The disappearing quasi-biennial oscillation under sustained global warming

Abstract

The stratospheric quasi-biennial oscillation (QBO) is a key modulator of interannual variability in global weather and climate. Over recent decades, the amplitude of the lower-stratospheric QBO has weakened, and in recent years the QBO has experienced unprecedented disruptions. However, the longer-term evolution of the QBO and its impact on tropospheric circulation remain uncertain. Here, based on CMIP6 models with extended projections beyond 2100 and targeted sensitivity experiments, we show that under ongoing global warming, the QBO exhibits a progressively weaker amplitude and shorter period, eventually risking complete disappearance. This is projected to reduce the predictability of 2–3-year climate forecasts in the troposphere. The weakening of the QBO amplitude arises from enhanced tropical upwelling, whereas the shortening of its period results from the combined influence of strengthened upwelling and intensified wave activity. The potential disappearance of the QBO poses new challenges for climate change under high emission.

Under sustained high greenhouse-gas emissions, the stratospheric quasi-biennial oscillation (QBO) may weaken and eventually disappear, potentially reducing short-term climate predictability, highlighting the risks of continued emissions for the middle and upper atmosphere.

Introduction

The quasi-biennial oscillation (QBO), features alternating westerly and easterly zonal winds in the tropical stratosphere, propagating downward with a ~ 28-month period, which primarily driven by a mix of Rossby gravity waves, Kelvin waves, and other gravity waves of varying scales^1–3. Although it originates in the tropical stratosphere, the QBO significantly influences both tropical and extratropical atmospheric circulation, thereby impacting tropospheric weather and climate^4–20.

However, of late, the lower stratospheric QBO has become less stable. In recent decades, while the amplitude of the QBO in the middle stratosphere (10–30 hPa) has increased, the amplitude in the lower stratosphere (50–70 hPa) has weakened²¹. Furthermore, the disruption of the QBO is first recorded in the 2015/16 period^22–25, followed by another in 2019/20²⁶. Recent advancements in model simulations have made it possible to project future changes in the QBO^27–29. CMIP6 model projections suggest that with increasing greenhouse gas emissions, the QBO’s amplitude will gradually weaken to 2100³⁰ (Fig. 1a–b, color lines), and QBO disruption events could become more frequent^31,32.

Fig. 1. Evolution of the 50 hPa quasi-biennial oscillation (QBO) under the extended SSP5-8.5 scenario.

a Time series of the QBO index and b Time series of the QBO amplitude. Colored lines denote different datasets and models: ERA5 (gray), MRI-ESM2-0 (magenta), CESM2-WACCM (dark blue), EC-Earth3-Veg (orange), and IPSL-CM6A-LR (cyan). Model data prior to 2015 represent historical simulations, while data following 2015 are based on the extended SSP5-8.5 scenario (Model selection, see Methods). The QBO amplitude values correspond to the midpoint of an 8-year sliding window. c–f Wavelet analysis results of the QBO index for the four models. Shaded regions indicate wavelet power passing the 95% confidence level Chi-square test.

Although previous studies suggest that global warming may influence the amplitude of the QBO, the longer-term evolution of the QBO under sustained warming remains unknown. Understanding the evolution of the QBO and its impact on the troposphere is critical for improving longer-term forecasting.

Here, we show that under sustained global warming, the QBO undergoes a progressive reduction in amplitude and a gradual shortening of its period, driven by intensified tropical upwelling and enhanced wave activity, and is likely to ultimately disappear. These alterations dampen the tropospheric QBO signal and consequently reduce the predictability of tropospheric climate forecasts on 2–3-year timescales.

Results

The disappearance of the QBO signal in the lower stratosphere

To examine the longer-term evolution of the QBO, we first analyze extended projections of the lower-stratospheric QBO using outputs from four selected CMIP6 models (CESM2-WACCM, EC-Earth3-Veg, IPSL-CM6A-LR and MRI-ESM2-0; See Methods). Under the extended SSP5-8.5 scenario, we find that both the westerly and easterly at 50 hPa simulated by the four models gradually weaken, and eventually stabilize (Fig. 1a). Similarly, these models project a pronounced weakening of the QBO amplitude under extended SSP5-8.5, followed by a plateau, albeit with slight differences in the timing of the transition (Fig. 1b). Notably, CESM2-WACCM shows a comparatively modest reduction in amplitude relative to the other models, with values remaining within 4–7 m s⁻¹. This suggests a significant shift in the tropical lower stratospheric circulation and the state of the QBO.

Modulations of the tropical lower stratospheric circulation would alter the periodicity of the QBO. Wavelet analysis of the QBO index at 50 hPa (see Methods) reveals that the QBO signal (16–36 months) in all four models progressively shortens and eventually disappears (Fig. 1c–f). The QBO disappearance occurs around 2075, 2150, and 2100 in CESM2-WACCM, EC-Earth3-Veg, and IPSL-CM6A-LR, respectively, while the MRI-ESM2-0 model exhibits intermittent disappearance after 2200. The timing of the QBO signal disappearance closely matches the inflection point of the QBO amplitude (Fig. 1b). After the disappearance of the QBO, wavelet analysis still reveals annual and semiannual signals at 50 hPa (Fig. 1c–f), and its disappearance manifests as a stepwise shortening of the periodic signals.

As shown in Supplementary Fig. 2a–c, for the CESM2-WACCM, EC-Earth3-Veg, and IPSL-CM6A-LR models, although the QBO disappears after the year 2150, the entire stratospheric zonal wind continues to exhibit alternating easterly and westerly regimes, albeit with a significantly shortened period compared to the pre-disappearance phase. In contrast, the MRI-ESM2-0 model shows little change in the upper stratospheric zonal wind (10–30 hPa), but the strength of easterly and westerly in the lower stratosphere (50 hPa) markedly weakens (Supplementary Fig. 2d).

It is found that the upper-level QBO disappears in CESM2-WACCM, EC-Earth3-Veg, and IPSL-CM6A-LR; however, signals at annual and semiannual periods persist after the QBO disappears (Supplementary Fig. 3a–c, 3e–g). This indicates that following the disappearance of the QBO, the tropical stratospheric zonal wind continues to exhibit alternating easterly and westerly regimes, but with a shortened period of one year or half a year. Although the MRI-ESM2-0 model maintains the quasi-biennial signal at high levels, the power of this signal gradually weakens after approximately 2200, suggesting that the upper-level QBO in MRI-ESM2-0 may also disappear over longer timescales (Supplementary Fig. 3d, 3h). The persistence of the upper-level QBO in MRI-ESM2-0 during the current simulation period may be attributed to its relatively weaker increase in wave forcing under global warming compared to other models. We will discuss this aspect in detail later.

The carbon dioxide (CO₂) increasing sensitivity experiments (see Methods) show that the QBO begins to disappear when CO₂ concentration reaches 6 or 8 times the pre-industrial level (Supplementary Fig. 4a–h). Supplementary Fig. 4i–j further show that the QBO also disappears when atmospheric CO₂ is held at the pre-industrial level, while sea-surface temperatures are warmed to those induced under six times CO₂. Together, these results suggest that QBO disappearance under global warming is not driven by a direct CO₂ effect on the QBO, but instead is associated with a cascade of responses to CO₂-induced sea-surface warming.

In contrast, simulations under the extended SSP1-2.6 scenario show no significant trends in either zonal wind variability or QBO amplitude within the tropical lower stratosphere, with the quasi-biennial signal maintaining coherence throughout the simulation period (Supplementary Fig. 3i–p, Supplementary Fig. 5 and Supplementary Fig. 6).

The mechanism of the disappearance of the lower stratospheric QBO signal

The weakening of the QBO amplitude (Fig. 1b) and the stepwise shortening of its period (Fig. 1c–f) are two manifestations of the QBO disappearance process. Using the zonal mean zonal momentum equation in the transformed Eulerian mean (TEM) framework, we conducted a momentum budget diagnosis in the tropical lower stratosphere at 50 hPa (see Methods; Because the ESGF database does not provide diagnostics associated with the TEM equation and vertical velocity for the EC-Earth3-Veg and IPSL-CM6A-LR, momentum budget analyses were not conducted for these models).

The reduction in the tropical lower-stratospheric QBO amplitude is inversely correlated with tropical upwelling, as the enhanced tropical upwelling inhibits the downward propagation of the QBO, an effect that outweighs the QBO-amplifying influence of increased wave activity³³, with the net effect being a damping of the QBO amplitude²¹. Both CESM2-WACCM and MRI-ESM2-0 simulate an enhancement of residual vertical velocity (see Methods) at 50 hPa in the tropics under the extended SSP5-8.5 scenario (Fig. 2a). This finding is further supported by sensitivity experiments with increasing CO₂ concentrations (Supplementary Fig. 7a).

Fig. 2. Residual vertical velocity, momentum budget analysis, at 50 hPa under the extended SSP5-8.5 scenario, and one-dimensional quasi-biennial oscillation (QBO) model results.

a The changes in residual vertical velocity (see Methods). b–e The meridional advection forcing, vertical advection forcing, resolved wave forcing, and gravity wave forcing terms from Eq. 2 in Methods. Blue and magenta lines denote CESM2-WACCM and MRI-ESM2-0, respectively. f Dependence of the QBO period on wave forcing and residual vertical velocity in the one-dimensional QBO model (see Methods); the prescribed upwelling values are grouped into three sets: orange circles indicate $w_{\mathrm{c}}=0.3mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.2mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.1mm{\mathrm{s}}^{-1}$; blue squares indicate $w_{\mathrm{c}}=0.4mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.3mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.2mm{\mathrm{s}}^{-1}$; and red triangles indicate $w_{\mathrm{c}}=0.5mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.4mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.3mm{\mathrm{s}}^{-1}$. The wave forcing $F$ is varied from $F_{\min }=1.0\times {10}^{-2}{\mathrm{m}}^2{\mathrm{s}}^{-2}$ to $F_{\max }=6.0\times {10}^{-2}{\mathrm{m}}^2{\mathrm{s}}^{-2}$, using $n_F=100$ equally spaced values. Each simulation corresponds to one combination of $F$ and $\left(w_{\mathrm{c}},w_{\mathrm{a}},w_{\mathrm{h}}\right)$, and is integrated for 100 years, with the first 20 years discarded as spin-up. The QBO period is diagnosed from the zonal-mean wind at 24 km by identifying successive onsets of westerly flow and calculating the interval between consecutive westerly onsets.

Meridional advection tends to damp the QBO³⁴. Figure 2b shows that under the extended SSP5-8.5 scenario, the meridional-advection forcing of zonal wind remains weak and exhibits no significant trend, indicating a limited influence on zonal-wind variability. Vertical advection promotes the downward propagation of the westerly phase of the QBO but inhibits that of the easterly phase, thereby producing the classic shear-zone asymmetry in descent rate¹. CESM2-WACCM shows an increase in the westerly forcing by vertical advection, which accelerates the descent of the westerly shear zones and further suppresses the descent of the easterly shear zones, whereas MRI-ESM2-0 exhibits no evident trend in the westerly forcing by vertical advection (Fig. 2c). The QBO arises from wave–mean flow interactions^1,35, with its period inversely proportional to wave momentum flux³⁶. Resolved waves and gravity waves are the sources of momentum driving the decent of zonal winds in the tropical stratosphere^1,34. Both models exhibit an increase in easterly and westerly forcing by resolved waves (Fig. 2d), as well as a significant strengthening of easterly forcing by gravity waves (Fig. 2e). The enhanced easterly gravity-wave forcing at 50 hPa after 2050, together with the lack of a significant change in westerly forcing (Fig. 2e), may be consistent with stronger filtering by the intensified westerlies in the 100–70 hPa layer (Supplementary Fig. 2).

It is worth noting that, under the extended SSP5-8.5 scenario, the simulated enhancements of the resolved wave (Fig. 2d), gravity wave forcing (Fig. 2e) and residual vertical velocity (Fig. 2a), are much weaker in the MRI-ESM2-0 model than in CESM2-WACCM. This difference likely explains why the upper-level QBO persists longer and the lower-level QBO disappears more gradually in the MRI-ESM2-0.

Sensitivity experiments with increasing CO₂ concentrations similarly indicate little change in meridional advection forcing, whereas vertical advection westerly forcing and both resolved wave forcing and gravity wave forcing—including their respective easterly and westerly components—increase with rising CO₂ levels (Supplementary Fig. 7b–e). The net effect of the momentum budget indicates that the downward propagation of both the westerly and easterly phases of the QBO is accelerated, thereby shortening the QBO period.

Using a one-dimensional QBO model (see Methods), we further demonstrate the role of enhanced wave forcing in the disappearance of the QBO. In simulations with gradually intensified wave forcing, the QBO period shortens in a stepwise manner³⁷, exhibiting phase locking at 24-month and 12-month periods before ultimately converging to ~6 months (Fig. 2f). This behavior provides a mechanistic explanation for how warming-induced strengthening of wave forcing would leads to a progressive shortening of the QBO period and, once the QBO disappears, to a regime in which annual and semiannual periodicities dominate the zonal wind variability (Fig. 1c–f). Moreover, the phase-locking behavior becomes more pronounced under stronger tropical upwelling (red triangles vs. yellow circles in Fig. 2f), explaining the persistent 12-month locking of the QBO period under enhanced tropical upwelling in the extended SSP5-8.5 scenario (Fig. 1c–f). These results suggest that under the extended SSP5-8.5 scenario, enhanced forcing by resolved and gravity waves may contribute to the disappearance of the QBO cycle.

Enhanced stratospheric wave activity is often linked to intensified tropospheric convection driven by sea surface temperature increases. Diagnostics of convection under the extended SSP5-8.5 scenario reveal a continuous intensification of convective activity in the tropical central-eastern Pacific which is indicative of enhanced wave generation (Supplementary Fig. 9a–d). It is also worth noting that changes in lower-stratospheric winds under the extended SSP5-8.5 scenario may modify the filtering of waves propagating upward from the troposphere into the stratosphere, thereby further contributing to the apparent increase in stratospheric wave activity.

Using wavenumber–frequency spectra to diagnose changes in individual equatorial wave types (see Methods), we find that under the extended SSP5-8.5 scenario the strengthened resolved waves are primarily associated with the symmetric components—Kelvin waves³⁸, inertio-gravity waves, and equatorial Rossby waves (Supplementary Fig. 10; Supplementary Fig. 11). In contrast, the antisymmetric components, including mixed Rossby–gravity waves and eastward-propagating inertio-gravity waves, exhibit a clear weakening (Supplementary Fig. 12; Supplementary Fig. 13). The contrasting behavior between symmetric and antisymmetric wave components may reflect the tendency for tropical convection to become more spatially concentrated under global warming, thereby modifying the excitation and structure of different equatorial wave modes^38–40.

In contrast to the extended SSP5-8.5 scenario, the extended SSP1-2.6 scenario shows no discernible long-term trend in the residual vertical velocity in the lower stratosphere (Supplementary Fig. 14a). Consistent with this, the momentum budget also exhibits no significant long-term trend (Supplementary Fig. 14b–e). This is associated with weaker changes in tropical convection (Supplementary Fig. 9e–h), leading to relatively stable wave activity (Supplementary Figs. 15–18). These features correspond to the persistent presence of the QBO and its sustained amplitude throughout the extended SSP1-2.6 scenario.

Decreased predictability of the 2–3-year signal of tropospheric circulation related to QBO disappearance

The weakening of the QBO amplitude, as well as the disappearance of the QBO, may have significant impacts on tropospheric weather and climate variability. Our focus here is on the subtropical jet, a system closely linked to tropospheric weather and climate⁴¹, and known to be modulated by the QBO⁴. Before this, we assessed the ability of the CMIP6 models to simulate the key tropospheric variables relevant to this study (Supplementary Figs. 19–21). Given that MRI-ESM2-0 exhibits substantial biases in its simulation of tropospheric zonal winds (Supplementary Discussion) and only a modest weakening of the QBO (Fig. 1f), we restrict our subsequent analysis to CESM2-WACCM, EC-Earth3-Veg and IPSL-CM6A-LR.

Under the extended SSP5-8.5 scenario, the time series of the 16–36 months cycle signal of zonal wind in three key regions influenced by the QBO on tropospheric zonal wind—the Southern Hemisphere (SH) subtropics, Northern Hemisphere (NH) subtropics, and NH midlatitudes (R1, R2, and R3; see Methods)—show that oscillation intensity was stronger during the earlier period when the QBO was present, and weaker after its disappearance, with all three regions showing a general weakening trend (Fig. 3a–c). The weakening of signal intensity may lead to reduced predictability. Signal-to-noise ratio (SNR) analysis (see Methods) reveals that under the extended SSP5-8.5 scenario, all three regions exhibit a weakening trend in the SNR of the quasi-biennial signal before the QBO disappears (Fig. 3d–f), and this trend flattens or stabilizes after the QBO disappearance. In contrast, under the extended SSP1-2.6 scenario, there are no significant changes in the oscillation intensity (Supplementary Fig. 23a–c) and SNR (Supplementary Fig. 23d–f) of zonal wind across the three regions.

Fig. 3. Potential impact of quasi-biennial oscillation (QBO) disappearance on the tropospheric zonal wind under the extended SSP5-8.5 scenario.

a–c Time series of the regionally averaged zonal-wind signal in three key regions where the QBO influences tropospheric zonal wind: R1 (100–500 hPa, 40°S–20°S; Southern Hemisphere (SH) subtropics), R2 (100–500 hPa, 20°N–40°N; Northern Hemisphere (NH) subtropics), and R3 (100–500 hPa, 40°N–60°N; NH midlatitudes) (see Methods). Purple arrows in a–c indicate the direction of change. d–f Signal-to-noise ratio (SNR) for each of the three regions (see Methods). Colored lines denote different models: CESM2-WACCM (blue), EC-Earth3-Veg (orange), and IPSL-CM6A-LR (cyan).

The results of two sensitivity experiments, with and without QBO forcing (see Methods), show that the 16–36 month zonal wind signal in three key regions (M1, M2, and M3; see Methods) is stronger with QBO forcing than without (Fig. 4a–c). The SNR of the zonal-mean zonal wind is consistently higher across all periods in these regions with QBO forcing than without (Fig. 4d–f). Note that, the weak trend-like fluctuations in SNR are most plausibly attributable to internal variability rather than to a forced response. In addition, in the sensitivity experiment with QBO forcing, the first EOF mode differs markedly from that without QBO forcing (Fig. 4g, h). The first EOF mode of CESM2-WACCM simulations under the extended SSP5-8.5 scenario during the first 50 years with QBO exist (Fig. 4i) closely resembles the corresponding sensitivity experiment results (Fig. 4g). During the last 50 years with QBO disappearance (Fig. 4j), it also closely resembles the corresponding sensitivity experiment results (Fig. 4h). When stratospheric signals are removed before calculating the EOF, this first EOF mode shift remains (Supplementary Fig. 25), indicating a significant phase change in the tropospheric 16–36 months zonal wind mode.

Fig. 4. Isolated response of tropospheric zonal wind to the presence or disappearance of the quasi-biennial oscillation (QBO) signal, as simulated by the CESM model.

a–c Time series of the 16–36 months zonal wind signal averaged over the three key regions (M1, M2 and M3, see Methods). d–f Corresponding Signal-to-noise ratio (SNR). Red and blue lines in a–f denote QBO_T (True, QBO included) and QBO_F (False, QBO excluded), respectively. First EOF modes of the 16–36 month zonal wind from the sensitivity experiments QBO_T (g) and QBO_F (h) (see Methods), and from the extended SSP5-8.5 scenario during the first 50 years with QBO present (i) and the last 50 years with QBO disappearance (j). In g–j, shading denotes the first EOF mode, and purple contours indicate the climatological zonal-mean zonal wind over the corresponding periods. The contour interval is 5 m s⁻¹, with the outermost contour at 10 m s⁻¹, and values increasing toward the center.

Here we show that, under a high-emission scenario, the QBO may vanish between 2075 and 2200, with potentially profound implications for short-term climate predictability in the troposphere. It calls for global mitigation efforts toward a development that is compatible with the 2 °C target of Paris Agreement. In addition, this raises an open question of whether the disappearance of the QBO under extended SSP5-8.5 scenario constitutes a climate tipping point, an issue that merits further investigation.

Methods

CMIP6 model data

To investigate the future evolution of the QBO and its impact on the troposphere, we utilized simulation data from the Sixth Coupled Model Intercomparison Project (CMIP6)⁴². Among the CMIP6 models, 15 are capable of simulating the QBO (Supplementary Fig. 1)²⁸. Given the focus of this study on the longer-term evolution of the QBO, we specifically selected models with extended simulation periods, with the longest simulations extending to 2299 or 2300. Of these 15 models, only CESM2-WACCM, EC-Earth3-Veg, IPSL-CM6A-LR and MRI-ESM2-0 meet the necessary criteria and are therefore used to assess future changes in the QBO.

Among the four selected models, only the SSP1-2.6 and SSP5-8.5 scenarios extend beyond 2100. The extended SSP1-2.6 scenario assumes global warming remains below 2.0 °C relative to 1850–1900 (median), with implied net-zero CO₂ emissions in the second half of the century, representing a low-emission pathway. In contrast, the extended SSP5-8.5 scenario is a high-emission pathway, assuming no additional climate policies are implemented, with CO₂ emissions projected to be approximately double the current levels by 2050. In addition, we use the CMIP6 historical simulations to examine the historical evolution of the QBO in these models.

QBO index

The QBO is considered to be zonally symmetric at a given time. Therefore, the QBO index is defined as the zonal mean zonal wind in the tropical region (from 5°S to 5°N) at specific pressure levels (10 hPa, 20 hPa, 30 hPa, 50 hPa, and 70 hPa)⁴³. Given that the zonal winds at 50 hPa in tropical regions are commonly used to define the QBO index in studies examining its influence on other atmospheric systems^8,44, our analysis of QBO variations in the lower stratosphere primarily focuses on this layer.

QBO amplitude

The QBO amplitude at a specific pressure level is calculated as the square root of two times the 8-year sliding standard deviation of the deseasonalized QBO index at that level³⁰. The calculation formula is as follows:

$${Amplitude}_{\mathrm{QBO}}=\sqrt{2}{\sigma }_{8\mathrm{years}}$$ 1

${Amplitude}_{\mathrm{QBO}}$ represents the amplitude of the QBO, and ${\sigma }_{8years}$ represents the standard deviation of the QBO index over an 8-year period. The sliding step size is 1 month. This method of calculating the QBO amplitude effectively represents the strength of the QBO oscillation.

Identifying the tropopause in the tropics

The tropopause serves as the transition layer between the troposphere, where temperature decreases with altitude, and the stratosphere, where temperature increases with altitude. The pressure corresponding to the point where the temperature begins to rise with altitude is commonly referred to as the tropopause pressure.

Wavelet analysis

To identify periodic signals in the QBO index, we performed wavelet analysis on the QBO index using the pycwt library (https://github.com/regeirk/pycwt)⁴⁵. The mother wavelet used was the Morlet wavelet with ${\omega }_0=6$.

The Transformed-Eulerian Mean (TEM) formulation

To diagnose the mechanism behind the disappearance of the QBO, we analyze the mean momentum budget at 50 hPa in the tropical region using the zonal mean zonal momentum equation in the transformed Eulerian mean (TEM) framework with spherical geometry and log-pressure coordinates⁴⁶. The equation is:

$${ū}_t={\overline{v}}^{*}\left[f-{\left(a\cos \varphi \right)}^{-1}{\left(ū\cos \varphi \right)}_{\varphi }\right]-{\overline{w}}^{*}{ū}_z+{\left({\rho }_{0}a\cos \varphi \right)}^{-1}\nabla \cdot \mathbf{F}+\overline{X}$$ 2

In the equation, ${ū}_t$ denotes the temporal derivative of the zonal mean zonal wind; ${\overline{v}}^{*}\left[f-{\left(a\cos \varphi \right)}^{-1}{\left(ū\cos \varphi \right)}_{\varphi }\right]$ represents advection by the residual meridional wind, ${\overline{w}}^{*}{ū}_z$ accounts for advection by the residual vertical wind, ${\left({\rho }_{0}a\cos \varphi \right)}^{-1}\nabla \cdot \mathbf{F}$ corresponds to forcing by resolved waves and $\overline{X}$ represents parameterized gravity waves. In addition, $\varphi$ is latitude, $z$ is altitude, ${\rho }_0$ is the air density, $u$ is zonal wind, $f$ is the Coriolis parameter, ${\overline{v}}^{*}$ and ${\overline{w}}^{*}$ are the transformed Eulerian mean meridional and vertical winds, ${\overline{v}}^{*}=\overline{v}-{\rho }_0^{-1}{\left({\rho }_0\overline{v^{\prime }{\theta }^{\prime }}/{\overline{\theta }}_z\right)}_z$, ${\overline{w}}^{*}=\overline{w}+{\left(a\cos \varphi \right)}^{-1}{\left(\cos \varphi \overline{v^{\prime }{\theta }^{\prime }}/{\overline{\theta }}_z\right)}_{\varphi }$, F is Eliassen-Palme (EP) flux. Overbars denote zonal means, and primes denote deviations from zonal means.

For the diagnostics under the extended SSP5-8.5 and extended SSP1-2.6 scenarios, vertical velocity fields are not available in the CMIP6 model outputs. Therefore, we could not directly calculate the zonal mean zonal momentum equation from CMIP6 data. Instead, we used the diagnosed quantities of this equation provided by the ESGF database. Moreover, as the ESGF database does not offer these diagnosed fields for the EC-Earth3-Veg and IPSL-CM6A-LR models, the TEM analysis was not conducted for these two models.

One–dimensional model of the QBO

We use a zonally averaged, one-dimensional QBO model^37,47–49 to further investigate the response of the QBO period to enhanced wave forcing. In this framework, the only prognostic variable is the zonal-mean zonal wind $ū\left(z,t\right)$ in the equatorial lower stratosphere. The governing equation for the zonal-mean momentum is

$$\frac{\partial ū}{\partial t}+w\left(z,t\right)\frac{\partial ū}{\partial z}=-\frac{1}{\rho \left(z\right)}{\sum }_i\frac{\partial F_i}{\partial z}+\kappa \frac{{\partial }^2ū}{\partial z^2}$$ 3

where $w\left(z,t\right)$ is the prescribed tropical upwelling, $\rho \left(z\right)$ is the background density, $F_i\left(z,t\right)$ are the vertically propagating wave momentum fluxes, and $\kappa$ is a constant eddy diffusivity representing small-scale mixing. We take $\kappa =0.3{\mathrm{m}}^2{\mathrm{s}}^{-1}$, as in previous one–dimensional QBO studies³⁷.

The atmosphere is assumed to be isothermal, so that the background density decreases exponentially with height,

$$\rho \left(z\right)={\rho }_0\exp \left(-\frac{z}{H}\right)$$ 4

where $H=7.6\mathrm{km}$ is the density scale height and ${\rho }_0$ is a reference density at the lower boundary.

In the one–dimensional QBO model, we idealize the QBO as being driven by the divergence of wave momentum flux associated with two oppositely propagating internal gravity waves. We consider two monochromatic waves with equal and opposite intrinsic phase speeds and identical horizontal wavenumbers, $c_1=+30\mathrm{m}{\mathrm{s}}^{-1}$, $c_2=-30\mathrm{m}{\mathrm{s}}^{-1}$, $k_1=k_2=\frac{2\pi }{40000\mathrm{km}}$, so that the upward wave momentum fluxes at the lower boundary satisfy

$$F_1=-F_2=F$$ 5

where $F$ is a control parameter representing the total wave forcing strength³⁷.

Above the lower boundary $z_l$, the vertical profile of each wave momentum flux $F_i\left(z,t\right)$ is obtained by integrating a Lindzen-type saturation condition⁵⁰. For each wave, the vertically varying flux is given by

$$F_i\left(z,t\right)=F_i\exp \left[-{\int }_{z_l}^z\frac{\mu N\alpha \left(\zeta \right)}{k_i{\left(ū\left(\mathrm{\zeta },t\right)-c_i\right)}^2}\mathrm{d}\zeta \right]$$ 6

where $N=2.16\times {10}^{-2}{\mathrm{s}}^{-1}$ is the Brunt–Väisälä frequency, $\mu ={10}^{-6}{\mathrm{s}}^{-1}$ is a Newtonian damping rate, and $\alpha \left(z\right)$ is a dimensionless height-dependent factor that enhances dissipation in the upper stratosphere and lower mesosphere. Specifically, we use

$$\alpha \left(z\right)=\left\{\begin{array}{c}\hfill 0.55+0.55\left(z-17\right)/6.5,z\le 30\mathrm{km}\hfill \\ \hfill 1.65,z>30\mathrm{km}\hfill \end{array}\right)$$ 7

as in Rajendran et al.³⁷.

The tropical upwelling $w\left(z,t\right)$ represents the mean ascent branch of the Brewer–Dobson circulation. It includes a time-mean and an annually varying component³⁷. In addition, we introduce a semiannual component, motivated by a wavelet analysis of the residual vertical velocity, which reveals not only an annual cycle but also a pronounced semiannual signal (Supplementary Fig. 8). It is prescribed as

$$w\left(z,t\right)=\left[w_{\mathrm{c}}+w_{\mathrm{a}}\cos \left(\frac{2\pi t}{360}\right)+w_{\mathrm{h}}\cos \left(\frac{2\pi t}{180}\right)\right]\exp \left(\frac{z-z_{\mathrm{t}}}{z_{\mathrm{t}}-z_{\mathrm{l}}}\right)$$ 8

where $t$ is time in days (with a 360-day year), $w_{\mathrm{c}}$ is the annual-mean upwelling, $w_{\mathrm{a}}$ is the amplitude of the annual cycle and $w_{\mathrm{h}}$ is the amplitude of the semiannual cycle. Here, we assume fixed periods of 360 days for the annual cycle and 180 days for the semiannual cycle, and the results from the one-dimensional QBO model should therefore be interpreted within this framework. The exponential factor confines the upwelling to the lower stratosphere, with magnitudes increasing upward between the lower and upper model boundaries $z_{\mathrm{l}}$ and $z_{\mathrm{t}}$. We adopt $z_{\mathrm{l}}=17\mathrm{km}$ and $z_{\mathrm{t}}=43\mathrm{km}$. The model domain extends from 17 to 43 km in the vertical, encompassing the lower and middle equatorial stratosphere, where the observed QBO has its largest amplitude. The model uses 200 vertical levels with a non-uniform grid spacing, refined near the lower boundary to better resolve thin shear layers³⁷.

At both the lower and upper boundaries we impose a zero-shear boundary condition on the zonal wind,

$$\frac{\partial ū}{\partial z}{\mid }_{z=z_{\mathrm{l}}}=0,\frac{\partial ū}{\partial z}{\mid }_{z=z_{\mathrm{t}}}=0$$ 9

This choice reduces the sensitivity of the solution to vertical diffusion at the lower boundary.

The governing equation is discretized in the vertical using second-order finite differences and integrated forward in time using an implicit Crank–Nicolson scheme. We use a time step of $\mathrm{\Delta }t=0.2$ days, which satisfies both accuracy and stability requirements for the range of wave forcing and upwelling considered here.

To explore the dependence of the QBO period on the wave forcing and the tropical upwelling, we perform parameter sweeps over the prescribed lower-boundary wave momentum flux $F$ and the mean, annual and semi-annual components of the tropical upwelling $\left(w_{\mathrm{c}},w_{\mathrm{a}},w_{\mathrm{h}}\right)$. The values of the upwelling are specified for three groups: group1:$w_{\mathrm{c}}=0.3mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.2mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.1mm{\mathrm{s}}^{-1}$; group2:$w_{\mathrm{c}}=0.4mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.3mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.2mm{\mathrm{s}}^{-1}$; group3:$w_{\mathrm{c}}=0.5mm{\mathrm{s}}^{-1}$, and $w_{\mathrm{a}}=0.4mm{\mathrm{s}}^{-1}$ and $w_{\mathrm{h}}=0.3mm{\mathrm{s}}^{-1}$. The wave forcing $F$ is varied from m $F_{\min }=1.0\times {10}^{-2}{\mathrm{m}}^2{\mathrm{s}}^{-2}$ to $F_{\max }=6.0\times {10}^{-2}{\mathrm{m}}^2{\mathrm{s}}^{-2}$, using $n_F=100$ equally spaced values.

Each simulation corresponds to one combination of $F$ and $\left(w_{\mathrm{c}},w_{\mathrm{a}},w_{\mathrm{h}}\right)$, and is integrated for 100 years, with the first 20 years discarded as spin-up. The QBO period is diagnosed from the zonal-mean wind at 24 km by identifying successive onsets of westerly flow and computing the interval between consecutive westerly onsets.

Identification of equatorial wave modes

The tropical region experiences a variety of waves³⁹, including Kelvin waves, equatorial Rossby waves, inertio-gravity waves, and mixed Rossby-gravity waves. To identify the contributions of different wave types to the QBO, we applied the wavenumber-frequency spectral analysis method published by Wheeler and Kiladis⁵¹. By filtering specific wavenumbers and frequencies in the daily OLR and zonal wind perturbation (zonal wind anomalies relative to the zonal mean) datasets, we isolated distinct wave types. In the wavenumber–frequency decomposition, Kelvin waves, inertio-gravity waves and a portion of the equatorial Rossby wave spectrum project onto the symmetric component about the equator, whereas mixed Rossby–gravity waves, eastward inertio-gravity waves, and the antisymmetric branch of equatorial Rossby waves are captured by the antisymmetric component⁵¹. The analysis was conducted using the wkSpaceTime_cam function provided by NCL.

Band-pass filtering

Since the QBO is a quasi-periodic signal, to investigate its impact on the troposphere, we applied a Butterworth band-pass filter to extract the 16–36 months period signals⁵². The butter function from the SciPy library (https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.butter.html) was used for this purpose, with a filter order of 6.

Models

The Community Earth System Model (CESM) is a coupled climate model developed by the National Center for Atmospheric Research (NCAR) that integrates multiple components of the Earth system, including the atmosphere, ocean, land, and ice sheets, to simulate and predict global climate change and its interactions. We conducted two separate sensitivity experiments using two different versions of the CESM model: CESM2.2.0 and CESM1.2.0.

The CESM2.2.0 version of the CESM⁵³, with the source code available at https://escomp.github.io/CESM/versions/cesm2.2/html/. The model’s ‘FWsc2000climo’ composite was employed, where both sea surface temperatures and greenhouse gas forcings were set to background values from around the year 2000. The chemical module was disabled during the simulations. We used the model grid f09_g17, which corresponds to an atmospheric resolution of 0.9° × 1.25° with a total of 70 vertical levels.

The CESM1.2.0 version of the CESM⁵⁴, with the source code available at https://www2.cesm.ucar.edu/models/cesm1.2/. We employed the model’s ‘F_2000_WACCM’ composite, where the sea surface temperature and greenhouse gas forcings match those of ‘FWsc2000climo’, while the chemistry module remains active. We used the model grid f19_g16, which corresponds to an atmospheric resolution of 1.9° × 2.5° with a total of 66 vertical levels.

Sensitivity experiments on increased CO₂ impacts on the QBO

To investigate whether the disappearance of the QBO is caused by increased CO₂ emissions, we designed a set of sensitivity experiments with multiplied CO₂ concentrations using CESM2.2.0. A total of five experiments were conducted (Table 1), each lasting 14 years for 3 years spin-up time. Output instantaneous zonal wind, meridional wind, vertical velocity, and temperature every 6 h, for calculating each term in the zonal mean zonal momentum equation in the transformed Eulerian mean (TEM) framework with spherical geometry and log-pressure coordinates.

Table 1.

Sensitivity experiment design for CO₂ doubling scenarios

Experiment Name	CO₂ Concentration (× Pre-industrial level, ~2.83 × 10⁻⁴ mol/mol)	Approximate Corresponding Year under extended SSP5-8.5	Sea Surface Temperature (SST) Increase Relative to 2000 Climatology (K)
x2CO2_SST1.9	2x	2050	+ 1.9
x4CO2_SST4.8	4x	2100	+4.8
x6CO2_SST7.1	6x	2150	+7.1
x8CO2_SST9.6	8x	2200	+9.6
x1CO2_SST7.1	1x	1850	+7.1

The first four experiments correspond to CO₂ concentrations at 2, 4, 6, and 8 times the pre-industrial levels under the extended SSP5-8.5 scenario, with sea surface temperatures (SSTs) increased relative to the 2000 climatology by approximately 1.9 K, 4.8 K, 7.1 K, and 9.6 K, respectively, corresponding roughly to the years 2050, 2100, 2150, and 2250. The fifth experiment uses the SSTs from the 6× CO₂ run but with CO₂ concentrations fixed at pre-industrial levels, designed to isolate the effect of SST warming from direct CO₂ forcing on the QBO disappearance. Detailed experimental design is provided in Table 1.

EOF decomposition

To identify the modes of QBO’s impact on the tropospheric zonal wind and to examine changes in atmospheric zonal wind patterns before and after QBO disappearance, we applied Empirical Orthogonal Function (EOF) decomposition using the eofs library (https://github.com/ajdawson/eofs/)⁵⁵. Prior to the EOF decomposition of the zonal-mean zonal wind, a 16–36 month band-pass filter was applied at each grid point to extract the relevant zonal wind signal. The spatial domain for EOF analysis covers 90°S to 90°N in latitude and 10 hPa to 1000 hPa in pressure. Each grid point was weighted by $\sqrt{\cos \varphi \cdot \frac{\mathrm{\Delta }P}{P_{\mathrm{s}}}}$, where $\varphi$ is latitude, $\mathrm{\Delta }P$ is the pressure difference between two levels, and $P_{\mathrm{s}}$ is the reference pressure, set to 1000 hPa.

When investigating changes in the dominant mode of the QBO signal in zonal wind before and after the QBO disappearance, we focused exclusively on the first mode.

Definition of three key regions influenced by the QBO on tropospheric zonal wind

To identify the key regions where the QBO influences tropospheric zonal wind, we reconstructed the QBO-induced tropospheric zonal wind pattern based on the first two EOF modes. Specifically, each of the first two spatial modes was multiplied by its respective variance contribution, and the results were summed to obtain the reconstructed pattern. The detailed calculation formulas are as follows:

$${EOF}_{1+2}={EOF}_1*{Var}_1+{EOF}_2*{Var}_2$$ 10

In the equation, $EOF$ denotes the spatial mode, and $Var$ indicates the explained variance.

Using ERA5 zonal wind data from 1959 to 2020, we reconstructed the QBO-induced tropospheric zonal wind pattern (Supplementary Fig. 22a). The QBO influences the tropospheric zonal wind in a horseshoe-shaped pattern, based on which we identified three key regions: R1 (100–500 hPa, 40°S–20°S; SH subtropics), R2 (100–500 hPa, 20°N–40°N; NH subtropics), and R3 (100–500 hPa, 40°N–60°N; NH midlatitudes). We then applied the same reconstruction approach to the QBO_T sensitivity experiment (Supplementary Fig. 22b) to identify the corresponding key regions in the sensitivity experiment where the QBO affects zonal wind. The resulting mode closely resembles that derived from ERA5, but is shifted approximately 10° toward the equator relative to ERA5 (Supplementary Fig. 22a). This equatorward displacement is likely attributable to a downward shift in the QBO EOF mode within the model, centered between 10 and 100 hPa. Accordingly, three model-based key regions were defined: M1 (100–500 hPa, 30°S–10°S), M2 (100–500 hPa, 10°N–35°N), and M3 (100–500 hPa, 35°N–60°N).

Sensitivity experiments on the tropospheric impact of QBO disappearance

To investigate whether the disappearance of the QBO leads to a weakening of the QBO signal in the tropospheric zonal wind and a reduction in the signal-to-noise ratio (SNR), we designed a set of sensitivity experiments using CESM1.2.0. These experiments differ based on the presence or absence of QBO forcing in the stratosphere.

The presence of the QBO signal was controlled by setting the parameter ‘qbo_use_forcing’ to either ‘.true.’ or ‘.false.’ in WACCM. When QBO forcing was present, we used the QBO forcing file provided by the CESM model team (https://svn-ccsm-inputdata.cgd.ucar.edu/trunk/inputdata/atm/waccm/qbo/qbocyclic28months.nc), which applies a 28-month cyclic signal in the range of approximately 4 hPa to 100 hPa and between 20°N and 20°S to represent the QBO.

Both experiments ran for 80 years. The tropical stratospheric zonal-mean zonal wind (5°S–5°N, 0°–360°) during the entire simulation period is shown in Supplementary Fig. 24. Detailed experimental design is provided in Table 2.

Table 2.

Sensitivity experiment design on tropospheric impact of quasi-biennial oscillation (QBO) disappearance

Experiment Name	CO₂ Concentration	Sea Surface Temperature (SST)	QBO Presence
QBO_T	2000 Climatology	2000 Climatology	QBO present
QBO_F	2000 Climatology	2000 Climatology	QBO absent

Signal-to-noise ratio (SNR) analysis

SNR is used to quantify the proportion of signal relative to the noise in a given dataset. A higher SNR indicates a clearer signal, which makes it easier to detect and predict. In this study, the 16–36 months periodic signal in the regional zonal wind is considered the signal, while the other frequency bands are treated as noise. The sliding 50-year SNR is calculated with a sliding step of 1 month. The value at the midpoint of a 50-year sliding window is calculated based on data within that 50-year window.

The 16–36 months signal was determined based on the dominant periodicity of the tropical zonal wind at 50 hPa, as shown in the wavelet analysis of the model simulations in Fig. 1c–f.

$$SNR={10\mathrm{\cdot }\log }_{10}\frac{Signal}{Noise}$$ 11

Signal refers to the power corresponding to the 16–36 month periodic component of the zonal wind. Noise is obtained by subtracting the Signal from the original data, representing the remaining frequency bands, and is associated with the power of those bands.

Author contributions

F.X. and W.S.T. contributed to the original idea. F.H.L. and F.X. wrote this paper drafted the figures and undertook the numerical simulations. T.J.Z., Y.L.N., Y.X., J.L.L., R.H.Z., Y.W., W.J.L. interpreted the results and discussed their implications.

Peer review

Peer review information

Nature Communications thanks Matthew H. Hitchman and the other, anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The ERA5 reanalysis⁵⁶ data used in this study are available in the Copernicus Climate Change Service (C3S) Climate Data Store⁵⁷ (10.24381/cds.6860a573). The CMIP6 model data⁴² used in this study are available in the Earth System Grid Federation (ESGF) database (https://esgf-metagrid.cloud.dkrz.de/search/cmip6-dkrz/). The HadISST data⁵⁸ used in this study are available from the UK Met Office Hadley Center (http://www.metoffice.gov.uk/hadobs/hadisst/data/download.html). The sensitivity experiment outputs and the source data underlying each figure that support the findings of this Article are available in the Zenodo repository⁵⁹.

Code availability

The code used for data analysis and figure generation in this study is available in the Zenodo repository⁵⁹. The source codes for CESM1 and CESM2 are freely available from the CESM website: https://www.cesm.ucar.edu/models/releases.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-68922-2.