 day running mean was used to smooth the variations of , which is shown as a function of time from October through April.
 In the ERA-40, the upward EP flux of wave 1 during the westerly QBO exceeded that during the easterly QBO in January and February at the 95% significance level, while there is no significant difference in other months. In the case of wave 2, significant differences were found only in November, when the upward EP flux during the westerly QBO was larger than that during the easterly QBO. These ERA-40 results during the 25 years from 1980 to 2004 are somewhat different from those reported by Ruzmaikin et al. , who used ERA-40 data for 1958–2002 (45 years) to show that the QBO modulation of the stationary planetary wave was robust in early winter for wave 1 and in late winter for wave 2.
 In the simulation, the upward EP flux of wave 1 during the westerly QBO also exceeded that during the easterly QBO in late January and February at the 95% significance level. Some differences, but at a lower level of confidence, can also be seen in December and March. For wave 2, the upward EP flux during the westerly QBO exceeded that during the easterly QBO in November and December, whereas in February and March, the easterly values exceeded the westerly QBO values. The quantitative differences between the observation and the simulation are much larger for wave 2 than for wave 1. Future investigation is required to explain this discrepancy.
 On the basis of the composite differences in zonal wind and EP flux (Figures 5b and 5d), we present a schematic overview of the equatorial QBO, planetary wave propagation, and extratropical circulation (Figure 8). The difference in planetary waves between the westerly and easterly QBO phases is directed downward as well as poleward. This feature contradicts the conventional Holton-Tan hypothesis, according to which stationary planetary waves during the westerly QBO are refracted equatorward through an extended westerly wind region (waveguide) in the extratropical stratosphere.
 However, Dunkerton and Baldwin  and Baldwin et al.  recognized that it is difficult to explain the modulation of the extratropical circulation by the equatorial QBO, as follows. From their investigation of the relationship between the EP flux and the QBO modulation, Dunkerton and Baldwin  concluded that only slight differences exist between the easterly and westerly phases, and that the planetary wave flux evidence adds no statistically independent information to the proposed association between tropical and extratropical QBOs. Furthermore, Baldwin et al.  found it difficult to formulate a simple quantitative model for the mechanism of the extratropical QBO for interaction of the equatorial mean flow with vertically propagating waves. The main complications were that the planetary waves propagate both vertically and meridionally, and the effects of critical lines on planetary wave propagation are not easy to predict theoretically.
 In summary, the horizontal components of the EP flux seem to be only slightly different between the westerly and easterly phases of the QBO (Figures 6b and 6d). However, quantitative evaluations of the horizontal component of EP flux and composite EP-flux differences (Figures 5b and 5d) demonstrate that planetary waves tend to propagate less poleward as well as less upward during the westerly QBO than during the easterly QBO.
 We strongly suggest that the upper equatorial QBO has a large influence on the extratropical circulation driven by QBO-induced meridional circulation [Gray et al., 2004; Anstey and Shepherd, 2008; Peña-Ortiz et al., 2008; Lu et al., 2009]. As a result, the QBO in the lower stratosphere has only a minor effect on the extratropical circulation. The NH winter circulation may be influenced by both the QBO and the 11 year solar cycle [e.g., Labitzke, 1987]. Several studies have suggested that stratospheric sudden warming (SSW) events are more prevalent in low solar activity years during the easterly QBO (LS/eQBO) and in high solar activity years during the westerly QBO (LS/wQBO). In contrast, the NH polar vortex tends to be strong throughout the winter in low solar activity years during the westerly QBO (LS/wQBO) and in high solar activity years during the easterly QBO (HS/eQBO), indicating that major midwinter SSWs seldom occur in LS/wQBO and HS/eQBO years [Labitzke, 1987; Naito and Hirota, 1997; Gray et al., 2004; Lu et al., 2009]. The present analysis of QBO influence on extratropical circulation in the NH winter included both solar minimum/solar maximum (LS/HS) years; thus, further research is needed to investigate the effects of the QBO–solar relationship on the NH stratosphere. Furthermore, although the QBO–solar relationship is statistically significant, an exception occurred in 2008/2009 year (LS/wQBO years), when a prominent mid-January SSW occurred with clear splitting of the polar vortex caused by the unusual development of wave 2 [e.g., Harada et al., 2010]. Future research using long-term data sets (both observation and simulation) should examine the mechanism of the solar–QBO influence on the NH polar vortex.
 We analyzed the extratropical effects of the equatorial QBO during 25 years (1980–2004) in the ERA-40 reanalysis (1980–2002) and ERA-interim analysis (2002–2004) data sets and in 125 years of ensemble simulated data sets (five members covering the period 1980–2004) by using the MRI-CCM, and we investigated the Holton-Tan relationship between the equatorial QBO and the polar vortex. The primary tools employed were composite differences in zonal wind, temperature, and EP fluxes. We tested statistically significant differences between the westerly and easterly QBOs, examining the independence of daily serial data by evaluating an effective sampling time teff. We found that daily data were more useful than monthly data because of the increased numbers of samples, especially for teff of 10 days or less.
 Not many GCMs can simulate the QBO realistically, but MRI-CCM, which includes the interaction between QBO dynamics and the ozone (hence heating) distribution, reproduces a self-generated QBO that is fairly realistic. A lack of dynamics-radiation feedback through ozone may reduce the relevance of GCMs to the real atmosphere, so CCMs with dynamics-ozone feedback are superior to GCMs without the feedback when it may affect the QBO simulation.
 The model realistically reproduced the equatorial QBO and the extratropical influences of the QBO. The simulated QBO power, however, was 20% smaller than the observed power, and the amplitudes of extratropical QBO signals such as zonal winds and temperatures were also 20 to 30% smaller.
 We demonstrated, by using MRI-CCM, that the conventional Holton-Tan explanation that the equatorial winds in the lower stratosphere act as a waveguide for midlatitude planetary wave propagation does not hold for winter circulation. Therefore, the QBO influence on the extratropical circulation does not come from the lower equatorial stratosphere. Our main finding was that, whereas the composite differences in zonal wind and temperature indicated a slight yet statistically significant Holton-Tan effect, that is, winters were warmer and more disturbed under easterly QBO conditions, the EP flux diagnostics did not show more poleward propagation in the midlatitude stratosphere. Rather, planetary waves propagate more equatorward as well as more upward during the easterly QBO than during the westerly QBO.
 The MRI-CCM simulation was made in part with the supercomputer at the National Institute for Environmental Studies, Japan. This work was supported in part by a Grant-in-Aid (20340129, 20340131, and 20244076) for Science Research of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.