The role of the stratosphere on the predictability of medium-range weather forecast during the northern hemisphere winter is examined using numerical experiments with a middle atmosphere climate model of the Meteorological Research Institute. It is found that in the winter of 2003/04 when the stratosphere exhibited a large variability called the Polar-night Jet Oscillation (PJO), the predictability of the model tended to be very good for large-scale zonal variability if the prediction is performed just before the occurrence of stratospheric sudden warmings (SSWs). The role of the stratosphere is examined by comparing experiments for the 2002/03 year and using the model with and without the stratosphere included. The results of the study suggest that taking account of the role of stratospheric variability (PJO) is crucial for improving the predictability of medium-range weather forecast in certain winters.
 Society requires forecasting centers to provide highly accurate medium-range weather forecast. However the chaotic nature of the atmosphere [Lorentz, 1963] prevents us from performing accurate weather forecasting for periods longer than about two weeks. For a discussion of the improvement in the skill of numerical prediction that has been achieved in recent years, see Simmons and Hollingsworth . One possible way to extend the current limit is to rely on the more slowly varying predictable boundary conditions from the ocean such as the El Niño Southern Oscillation (ENSO) [Kanamitsu et al., 2002]. Recently another possibility of extending predictability using the slow variability of the stratosphere was proposed. For example, Baldwin and Dunkerton  considered the statistical predictability of the hemispheric annular variability called the Northern Annular Mode (NAM), and found that the lowermost stratospheric NAM in mid-winter can be used as a better predictor for the surface NAM in mid-winter.
 A slow long-term variability called the Polar-night Jet Oscillation (PJO) exists in the winter stratosphere [Kuroda and Kodera, 1999, 2001, 2004]. The northern hemisphere-PJO shows a quasi-periodicity of 3 to 5 months and indicates poleward and downward movement of anomalous zonal-mean zonal wind in the stratosphere, if the anomaly is defined by the departure from climatology. The anomalous wind often reaches the surface and creates the NAM with the progression of the PJO. Anomalous polar temperature associated with the PJO extends from the tropopause to the upper stratosphere [Kuroda and Kodera, 2001, 2004].
 As the stratospheric process shows slow regular variability, it may be used as a potential predictor of tropospheric climate, such as the ENSO for medium-range weather forecast. Thus it will be interesting to examine whether the PJO can be predicted reliably using a sophisticated numerical prediction model. It is also interesting to examine whether the tropospheric climate is well-predictable if the PJO is also well-predictable by the model. We will examine these problems in this paper. We will also examine the role of the stratosphere in improving the predictability of forecasting by comparing model results obtained with and without the stratosphere included.
 This paper is organized as follows. The numerical model used in the present study and the principal analytical method are described in Section 2. Section 3 provides the results of the analysis, and Section 4 presents the discussion and remarks.
2. Model and Method of Analysis
 The numerical model used in the present study is the general circulation model (GCM) developed with the cooperation of the Japan Meteorological Agency (JMA) and the Meteorological Research Institute (MRI) of Japan, for use as the next generation model for seasonal prediction by JMA [Mizuta et al., 2006]. In the present study, we used a version of the model with horizontal parameters triangularly truncated at a total wave number of 95 (~200 km grid) and with a 40-layer hybrid pressure-sigma coordinate system with an upper boundary at 0.4 hPa (~55 km height). See Mizuta et al.  for further detail of the model. We have integrated the model from initial conditions determined from the objective analysis data produced by JMA. To calculate the initial value problem from analyzed data, the data is first modified according to the non-linear normal mode initialization method [Machenhauer, 1977] to remove the initial shock from the fast gravity wave, and then integrated. Land processes are included in the model, and their initial values are also obtained from JMA analysis. As the model cannot predict the sea surface temperature (SST), it is assumed that the analyzed anomalous SST at the initial time persists throughout (since the climatological SST varies with the day of the year, SST varies with forecasting time).
 Numerical prediction has been performed for every 6 hours from the time of the objective analysis data provided by JMA. Predictability was then estimated from runs with different initial times within a 5 day period. The total number of runs used for the statistical analysis was 20 so the present ensemble prediction is substantially the Lagged Averaged Forecasting (LAF) Method.
 If the spread of the ensemble runs were smaller and the ensemble mean were shifted significantly from the climatology, the ensemble runs would predict a future weather shift. In contrast, if the spread of the ensemble runs were large and the ensemble mean were very close to the climatology, there would be almost no information for prediction. Predictability will thus be evaluated by the Student’s t-test. It should be noted that the Student’s t-test simply gives the significance of the prediction.
 Here, we have compared anomalous zonal-wind at around 60°N as a simple index of the NAM (which is also called the Arctic Oscillation (AO) at the surface) [Thompson and Wallace, 1998; Baldwin and Dunkerton, 2001] for the observations and the predictions. This definition of the NAM index has the advantage that it simply captures the strength of the polar vortex and is not concerned with details of the modeled pattern. The observational data we used is the reanalysis data of the National Center of Environmental Prediction (NCEP)/National Center of Atmospheric Research (NCAR) [Kalnay et al., 1996; Kistler et al., 2001]. Daily climatological data was created from this data for the period 1958 to 2001 and then the anomalous wind was defined as a departure from daily climatology both for the observations and model results.
 The target period for the present experiment was the winters of 2002/03 and 2003/04. These two winters had contrasting features. The activity of the PJO in winter 2002/03 was small, while in 2003/04 the PJO was very active, as can be seen from the 31-day-running average anomalous polar temperature shown in Figure 1. In fact, prominent signals are limited only to the middle stratosphere in the winter of 2002/03, but they have larger amplitude and extend to the tropopause in 2003/04. Note that the major stratospheric sudden warming (SSW) occurs in both winters.
 Firstly, we performed a numerical prediction for the winter of 2002/03 when the activity of the PJO was small. Figure 2 (top) shows the observed features of NAM variability observed from December 1, 2002 to April 1, 2003. In this winter about four SSWs took place. They occurred on January 1, January 19, mid-February, and March 8. Note that the SSW on 19 January is a peak day of the major SSW defined by the strongest easterly zonal wind averaged from 55° to 65°N at the 10-hPa level. Corresponding with these SSWs, the polar vortex weakened. However, these signals are rather independent and do not create large low frequency variability as seen in Figure 1. It is interesting to note that the weaker polar vortex associated with the major SSW on January 19 propagates downward and creates AO-like variability in the surface on January 21.
Figure 2 (bottom) indicates the ensemble mean (contour) of the predictions and its statistical significance (shading), obtained using initial times between 06Z January 9 to 00Z January 14. It can be seen that a weak predictability exists for about one month in the stratosphere, but only for about three weeks in the troposphere. It is interesting to note that the downward propagation of the NAM signal is weakly predicted by the model. The predictability in the troposphere is found to be rather longer in this case. In fact, by changing the initial time of the prediction, it is found that the predictable period becomes shorter in the troposphere if the time between the initial time and the occurrence of the major SSW is increased. For example, for the prediction started from an initial time of 06Z January 1 to 00Z January 6, the significant predictable period is reduced to just 5 days in the troposphere (not shown).
 Next, we examined the numerical prediction for the winter of 2003/04 when the activity of the PJO was very large. Figure 3 (top) shows the observed features of the NAM variability. It is found that the polar vortex in the stratosphere became weaker from mid-December, and had a peak around January 9 when the major SSW took place and the weaker polar vortex lasted until the end of February. The polar vortex then became stronger after March. Such a long-lasting weaker vortex tends to propagate downward. Hence deep low frequency variability was more dominant in this winter compared with the winter of 2002/03, as seen in Figure 1. The weaker vortex signal in the stratosphere tended to propagate downward with time. Though the NAM signal in the troposphere was negative throughout, after the occurrence of the SSW, the signal fluctuated and sometimes turned positive.
Figure 3 (bottom) shows the result of the prediction performed using initial times from 06Z December 27 to 00Z January 1, just before the occurrence of the major SSW. It is interesting to note that the significance of this prediction is very high, and captures rather nicely the real time evolution of the zonal wind. In fact, the predictability in the stratosphere is extremely high, and the period of predictability is almost three months. The slow downward propagation of the zonal wind is also well captured although short-term fluctuations cannot be captured by the model. Furthermore it is noteworthy that the predictability in the troposphere is also very high and has a predictable time scale of about two months. It is interesting to note that although the prediction cannot capture well the occasional positive NAM signals, it does capture well the strong downward signals appearing around January 7, the end of January, mid-February, and the end of February. With an increase in the lead time from the initial time to the time of the major SSW, the predicted stratospheric and tropospheric signals tend to be weaker, but a positive AO-like signal is still predicted in the surface throughout the winter even if the prediction is started as early as December 15 (not shown).
 To examine the role of the stratosphere on the predictability for the winter of 2003/04, we performed the same numerical prediction using a model without the stratosphere included. The model used was the same except that the top of the model was set to be 40-hPa, so that 29 vertical layers remained after removing the upper (stratospheric) levels of the original model. In this model, we have included the Newtonian cooling toward the global mean temperature with time scales of 10 to 20 days for levels above 110-hPa to reduce the bias of stronger zonal wind. We used the same initial times, and Figure 4 (top) shows the results. It can be seen that the prediction in the troposphere is almost the same until January 10 but the NAM signal in the troposphere that appears after mid-January is not predicted by the model. A similar result was obtained in the troposphere by the model without Newtonian cooling (not shown). So removing the stratosphere primarily affects the predictability of the troposphere for this particular winter.
 Surface conditions should have a large impact on predictability, as is the case for the ENSO. To see the effect surface conditions have on the predictability, we performed the same prediction but set the surface condition, including the SST and the initial land conditions, as the climatology. The model used was the standard model with the stratosphere included. The result is shown in Figure 4 (bottom). It is apparent that the predictability is worse both in the troposphere and stratosphere. However, the predictability in the stratosphere is not entirely bad and there still is improved predictability over about two months. Compared with the stratosphere, predictability in the troposphere is rather worse, with significant signal only until the beginning of February, except for the weakening signal in mid-January. Compared with the effect on the prediction made without the stratosphere in the model, the effect of the surface is found to be smaller for this year.
4. Discussion and Remarks
 In summary, this study indicates that the ensemble prediction performed just before the occurrence of the major SSW in the winter 2003/04 shows that predictability of behaviour during this winter is very good both for the stratosphere and the troposphere. The predictability has been compared with that for the winter of 2002/03. In both winters, major SSWs occurred but the activity of the PJO in the winter of 2002/03 was small whereas in 2003/04 it was large. Hence the activity of the PJO can be considered a key process to producing an extended range of predictability. In fact, the experiment of setting climatological lower boundary conditions produced larger predictability in the stratosphere. This indicates that stratospheric internal variability is important for increasing predictability in the stratosphere. Also an experiment without the stratosphere included in the model showed worse predictability, confirming this hypothesis.
 The PJO includes quasi-periodic occurrence of stronger and weaker polar vortices. A weaker polar vortex corresponds to the SSW and a stronger one is called the vortex intensification (VI) [Limpasuvan et al., 2005]. Previous studies have demonstrated that the effects of the stratosphere and troposphere associated with the SSW and VI are in many respects very similar except for the polarity [Limpasuvan et al., 2005; Kuroda, 2008]. It will therefore be interesting to examine whether higher predictability can also be obtained before or during a VI. We examined this problem from late winter to spring 2004 when the VI occurs. The results indicate that very high predictability in the troposphere (with a time scale of one month or more) cannot be obtained. The predictable period of NAM in the troposphere was at most half a month (not shown). These experiments suggest that higher predictability of surface NAM can be obtained only for the SSW stage of the PJO.
 To reinforce the hypothesis that higher predictability can be obtained if the prediction is performed just before an SSW of a larger PJO, we performed additional experiments in the winter of 2005/06 when a prominent PJO appeared as in the winter of 2003/04. The results demonstrate that higher predictabilities of two or more months were obtained if the prediction was performed just before the major SSW on January 27, 2006. The result is very similar to those obtained in winter of 2003/04 (not shown). However, experiments were performed for only a few winters, so a more extended study will be needed in the future.
 It will be interesting to examine why the tropospheric NAM index is so well predicted in the winter of 2003/04. It is found from the result of the forecast with the climatological surface condition, that the PJO in the stratosphere is well predictable in this winter. In fact, anomalous polar cap temperature shows clear downward movement with time, which persists until mid-March. At the same time, the SST was rather higher than normal in the Atlantic Ocean in this winter. So the troposphere will be sandwiched between higher temperature boundaries above and below it. As a reaction to these thermal forcings, a negative AO-like signal will be preferentially created in the troposphere after the SSW.
 In the real data the tropospheric NAM index is sometimes perturbed to a positive signal. How can we understand this from the point of ensemble forecasting? According to the forecasted data, the tropospheric NAM is largely forced to negative NAM throughout in this winter. However, tropospheric intrinsic NAM variability should be superposed on this signal. So real data, which should be considered as one realization of forecasting, will sometimes indicate a positive NAM signal. Strong negative NAM signals in the real data should be regarded as having a more direct influence on the stratosphere because the signals seem to nicely coincide with those of the ensemble prediction (Figure 3).
 The author is grateful to H. Yoshimura for providing numerical models used in the present study. He is also grateful to K. Yamazaki of Hokkaido University and anonymous reviewers for useful comments. This work was supported in part by a Grant-in-Aid (16340144, 18204043, 19340135, 20340131) for Science Research of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.