Role of tropical lower stratosphere winds in quasi-biennial oscillation disruptions.

In 2016, the westerly quasi-biennial oscillation (WQBO) in the equatorial stratosphere was unprecedentedly disrupted by westward forcing near 40 hPa; this was followed by another disruption in 2020. Strong extratropical Rossby waves propagating toward the tropics were considered the main cause of the disruptions, but why the zonal wind is reversed only in the middle of the WQBO remains unclear. Here, we show that strong westerly winds in the equatorial lower stratosphere (70 to 100 hPa) help to disrupt the WQBO by hindering the wind reversal at its base. They also help equatorial westward waves propagate further upward, increasing the negative forcing at around 40 hPa that drives the QBO disruptions. Tropical westerly winds have been increasing in the past and are projected to increase in a warmer climate. These background wind changes may allow more frequent QBO disruptions in the future, leading to less predictability in atmospheric weather and climate systems.

INTRODUCTION

The quasi-biennial oscillation (QBO) in the tropical stratosphere is the dominant form of interannual variability in the zonal-mean zonal wind from 5 to 100 hPa; it consists of alternating, downward-propagating easterly and westerly winds with an irregular period of 20 to 35 months (Fig. 1). It has been shown that the QBO is generated by wave-mean flow interaction, where the waves include equatorial Kelvin, Rossby, mixed Rossby–gravity (MRG), inertia gravity (IG), and small-scale gravity waves (GWs) (). Since radiosonde observations in the equatorial stratosphere began to be recorded (, ), the QBO has shown downward propagation with time.

Fig. 1.

Zonal wind in Singapore radiosonde station (2000–2020).

Time-height cross-section of the monthly mean zonal wind from Singapore radiosondes (1°N, 104°E). Red and blue boxes denote 2015/16 and 2019/20 QBO disruption periods, respectively.

In winter 2015/16, however, the downward-propagating westerly QBO (WQBO) phase was interrupted by very localized easterlies for the first time, resulting in two split equatorial westerly jets, one propagating upward and one downward (red box in Fig. 1). This phenomenon is referred to as a QBO disruption (). Some considered this phenomenon as an exceptional event, a so-called “black swan” (). Others suspected that this is one of the responses to anthropogenic climate change (), as the atmospheric zonal mean structure during this period () was similar to the one projected in the future climate (). Unexpectedly, the QBO was disrupted once again in winter 2019/20 (blue box in Fig. 1), evidencing that a QBO disruption can no longer be considered a one-off event.

Theoretically, vertically propagating equatorial waves dissipate in the region where the vertical wind shear is strong (), e.g., westward wave breaking in the region of negative vertical wind shear. This normally happens at the top and bottom of each phase of the QBO (Fig. 2A). However, during the two QBO disruptions, equatorial waves dissipated in the middle of a descending WQBO concurrent with the development of very localized easterly winds (Fig. 2, B and C) (). Those easterly winds partly resulted from horizontally propagating waves (blue arrows) and were further strengthened by feedback processes such as the secondary circulation and meridional potential vorticity gradient in the subtropics (). Therefore, extratropical Rossby waves propagating into the tropics have been considered as a key driver of the QBO disruptions (, , , , , ). However, the contribution of extratropical Rossby waves to the total negative wave forcing at ~40 hPa was only 46% in the 2015/16 QBO disruption (ranging from 30 to 78% from October 2015 to March 2016) and 38% (ranging from 19 to 65% from June 2019 to January 2020) in the 2019/20 QBO disruption [table 1 of Kang et al. (, )]. In addition, the extratropical Rossby wave forcing alone cannot fully explain why the zonal winds continue to decelerate only in the middle of the WQBO, without decelerating at its top or bottom.

Fig. 2.

Schematic diagrams of the typical WQBO, 2015/16 QBO disruption, and 2019/20 QBO disruption.

Schematics represent the equatorial waves and small-scale CGWs (red arrows) and extratropical Rossby waves (blue arrows) and their breaking on the evolution of the (A) typical WQBO during NH winter, (B) 2015/16 QBO disruption, and (C) 2019/20 QBO disruption. Red and blue explosion marks indicate the breaking of equatorial planetary/GWs and extratropical Rossby waves, respectively.

For the 2015/16 QBO disruption, it was first argued that extratropical Rossby waves from the Northern Hemisphere (NH) disrupted the QBO (, , ). However, recent studies revealed that equatorial wave flux was also exceptionally strong (). In particular, strong MRG wave forcing () and IG wave forcing () weakened the WQBO in the early stage of the disruption (October to November 2015; left panel of Fig. 2B), making the QBO more susceptible to the extratropical Rossby wave breaking in the deep tropics. In the later stage (February 2016; right panel of Fig. 2B), vertically propagating equatorial Rossby waves and small-scale convective GWs (CGWs) substantially decelerated the WQBO in addition to the extratropical Rossby waves ().

In the case of 2019/20, strong extratropical Rossby wave forcing from the Southern Hemisphere (SH) initiated the QBO disruption () (left panel of Fig. 2C), but the MRG wave forcing and vertically propagating equatorial Rossby wave forcing became stronger in October 2019 and finally induced the disruption in January 2020 () (right panel of Fig. 2C).

Although the temporal evolution of each type of wave forcing is different in each case, both QBO disruptions show strong equatorial waves as well as equatorward-propagating extratropical Rossby waves. According to Kang et al. (, ), those enhanced waves during the QBO disruptions were attributable to (i) strong extratropical Rossby wave flux toward the equator, (ii) enhanced convective activity in the equatorial troposphere, and (iii) westerly wind anomalies in the equatorial lower stratosphere. While the first factor is well discussed in the literature, the second and third factors, which are related to the increase in the tropical wave flux, require further analysis.

Convective activity is an important source of equatorial waves, and an increase in convection strength or variability generally leads to a strong wave flux into the equatorial stratosphere (). Westerly anomalies in the lower stratosphere favor the propagation of westward tropical waves (i.e., Rossby, MRG, and westward GWs) by reducing critical-level filtering of westward waves (). Between (ii) and (iii), the changes in the equatorial lower stratospheric wind (iii) are likely the more important factor driving the QBO disruptions, as the convective activity during the 2019/20 QBO disruption was similar to the climatology ().

Here, we show that the third factor not only can explain the increased equatorial wave forcing at 40 hPa but also is consistent with the zonal wind reversal being confined near 40 hPa. We also show the possibility of more frequent occurrence of QBO disruptions in the future due to accelerating zonal wind in the equatorial lower stratosphere.

RESULTS

Zonal wind changes and their relation to QBO disruptions

Figure 3 (A to C) shows the difference in the equatorial zonal-mean zonal wind between 2015/16 winter [December-January-February (DJF)] and the WQBO winter climatology (Fig. 3A), that between 2019/20 winter and the WQBO winter climatology (Fig. 3B), and the zonal-mean zonal wind trend during WQBO winters (shading in Fig. 3C) over the period of 1980–2019 in the MERRA-2 reanalysis. The zonal wind at approximately 40 hPa in Fig. 3 (A and B) is much weaker than the WQBO climatology (by more than 1 SD of the year-to-year variation of WQBO winters) due to the development of easterly winds during the disruptions (see contours). Here, it is important to note that the equatorial zonal wind in the lowermost stratosphere shows strong westerlies during the two QBO disruptions. The zonal wind difference in the tropics below 60 hPa as well as that in the SH at 30 to 100 hPa are positive in Fig. 3 (A and B).

Fig. 3.

Differences in the zonal-mean zonal wind between QBO disruption winters and WQBO winter climatology along with the zonal wind trends over the period 1980–2019 in MERRA-2 and historical trends in the zonal wind in radiosonde data.

(A and B) Zonal-mean zonal wind (gray line contours; contour interval: 2 m s−1; thick solid lines: zero zonal wind speed) in DJF 2015/16 and DJF 2019/20 overlaid with their differences (shading) with respect to the DJF WQBO climatology for the 40-year period from 1980 to 2019. Regions where the zonal wind differs from the DJF WQBO climatology by more than its one SD are stippled. (C) Linear trend of the zonal-mean zonal wind (shading) for the DJF WQBO mean over the 40-year period from 1980 to 2019, overlaid with its 1980–2019 climatology (gray line contours) in the MERRA-2 reanalysis data. Regions with statistically significant trends (bootstrap test, P < 0.05) are stippled. Time series of the (D) zonal wind from Singapore (1.4°N, 103.9°E) and (E) Kuching (1.5°N, 110.3°E) radiosonde stations at 70 to 80 hPa for WQBO winters and its linear trend (black dashed lines); the 2015/16 and 2019/20 disruptions are highlighted in red. The text in the upper-right corner represents the slope of linear trend. The number of asterisks indicates the level of significance: one, two, and three indicate P < 0.1, P < 0.05, and P < 0.01, respectively.

The zonal-mean zonal wind trend during WQBO winters (Fig. 3C) shows a dipolar pattern in the deep tropics. The zonal wind in the lower stratosphere, below approximately 60 hPa, is shifting toward stronger westerlies, while the zonal wind above 60 hPa shows the opposite trend. A similar trend was also found in the ERA5 and JRA-55 reanalyses (fig. S1) and in the radiosonde data (Fig. 3, D and E).

As the anomalous zonal winds in the equatorial region during both QBO disruptions (Fig. 3, A and B) are consistent with the features shown in the long-term trends (Fig. 3C), the QBO disruptions may be at least in part associated with the long-term changes in the equatorial zonal wind. Previous studies have shown that the QBO amplitude in the lower stratosphere has weakened since the 1950s (), consistent with the negative trends of WQBO above 60 hPa (blue shading in Fig. 3C; see also fig. S2). Note that we consider WQBO in DJF only, and the maximum easterly winds at 70 hPa were weakened until 2010 [blue line in fig. S3; figure S4 in ()] so that the amplitude of the QBO could be reduced at 70 hPa () despite the strengthening westerly winds.

Strong tropical westerlies, which could result from long-term climate changes, have an important implication to the QBO disruption. As discussed above, they allow more westward waves to propagate into the equatorial stratosphere. These waves may induce negative forcing to develop QBO disruptions, once extratropical Rossby waves and their breaking generate a local critical level (fig. S4). Moreover, Rossby waves propagating from the extratropics might be unable to reverse the westerly wind at altitudes lower than 70 hPa if strong westerlies are sustained by the eastward forcing at those levels (figs. S4 and S5) (). Given that the extratropical Rossby wave breaking near the equator occurs mostly at 30 to 80 hPa due to the wave guide in the subtropics () and that the eastward forcing is evident below 70 hPa, the strong westerlies at the base of the WQBO can explain why the easterly winds are confined to altitudes above 70 hPa during the two QBO disruptions, creating two split branches of the westerly jet (Fig. 2, B and C).

Figure 3 (D and E) shows the time series of the zonal wind at Singapore station (1.4°N, 103.9°E) and Kuching station (1.4°N, 110.3°E) at 70 to 80 hPa during WQBO winters and their long-term trends. Both trends are positive (0.6 and 1.03 m s−1 per decade) as in the reanalysis data (Fig. 3C), but only the long-term trend at Kuching (Fig. 3E) is statistically significant. According to the linear trend, the increase in the westerlies from 1979 to 2020 at 70 to 80 hPa is about 2.5 to 4 m s−1. Positive westerly trends are also seen for the period before the emergence of easterlies in 2016 (November-December-January) and 2020 (October-November-December mean; fig. S6), suggesting that strong westerlies below 70 hPa play a role in preconditioning the QBO disruptions. Seven radiosonde stations located at 5° to 10°N and 102°E to 172°E (fig. S7) mostly show the increasing trend in the zonal wind but without statistical significance, which is also consistent with the reanalysis data. Similar time series at 30 to 50 hPa (fig. S8) reveal that there is a negative trend at those pressure levels (see Fig. 3C).

Note that westerly winds in the two disruption winters are not the strongest in the observational record. This is because the strong extratropical Rossby wave flux toward the equator during the two disruptions also decelerates the base of the QBO (). However, we hypothesize that the winds were able to remain rather strong due to the strong eastward equatorial wave forcing (figs. S4 and S5).

In fig. S3, the entire time series between 70 and 100 hPa are presented. When the years with the maximum westerly wind are considered (red dots), the zonal wind trends are significant even at the 99% confidence level. This result implies that a westerly acceleration over the period 1979–2020 could be relevant to the increasing trend in the peak of the westerly wind.

Changes in the waves related to the zonal wind changes

Figure 4 illustrates how the increased westerly winds in the equatorial lower stratosphere are expected to affect the generation, propagation, and dissipation of the equatorial planetary/gravity waves. The schematic in Fig. 4A shows that (i) equatorial westward waves (MRG waves) are generated at the edges of the QBO (5° to 10°N/S) at altitudes between 70 and 90 hPa, propagating upward (pathway B); (ii) westward waves (equatorial Rossby waves and westward IG waves) propagate farther upward (pathways C and D); and (iii) eastward waves (CGWs and Kelvin waves) dissipate at approximately 85 hPa in response to the zonal wind acceleration (pathways E and F). To quantify this schematic picture, we now calculate each wave forcing and flux using the MERRA-2 reanalysis and CGW parametrization (Materials and Methods) for WQBO winters. Values of the equatorial wave flux/forcing illustrated in Fig. 4A are denoted by colored dots in Fig. 4 (B to F), where the colors indicate the zonal wind strength averaged over 5°N to 5°S and 70 to 90 hPa.

Fig. 4.

Trends in equatorial waves related to zonal wind changes in MERRA-2.

(A) Schematic of the changes in the wave flux and forcing in response to the zonal wind changes in the equatorial lower stratosphere (70 to 90 hPa) during the NH winter. Letters B to F in the schematic plot refer to the various waves whose changes are documented in the other panels of the figure. Time series of (B) the Eliassen-Palm (EP) flux divergence of MRG waves averaged over 70 to 90 hPa at 5°N to 10°N and 5°S to 10°S; (C) vertical EP flux of Rossby waves and (D) westward-eastward IG waves at 70 hPa and 5°N to 5°S; (E) EP flux divergence of CGWs and (F) Kelvin waves at 85 hPa and 5°N to 5°S for the DJF mean during the WQBO phase and their linear trends in MERRA-2. The text in the upper-left corner represents the slope of each linear trend. Asterisks denote statistically significant trends using the bootstrap test. The number of asterisks indicates the level of significance: One, two, and three indicate P < 0.1, P < 0.05, and P < 0.01, respectively. “W” indicates WQBO.

According to Kang et al. (, ), the MRG waves made large contributions to the 2015/16 and 2019/20 QBO disruptions. In both cases, MRG waves that mostly propagate upward (, ) were found to be generated mainly from barotropic instability at the edges of the QBO in the lower stratosphere. Since barotropic instability occurs when the curvature of the equatorial jet is strongly positive, if the wind at the jet core is strengthening more than the edges, instability should occur more frequently (, ). Recall from Fig. 3 that the WQBO jet core at altitudes lower than 70 hPa and higher than 90 hPa becomes stronger with time and was strong during the disruption events. Accordingly, generation of MRG waves would be expected to be stronger at the QBO edges during the two disruptions (fig. S9). Figure 4B further shows an increasing trend of MRG wave generation at 70 to 90 hPa, 5° to 10°N/S, significant at the 95% confidence level. The magnitude of MRG wave generation (Fig. 4B) is linearly correlated with the strength of the westerly wind at 5°N to 5°S, 70 to 90 hPa with a correlation coefficient of 0.52.

Under stronger westerly winds in the equatorial lower stratosphere, more westward-propagating waves can reach the middle stratosphere due to the reduced critical-level filtering range. This is evident in the increased equatorial Rossby wave flux (Fig. 4C) and increased westward IG wave flux (Fig. 4D) at 70 hPa over time, which are statistically significant at the 99% level. Their correlation coefficients with the zonal wind at 70 hPa are 0.62 and 0.79, respectively. In summary, more westward waves (blue arrows in Fig. 4A) are generated or propagate toward the equatorial stratosphere, contributing to the deceleration of the WQBO at an altitude of 40 hPa (fig. S10) due to the strong westerly winds in the equatorial lower stratosphere.

Last, positive momentum forcing by eastward CGWs (Fig. 4E) and Kelvin waves (Fig. 4F) at 85 hPa has increased over time, either because the wave flux entering the stratosphere has increased (fig. S11) () or because the wind acceleration induces stronger positive vertical wind shear in the lowermost stratosphere, enabling more critical-level filtering of the eastward waves. The correlation coefficient between the zonal wind and CGW forcing at 85 hPa and that between the zonal wind and Kelvin wave forcing are 0.66 and −0.21, respectively, with the former being statistically significant at the 99% level. The increased positive wave forcing by CGWs can again cause stronger equatorial westerly winds; this could be one of the reasons for the stronger positive trend in the maximum westerly winds than in the entire time series of the zonal wind (fig. S3). The positive wave forcing by the equatorial waves is important as it mainly acts to sustain the westerly winds over 70 to 90 hPa, despite the strong extratropical wave forcing (fig. S4). The same analysis as in Fig. 4 but using ERA5 model-level data also shows increasing trends in equatorial wave forcing and flux (fig. S12). However, details in the MRG and Kelvin wave forcing are somewhat different from each other. This is likely because MRG and Kelvin waves have relatively short vertical wavelengths, highly sensitive to vertical resolution, and thus might be difficult to assimilate accurately in the reanalyses.

In Fig. 4F, Kelvin wave forcing shows a statistically insignificant trend, and this could originate from the uncertainties in representing Kelvin wave forcing in the reanalysis. Kelvin waves have a small vertical wavelength, so high vertical resolution (~500 m) is apparently required to properly represent Kelvin wave forcing (). Furthermore, the vertical velocity fields in the equatorial stratosphere, which are used to calculate the vertical momentum flux of the Kelvin waves, are difficult to represent well in the reanalysis due to poor constraint by observations (, ). Kelvin wave forcing shows the largest spread among the reanalyses (, ), suggesting that Kelvin waves are the most uncertain part among the equatorial waves. This may explain why Kelvin waves do not respond significantly to the changes in the zonal wind, although further studies are needed to confirm this argument.

Here, it is important to state that the occurrence of stronger westerlies at the base of the QBO is a necessary but not sufficient condition for the QBO disruption. In other words, even if the westerly winds are record-breaking, the QBO disruption would not occur without strong Rossby wave flux. As shown in Fig. 4A (gray arrows), the increased extratropical Rossby wave flux into the tropics is an important contributor to the QBO disruptions (, ). For example, despite the strong westerlies in 2013/14, there was no QBO disruption, likely because the equatorward Rossby wave flux at 10°N and 40 to 90 hPa was only about half of that in 2015/16. However, strong westerlies at 70 to 90 hPa favor larger negative wave forcing by most types of equatorial waves at 40 hPa, promoting QBO disruptions. In addition, without the strong westerlies at 70 to 90 hPa, the base of the WQBO would be more easily decelerated; if this were the case, it would be difficult for the WQBO to bifurcate (fig. S4).

Future projection

How will the equatorial wind change in the future? Figure 5A shows the time series of the zonal-mean zonal wind averaged over 5°N to 5°S, 70 to 100 hPa, for the Sixth Coupled Model Intercomparison Project (CMIP6) historical run for 10 models (1960–2014), the reanalysis (1980–2020), and the shared socioeconomic pathway (SSP) 3-7.0 scenario experiments (2015–2100) for 10 models (see Materials and Methods). This figure represents the changes in zonal winds in the equatorial lowermost stratosphere in response to anthropogenic climate changes (see also fig. S13 for trends over 1979–2020 in the CMIP6 models). A positive zonal wind trend is shown (significant at the 99% level), with a difference in the 12-month running mean zonal wind between 1960 and 2100 being 3 m s−1. Note that year-to-year differences reach ~8 m s−1.

Fig. 5.

Time series of the zonal wind at 5°N to 5°S, 70 to 100 hPa in CMIP6 historical simulations (1850–2014), reanalysis (1979–2020), and SSP3-7.0 experiments (2015–2100) and composite for the QBO disruption–like events and normal WQBO in SSP3-7.0 (2050–2000) along with typical WQBO composite in historical simulation (1960–2010).

(A) Time series of the zonal wind averaged over 5°N to 5°S, 70 to100 hPa in the 10 CMIP6 historical simulations (1850–2014), 2 reanalysis datasets (ERA5 and MERRA-2, 1979–2020), and 10 SSP3-7.0 simulations (2015–2100), overlaid with DJF averages (thick line). (B) Composite of the QBO disruption–like events in five SSP3-7.0 simulations (2050–2100) (19 cases) as a time-height cross-section, where month “0” indicates when the localized easterlies start to appear. (C) Time-height cross-section of the typical WQBO phase with easterly to westerly phase transition at month “−3” in SSP3-7.0 simulations (2050–2100, 107 cases) (D) and that in historical simulations (1960–2010, 142 cases). See Materials and Methods for detecting QBO disruption–like events.

The westerly acceleration at 70 to 100 hPa found in this study suggests more frequent occurrences of QBO disruptions in the future (Fig. 5, C and D). QBO disruption–like events (Materials and Methods) occur in SSP3-7.0 simulations (Fig. 5B) but never in the historical simulations (table S1). It is found that QBO disruption–like events show strong westerlies at 70 to 100 hPa (Fig. 5B) compared to the typical QBO cases in SSP3-7.0 simulations (Fig. 5C), being much stronger compared to the historical simulations (Fig. 5D). Rossby wave flux toward the equator, another important factor inducing the QBO disruption, is also projected to increase in SSP3-7.0 scenario (fig. S14) (), supporting more frequent occurrences of the QBO disruption–like events in the future.

There are two possible causes of the westerly anomaly. First, in response to increased CO2 concentration, the atmospheric temperature increases in the troposphere but decreases in the stratosphere (, ). Since tropopause height is highest at the equator and decreases toward the poles, the temperature gradient is enhanced near the tropical tropopause (fig. S15A). As shown in fig. S15C, the air temperature at 80 to 120 hPa increases more at the equator than in the subtropics, resulting in an increase of the vertical wind shear by the thermal wind balance on an equatorial beta plane (). This could, in turn, lead to the westerly acceleration at 70 to 100 hPa (fig. S15B). The increased vertical wind shear could allow more eastward waves to dissipate, hence accelerating the westerly winds through a positive feedback process. Another reason for the increase in westerly winds could be the increased wave source. As the Kelvin wave activity in the troposphere is expected to increase under higher CO2 (fig. S16) (), stronger wave forcing can be exerted on the shear zone.

DISCUSSION

Strong westerly winds in the equatorial lower stratosphere provide favorable conditions for QBO disruptions by allowing westward tropical waves to propagate more readily above 70 hPa and inhibiting zonal wind reversals in the lower stratosphere. The westerly winds in the lowermost stratosphere have been strengthened and are projected to strengthen further in a warmer climate. In some previous studies, quadrupled CO2 simulations show westerly anomalies compared to present-day simulations at altitudes between 120 and 80 hPa (), resulting in a stronger westward Eliassen-Palm (EP) flux at 70 to 85 hPa [see figure 14 in ()], which supports the current results. This may enhance the westward wave forcing at the negative shear zone, potentially speeding up the westerly-to-easterly phase transition of the QBO.

It is worth noting that the climate simulation results (Fig. 5) of the QBO are very different among models, largely due to the uncertainties in the treatment of unresolved convection and the associated uncertainties in the parametrized GWs (). In addition, there is a well-known bias in the simulated QBO, namely, weak penetration of the WQBO into the lower stratosphere (, , ) [compare Fig. 5 (C and D) with fig. S17]. For the QBO to propagate down to lower levels, high vertical resolution (~500 m) is required, presumably because equatorial waves and their interactions with the mean flow are relatively well represented in a model with a sufficient vertical resolution (). Better representation of the QBO will enable us to understand the QBO disruptions in a warming climate comprehensibly through the improved simulation of the wave-mean flow interaction in the lower stratosphere.

The quasi-regular variability and long periodicity of the QBO have made it possible to predict its phase in advance (), potentially improving the seasonal forecasts of the atmospheric circulations related to the QBO, such as the Madden-Julian oscillation (MJO) (), the stratospheric winter polar vortex (), and the North Atlantic oscillation (NAO) (, ). Abrupt changes in the QBO in the future climate, including unexpected short or long QBO periods (fig. S18), may lead to less predictability of the aforementioned phenomena.

Last, the strengthening of the westerly winds in the equatorial lowermost stratosphere is also important to understand a typical QBO in the future, as the enhanced westward flux entering the stratosphere due to the westerly acceleration () may contribute to the fast QBO phase progression rate. In a future climate, both wave sources in the troposphere and tropical upwelling in the stratosphere are expected to increase (, ). Considering those factors along with the strengthened westerlies in the lowermost stratosphere will shed light on the future behavior of the QBO.

MATERIALS AND METHODS

Data

We use 3-hourly output from MERRA-2 on native model levels (13 levels between 10 and 100 hPa) () to calculate the zonal wind trend and the equatorial wave flux/forcing from 1980 to 2020. We use MERRA-2 because it (i) uses a forecast model that internally generates a QBO-like oscillation and (ii) provides a variable named “temperature tendency due to the moist physics” during the QBO disruption periods, which is required to calculate CGW forcing. Six-hourly output from ERA5 on native model levels (31 levels between 10 and 100 hPa) at a horizontal resolution of 1.5° × 1.5° () is also used to support the MERRA-2 result from 1979 to 2020. Note that MERRA-2 and ERA5 are the only two reanalysis forecast models that internally generate QBO-like oscillations. Monthly averaged zonal-mean zonal wind data are also obtained from JRA-55 on native model levels from 1958 to 2020 (). Monthly zonal winds at Singapore and Kuching stations, the only stations within 5°N to 5°S having fewer than 10% missing values at 70 to 100 hPa from 1979 to 2020, are provided by the Integrated Global Radiosonde Archive version 2 [IGRA version 2; ()] for 42 years (1979–2020). Monthly mean zonal winds at each station are derived by averaging the zonal wind for each month at 10-hPa intervals from 30 to 100 hPa.

The years with a WQBO phase are selected when the zonal-mean zonal wind provided by the Free Berlin University (FUB) () is westerly at both 30 and 50 hPa for at least 4 months during the extended NH winter (from October to March). On the basis of these criteria, a total of 15 WQBO years is selected: 1980/81, 1982/83, 1985/86, 1987/88, 1990/91, 1992/93, 1999/2000, 2004/05, 2006/07, 2008/09, 2010/11, 2013/14, 2015/16, 2016/17, and 2019/20.

We use the CMIP6 experiments () for the historical simulations for 1850–2014 and the SSP3-7.0 simulations () for 2015–2100. Here, SSP3-7.0 represents a scenario in which the radiative flux reaches ~7.0 W m−2 in 2100. Only 10 models that simulate a QBO-like oscillation () are examined. They are AWI-CM-1-1-MR, BCC-CSM2-MR, CESM2-WACCM, CNRM-CM-6-1, CNRM-ESM2-1, EC-Earth3-Veg, GFDL-ESM4, IPSL-CM6A-LR, MIROC6, and MRI-ESM2-0.

Significance test

Trends in the zonal-mean zonal wind are calculated on the basis of a least square fit, and the significance tests are conducted using a bootstrap method (), as follows: 15 WQBO winters are randomly resampled 1000 times to produce a null hypothesis distribution of the trends. If a trend lies in the tails of the distribution outside the given confidence level (two-tailed), the trend is considered to be statistically significant.

Detection of the QBO disruption–like events

QBO disruption–like event is defined when easterly wind develops in the middle of WQBO and lasts at least 3 months as follows: U > 0, U > 0, U > 0, U > U, U < 0, U > U, U < 0, U < 0, where U is the zonal-mean zonal wind averaged over 5°N to 5°S, and t and z indicate certain time and height, respectively. Here, z is set to 50 hPa, which is the closest altitude to 40 hPa in the available model data. Accordingly, z − 1 and z + 1 are determined as 70 and 30 hPa, respectively. Among 10 models used, five models show QBO disruption–like events (AWI-CM-1-1, BCC-CSM2-MR, CESM2-WACCM, IPSL, and MRI-ESM2-0). When Singapore sonde and MERRA-2 model level data are used, z − 1, z, and z + 1 are set to 60, 40, and 30 hPa, respectively (fig. S17).

The wave flux and forcing of the Kelvin, MRG, and IG waves are obtained by calculating the EP flux and its divergence (). The meridional and vertical components of the EP flux are calculated as followswhere

The EP flux divergence is calculated as follows

Each type of wave is classified on the basis of its dispersion relationship and theoretical characteristics, following Kim and Chun (). First, a two-dimensional Fourier transform is applied to the 90-day time series centered on a target month (30 days) with sine and cosine windows for the first and last 30 days, respectively. For the symmetric components with respect to the equator, those with F that have a momentum flux component (Eq. 3B) larger than the heat flux component (Eq. 3A) (i.e., ∣F∣>∣F∣) for the spectral range of 0 < k ≤ 20 and ω < 0.75 cycles per day (cpd) are classified as Kelvin waves, where k and ω are zonal wave number and frequency, respectively. For the antisymmetric components with respect to the equator, those that have opposite sign of the heat flux and momentum flux components (F × F < 0) for the spectral range of ∣k∣≤ 20 and 0.1 ≤ ω ≤ 0.5 cpd are classified as MRG waves. The spectral components that are not classified as Kelvin or MRG waves for ∣k∣≤ 20 and ∣ω∣ ≤ 0.4 cpd are classified as equatorial Rossby waves, and the remainder are classified as IG waves.

To obtain the small-scale CGW flux and forcing, an offline CGW parameterization () is used on the basis of Song and Chun (). The parameterization calculates the convective heating-induced momentum flux at the top height of the convective heating (i.e., cloud top) by evaluating an analytic solution. From cloud top to the stratosphere, the saturated wave momentum flux and the resultant wave drag are calculated on the basis of Lindzen’s saturation theory (). To prevent overestimation or underestimation of the CGW forcing, a parameter c (conversion factor) of the CGW parameterization () is adjusted to obtain the magnitude of the CGW momentum flux comparable to the GW momentum flux observed from superpressure balloons in the tropical region at 50 hPa during February to May 2010 (). More details on the equatorial waves and CGW parameterization can be found in the study of Kang et al. ().