behavior of planetary waves before and after stratospheric ...€¦ · over 10 000 days by sweeping...

Behavior of Planetary Waves before and after Stratospheric Sudden Warming Eventsin Several Phases of the Equatorial QBO

YOKO NAITO AND SHIGEO YODEN

Department of Geophysics, Kyoto University, Kyoto, Japan

(Manuscript received 14 July 2005, in final form 3 November 2005)

ABSTRACT

Almost a thousand stratospheric sudden warming (SSW) events are obtained through long time integra-tions with a simple global circulation model, and a statistical analysis based on such a large number ofsamples is made to investigate behavior of planetary waves before and after SSW events depending on thephase of the equatorial quasi-biennial oscillation (QBO). An idealized zonal momentum forcing to mimica phase of the QBO is imposed under a perpetual winter condition, and eight phases of the QBO-windforcing are examined for 8 � 10 800-day datasets.

Some systematic dependence on the phase of the QBO-wind forcing is seen in the anomaly of theEliassen–Palm (EP) flux in the winter hemisphere, both in the 10 800-day average and in the composites forSSW events. The composite analysis shows that before SSW events, the upward EP flux in the troposphereand midlatitude lower stratosphere as well as the equatorward flux above the tropopause is larger in thewesterly forcing runs than in the easterly forcing runs. After SSW events, the upward EP flux in thetroposphere is still larger in the westerly forcing runs. Correlation associated with the differences amongSSW events that occurred in each run is significantly positive between the magnitude of the warming andthe planetary wave activity flux before all the events in QBO-wind forcing in the stratosphere, but only inthe easterly forcing runs in the troposphere.

1. Introduction

Occurrence of stratospheric sudden warming (SSW)events is an important factor in intraseasonal and inter-annual variations of winter stratospheric circulation inthe Northern Hemisphere (NH). The relationship be-tween the interannual variation and the equatorialquasi-biennial oscillation (QBO) has been investigatedsince the 1980s. The stratospheric polar vortex isweaker, warmer, and more disturbed during winters inthe easterly phase of the QBO (Holton and Tan 1980,1982), and a major SSW tends to occur in the easterlyphase (Labitzke 1982). The weaker polar vortex in theeasterly phase of the QBO is associated with a largerupward component of the Eliassen–Palm (EP) fluxfrom the troposphere to the stratosphere (Dunkertonand Baldwin 1991). In the Holton–Tan relationship de-scribed above, modulation of the propagation route ofplanetary waves associated with the QBO, for example,

latitudinal shifts of the zero-wind line (i.e., a critical linefor stationary waves), is considered to play an impor-tant role.

When a SSW occurs, planetary waves propagatingfrom the troposphere to the stratosphere are an essen-tial ingredient in the process (e.g., McIntyre 1982). Thewave driving in the stratosphere induces the mean me-ridional circulation in form depending on its time scale,according to the “downward control” principle (Hayneset al. 1991). Fusco and Salby (1999) showed that inter-annual variations of total ozone in midlatitudes of theNH, which are associated with the mean meridionalcirculation, operate coherently with variations of up-welling planetary wave activity from the troposphere.Further quantification of the space–time relationshipsbetween column ozone tendency and lower strato-spheric EP flux was done by Randel et al. (2002) forboth hemispheres. Newman et al. (2001) tested thetime-integrated effects of the upward EP flux on thepolar temperature in the lower stratosphere. Theyshowed that the tropospheric eddy heat flux in middleto late winter (January–February) is highly correlatedwith the mean polar stratospheric temperature during

Corresponding author address: Yoko Naito, Dept. of Geophys-ics, Kyoto University, Kyoto 606-8502, Japan.E-mail: [email protected]

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© 2006 American Meteorological Society

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March. Hio and Yoden (2005) investigated dynamicalfeatures of the interannual variations of the seasonalmarch in the Southern Hemisphere (SH) stratosphere,and characterized the unprecedented year 2002 inwhich a major SSW occurred. They showed that thestronger wave activity in the lower stratosphere is as-sociated with the earlier “shift down” of the polar-nightjet and that the large deviation in 2002 is consistent withthe tendency of the fluctuations in the other years ex-cept for its extreme nature.

Propagation of the stratospheric variation into thetroposphere has also been reported. Baldwin andDunkerton (1999) examined the leading mode of low-frequency variability of wintertime geopotential be-tween 1000 and 10 hPa and showed that Arctic Oscil-lation (AO) anomalies typically appear first in thestratosphere and propagate downward. Taguchi andHartmann (2005) showed that SSWs and the El Niño–Southern Oscillation interfere and induce significantsurface climate anomalies in northern midlatitudes dur-ing winter.

Naito et al. (2003, hereafter referred to as N03) in-vestigated the effects of the equatorial QBO on SSWevents by performing perpetual winter integrationswith a simplified three-dimensional global mechanisticcirculation model (MCM) of the atmosphere in whichzonal momentum forcing was imposed in the equatorialstratosphere to mimic a westerly or easterly phase ofthe QBO. In a series of experiments to sweep a param-eter of the equatorial wind forcing from a case withstrong westerly to a case with strong easterly through acase with zero forcing, statistical and dynamical char-acteristics of SSW events showed systematic depen-dence on the equatorial wind forcing. Composite analy-sis for a large number of the obtained SSW events wasmade to describe daily evolution of the temperaturefield during the events, particularly the aftereffect onlower levels. The statistical significance of the compos-ite difference was tested with the large sample method.A significant difference between a case with westerlywind forcing and another case with easterly wind forc-ing was detected even in the troposphere in high lati-tudes. Naito and Yoden (2005) analyzed 46 years of theNational Centers of Environmental Prediction (NCEP)Reanalysis data and showed that a difference in thepolar temperature between the westerly and easterlyphases of the QBO is significant even in the tropo-sphere.

In the present study, the same MCM as was used byN03 is employed to investigate the dynamical processesthrough which the equatorial QBO influences SSWevents. Perpetual winter integrations are performedover 10 000 days by sweeping a parameter that deter-

mines the vertical profile of the equatorial wind forcing.Composite analysis for a large number of the obtainedSSW events is made to investigate behavior of the zonalmean temperature and the EP flux before and after theevents both in the stratosphere and in the troposphere.As was done by N03 and Naito and Yoden (2005), sta-tistical significance is tested with the large samplemethod.

The present paper is organized as follows. Section 2describes the model and the experimental setup. Sec-tion 3 overviews time–mean states, and section 4 de-scribes the results of statistical analysis for SSW events.Discussion is in section 5 and conclusions are in section 6.

2. Model and experimental setup

The model used in this study is basically the same asin N03, and the details are documented there. Themodel is a three-dimensional global primitive equationmodel (Swamp Project 1998), which explicitly describeslarge-scale motions with a horizontal resolution of T21spherical harmonics truncation and a vertical represen-tation of 42 � levels (� � p/psurface; p is pressure) fromthe surface to the mesopause. The model includes sim-plified physical processes such as Newtonian heating/cooling to a perpetual winter condition in the modelNH, dry atmosphere without moist processes, Rayleighfriction at the surface, and so on. A sinusoidal surfacetopography of zonal wavenumber 1 and amplitude h0 �1000 m is included in the model NH; a parameter sweepstudy with a similar MCM by Taguchi et al. (2001)showed that the parameter range around h0 � 1000 mcorresponds to a regime close to the intraseasonalvariations in the NH winter stratosphere with intermit-tent occurrence of SSW events.

To produce a westerly or easterly phase of the QBO,an additional source term is imposed in the zonal mo-mentum equation:

�u��t � · · · � �QBO�u � UQBO�, �1�

where u(�, , �, t) is the local zonal wind at any pointof longitude �, latitude , and level �; and a relaxationrate QBO and a profile UQBO of the perpetual QBO-wind forcing are prescribed as functions of and � asfollows:

�QBO��, �� 1

30��, �� day�1�, �2�

UQBO��, �� 45��, �� cos�2�� 3

6 � �m s�1�,

�3�

1638 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 63

where � � �log �, and �(, �) is a weighting functionto confine both QBO and UQBO to the equatorialstratosphere:

��, �� exp��

17�2�

� �exp�� 2.7

0.68 �2�, for � � 2.7,

1, for 2.7 � � � 3.6,

exp�� 3.61.37 �2�, for � � 3.6,

�4�

(e.g., Horinouchi and Yoden 1997). The forcing in theupper stratosphere is not very large, though Gray et al.(2001, 2003) mentioned the sensitivity of the NorthernHemisphere stratospheric winter circulation to theequatorial wind in the upper stratosphere.

The phase � in Eq. (3) is changed as an experimentalparameter by using eight values from 0 with an incre-ment of �/4. Figure 1 shows the vertical profiles ofUQBO at the equator � 0°. Here four letters, combi-nations of W and E, indicate the vertical profile of theforcing in each experiment: for example, WWEE (� �3�/2) denotes a westerly shear phase. Similarly, theequatorial zonal wind in the lower stratosphere isforced to be westerly in WWWW (� � 0), while it isforced to be easterly in EEEE (� � �). In each of eight

FIG. 1. Vertical profiles of the QBO-wind forcing at � 0° for the eight runs. Scales onthe rhs show approximate pressure in units of hPa.


runs, time integration is performed with �t � 15 min for12 000 days with a perpetual winter condition. Dailydata for the last 10 800 days, excluding the initial tran-sient time, are analyzed after vertical interpolation ontosurfaces of constant pressure.

3. Time–mean states

Figure 2 shows time–mean fields of the zonal–meanzonal wind [u] and the EP flux F � (Fy, Fz) for 10 800days in the eight runs. Here square brackets denote thezonal mean, and an overbar the time mean. As Taguchiet al. (2001) discussed with their Fig. 1e, general fea-tures of [u] in the present experiment agree with thoseobserved in the real atmosphere qualitatively: the west-erly subtropical jet in both hemispheres and the west-erly polar night jet in the NH extratropical strato-sphere. The EP flux is generally upward in the extra-tropical westerlies from the surface to the upperstratosphere in the NH, and only below the lowerstratosphere in the SH. The upward flux turns equator-ward in the subtropics around the tropopause. Thesefeatures of the EP flux also agree with the observationsof the atmosphere qualitatively.

In response to the QBO-wind forcing, the zonal–mean zonal wind in the equatorial lower stratosphere iswesterly in the westerly forcing runs such as WWWWand is easterly in the easterly forcing runs such asEEEE. The runs with shear-phase forcing such asEEWW or WWEE show zonal–mean zonal wind withthe corresponding shear profile in the equatorial lowerstratosphere. Consequently the shape of the zero-windline (i.e., a critical line for stationary waves) also de-pends on the phase of the QBO-wind forcing. Theequatorward EP flux in the lower stratosphere reacheslower latitudes in the westerly forcing runs than in theeasterly forcing runs.

Influence of the QBO-wind forcing on the extra-tropical stratospheric circulation appears as a system-atic change in strength of the winter polar night jet inthe NH. The polar night jet is strongest in WWWW andweakest in EEEE. These are consistent with the Hol-ton–Tan relationship as was also confirmed in N03. Thestrength of the polar night jet changes gradually as thephase of the QBO-wind forcing changes betweenWWWW and EEEE.

Figure 3 shows the grand average of [u] and F overthe eight runs (center) and the anomaly fields for each

FIG. 2. Latitude–height sections of the 10 800-day mean fields of the zonal–mean zonal wind [u] (m s�1) and the EP flux F (kg s�2)in the eight runs. Contour interval of [u] is 20 m s�1 and the zero-wind line is drawn by a thick solid line. Vectors below 100 hPa aremultiplied by a factor of 1/5. The unit vectors are shown on the rhs of the bottom row. Too-small vectors are not plotted.


run from the grand average. As was seen in Fig. 2,anomaly of the zonal–mean zonal wind in the equato-rial stratosphere is the direct response to the QBO-wind forcing, while that in the extratropical upperstratosphere is a remote response. The polar night jet isstrongest in WWWW and weakest in EEEE. Theanomaly vectors of the EP flux in the high-latitudestratosphere are upward in the easterly forcing runs,particularly in EEEE, indicating that the upward EPflux is larger compared to the grand average. Theweaker polar night jet associated with the larger up-ward EP flux in the easterly phase of the QBO isconsistent with the observational result by Dunkertonand Baldwin (1991). The anomaly vectors in the tropi-cal lower stratosphere are poleward in the easterly forc-ing runs, indicating that the equatorward EP flux issmaller. The height range of the poleward anomalyvectors in the equatorial stratosphere corresponds to

that of the negative (or easterly) wind anomaly. Theanomaly vectors in the midlatitude troposphere aredownward in the easterly forcing runs, indicating thatthe upward EP flux is smaller in the easterly forcingruns.

The anomaly vectors of the EP flux in WWWWare roughly in the opposite direction to those in EEEEwith similar magnitudes. The stronger polar night jetis associated with the smaller upward EP flux inthe high-latitude stratosphere and the larger equator-ward EP flux in the tropical stratosphere. The anomalyvectors vary gradually depending on the QBO-windforcing from EEEE to WWWW through the westerlyshear phases. On the other hand, they vary ratherabruptly in the easterly shear phases between EWWWand EEWW. The QBO-wind forcing is the same mag-nitude with opposite sign between EEWW andWWEE, while the anomaly fields do not have such

FIG. 3. (central panel) Grand average of the 10 800-day mean fields of the zonal–mean zonal wind [u] (m s�1)and the EP flux F (kg s�2) over the eight runs. Note that only the NH below 1 hPa is shown; contour interval andvectors are the same as in Fig. 2. The unit vectors are shown on the rhs of the middle row. (other panels) Anomalyfields of the 10 800-day mean for each run from the grand average. Negative values shaded with diagonal linesindicate weaker westerly (or stronger easterly) compared with the grand average.


antisymmetry, although the anomalies are not verylarge.

4. Composite analysis for SSW events

Time variations of the zonal–mean temperature [T ]around the North Pole in the upper stratosphere areshown in Fig. 4 for the last 2000 days in each run. ManySSW events are seen for all runs. Here we define a SSWevent from these time series following N03 as a periodduring which the temperature is continuously above235 K and its maximum is greater than 270 K. Denotedby a circle is the day of maximum temperature in eachevent period. Total number N of the defined SSWevents in 10 800 days for each run is shown on the rhsof the panel. A total of 954 SSW events are obtained inthe eight runs. In WWWW, the occurrence of SSWevents is the least frequent in all of the runs. The totalnumber N increases monotonically from WWWW toEEEE both through the easterly shear phases andthrough the westerly shear phases. The number of SSWevents increases monotonically with the increase ofdepth of the layer of equatorial easterly wind in thelower stratosphere (Figs. 1 and 2).

a. Composite time-variation of polar temperatureand upward EP flux

Composites of the time variation of polar tempera-ture before, during, and after SSW events are shown inFig. 5, in a similar way to Figs. 11 and 14a of N03. Thekey day, corresponding to lag � 0 day on the abscissa,is defined as the day of maximum temperature at p �2.6 hPa in each event (denoted by a circle in Fig. 4). Atp � 2.6 hPa, the SSW events appear as a sharp increaseof the temperature by �50 K from lag ��10 days,rather independently of the QBO-wind forcing. Thesuperficial independence in the maximum temperatureis found only at neighboring levels around p � 2.6 hPa.The maximum temperature is highest in WWWW orWWWE at p � 1.2 hPa and above, while it is lowest inWWWW at p � 3.8 hPa and below (not shown). At p �12 hPa, the maximal temperature just after the key dayis about 10 K lower in WWWW than in the easterlyforcing runs, and the composite temperature is lower inthe westerly forcing runs, especially in WWWW, duringthe gradual decay for 30 days after the event. Note alsothat the composite temperature before lag � �10 dayhas some variation depending on the QBO-wind forc-

FIG. 4. Time series of the zonal-mean temperature [T ] (K) at � 86°N and p � 2.6 hPa for 2000 days in the eight runs. Horizontallines at 235 and 270 K denote the two thresholds for the definition of SSW events. Periods of warming events are shaded with dots. Acircle denotes the key day of each warming event. The total number of events in 10 800 days for each run is shown on the rhs of thepanel.


ing related to the occurrence of the previous SSWevent. The effect of the QBO-wind forcing is more evi-dent in the lower stratosphere (p � 120 hPa). The com-posite temperature increases gradually for a month orso before and after the key day in the three westerlyforcing runs (WWWE, WWWW, and EWWW). In themidtroposphere (p � 449 hPa), the temperature is sig-nificantly higher throughout SSW events in the westerly

forcing runs than in the easterly forcing runs, althoughthe difference is about 1 K or so (see Fig. 14b in N03).

Composites of the upward EP flux are shown in Fig.6 after being averaged over middle and high latitudes.The upward EP flux at p � 57 hPa has a maximumseveral days before the key day. The flux before themaximum is larger in the westerly forcing runs, espe-cially in WWWE. The flux after the key day, on theother hand, tends to be larger in the easterly forcingruns. The upward EP flux at p � 120 hPa also has amaximum several days before the key day. The flux

FIG. 6. As in Fig. 5 but for the vertical component of the EP fluxFz cos (kg s�2) averaged from � 30°N to 86°N at (top) p � 57,(second) 120, (third) 254, and (bottom) 449 hPa.

FIG. 5. Composite time series of the zonal-mean temperature[T ] (K) for SSW events in the eight runs at � 86°N and (top)p � 2.6, (second) 12, (third) 120, and (bottom) 449 hPa. The keyday corresponds to lag � 0 day.


before the maximum is larger in WWWE and WWEEthan in the other phases. The flux after the key day islarger in the easterly forcing runs at p � 120 hPa aswell as at p � 57 hPa. The upward EP flux in thetroposphere (p � 254 and 449 hPa) gradually increasesfor a few weeks and suddenly decreases several daysbefore the key day. The upward flux during the in-crease phase is larger in the westerly forcing runs thanin the easterly forcing runs. The difference dependingon the QBO-wind forcing becomes small after the sud-den decrease.

b. Latitude–height section of EP flux vectors

Figure 7 shows SSW event composites of the EP fluxvectors F averaged from lag � �30 day to the key day.The grand composite for the total 954 SSWs (shown inthe central panel) is subtracted from the composites forSSWs that occurred in each run (shown in the otherpanels). The large sample method is used to test statis-

tical significance for the difference in the vertical com-ponent Fz between the composite for the SSWs thatoccurred in a particular run and the composite for theSSWs that occurred in the other seven runs. In thetroposphere, the upward EP flux is significantly largerin the westerly forcing runs and smaller in the easterlyforcing runs, as already shown in the latitudinally aver-aged time series in Fig. 6. In particular, the large mag-nitude of Fz around � 50°N, p � 300 hPa in WWWEhas statistical significance of more than 99.99999%.Above the tropopause, the equatorward flux in low lati-tudes is larger in the westerly forcing runs (particularlyin WWWE) while smaller in the easterly forcing runs(particularly in EEEE). In the westerly forcing runs,the upward flux is larger in the midlatitude lowerstratosphere while smaller in high latitudes. The oppo-site sign of the anomaly Fz between midlatitudes andhigh latitudes in each run indicates a latitudinal shift ofthe dominant zone of the upward EP flux: equatorwardshift in the westerly forcing runs while poleward shift in

FIG. 7. (central panel) Grand composite of the EP flux F (kg s�2) for the total 954 SSWs, averaged from lag ��30 day to 0 day. The unit vectors are shown on the right side of the middle row. (other panels) Anomalies of SSWevent composites of F in each run from the grand composite. The unit vectors are shown on the rhs of the bottomrow. See text for statistical significance denoted by gray shades. Too-small vectors are not plotted.


the easterly forcing runs. The pattern of the EP fluxanomalies similar to WWWE is seen in a broad range ofthe phase from WWEE to EWWW, although theanomaly in the high-latitude stratosphere is not verylarge in EWWW. On the other hand, the similar patternto EEEE appears only in EEEW. The composite of theEP flux anomalies before SSW events has large asym-metry with respect to the opposite sign of the QBO-wind forcing.

Figure 8 shows SSW event composites of the EP fluxvectors F averaged from the key day to lag � 30 day.Overall patterns of the anomaly vectors after SSWevents depending on the QBO-wind forcing are similarto those before SSW events as shown in Fig. 7. How-ever, the statistically significant regions are largely re-duced in the troposphere, particularly in middle andhigh latitudes. The upward flux in midlatitudes is stillsignificantly larger in WWWW while smaller in EEEE.The equatorward flux in low latitudes above the tropo-pause is larger in the westerly forcing runs (WWEE toEWWW). The upward flux in the high-latitude lowerstratosphere is smaller in the westerly forcing runswhile larger in EEEE and EEWW.

c. Relationship between polar temperature andupward EP flux

According to the argument by Newman et al. (2001),polar temperature in the lower stratosphere is depen-dent on the time-integrated effects of the troposphericupward EP flux. In Fig. 9, SSW event composites of thepolar temperature at p � 12 hPa averaged for 6 daysjust after the key day are plotted against composites ofthe upward EP flux averaged from lag � �30 day to 0day over middle and high latitudes at four levels (p �57 hPa, 120 hPa, 254 hPa, and 449 hPa) for eight runs.The composites of the polar temperature and the up-ward EP flux show roughly negative correlation exceptfor those at p � 120 hPa; the polar temperature is lowerwhile the upward EP flux is larger in the westerly forc-ing runs than in the easterly forcing runs.

For each composite a confidence ellipse is deter-mined so that the ellipse encloses an area in which an-other possible composite for a set of events in each run(the number of events is supposedly the same as thepreviously obtained sample) would appear with prob-ability 90% (see Wilks 1995). Since the estimated vari-

FIG. 8. As in Fig. 7 but averaged from lag � 0 day to 30 day.


ance of possible composites is �2/N (where �2 is a vari-ance of the sample set of events and N is the number ofevents in the set), a confidence ellipse for possible com-posites is determined by reducing the size of a confi-dence ellipse evaluated for events with a scaling factorof 1/�N. The ellipses show that separation betweenthe composites in the westerly forcing runs (WWWE,WWWW, and EWWW) and those in the others is sta-tistically significant at p � 449 and 254 hPa. Heavieroverlapping of the ellipses at p � 120 hPa means thatthe separation is less significant.

The anisotropy of a confidence ellipse indicates thecorrelation between the time-averaged temperatureand the upward EP flux among the SSW events in eachrun. Most of the ellipses are elongated diagonally frombottom left to top right in the lower stratosphere, whichindicates the positive correlation between the polartemperature and the upward EP flux; stronger SSWevents follow with larger upward EP flux. The ellipsesat p � 254 and 449 hPa are hardly tilted in the westerlyforcing runs.

Figure 10 shows a similar relationship between thepolar temperature and the upward EP flux as in Fig. 9but the flux is averaged from lag � 0 day to 30 day.After SSWs, the upward EP flux is smaller in the west-erly forcing runs than in the easterly forcing runs at p �57 and 120 hPa, while it is larger in the westerly forcingruns at p � 254 and 449 hPa. The separation betweenWWWW and EEEE, for instance, is still significant atall levels. The anisotropy of the confidence ellipsesshows that composites of the polar temperature havepositive correlation with the upward EP flux at p � 57and 120 hPa and negative correlation with the upwardEP flux at p � 254 and 449 hPa.

Figure 11 shows a quantitative summary of the an-isotropy of confidence ellipses, or the correlation coef-ficients between the temperature just after the key dayin the polar midstratosphere and the latitudinally aver-aged upward EP flux averaged over 31 days before(Fig. 11a) or after (Fig. 11b) SSWs at the four lowerlevels. The correlation coefficient with the upward EPflux before SSW events is significantly positive in alleight runs at p � 57 and 120 hPa, while it is significantlypositive only in the easterly forcing runs (from EEWWto WWEE) at p � 254 and 449 hPa. The maximumcorrelation is obtained in WEEE: 0.44 at p � 57 hPa,

←

254, and (bottom) 449 hPa. The composites are denoted by plussigns and linked by thin lines in the order of the phase of theQBO-wind forcing. An ellipse denotes 90% confidence limit ofpossible composites for each run. See text for details.

FIG. 9. Composites for SSWs of the zonal–mean temperature[T ] (K) at � 86°N and p � 12 hPa averaged from lag � 1 dayto 6 day, plotted against composites of the vertical component ofthe EP flux Fz cos (kg s�2) averaged from � 30° to 86°N andfrom lag � �30 day to 0 day at (top) p � 57, (second) 120, (third)


0.58 at p � 120 hPa, 0.43 at p � 254 hPa, and 0.47 atp � 449 hPa. The correlation coefficient with the up-ward EP flux after SSW events at p � 57 and 120 hPais significantly positive in the westerly or easterly shearforcing runs, particularly in EWWW and EEWW. Thecorrelation coefficient at p � 254 and 449 hPa is sig-nificantly negative in the easterly forcing runs, particu-larly in EEEE.

5. Discussion

Time–mean states of the EP flux (Figs. 2 and 3) showthat the planetary waves propagate more easily toward

FIG. 10. As in Fig. 9 but the vertical component of the EP fluxFz cos (kg s�2) is averaged from lag � 0 day to 30 day.

FIG. 11. Correlation coefficient of the zonal-mean temperature[T ] (K) at � 86°N and p � 12 hPa averaged from lag � 1 dayto 6 day with the vertical component of the EP flux Fz cos (kgs�2) averaged from � 30° to 86°N at p � 57, 120, 254, and 449hPa: (a) from lag � �30 day to 0 day and (b) from lag � 0 day to 30 day. Note that the run WWWW is plotted at both ends. Grayshades denote statistical significance.


the equator in the westerly phase of the QBO becausethere is no zero-wind line (i.e., a critical line for sta-tionary waves) in the lower stratosphere. The compos-ite analysis of the EP flux shown in Figs. 7 and 8 dem-onstrates the behavior of planetary waves before andafter SSW events depending on the phase of the QBO-wind forcing with statistical significance based on largenumbers of samples—at least 70 events in each phase.The result shows that the equatorward EP flux beforeSSWs is larger in the westerly forcing runs. This prop-erty of the wave propagation results in the inefficiencyof the wave driving to induce a warming event in thewesterly forcing runs; occurrence of SSW events is lessfrequent (Fig. 4) and, even if an event occurs, the in-crease of temperature is smaller despite the larger up-ward EP flux (Figs. 5, 6, and 9). The upward flux afterSSW events is still significantly larger in the westerlyforcing runs than in the easterly forcing runs (Fig. 8). Apair of confidence ellipses (e.g., for WWWW andEEEE) shown in Fig. 10 are well separated in the tro-posphere, indicating that the composite difference ofthe upward flux between the two phases is statisticallysignificant. The difference in the impact of the strato-spheric warming event on the tropospheric waves de-pending on the phase of the QBO is newly demon-strated in the present study.

Each confidence ellipse shown in Figs. 9 and 10 in-dicates correlation associated with difference amongSSW events that occurred in each run, and the corre-lation coefficient is given in Fig. 11. The correlation ofthe polar temperature in the upper stratosphere withthe upward EP flux in the lower stratosphere beforeSSWs is significantly positive in all phases of the QBO-wind forcing. It is easy to understand because largerupward EP flux and its consequence of larger wavedriving result in a stronger warming event in the strato-sphere. The correlation with the upward EP flux beforeSSWs in the troposphere is still significantly positive inthe easterly forcing runs, while it is not significant in thewesterly forcing runs. The loss of significant correlationcan be due to large variability of the fraction of the EPflux toward the equatorial region above the tropo-pause.

The confidence ellipses in Figs. 9 and 10 are larger inthe westerly forcing runs than in the easterly forcingruns. This difference of size is mostly due to the smallersample size in the westerly forcing runs (remember thata confidence ellipse for possible composites is 1/�Ntimes the size of a confidence ellipse evaluated for asample set of events). The ellipses for possible eventsoverlap each other heavily (not shown). Also, varia-tions of the variances of the upward EP flux and thetemperature depending on the phase of the QBO-wind

forcing are another factor determining the size of aconfidence ellipse, although the variations are quitesmall.

The SSW events shown in Fig. 4 are sometimes clus-tered in time integrations under perpetual winter con-dition. In the real atmosphere, a sequence of minorSSWs is sometimes observed. The condition when aSSW event occurs for the first time in a season maydiffer from the condition when another event follows.A further study focusing on the first events in a seasonmay improve our understanding about the dependenceof SSW occurance on QBO-wind forcing.

6. Conclusions

To investigate how the planetary wave activity beforeand after a stratospheric sudden warming (SSW) eventdepends on the phase of the equatorial quasi-biennialoscillation (QBO), a statistical analysis was made basedon almost one thousand SSW events that were obtainedby a numerical experiment. An idealized zonal momen-tum forcing to mimic a phase of the QBO was imposedin the equatorial stratosphere in a simple global circu-lation model. By changing the phase of the perpetualQBO-wind forcing as an experimental parameter, eightintegrations were performed for 12 000 days under per-petual winter condition. Time-mean states of the zonal-mean zonal wind and the Eliassen–Palm (EP) flux de-pending on the QBO-wind forcing reconfirmed the pre-viously obtained relationship between the phase of theQBO forcing and the responses in middle and high lati-tudes (Figs. 2 and 3).

The EP fluxes before and after SSW events were alsocompared among the several phases of the QBO forc-ing. Such analysis is not possible without a large num-ber of samples of SSW events during each phase of theQBO. Composite analysis of the EP flux before SSWevents (Figs. 6 and 7) showed that the upward flux inthe troposphere is larger in the westerly forcing runsthan in the easterly forcing runs. As well as the equa-torward flux above the tropopause, the upward flux inthe midlatitude lower stratosphere is also larger in thewesterly forcing runs (Fig. 7). The larger upward fluxplays a key role when a SSW event takes place, even inthe westerly forcing runs in which the upward flux is notvery large in the high-latitude lower stratosphere. AfterSSWs, composites of the EP flux still have a statisticallysignificant difference depending on the QBO-windforcing (Fig. 8); the upward flux in the midlatitude tro-posphere is larger in the westerly forcing runs than inthe easterly forcing runs.

Relationship between the temperature in the polarstratosphere just after SSW events and the latitudinally


and temporally averaged upward EP flux in the lowerstratosphere and troposphere was investigated (Figs. 9and 10). The composite of the polar temperature islower while the upward EP flux, averaged over 31 daysbefore SSW events, is larger in the westerly forcing runsthan in the easterly forcing runs with statistical signifi-cance (Fig. 9). Similarly the upward EP flux, averagedover 31 days after SSW events, is larger in the westerlyforcing runs in the troposphere while it is smaller in thestratosphere (Fig. 10).

The anisotropy of each confidence ellipse also indi-cates the correlation between the polar temperatureand the time-averaged upward EP flux for SSW eventsin each run. In the stratosphere, stronger SSW eventsfollow larger upward EP flux for all QBO-wind forcing,while the correlation with the upward EP flux in thetroposphere is significant only in the easterly forcingruns. In the westerly forcing runs, on the other hand,the correlation is not significant because a large fractionof the tropospheric upward EP flux can turn toward theequatorial region.

Acknowledgments. The graphic tools that we usedare based on the codes in the GFD-DENNOU Library(SGKS Group 2001). Time integrations were done onVPP800 of the Academic Center for Computing andMedia Studies of Kyoto University. Calculation ofthresholds for a standard normal variable correspond-ing to statistical significance was done with the programon the web site by Aoki (1996). This work was sup-ported in part by the Grant-in-Aid for Scientific Re-search of the Ministry of Education, Culture, Sports,Science, and Technology (MEXT) of Japan, and by theKyoto University Active Geosphere Investigations forthe 21st Century COE (KAGI 21), which was approvedby the MEXT of Japan.

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