A full troposphere-stratosphere-mesosphere global circulation model is used in a set of idealised experiments to investigate the sensitivity of the Northern Hemisphere winter stratospheric flow to improvements in the equatorial zonal winds. The model shows significant sensitivity to variability in the upper equatorial stratosphere, the imposition of SAO and QBO like variability in this region advances the timing of midwinter sudden warmings by about one month. Perturbations to the lower equatorial stratosphere are mainly found to influence early winter polar variability. These results suggest that it is important to pay attention to the capability of models to simulate realistic variability in the upper equatorial stratosphere.
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 The winter season in the northern polar stratosphere is dominated by a vortex of westerly winds. However, the polar vortex is vulnerable to disruption by planetary waves which can propagate through the westerly flow. Occasionally a planetary wave may undergo rapid growth and become so large that the resulting flow acts to move the vortex away from the pole or split the vortex in two [Matsuno, 1970; Labitzke, 1982; McIntyre, 1982]. These events can result in a sudden warming of around 50 K in just a few days [Andrews et al., 1987].
 Many global circulation models (GCMs) are unable to capture the full extent of wintertime stratospheric polar vortex variability and consequently suffer from a significant cold bias at high latitudes. The use of parametrization schemes to simulate the influence of both orographic [Miller et al., 1989] and non-orographic gravity waves [Garcia and Boville, 1994] has gone some way to reduce the stratospheric cold bias. However, the introduction of these gravity wave schemes has also been shown to substantially improve the simulation of the semi annual oscillation (SAO) [Jackson and Gray, 1994], thus dramatically increasing the variability in the equatorial upper stratosphere. In recent years the introduction of gravity wave schemes has also resulted in the simulation of the quasi-biennial oscillation (QBO) [Scaife et al., 2000; Giorgetta et al., 2002; Shibata and Deushi, 2005].
 In the lower stratosphere the QBO contributes to polar vortex variability through the modification of planetary wave propagation [Holton and Tan, 1980, 1982]. For more recent reviews of this subject see Baldwin et al.  and Pascoe et al. . However, recent studies have shown that there is an additional influence on polar variability from upper stratospheric equatorial winds [Gray et al., 2001a; Gray, 2003]. Observations and model studies have suggested that the lower stratospheric QBO may be most influential in early winter when the flow is more linear and that the influence from the upper stratospheric equatorial wind (SAO and QBO) is greatest in mid to late winter when the flow is highly non-linear [Gray, 2003; Gray et al., 2004].
 In this paper, we describe a set of GCM experiments in which idealised SAO and QBO variability is introduced via the relaxation of the equatorial winds over different height regions. The impact of the imposed equatorial variability on the simulated variability of Northern Hemisphere polar stratospheric temperatures is assessed, with particular attention to the impact on the timing of sudden warmings. A self-consistent QBO generated by a gravity wave parameterisation was not used in this suite of experiments because we wished to have greater control over the height region of the imposed variability. The model and details of the experiments are described in section 2, the results are provided in section 3 and the primary conclusions are summarized and discussed in section 4.
 The model employed was the UK Met. Office's Unified Model version 4.5 which is a hydrostatic primitive-equation model based on a 2.5° by 3.75° latitude-longitude grid. The model has an extended vertical range with 64 levels between 1000 and 0.01hPa (0–80 km). The model was configured in an atmosphere only mode and utilised an annually periodic sea surface temperature climatology based on a 360 day approximation to the annual cycle. Rayleigh friction was imposed on the upper model levels above 50 km. For further details of the model see Austin  but note that the coupled chemistry was not included in this study.
 Four 28 year simulations have been performed in order to test the sensitivity of the winter stratosphere to equatorial winds: a control simulation with no modification of the equatorial wind field and three further experiments where the equatorial zonal mean winds were relaxed toward more realistic representations of the SAO and QBO. The control exhibited constant weak easterlies in the lower stratosphere peaking at 17 ms−1 at 25 km and SAO variability at the stratopause with strong easterlies of around 30 ms−1 in January and July and weak easterlies of around 15 ms−1 in April and October.
 The first perturbation experiment imposed only the idealised SAO momentum forcing above 30 km described by the solid profile in Figure 1. The second experiment imposed the SAO momentum forcing and also a ‘shallow’ QBO confined only to the lower stratosphere (15–35 km), as shown by the dotted profile, so that the additional influence on polar variability solely from the lower stratospheric QBO can be assessed. The third experiment was identical to experiment two except that a more realistic ‘deep’ QBO was imposed throughout the height region 15–65 km (dashed profile). In this way the additional influence on polar vortex variability from the upper equatorial QBO can be assessed. The Deep QBO (Fdeep), Shallow QBO (Fshlw) and SAO (Fsao), momentum forcing functions are described explicitly in the Appendix. The amplitude of the SAO and QBO momentum forcing was symmetrical about the equator and diminished with latitude, θ, following the Gaussian expression exp[−(12 θ/π)2].
 The phase of the imposed QBO varied with respect to height and time as described by equation (1) following the method of Hamilton .
where t is time in months and z is height in kilometers. It describes a QBO with a period of 27 months and a time evolution that is fairly realistic, being closer to a square wave than a sinusoid. Fqbo(z) is the chosen QBO momentum forcing function shown in Figure 1. The harmonic amplitudes, An, are 1.0, 0.15, 0.20, 0.08, 0.04 and 0.02 for n = 1, 2, 3, 4, 5 and 6, respectively [Hamilton, 1998].
 A similar method was used to describe the time evolution of the SAO, equation (2). A phase shift, Δt = 1 month, was inserted to ensure that maximum (1 hPa) SAO easterlies occurred in January and July.
 The equatorial zonal wind field was relaxed toward the idealised QBO and SAO perturbations using a relaxation timescale that reduced smoothly from 5 days at 17 km to 0.5 days at 40 km and increased with distance from the equator following the formula:
where C is the relaxation timescale and y is latitude in degrees.
 The west and east phases of the idealised QBO and SAO perturbations are symmetrical, in the sense that they have equal magnitude, duration and latitudinal extent. However, the descending westerly shear of the QBO is stronger than the easterly shear to reflect the more rapid descent of westerlies in the observed QBO [Pascoe et al., 2005]. Examples of the resulting equatorial zonal mean zonal wind time series for the shallow QBO and deep QBO simulations are shown in Figure 2. Zonal wind variability is greatest in the stratopause region of the Deep QBO experiment where the SAO and QBO perturbations superpose (Figure 2b).
Figure 3 shows the standard deviation of the interannual distribution of lower stratospheric (50 hPa) daily mean North Pole temperature for each of the four runs: control (shaded), SAO-only (dotted), Shallow QBO (dashed), and Deep QBO (solid). The standard deviation gives a measure of interannual polar vortex variability and rises rapidly once a simulation begins to exhibit midwinter sudden warmings. The most dramatic differences between the simulations occur as a result of changes in the timing of midwinter warming activity. However, persistent differences between the simulations are also found in early winter.
 Middle atmosphere equatorial winds in the control are never westerly and the zero wind line which influences planetary wave propagation to the stratosphere is always in the Northern Hemisphere. Yet, warmings in the control run occur later than observations and of all the simulations, the control run exhibits the least amount of midwinter variability. The largest standard deviation values are found at the beginning of March during the period of final winter warmings, reflecting the fact that many of the winters in the control run do not achieve a midwinter sudden warming.
 The relaxation to the idealised SAO results in slightly weaker easterlies in the lower equatorial stratosphere than the control. The associated equatorward movement of the critical line might be expected to reduce the likelihood of sudden stratospheric warmings but instead the onset of these events are brought forward. The maximum variability in the SAO-only run occurs at the beginning of February, a month earlier than in the control. The addition of the lower stratospheric Shallow QBO to the SAO perturbation makes no appreciable difference to the timing of midwinter warmings with respect to the SAO-only run. The addition of a Deep QBO to the SAO perturbation, while not changing the position of the maximum variance, nevertheless advances the onset of the midwinter warming activity. The advance is two weeks with respect to the SAO-only and Shallow QBO runs and a whole month with respect to the control run. This indicates that a number of winters in the Deep QBO simulation have late December/early January warmings, which is much more representative of reality.
 The autumn/early winter buffeting of the polar vortex begins first in the experiments with QBO-like variability in the lower stratosphere. The standard deviation profiles in the Shallow QBO and Deep QBO experiments show very similar early winter behaviour, rising to 4 K in mid November, but this level of variability is not exceeded until the onset of sudden warmings. The buffeting of the polar vortex begins later in the SAO only experiment but the magnitude of the disruption is greater rising to 5.5 K in mid December. The control simulation which had no equatorial relaxation showed very little early winter disruption of the polar vortex.
 As well as having the most realistic equatorial QBO distribution, Figure 3 shows that the Deep QBO run also results in the most realistic variability in sudden warming activity. The onset of sudden warmings and the timing of maximum variability in the Deep QBO run both occur about one month ahead of the same features in the control run. Therefore, we compare the Deep QBO and control runs to make an objective assessment of the improvement to polar variability that is achieved via the introduction of equatorial variability.
Figures 4a and 4b show plots of the daily mean North Pole temperature time series at 50 hPa for every year of the Control and Deep QBO simulations. The sudden warming activity implied by the standard deviation time series (Figure 3) is clearly apparent during the January of the Deep QBO simulation which contains several years with instances of sudden warmings. In contrast to this, the Control simulation has just one January warming.
Figures 4c and 4d are histograms of 50 hPa daily mean North Pole temperature which show the different January temperature distributions of the Control and Deep QBO experiments. The mean, variance, skewness (asymmetry) and kurtosis (peakedness) of these two distributions are listed in Table 1. Both distributions are positively skewed and have similar mean temperatures. However, the Deep QBO temperature has a higher variance and the distribution is flatter with a fatter tail.
Table 1. Statistics Which Describe the Shape of the 50 hPa Daily Mean January North Pole Temperature (K) Distribution for the Control and Deep QBO Simulations
 A chi-square probability test has been performed to test whether the Control and Deep QBO distributions of 50 hPa January North Pole temperature are significantly different given a confidence interval of 90 percent. The chi-square test is designed to be performed on independent data but the daily data have significant autocorrelation (approximately 0.85). To account for this the temperature time series was sampled at intervals of seven days (where the autocorrelation fell to less than 0.05) giving 5 samples per month, and hence 140 (5 × 28 years) data points to form a subset of the data. Further subsets were selected by shifting the data sampling by 1 and 2 days. Three subsets, were thus selected from the two simulations and a chi-square test with a bin size of 2 K was performed on all possible pairing combinations which yielded a mean chi-square probability of 0.945. This result objectively confirms that the modification applied to the equatorial middle atmosphere in the Deep QBO simulation has significantly improved the midwinter polar vortex variability.
 This study clearly demonstrates that the introduction of realistic equatorial variability to the GCM simulations significantly improves the cold bias in the polar stratosphere. The improvement is achieved by bringing forward the onset of midwinter sudden stratospheric warming activity. The timing of the onset of warmings changes according to the height region of the imposed equatorial perturbation such that:
 1) With no equatorial relaxation the control experiment has the standard cold pole problem and very low variability during early and midwinter.
 2) Increasing the variability in the SAO region (above 30 km) results in a one month advance of the mid winter warming maximum.
 3) Increasing the variability in the SAO region even more by adding a deep QBO brings forward the onset of midwinter variability by about another two weeks.
 4) The introduction of the shallow QBO appears to primarily affect the early winter variability.
 These findings suggest that the lower equatorial stratosphere influences early winter polar variability, whereas the upper equatorial stratosphere influences midwinter polar variability. These GCM results are in agreement with the idealised experiments of Gray , who used a stratosphere-mesosphere model to asses the sensitivity of mid winter warmings to idealised equatorial perturbations.
 One consequence of the improved SAO and QBO is the introduction of a more realistic westerly phase with an associated shift of the zero wind line. This might be expected to influence the propagation of planetary waves so that the frequency of warmings is reduced but more midwinter warmings were present in the SAO and QBO experiments. In fact, it was the introduction of the more realistic SAO that showed the largest impact, reinforcing the hypothesis that variability in the equatorial upper stratosphere is a crucial factor in the timing of sudden warmings. Further investigation is required to fully understand the mechanism of this influence. Recent work of Gray et al. [2001b, 2004] suggests that the details of the equatorial/subtropical zonal winds (and possibly their vertical wind shear) are important.
 We note that the symmetric QBO and SAO defined by equations (1) and (2) have zero zonal mean zonal winds when integrated over a full cycle, and hence the zonal momentum integrated over time is zero at every level. In the control experiment, on the other hand, the climatological annual mean of the zonal mean zonal wind profile at the equator is different from zero and depends on the level. Thus, there is a small difference in height-integrated zonal momentum between the control and the experiments (but not between the experiments themselves). However, we believe that the net effect of this discrepancy is small.
 The Deep QBO momentum forcing function, Fdeep, takes the form of a Weibull function with parameters α = 3.5, β = 0.27 and γ = 3.2335:
where RD = 40.0 m s−1, ZD = (z − 15)/20 and z is the height in kilometers.
 The Shallow QBO momentum forcing function, Fshlw, takes the form of a Gamma function with parameters a = 4.0 and b = 2.0:
where RS = 47.7 m s−1 and ZS = (z − 15)/7.2.
 Where 30 < z < 50 the SAO momentum forcing function, Fsao, takes the form of a Gamma function with parameters a = 2.7 and b = 0.48 where RS = 17.8 m s−1 and ZS = (z − 30)/45. Above 50 km the SAO momentum forcing function has a constant amplitude of 40 m s−1.
 This work was supported by the United Kingdom Natural Environment Research Council through the Upper Troposphere Lower Stratosphere thematic program. The authors would like to acknowledge Kevin Hamilton for providing the algorithm that was used to govern the phase of the QBO and SAO in our simulations.