Attribution of variations in the quasi biennial oscillation period from the duration of easterly and westerly phases

Transcription

1 Clim Dyn DOI.07/s Attribution of variations in the quasi biennial oscillation period from the duration of easterly and westerly phases Mengmiao Yang 1 Yueyue Yu 2,3 Received: June / Accepted: 6 December Springer-Verlag Berlin Heidelberg Abstract This study reports the main features of quasibiennial oscillation (QBO) period variability at stratospheric levels from to hpa and its attribution from the duration variability of westerly and easterly phases using monthly mean zonal wind data from August 1956 to July 13, archived by Free University of Berlin. A total of 24 QBO events have been distinguished based on the zonal wind field and wavelet analysis for it. The QBO period varies in phase at various stratospheric levels and shows no significant long-term trend but decadal to multi-decadal variability. The noted case-to-case variations in QBO period are due to variations in durations of the westerly and easterly phases at the same level. The highly coupled variability of the easterly duration in the upper levels above hpa and westerly durations in the lower levels below, which manifests the stalling or accelerating of the descent rate of easterly wind regimes around hpa, is found to be the dominant variability of the easterly and westerly durations at various stratospheric levels. Accordingly, the period of QBO in the lower levels below hpa/upper levels above hpa is determined by the westerly/easterly durations there in about 75 % of the 24 QBO events; and at hpa, variations in the durations of both easterly and * Yueyue Yu yuyueyue1987@hotmail.com 1 Ministry of Education Key Laboratory for Earth System Modeling, Center for Earth System Science, Tsinghua University, Beijing 0084, China 2 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 0029, China 3 University of Chinese Academy of Sciences, Beijing 0049, China westerly phases contribute to the QBO period variability. On the contrary, in only 4 out of 24 QBO events, the variations of the westerly/easterly durations in the upper/lower levels are greater than the variations of the easterly/westerly durations in the upper/lower levels, making deterministic contributions to the QBO period variability. Keywords Quasi-biennial oscillation period Wavelet analysis Multi-variance EOF analysis Westerly and easterly phases 1 Introduction The quasi-biennial oscillation (QBO) is a dominant oscillation mode in the equatorial stratosphere discovered independently by Reed et al. (1961) and Veryard and Ebdon (1961). The QBO is characterized by an alternating pattern of downward-propagating easterly and westerly wind regimes in the equatorial stratosphere with a period of about 28 months. Lindzen and Holton (1968) and Wallace and Kousky (1968) developed a theory of equatorial waves on this alternating regime descent phenomenon, which was further refined in Holton and Lindzen (1972) and supported by the laboratory experiment of Plumb and McEwan (1978). They documented that the westerly phase of the QBO is mainly due to the upward transport of westerly momentum by the upward propagating Kelvin waves from the tropical troposphere, while the easterly phase is contributed from the upward transport of easterly momentum by the upward propagating Rossby-gravity waves. Besides these two waves, a broad spectrum of gravity waves from a variety of sources (e.g., convection and frontal systems) (Takahashi and Boville 1992; Dunkerton 1997; Kawatani et al. ) also play an important role in driving the

2 M. Yang, Y. Yu observed oscillation. Then through internal interactions between the waves and the mean flow in the equatorial stratosphere, the westerlies or easterlies exhibit a downward propagation without loss of amplitude. The wavemean flow interaction mechanism for the QBO includes the wave-breaking processes (e.g., Lindzen and Holton 1968; Holton and Lindzen 1972) and the continuously alternating downward transfer of westerly and easterly angular momentum by westward-tilted, westward-propagating waves and eastward-tilted, eastward-propagating waves (Ern and Preusse 09; Cai et al. 14; Ern et al. 14). Only a few climate models can simulate the alternation between easterlies and westerlies in the tropical stratosphere, including the full radiative-dynamical model (Gray and Pyle 1989), the 2-D middle atmosphere model (Mengel et al. 1995; Burrage et al. 1996), and general circulation models (GCMs) (Takahashi 1996, 1999). However, issues remain in simulating the realistic period of QBO events. The simulated QBO period varies from 1 to 2.3 years (Horinouchi and Yoden 1998; Untch 1998; Hamilton et al. 1999; Takahashi 1999), which is shorter than the average period of realistic QBO events. To provide useful guidance for improving the model simulations of QBO events, it is important to investigate the QBO period variability and reveal its possible mechanism. Although an average QBO period is approximately 28 months, it has interannual variations of a few months, particularly from 22 to 34 months (Baldwin et al. 01). The total period of QBO events depends on the variations in both easterly and westerly phase durations at the same level. These durations at a given level are further related to those at other levels through the anomalous downward propagation of an easterly or a westerly wind regime. One potential mechanism used to explain the variability of the QBO period is the stalling of easterlies, which is represented by a longer easterly duration above the stalling level and a longer westerly duration below. The stalling of easterlies tends to occur more frequently than that of westerlies (e.g., Fischer and Tung 08), which can be attributed to three main factors according to previous studies: (i) the QBO self-induced secondary circulation due to thermal wind balance (Plumb and Bell 1982; Baldwin et al. 01; Ribera et al. 04; Punge et al. 09) is upward for the easterly phase, thus favors the stalling of easterly wind regime; (ii) the Brewer-Dobson circulation (BDC) in the tropics tends to be stronger during the easterly phase of the QBO and therefore the slowdown of the descent of the easterlies caused by the upward branch of the BDC is stronger than that of the westerlies (Plumb and Bell 1982; Kinnersley and Pawson 1996; Niwano et al. 03; Flury et al. 13); and (iii) variability of the QBO period is also modulated by external forcing (i.e., volcanic aerosols at equator via inducing local heating as in Dunkerton 1983 and Marquadt 1997, El Niño Southern Oscillation (ENSO) via modulating wave activities as in Maruyama and Tsuneoka 1988, and the 11-year solar cycle as in Fischer and Tung 08) and remote circulation anomalies, such as the polar downwelling associated with Stratospheric Sudden Warming (SSW) events, which are caused by the planetary wave breaking and dissipation in the polar stratosphere (Dunkerton 1990; Holton et al. 1995; Randel et al. 02; Hood and Soukharev 03). SSW events tend to favor a longer QBO period since the downwelling at the pole associated with SSWs remotely strengthens the upwelling at the equator, which helps decrease the decent rate of wind regimes in tropics and lengthens the QBO period. In addition, the SSW events were observed to occur more frequently in late winter in Northern Hemisphere during solar maximums than during solar minimums (Labitzke 1982; Camp and Tung 07; Gray et al. ), which is probably due to the modification of solar heating in the winter polar stratosphere on the upward propagation of planetary waves (Marchand et al. 12). So it is proposed that QBO periods should be longer during solar maximums. However, such linkage turns out to be nonstationary: before 1990s, solar minima corresponds to the longer QBO period, while in the remaining three solar cycles after 1990s, the QBO period is lengthened at solar maxima (Salby and Callaghan 00; Soukharev and Hood 01; Gabis and Troshichev 06; Fischer and Tung 08). This suggests that the role of the stalling of easterlies in determining the variability of QBO period and its underlying mechanism are still not convincingly established and need further investigation. Several previous studies have also examined the relation between the variability of durations of easterly and westerly phases at the same level and different levels respectively, but observational evidence and model simulations are controversial and few generally acknowledged conclusions have been drawn. Salby and Callaghan (00) reported that the descent of the easterly shear zone tends to stall near hpa during the solar minimum, leading to a longer duration of the westerly phase in the middle and lower stratosphere, particularly at and hpa, whereas the duration of the easterly phase at the same level is maintained for approximately 12 months, contributing to the longer QBO period below hpa. This has been confirmed by Pascoe et al. (05) using the ERA- data set. Distinctly, Soukharev and Hood (01) found that the durations of both the westerly and easterly phases in the middle and lower stratospheres tend to be prolonged during solar minima. In a series of general circulation model (GCM) experiments conducted by Palmer and Gray (05), the durations of both easterly and westerly phases at 26 hpa are shortened during solar maxima. The 2-D photochemicaldynamical middle atmosphere model experiments of McCormack (03) show that at 32 hpa, the westerly duration is

3 Attribution of variations in the quasi-biennial oscillation period from the duration of significantly shortened during the solar maximum, whereas the easterly duration is lengthened. Using Singapore wind data of for the lower stratosphere, courtesy of Barbara Naujokat of Free University of Berlin, and continuous wavelet transform analysis, Fischer and Tung (08) demonstrated that the easterly duration at hpa and the westerly duration at hpa vary synchronously and dominate the decadal variation up to 12 years in the total periods of QBO events above hpa and below, respectively. Following the work of Fischer and Tung (08), we examine in the present study the case-to-case variations of the QBO period and elucidate the contributions of the variability of westerly and easterly durations to the total period variability of the QBO at various stratospheric levels. For this analysis, we obtained updated monthly mean zonal wind datasets of from Free University of Berlin. In the following section, we briefly describe the dataset used in this study and methods for distinguishing a QBO event in addition to criteria used for dividing the event into easterly and westerly phases. Section 3 shows the temporal variations of the QBO period using wavelet analysis and the corresponding variations of easterly and westerly durations in each QBO event. In Sect. 4, we investigate the dominant spatial patterns or vertical profiles of the QBO period, the westerly and easterly durations via empirical orthogonal function (EOF) analysis, and further establish the relationship between the QBO periods and westerly and easterly durations using multivariate EOF (MV EOF; Wang 1992) analysis. Section 5 shows the statistical analysis of the relationship among the QBO period, the westerly and easterly durations at different levels on a case-by-case basis. The concluding remarks are provided in Sect Data and methodology The data used in this study, monthly mean zonal winds for seven stratospheric levels, i.e.,,,,,,, and hpa, were obtained from Free University of Berlin. This dataset was produced by combining the observations of three radiosonde stations: Canton Island (3 S/172 W, January 1956 August 1967), Gan/Maledive islands (1 S/73 E, September 1967 December 1975), and Singapore (1 N/4 E, 1976 present). This dataset is considered to be representative of the entire equatorial belt because many studies (e.g., Hamilton et al. 04) have shown that longitudinal differences in the QBO phase are negligible. In this study, we selected 24 QBO events at each stratospheric level in the period A QBO event is defined as the period from the first month of the westerly phase to the last month of the easterly phase at a given level. Based on this definition and the downward propagating features of a westerly or an easterly wind regime, the timespans of data selected for various levels differed slightly. Lower levels related to more timespan shifting toward later months. Specifically, we used data for the periods of August 1956 April 12 for hpa, September 1956 June 12 for hpa, November 1956 September 12 for hpa, March 1957 January 13 for hpa, April 1957 March 13 for hpa, June 1957 May 13 for hpa, and September 1957 July 13 for hpa. We then obtained the total period and durations of the westerly and easterly phases of each of the 24 QBO events. Since the temporal lag of the transit between easterly and westerly wind regime at hpa compared to that at hpa is 12 months in average, about 2 4 months less than half of the average period of QBO, the timespan of the easterly phase at hpa largely overlays with the timespan of the westerly phase at hpa in terms of time. We found that there were several transition periods when the values of zonal winds in the equatorial stratosphere fluctuated near zero, which is difficult to determine the phase to which they belong. The transition period defined here starts at the day when the monthly mean zonal wind reaches 0, and afterwards continuously fluctuates around 0 with an amplitude less than % of the mean amplitude of the zonal wind velocity during the westerly and easterly phases and ends at the day before the monthly mean zonal wind exceeds the same criteria. The number and duration of the transition periods at each of the seven stratospheric levels in the period are listed in Table 1. It is seen that Table 1 The number, time range and duration of the transition periods at 7 stratospheric levels Level Number of transition period Time range hpa hpa 0 hpa hpa hpa hpa hpa Duration (months)

4 M. Yang, Y. Yu among the 24 QBO events, there is only one or no transition period at all the 7 stratospheric levels except and hpa. Even at and hpa, where there are 9 and 4 transition periods, respectively, the duration of transition periods is comparatively shorter than the westerly and easterly durations before and after them with a ratio between the transition period and the westerly and easterly durations at about 0.3. Those features of the transition period provide the rationale for simply dividing the transition period into two halves with the former and latter half allocated to the phase periods prior to and after that point, respectively. It is admitted that this procedure may create some subjectivity in the method of calculating the westerly and easterly durations and the total period, but the validity of this method can be justified: on the one hand, an objective method, wavelet analysis of zonal winds, has been used, as shown in the next section; on the other hand, considering that filtering methods may help reduce the occurrence of transition period, we conducted the filtering methods, including Fourier transform (Cooley et al. 1969) and ensemble empirical decomposition (EEMD, Wu and Huang 09; Huang et al. 12), on the monthly mean zonal wind, and found that the main results are not sensitive to the use of the filtering process. 3 Variations of the QBO period The local period of the QBO at seven pressure levels in the stratosphere can be objectively determined from the maxima of wavelet power spectra of zonal winds at corresponding levels during the period (dashed curves in Fig. 1). The periods of QBO at various pressure levels in the stratosphere tend to exhibit strong variations in phase and show little significant differences in duration. The periods of the QBO at all seven levels vary within a range of months, showing decadal to multi-decadal fluctuation from a mean period of 28 months but no significant long-term linear trend. This finding indicates that the QBO generally exhibits a stable periodic oscillation with an average period of 28 months; this result is consistent with those in previous reports (Ebdon and Veryard 1961; Veryard and Ebdon 1961; Naujokat 1986; Baldwin et al. 01). The decadal variability of the QBO period shows close relationship with the solar cycle. Specifically, before 1990s, the period of the QBO reached its maximum during the three solar minimums of 1965, 1976, and 1986, which were mentioned by Salby and Callaghan (00). After 1990s, their out-of-phase relation changed to in-phase relation: the period of the QBO reached its maximum during the solar maximum of 00 and reached minimums during the solar minimums of 1997 and 07, which is consistent with Gabis and Troshichev (06) and Fischer and Tung (08). See Fischer and Tung (08) and references therein for detailed information about the linkage of the decadal variability of QBO period to the 11-year solar cycle. Hereinafter, we focus on the case-to-case variations of the QBO period. The total period of the 24 QBO events, denoted by the thick solid black curves in Fig. 1, was selected according to the stratospheric zonal wind field (Fig. 2a) following the method introduced in the previous section. This period strongly correlates with the maxima of the wavelet power spectrum (dashed black curves in Fig. 1) at all 7 levels, confirming that the method of manually selecting QBO events and counting their periods is reliable. Moreover, we manually selected the westerly and easterly phases of each QBO event at seven stratospheric levels and displayed the time series of the total period of QBO events and the durations of the westerly and easterly phases of QBO in Fig. 2b d. The westerly phase tends to have longer durations at lower levels than those at upper levels. The opposite is noted for the easterly phase with longer durations at upper levels than those at lower levels. At the middle levels of the stratosphere (i.e., hpa), the westerly and easterly durations have nearly the same magnitude. These features of westerly and easterly phases at different levels agree with the research of Salby and Callaghan (00) and Gabis and Troshichev (06). A comparison of the total period of QBO events (Fig. 2b) with the easterly (Fig. 2d) and westerly durations (Fig. 2c) sketches out a generally inphase relation of the variations in the total periods of QBO events with variations of the westerly durations in the lower stratosphere and those of the easterly durations in upper levels, which supplements the findings of Fischer and Tung (08), obtained from two levels, and hpa. 4 Dominant vertical profiles of the variations of the QBO period and easterly and westerly durations In this section, we investigate the dominant spatial patterns or vertical profiles of the variations of the total period of QBO events and the durations of the westerly and easterly phases of QBO events through EOF analysis. The roles of case-to-case variations of the westerly and easterly durations in determining the variations of the QBO period can be examined by determining the relationships among the time coefficients of dominant EOF modes of the three variables. The spatial patterns and their corresponding time coefficients of the two leading EOF modes of the total period of QBO events during the period are displayed in Fig. 3. The EOF 1 mode is strongly dominant and explains 82.8 % of the total case-to-case variance of the QBO

5 Attribution of variations in the quasi-biennial oscillation period from the duration of Fig. 1 Local period in months of zonal wind data from the Free University of Berlin (FUB) at seven stratospheric levels as determined by the Morlet wavelet power spectra and the distribution of variance: a hpa, b hpa, c hpa, d hpa, e hpa, f hpa, g hpa. The black dashed curves represent the maxima of the wavelet power at each level. The areas encircled by the yellow contours are above the 95 % statistical significance level, and the black solid curves denote the wavelet edge. The superimposed thick black solid curves represent the total periods of quasi-biennial oscillation (QBO) manually selected on the basis of westerlies and easterlies at each pressure level

6 M. Yang, Y. Yu Fig. 2 a Time height section of monthly mean zonal wind data obtained from Free University of Berlin (FUB), based on which 24 quasi-biennial oscillation (QBO) events were detected and the associated total period and durations of westerlies and easterlies for each QBO event were manually selected. Also shown are the time series of the manually selected, b total period of QBO, c westerly duration, and d easterly duration at seven stratospheric levels

7 Attribution of variations in the quasi-biennial oscillation period from the duration of Fig. 3 The first two empirical orthogonal function (EOF) modes of the total periods of the quasi-biennial oscillation (QBO) for the 24 QBO events. a, b are the spatial patterns of EOF 1 and EOF 2 modes, and c, d are the corresponding time coefficients (a) EOF 1 (82.8%) (b) EOF 2 (13.7%) (c) Time coefficient of EOF (d) Time coefficient of EOF Table 2 Correlations between the mean Multivariate ENSO Index (MEI) and the QBO period at seven stratospheric levels in the period Pressure level (hpa) Correlation 0.* 0.45* 0.41* Correlations with asterisks are above 95 % statistical significance level periods. The spatial pattern or vertical profile of the EOF 1 mode exhibits values with the same sign throughout all the seven stratospheric levels from to hpa, indicating vertical coherence in the variability of the QBO period, which is consistent with Figs. 1 and 2b. A maximum at hpa can be observed that decreases with increasing height above hpa; that below hpa increases with increasing height. The time coefficients of EOF 1 (Fig. 3c) shows a nearly perfect correlation with the time series of the total period of the 24 QBO events shown in Fig. 2b; their correlation is This result also confirms that the EOF 1 variations can represent the temporal and vertical variations of the QBO period. The EOF 2 mode, accounting for 13.7 % of the total variance, represents the out-of-phase relation profile of the QBO period at levels above and below hpa. The time coefficients of the EOF 2 mode present an oscillation with a period of approximately 4 6 years, which is right at the timescale of ENSO. We have made a brief investigation on the relation between the QBO period and ENSO in the period via correlation analysis of the QBO period at seven stratospheric levels and the Multivariate ENSO Index (MEI, Wolter and Timlin 1993, For easy comparison, the mean MEI corresponding to each QBO event is obtained via doing average over the period of each QBO event at different levels. As shown in Table 2, the correlations between ENSO and the total period of QBO at and below hpa are statistically significantly positive, which means that there exists robust linkage between the two. Such linkage is possibly associated with the modulation of the Kelvin wave activities and mixed Rossby-gravity wave activities in the middle and lower stratosphere due

8 M. Yang, Y. Yu Fig. 4 The same as Fig. 3, but for the duration of the easterly phase of quasi-biennial oscillation (QBO) events (a) EOF 1 (47.4%) (b) EOF 2 (26.7%) (c) Time coefficient of EOF (d) Time coefficient of EOF to different phases of the ENSO, as reported in Maruyama and Tsuneoka (1988) and Calvo et al. (09). The EOF analysis was also applied to the easterly and westerly durations at various levels. Their two leading EOF modes and corresponding time coefficients are respectively shown in Figs. 4 and 5. The EOF 1 of the easterly duration explains 47.4 % of the total case-to-case variances of the easterly durations. The spatial pattern of EOF 1 (Fig. 4a) shows out-of-phase variations between levels at and above hpa and those below hpa. Note that in the spatial pattern of the EOF 1 of the easterly duration, the absolute values are significantly larger in the upper levels at and above hpa than those in the levels below with the opposite signs. It is also found that the correlations between the time coefficients of EOF 1 of easterly duration and the time series of easterly duration at upper levels are statistically significant, while their positive correlations in lower levels are not (blue solid curve in Fig. 6a). Therefore, the EOF 1 mode of easterly duration mainly captures the variability of durations at upper levels. The spatial pattern of the EOF 2 mode of the easterly duration, only explaining 26.7 % of the total variance, represents an out-of-phase vertical profile with that of the EOF 1 mode of easterly duration but with larger absolute values at lower levels. The variability of this pattern represents the easterly duration variability at lower levels instead of upper levels, manifested by the positive/small correlations between time coefficients of EOF 2 and the time series of easterly duration at lower/upper levels, as shown by the dashed blue curve in Fig. 6a. Since the EOF 1 mode is the most dominant vertical pattern, the variability of easterly duration in upper levels is much larger than that in lower levels. The out-of-phase vertical profile between the upper (above hpa) and lower stratospheric levels below is also the dominant mode (EOF 1, explaining 46.4 % of the total variance) of the variability of the westerly duration, although the separation level is slightly higher and the absolute values in the lower levels are larger than those in upper levels (Fig. 5a). The EOF 1 mode of the westerly duration mostly represents the duration variability in the lower levels, manifested by the statistically significant positive correlations between the time coefficients of EOF 1 and the time series of westerly duration there but statistically insignificant negative correlations in the upper levels (red solid curve in Fig. 6b). The EOF 2 mode of the

9 Attribution of variations in the quasi-biennial oscillation period from the duration of Fig. 5 The same as Fig. 3, but for the duration of the westerly phase of quasi-biennial oscillation (QBO) events (a) EOF 1 (46.4%) (b) EOF 2 (.6%) (c) Time coefficient of EOF (d) Time coefficient of EOF Fig. 6 a Correlations of the time coefficients of EOF 1 and EOF 2 modes of the easterly duration with the time series of the easterly duration during the 24 QBO events at seven stratospheric levels. b Is the same as (a), but for the westerly duration. Dots indicate correlations above the 95 % statistical significance level (a) E-PC1 & E E-PC2 & E (b) W-PC1 & W W-PC2 & W

10 M. Yang, Y. Yu westerly duration (explaining.6 % of the total variance of the westerly duration) represents consistent variability throughout all levels, with a maximum at hpa. This pattern is more closely related to the variability of westerly duration in the upper levels as indicated by Fig. 6b. The much larger variance explained by EOF 1 than EOF 2 reveals that the largest variability of westerly duration lies in the lower stratospheric levels. The time coefficients of EOF 1 modes of easterly and westerly durations are highly positively correlated with the correlation as high as This indicates that a longer/ shorter easterly duration at the upper levels at and above hpa is always accompanied by a longer/shorter westerly duration at levels below. Such relation indicates that if the descent of the easterlies stalls at mid-stratospheric levels, the easterly phase will last longer in the upper stratospheric levels, and meanwhile, the duration of the westerly phase, which has already propagated into the lower stratosphere, will also extend because of the delay of the take-over by the easterly wind regime. The opposite can be said for an acceleration of the descent rate of the easterlies at midstratospheric levels. Therefore, the variability of the dominant modes of the westerly and easterly durations reflects the stalling or accelerating of the descent rate of easterlies, rather than that of the westerlies, suggesting that the stalling or accelerating of easterlies is much stronger and occurs more frequently than that of westerlies, which can be also seen clearly from Fig. 2a. At the two mid-stratospheric levels ( and hpa), where easterly wind regime tends to stall as reported by previous studies (e.g., Fischer and Tung 08), EOF 1 modes of the durations of the westerly and easterly phases vary in phase. Comparing Figs. 4 and 5 with Fig. 3, the contribution to the variability of the total period of QBO from the duration of each phase at different levels can be figured out. The time coefficients of EOF 1 modes of both easterly durations (Fig. 4c) and westerly durations (Fig. 5c), show statistically significant positive correlations with the time coefficient of EOF 1 of the total period (Fig. 3c); the coefficient is 0.92 and 0.86, respectively. In contrast, the correlation of the time coefficients of the dominant mode of the total period (Fig. 3c) with the time coefficients of the EOF 2 mode of easterly durations is negligibly small ( 0.05) and that with the time coefficients of the EOF 2 mode of westerly durations is also small at 0.37, though above the 90 % statistical significance level. These results help to explain the general variations in the total period under the following conditions: in phase with westerly durations in the lower levels at and below hpa; in phase with easterly durations in the upper levels at and above hpa; and in phase with both westerly and easterly durations at and hpa, respectively; not robustly related to variations of the easterly/westerly duration in the lower/upper stratospheric levels. In addition, the positive correlation between the time coefficients of the EOF 2 mode of the westerly duration and the time coefficients of the EOF 1 mode for the total period, together with the results showing that the variance of the westerly duration explained by its EOF 1 mode is slightly smaller than that of the easterly duration, suggests that variations of the westerly duration in upper levels can also make weak positive contributions to the total period variability of QBO in corresponding levels, despite the dominant contribution is from the duration variability of easterly phase. We also investigate the dominant patterns in the spatial phase relationships among the total period and the durations of westerly and easterly phases through MV EOF analysis (Wang 1992). Compared with the conventional EOF analysis, the MV EOF analysis is conducted on the basis of both spatial and intervariable coherence and thus can help to explain the interactive processes. Figure 7 shows the first MV EOF mode of the total period and westerly and easterly durations. The spatial patterns (Fig. 7a c) are very close to the corresponding EOF 1 modes of each of the three variables (Figs. 3a, 4a, 5a). Moreover, the time coefficients of the MV EOF 1 mode have a high positive correlation (0.89, above the 99 % statistical significance level) with the time series of the total period of QBO events (Fig. 2b). Results derived from the MV EOF analysis clearly show the vertical consistency of the variability of the QBO period, and the coupling of anomalies of the total period, easterly durations in the upper levels above hpa and westerly durations in the levels below. This confirms the results of EOF analysis that it is the stalling/accelerating of the descent rate of the easterly wind regime that dominates the variability of easterly durations and westerly durations in the stratosphere and plays a key role in lengthening/shortening the total period of QBO events. 5 Case to case investigation of variations of the total period and durations of westerly and easterly phases After identifying the dominant vertical patterns of the total period of QBO events and the westerly and easterly durations and revealing their relationships, we in this section directly investigate the relationship among the total period of QBO events and the westerly and easterly durations via statistical analysis on a case-by-case basis. Seen from the correlations of westerly durations between different levels (Fig. 8a), the westerly durations in any two of the lower levels at and below hpa are positively correlated, but such relation can hardly be seen in the upper levels. The westerly durations in the lower levels show statistically insignificant negative correlations with those in the upper levels. And the similar features can be seen from

11 Attribution of variations in the quasi-biennial oscillation period from the duration of (a) Total QBO period (b) Westerly Duration (c) Easterly Duration (d) Time coefficient Fig. 7 The first multivariate empirical orthogonal function (MV EOF) mode of the total quasi-biennial oscillation (QBO) period, the westerly duration, and the easterly duration during the 24 QBO events. The spatial patterns are shown in (a c) and the corresponding time coefficients are shown in (d). MV EOF 1 explains % of the total variance the correlations of easterly durations between different levels (Fig. 8b). The statistically significant positive correlations of the easterly durations between any two levels can be found only at the upper levels above hpa. The easterly durations in the lower levels and those in the upper levels vary independently, manifested by the statistically insignificant negative correlations. This result indicates that the variations of westerly/easterly durations are vertically consistent in the lower/upper levels, and the dominant vertical profile for the westerly/easterly durations, represented by the spatial patterns of its EOF 1 modes (Figs. 4a, 5a) which is out of phase between upper and lower levels, are not typical nor robust. Displayed in Fig. 8c are the correlations between the westerly and easterly durations at different levels. Firstly, the correlations of the easterly durations at a given level from to hpa with the westerly durations at a different level show larger positive values towards the top left corner, where the level for the westerly duration is lower and the level for the easterly duration is higher. The maximum correlations are achieved between levels at and above hpa for the easterly duration and level hpa for the westerly duration. This suggests that the easterly durations at the upper levels vary in phase with the westerly durations at the lower levels, but the variations of the westerly durations at the upper levels and the variations of easterly durations at the lower levels have no robust relationship. It can also be seen from the correlations between the durations of the westerly and easterly phases at the same level for the 7 stratospheric levels (along the diagonal line in Fig. 8c) that durations of the westerly and easterly phases show anti-correlations, but not statistically significant, particularly for and hpa. This indicates that prior to a longer/shorter easterly duration in the upper levels, the westerly phase in the same level tends to be slightly shorter/longer in average, but it is not necessarily true for most of the QBO events. Such statistically insignificant relation between the case-to-case variations of the easterly durations and westerly durations at the same level explains why a discrepancy is found on this relation, as reported by numerous studies based on records with limited

12 M. Yang, Y. Yu Fig. 8 Correlations between different levels of a the westerly duration and b the easterly duration, and c correlations between the westerly duration and the easterly duration at different stratospheric levels during the 24 QBO events. Dots indicate correlations above the 95 % statistical significance level Fig. 9 Correlations of the total period of QBO events with the westerly duration and the easterly duration at the same level during the 24 QBO events. Dots indicate correlations above the 95 % statistical significance level sample size (Salby and Callaghan 00; Soukharev and Hood 01; McCormack 03; Palmer and Gray 05). The correlations of the total period of QBO respectively with the westerly durations (red curve) and easterly durations (blue curve) at the same level are displayed in Fig. 9. It is seen that the total period of QBO events at hpa and levels below have a strong positive correlation with the westerly duration and the correlation decreases with an increase in height, while the total QBO period at hpa and above has a statistically significant positive correlation with the easterly duration, which increases with an increase in height until reaching its maximum at hpa. The statistically significant positive correlations of the QBO period with the westerly durations are found only at lower levels and those with the easterly durations are found only at upper levels. This provides more evidence for the dominant role of variations of the westerly duration at lower levels and variations of the easterly duration at upper levels (i.e., anomalous descent rate of easterlies) in contributing to variations of the QBO period.

13 Attribution of variations in the quasi-biennial oscillation period from the duration of Fig. Vertical distributions of anomalies of a the total period of QBO events and b the durations of the easterly phase (shadings) and the westerly phase (contours, negative values represented by dashed contours and positive values represented by solid contours, with a contour interval of 2) for the 24 QBO events in the period The abscissa denotes the number of QBO events and ordinate denotes the 7 stratospheric levels from to hpa Table 3 The probability of the occurrence (PO) of three categories PO/Level hpa hpa hpa hpa hpa hpa hpa W 16/24 8/22 5/ 7/24 6/24 4/24 4/ E 2/24 3/22 2/ 4/24 7/24 /24 11/ W&E 6/24 11/22 13/ 13/24 11/24 /24 9/ Total events W indicates that the total period anomaly has the same sign as that of the westerly duration anomaly but an opposite sign as that of the easterly duration anomaly. E indicates that the total period anomaly has the same sign as the easterly duration anomaly but an opposite sign as that of the westerly duration anomaly. W&E indicates that the total period anomaly has the same sign as both the easterly and westerly duration anomalies. Quasi-biennial oscillation (QBO) events with average total period are excluded To gain more detailed insight into the contributions to the variability of QBO period from variations of durations of westerlies and easterlies on a case-by-case basis, we investigate the probability of occurrence of different collocation of anomalies of the total period and the durations of westerly and easterly phases in each of the 24 QBO events. The anomaly fields were obtained by removing their climatological mean values averaged over the 24 QBO events and shown in Fig.. Three categories of collocation were identified: W refers to QBO events of which the total period anomaly shares the same sign with the westerly duration anomaly but has a sign opposite to that of the easterly duration anomaly or those in which the variability of the QBO period is contributed positively by the westerly duration anomaly but negatively by the easterly duration anomaly. E refers to QBO events of which the variability of the total period is contributed positively by the easterly duration anomaly but negatively by the precedent westerly duration anomaly. W&E refers to QBO events of which the total period anomaly is positively contributed by both easterly and westerly duration anomalies. The occurrence of these three categories and their ratios to the total numbers of QBO events, known as the probability of occurrence, are listed in Table 3. Consistent with the

14 M. Yang, Y. Yu results shown above, the probability of the occurrence of W decreases with an increase in height, with a maximum of 67 % achieved at hpa. In contrast, the probability of the occurrence of E increases with an increase in height and reaches its maximum at hpa (46 %). It is noteworthy that the probability of occurrence of W&E is maintained at approximately % with no remarkable changes with height, although its maximum is at hpa. Accordingly, except for those at and hpa, W&E is the most common category. Therefore, besides confirming that the easterly/westerly duration dominates the variability of the QBO period in upper/lower levels, these results suggest that in more than half of the cases at most of the stratospheric levels, the variations of both of the westerly and the following easterly durations contribute positively to the case-to-case variations of QBO period. Furthermore, more than % of the 24 QBO events are dominated by the variability of the easterly/westerly duration in lower/upper levels. Next we wish to quantify how dominant the stalling/ accelerating of the descent rate of easterlies is in determining the variations of QBO period via examining the probability of occurrence of QBO events whose period variations involve the stalling/accelerating of the descent rate of the easterlies at mid-stratospheric levels ( hpa) during the period Such an event can be identified when the total period anomalies are almost vertically consistent (allowing exceptional sign at one level, events in total) and share the signs with easterly duration anomalies at upper levels above or hpa and westerly duration anomalies below (exceptional sign at one level is also allowed), based on the vertical profiles of anomalies of the total period (Fig. a), westerly duration (contours in Fig. b) and easterly duration (shadings in Fig. b). Note that the four events in which the total period anomalies are vertically inconsistent are caused by the diversity of stalling level of easterlies (1 and 16) or the dominant contributions from easterly duration anomalies at lower levels and westerly duration anomalies at upper levels when the two have opposite signs (12 and 24). Results show that, there were 9 QBO events (3, 4, 5,, 11, 13, 14, 19 and 23) with lengthened periods associated with a stalling in the descent rate of the easterly wind regime around the middle stratosphere and 9 events (2, 6, 7, 8, 17, 18,, 21 and 22) with shortened period related to an accelerating of the descent rate of easterlies. Among the 18 events, the periods of 7 QBO events (4, 6,, 14, 19, 21 and 23) were positively contributed by the anomalous stalling of easterlies but little or negatively contributed by variations of the westerly duration at upper levels and easterly duration at lower levels. For the remaining 11 events related to anomalous descent of easterlies, variations of the westerly duration at upper levels and easterly duration at lower levels (especially the former) also contribute positively (i.e., anomalies of westerly duration at upper levels and easterly duration at lower levels have the same sign with anomalies of the total period of QBO) and even dominantly (i.e., positive contributions to the total period variability from variations of the westerly duration at upper levels and easterly duration at lower levels are larger than those from variations of the easterly duration at upper levels and westerly duration at lower levels) in 2 events (8 and 17). 2 QBO events (9 and ) out of the QBO events with vertically consistent period variability are also found dominated by the in-phase variations of the westerly duration at upper levels and easterly duration at lower levels, but negatively contributed by the coupled variations of the easterly duration at upper levels and the westerly duration at lower levels (i.e., a/an stalling/accelerating of the descent rate of easterlies). The existence of these events related to the coupling variability of westerly duration at upper levels and easterly duration at lower levels explains the positive but statistically insignificant correlations of the total period with the westerly duration in the upper levels and easterly duration in the lower levels (Fig. 9), and coincide with the large probability (up to %) of occurrence of the QBO events which is positively contributed by variations of both easterly and westerly durations and the existence of the QBO events ( %) which is positively contributed by variations of westerly durations but negatively contributed by variations of easterly durations (Table 3). To sum up, in the period , the stalling/accelerating of the descent rate of easterlies in middle stratosphere does occur frequently and overwhelm other factors, such as anomalous descent of westerlies associated with variability of westerly duration at upper levels and easterly duration at lower levels, in determining variations of the period of most of the QBO events (18/24). The variations of the westerly duration at upper levels and easterly duration at lower levels also contribute positively to the period variability of more than % of the total events of QBO (13/24), but dominate in a very small portion of the total events (4/24) when both variations of the westerly duration at upper levels and easterly duration at lower levels, and variations of the easterly duration at upper levels and westerly duration at lower levels contribute positively to the total period variability, but the contribution from the former is larger, or variations of the westerly duration at upper levels and easterly duration at lower levels contribute positively to the total period variability, but variations of the easterly duration at upper levels and westerly duration at lower levels contribute negatively to the total period variability. 6 Concluding remarks Using the wavelet method, EOF, and MV EOF analysis with updated data obtained from Free

15 Attribution of variations in the quasi-biennial oscillation period from the duration of University of Berlin, we have studied the features of the temporal-spatial variations of the period of QBO events. This study includes investigating the variations of the total period of QBO events and the durations of the easterly and westerly phases, respectively, at various stratospheric levels, in addition to the contributions to the variations of the QBO period from the duration variations of the easterly and westerly phases. The results show that the QBO is a vertically consistent and stable periodic oscillation with an average period of 28 months. The QBO period shows decadal to multidecadal variability at each stratospheric level associated with the 11-year solar cycle, but no long-term trend. The noted case-to-case variations in QBO period are by nature attributed to variations in westerly and easterly durations. The EOF and MV EOF analyses have been conducted on the total period of QBO and the westerly and easterly durations to investigate their dominant vertical profiles and their relationships. It is found that the dominant vertical structure of easterly duration shows out-of-phase variations between levels at and above hpa and those below hpa, but this dominant pattern mainly represents the easterly duration variations in upper levels above hpa. The variations of the westerly duration are also dominated by an out-of-phase vertical profile between upper levels above hpa and lower levels at and below hpa, but this pattern mainly captures the westerly duration variability in lower levels. This indicates that the largest variability of the easterly/westerly durations in the stratosphere lies in upper/ lower levels. The two dominant modes, which respectively capture the variations in the easterly duration at upper levels and westerly duration at lower levels, vary strongly in phase. In other words, a longer/shorter duration of easterlies at upper levels above hpa tends to be accompanied by longer/shorter duration of westerlies at lower levels below, indicating a/an stalling/accelerating of the descent rate of the easterly wind regimes around mid-stratospheric levels. In contrast, no robust relationship has been found between variations in the westerly durations at upper levels and the easterly durations at lower levels. The dominant modes of westerly and easterly durations, namely the coupled variations of the easterly durations in upper levels and westerly durations in lower levels, have statistically significant in-phase relation with the variations of the total period of QBO events at corresponding levels. This provides evidence that it is the anomalous stalling/accelerating of the descent rate of the easterlies around hpa that plays a critical role in extending/shortening the QBO period at upper levels above hpa and at lower levels below hpa. In the middle stratosphere at and hpa, the variations in durations of both westerly and easterly phases tend to contribute positively to the total period of QBO. The correlation analysis, as well as the occurrence probability of QBO events belonging to different categories based on the collocation of anomalies of the total period and westerly and easterly durations, confirms that the easterly/westerly duration tends to dominate the variability of the QBO period at upper/lower levels. It is noteworthy to mention that the contributions to QBO period variability from the variations in the easterly duration in lower levels and the westerly duration in upper levels are not robustly positive but unnegligible because in more than half of the 24 QBO events during , easterly/westerly duration in lower/upper levels, together with easterly/westerly duration in upper/lower levels, contribute positively to the total period of QBO, and in addition, % of the 24 QBO events are dominated by easterly/westerly duration in lower/upper levels, instead of easterly/westerly duration in upper/lower levels. Further investigation on the probability of occurrence of QBO events whose period variations involve the coupling of the easterly durations at upper levels and westerly durations at lower levels (i.e., stalling/ accelerating of the descent rate of the easterlies at midstratospheric levels) in the period shows that the stalling/accelerating of the descent of easterlies in middle stratosphere occurs frequently and overwhelmingly determines the variations of the period of up to 75 % of the total events of the QBO. The variations of the westerly duration at upper levels and easterly duration at lower levels, which are related to stalling/accelerating of the decent rate of westerly wind regimes that occurs less frequently and weaker than that of easterlies, contribute positively to the variability of total period for more than half of the QBO events, but only plays a dominant role in 17 % of the 24 QBO events. The stalling of easterly and westerly wind regimes can be explained in view of the anomalous momentum transport by the westward propagating waves, such as Rossbygravity waves, and the eastward propagating Kelvin waves. When the westerly phase has a longer duration time in the lower stratosphere, the basic flow favors upward propagation of the westward propagating waves, such as Rossbygravity waves, transporting easterly momentum to upper levels. As a result, the duration of the easterly phase tends to be longer. When the easterly duration is longer in the lower stratosphere, eastward propagating waves, such as Kelvin waves, can propagate upward, leading to a gain of westerly momentum. Consequently, the westerly regime stalls for a longer time in the upper stratosphere. Takahashi and Boville (1992) and Dunkerton (1997) have reported that gravity-inertial waves and smaller scale gravity waves also play important roles in momentum transport, which is the main driving force of the QBO events in the tropical stratosphere. Therefore, further research is needed to