The disappearing quasi-biennial oscillation under sustained global warming

Domain: neuroscience
Published: 2026-01-29
Editorial outcome: major_revision

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.

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 scales1–3. Although it originates in the tropical stratosphere, the QBO significantly influences both tropical and extratropical atmospheric circulation, thereby impacting tropospheric weather and climate4–20.

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 period22–25, followed by another in 2019/2026. Recent advancements in model simulations have made it possible to project future changes in the QBO27–29. 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 frequent31,32.

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 ms⁻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).

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 interactions1,35, 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 stratosphere1,34. 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 lead 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 modes38–40.

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.

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 month zonal wind mode.

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 examine the future evolution of the QBO and its impact on the troposphere, we utilized the simulation data from the 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 simulations extending to 2299 or 2300. Of the 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 systems8,44, 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 = 2σ_QBO_8years (1)

Amplitude represents the amplitude of the QBO, and σ_QBO_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 ω_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:

∂u̅/∂t = v̅* [f - (acosϕ)⁻¹(u̅cosϕ)_ϕ] - w̅*u̅_z + (ρ_0 acosϕ)⁻¹∇·F + X (2)

In the equation, u̅ denotes the temporal derivative of the zonal mean zonal wind; v̅* [f - (acosϕ)⁻¹(u̅cosϕ)_ϕ] represents advection by the transformed Eulerian mean meridional wind, w̅*u̅_z corresponds to advection by the transformed Eulerian mean vertical wind, (ρ_0 acosϕ)⁻¹∇·F corresponds to forcing by resolved waves and X represents parameterized gravity waves. In addition, ϕ is latitude, z is altitude, ρ_0 is the air density, u is zonal wind, f is the Coriolis parameter, v̅* and w̅* are the transformed Eulerian mean meridional and vertical winds, v̅*=v̅+ρ_0⁻¹(ρ_0 v' θ' / θ̅_z)_z, w̅*=w̅+(acosϕ)⁻¹(cosϕv' θ' / θ̅_z)_ϕ, F is Eliassen-Palm (EP) flux. Over bars 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 model37,47–49 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 u̅(z,t) in the equatorial lower stratosphere. The governing equation for the zonal-mean momentum is

∂u̅/∂t + w(z,t) ∂u̅/∂z = - 1/ρ(z) ∑ ∂F_i/∂z + κ ∂²u̅/∂z² (3)

where w(z,t) is the prescribed tropical upwelling, ρ(z) is the background density, F_i(z,t) are the vertically propagating wave momentum fluxes, and κ is a constant eddy diffusivity representing small-scale mixing. We take κ=0.3 m²s⁻¹, as in previous one–dimensional QBO studies37.

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

ρ(z)=ρ_0 exp(-z/H) (4)

where H=7.6 km is the density scale height and ρ_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 ms⁻¹, c_2=-30 ms⁻¹, k_1=k_2= 2π/40000 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(z,t) is obtained by integrating a Lindzen-type saturation condition50. For each wave, the vertically varying flux is given by

F_i(z,t)=F_i exp [ - ∫_z_l^z (μNα(ζ) / k_i |u̅(ζ,t)-c_i|²) dζ ] (6)

where N=2.16×10⁻² s⁻¹ is the Brunt–Väisälä frequency, μ=10⁻⁶ s⁻¹ is a Newtonian damping rate, and α(z) is a dimensionless height-dependent factor that enhances dissipation in the upper stratosphere and lower mesosphere. Specifically, we use

α(z) = 0.55+0.55(z-17)/6.5, z≤30 km
1.65, z>30 km (7)

as in Rajendran et al.37.

The tropical upwelling w(z,t) 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(z,t)= [w_c + w_a cos(2πt/360) + w_h cos(2πt/180)] exp((z-z_l)/(z_t-z_l)) (8)

where t is time in days (with a 360-day year), w_c is the annual-mean upwelling, w_a is the amplitude of the annual cycle and w_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_l and z_t. We adopt z_l=17 km and z_t=43 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,

∂u̅/∂z |z=z_l = 0, ∂u̅/∂z |z=z_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 timestep of Δt=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 (w_c, w_a, w_h). The values of the upwelling are specified for three groups: group 1: w_c=0.3 mm s⁻¹, and w_a=0.2 mm s⁻¹ and w_h=0.1 mm s⁻¹; group 2: w_c=0.4 mm s⁻¹, and w_a=0.3 mm s⁻¹ and w_h=0.2 mm s⁻¹; group 3: w_c=0.5 mm s⁻¹, and w_a=0.4 mm s⁻¹ and w_h=0.3 mm s⁻¹. The wave forcing F is varied from F_min=1.0×10⁻² m²s⁻² to F_max=6.0×10⁻² m²s⁻², using n_F=100 equally spaced values. Each simulation corresponds to one combination of F and (w_c, w_a, w_h), 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, mixed Rossby–gravity waves, and inertio-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.

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 1.9K, 4.8K, 7.1K, and 9.6K, 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 √cosϕ * ΔP, where ϕ is latitude, ΔP is the pressure difference between two levels P_s and P_s+1, and P_ref 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.

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 log_10 (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.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is my third time reviewing this paper. (The previous two times were for a different journal which regrettable decided to reject the paper.) Both previous times I asked for major revisions and requested numerous additional analyses which the authors have since performed. I think the paper is much stronger than the original version, and at this point I suggest only minor revisions for clarity.\n1. There is a new paper that just came out of relevance to this paper: Garfinkel et al 2025. This paper focuses on the historical record and finds a weakening of the QBO and more disruptions under GHG forcings, while aerosols strengthen the QBO. They don't find any evidence for robust changes in period unlike the present paper, however the climate forcings in their paper are much weaker than the end of century SSP585. I suggest citing near e.g., line 56\nline 34: \"shift the tropospheric westerly jet\" I don't think strong evidence is provided for this. The EOF pattern does shift, but that doesn't mean the jet actually shifts. It just means that the dominant mode of variability becomes the polar vortex (as I wrote in previous reviews). I suggest deleting these words\nline 68-69: \"experience a modest increase\" I don't see any increase in the corresponding figure. Please clarify (or delete)\nline 142-143: vertical advection inhibits downward propagation for both QBO phases. It is just that for wQBO the anomalous w associated with the QBO weakens the BDC, so the inhibition is less pronounced than for eQBO.\nline 257-260: please rewrite for clarity\nGarfinkel, C. I., Avisar, D., Osprey, S., & Smith, D. (2025). The response of the QBO to external forcings: Implications for disruption events. Journal of Geophysical Research: Atmospheres, 130(22), e2025JD044438.", "reviewer_2": "I have read the second revision of the manuscript, together with replies to three reviewers. The authors addressed my questions from the previous review. They included new results from a 1D model, which adds another dimension to the paper. They have shown that under severe GH gas loading the QBO is likely to have a reduced amplitude and reduced period and less of an influence on the STJs. The exploration of possible terraced future QBO regimes is interesting. I recommend publication with minor revision. I have some comments and suggestions below.\n1. l27: “In recent years, the amplitude of the lower-stratospheric QBO has weakened” - Is this known for sure? Perhaps mention in text and cite source if you this it is. (It is unusual to state something such as this in an abstract without mention in the text.)\n2. l71-72: For completeness, suggest stating that the CESM2-WACCM did not show a significant reduction in amplitude, with values all within the range 4-7 m/s in panel b).\n3. Figure 1: For panels 1c-f, if you deleted white space between and the y-axis label and expanded each window, readers could more easily see the data. Figures 3 and 4 would benefit from this treatment as well.\n4. Discussion beginning l160: This exploration of very large CO2 loadings is interesting. It invites consideration of what else in the climate system would also change. In such a large CO2 loading scenario, what other changes do you think might occur in the earth system that could be larger than the effect that you found and possibly cause different results for the QBO?\n5. Fig. 2: What causes the large growth in easterly GWD at 50 hPa after 2050 in WACCM (Fig. 2e)? Is this due to filtering by stronger mean westerlies at 100-70 hPa? Fig. 2f - please explain colors in caption. Why are R1, R2, R3 chosen to be slightly different from M1, M2, and M3?\n6. Fig. 4 Please include descriptions of shading and purple contours.\n7. Discussion following l272: The result in Fig. RA4 (panels a and i) shows that the QBO amplifies from 1 to 2x CO2, which may be in 2050. Perhaps this is worthy of mentioning? It would be in the opposite direction of the trend that you mentioned in the abstract.\n8. Equation 8: It is highly likely that the changes in the wave forcing which led to changes in the QBO would also change the properties of the SAO. It is also likely that the annual cycle would not be fixed in an increasing loading scenario. Perhaps these aspects should be mentioned. This is in the same spirit as comment 4 above. If you discuss such future scenarios, then it seems reasonable to try to imagine other aspects of strong changes that would occur. I think it’s fine to show the 1D model results as they are – it is too hard to parameterize changes in the SAO and annual cycle. But perhaps mention whatever caveats you think should be pointed out along these lines."}, "author_response": "We sincerely appreciate the editor and reviewers’ constructive comments and valuable suggestions. Below, the reviewers’ comments are included in black text, and our responses are presented in blue.\nReviewer #1 (Remarks to the Author):\nThis is my third time reviewing this paper. (The previous two times were for a different journal which regrettable decided to reject the paper.) Both previous times I asked for major revisions and requested numerous additional analyses which the authors have since performed. I think the paper is much stronger than the original version, and at this point I suggest only minor revisions for clarity.\nResponse: We appreciate the reviewer’s careful reading of our manuscript and the constructive comments provided. These suggestions have helped us to improve the manuscript. Below, we respond to each point in turn.\n1. There is a new paper that just came out of relevance to this paper: Garfinkel et al 2025. This paper focuses on the historical record and finds a weakening of the QBO and more disruptions under GHG forcings, while aerosols strengthen the QBO. They don't find any evidence for robust changes in period unlike the present paper, however the climate forcings in their paper are much weaker than the end of century SSP585. I suggest citing near e.g., line 56\nResponse: Thanks for the reviewer’s suggestion. We have added a citation to Garfinkel et al. (2025) at the suggested location.\nReference:\nGarfinkel, C. I., Avisar, D., Osprey, S., & Smith, D. (2025). The response of the QBO to external forcings: Implications for disruption events. Journal of Geophysical Research: Atmospheres, 130(22), e2025JD044438.\nline 34: \"shift the tropospheric westerly jet\" I don't think strong evidence is provided for this. The EOF pattern does shift, but that doesn't mean the jet actually shifts. It just means that the dominant mode of variability becomes the polar vortex (as I wrote in previous reviews). I suggest deleting these words\nResponse: Thanks for the reviewer’s suggestion. We have deleted this wording as recommended.\nline 68-69: \"experience a modest increase\" I don't see any increase in the corresponding figure. Please clarify (or delete)\nResponse: Thanks for the reviewer’s suggestion. We have deleted this statement accordingly.\nline 142-143: vertical advection inhibits downward propagation for both QBO phases. It is just that for wQBO the anomalous w associated with the QBO weakens the BDC, so the inhibition is less pronounced than for eQBO.\nThis interpretation is consistent with Reviewer#1’s Comment#1 from the previous review round and with the description in Baldwin et al. (2001), who noted that “downward advection of momentum associated with the westerly shear zone enhances the descent of the westerlies, while the upward advection of momentum associated with easterly shear inhibits the descent of easterlies.” We therefore retain our original wording.\nReference:\n[1] Baldwin M P, Gray L J, Dunkerton T J, et al. The quasi‐biennial oscillation[J]. Reviews of Geophysics, 2001, 39(2): 179–229.\nline 257-260: please rewrite for clarity\nResponse: Thanks for the reviewer’s suggestion. We have rewritten this passage for clarity. The revised text now reads:\n“The first EOF mode of CESM2-WACCM simulations under the extended SSP5-8.5 scenario during the first 50 years, when the QBO is present (Fig. 4i), closely resembles the corresponding sensitivity experiment (Fig. 4g). During the last 50 years, when the QBO disappears (Fig. 4j), it similarly resembles the corresponding sensitivity experiment (Fig. 4h).” (Page 11, lines 240–245 in the revised manuscript.)\nI have read the second revision of the manuscript, together with replies to three reviewers. The authors addressed my questions from the previous review. They included new results from a 1D model, which adds another dimension to the paper. They have shown that under severe GH gas loading the QBO is likely to have a reduced amplitude and reduced period and less of an influence on the STJs. The exploration of possible terraced future QBO regimes is interesting. I recommend publication with minor revision. I have some comments and suggestions below.\nResponse: We sincerely thank the reviewer for the time and effort devoted to evaluating our manuscript. The reviewer’s comments and suggestions have been very helpful in improving the quality and clarity of the manuscript. Below, we provide a point-by-point response to each comment.\n1. l27: “In recent years, the amplitude of the lower-stratospheric QBO has weakened” - Is this known for sure? Perhaps mention in text and cite source if you this it is. (It is unusual to state something such as this in an abstract without mention in the text.)\nResponse: Thanks for the reviewer’s comment, and we apologize for the inaccurate wording in the previous version. We have corrected the words accordingly. The study by Kawatani et al. (2013) reports a weakening of the lower-stratospheric QBO amplitude over the past several decades. The sentence has now been revised to read:\n“Over recent decades, the amplitude of the lower-stratospheric QBO has weakened, and in recent years the QBO has experienced unprecedented disruptions.” (Page 2, lines 26–28 in the revised manuscript.)\nIn addition, detailed discussion and relevant references are provided in the Introduction section (Page 3, lines 47–51 in the revised manuscript.).\nReference:\n[1] Kawatani Y, Hamilton K. Weakened stratospheric quasi biennial oscillation driven by increased tropical mean upwelling[J]. Nature, 2013, 497(7450): 478–481.\n2. l71-72: For completeness, suggest stating that the CESM2-WACCM did not show a significant reduction in amplitude, with values all within the range 4–7 m/s in panel b).\nResponse: Thanks for the reviewer’s suggestion. Although the amplitude change in CESM2-WACCM is indeed weaker compared with other models, we have calculated its linear trend, which shows a statistically significant decrease at the 99% confidence level. The sentence has now been revised to read:\n“Notably, CESM2-WACCM shows a comparatively modest reduction in amplitude relative to the other models, with values remaining within 4–7 m s⁻¹.” (Page 4, lines 73–75 in the revised manuscript.)\n3. Figure 1: For panels 1c-f, if you deleted white space between and the y-axis label and expanded each window, readers could more easily see the data. Figures 3 and 4 would benefit from this treatment as well.\nResponse: Thanks for the reviewer’s suggestion. We have revised Fig. 1 by removing the white space between the panels and the y-axis labels and by expanding each panel to improve the visibility of the data. The same adjustments have also been applied to Figs. 3 and 4. Please refer to the Figs. 1, 3 and 4.\n4. Discussion beginning l160: This exploration of very large CO2 loadings is interesting. It invites consideration of what else in the climate system would also change. In such a large CO2 loading scenario, what other changes do you think might occur in the earth system that could be larger than the effect that you found and possibly cause different results for the QBO?\nResponse: We thank the reviewer for the comment. We acknowledge that under a large CO₂ loading scenario, many components of the Earth system may change, including, as noted by the reviewer in Comment #8, the annual cycle and the semiannual oscillation. As the reviewer pointed out, it is challenging to parameterize changes in the SAO and the annual cycle. We therefore followed the reviewer’s suggestion and have clarified this limitation in the Methods section:\n“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.” (Page 16, lines 370–372 in the revised manuscript.)\nIn addition, the disappearance of the QBO under high CO₂ forcing is supported by both the CMIP6 simulations and our sensitivity experiments. In the sensitivity experiments, the imposed CO₂ increases were designed to follow the CO₂ trajectory under the SSP5-8.5 scenario. When CO₂ reaches four times its baseline concentration (approximately corresponding to SSP5-8.5 around 2100), the QBO period is already substantially weakened (Supplementary Fig. 4c,d). When CO₂ reaches six and eight times its baseline concentration, roughly corresponding to SSP5-8.5 around 2150 and 2200, respectively, the QBO disappears entirely (Supplementary Fig. 4e–h). The mechanisms analysed in the manuscript are consistently supported by the CMIP6 models, the sensitivity experiments, and the one-dimensional QBO model. We therefore conclude that the mechanisms discussed in the manuscript play an important role in the disappearance of the QBO.\nWe note that, as the reviewer suggested, additional changes under high CO₂ loading (for example, changes in the annual cycle and the semiannual oscillation) may also influence the QBO and could contribute to its disappearance. However, given the scope and length constraints of the present manuscript, and the complexity of quantifying these effects, we do not pursue a detailed discussion here.\n5. Fig. 2: What causes the large growth in easterly GWD at 50 hPa after 2050 in WACCM (Fig. 2e)? Is this due to filtering by stronger mean westerlies at 100–70 hPa?\nResponse: Thanks for the reviewer’s comment. We have added this discussion to the revised manuscript:\n“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).” (Page 7, lines 151–154 in the revised manuscript.)\nFig. 2f - please explain colors in caption.\nResponse: Thanks for the reviewer’s comment. We have revised the figure caption as follows:\n“The prescribed upwelling values are grouped into three sets: orange circles indicate 𝒘 = 𝟎.𝟑 𝒎𝒎 𝐬−𝟏 , and 𝒘 = 𝟎.𝟐 𝒎𝒎 𝐬−𝟏 and 𝒘 = 𝟎.𝟏 𝒎𝒎 𝐬−𝟏 𝒄 𝒂 𝒉 blue squares indicate 𝒘 = 𝟎.𝟒 𝒎𝒎 𝐬−𝟏 , and 𝒘 = 𝟎.𝟑 𝒎𝒎 𝐬−𝟏 and 𝒘 = 𝒄 𝒂 𝒉 𝟎.𝟐 𝒎𝒎 𝐬−𝟏 and red triangles indicate 𝒘 = 𝟎.𝟓 𝒎𝒎 𝐬−𝟏 , and 𝒘 = 𝒄 𝒂 𝟎.𝟒 𝒎𝒎 𝐬−𝟏 and 𝒘 = 𝟎.𝟑 𝒎𝒎 𝐬−𝟏.” (Caption for Fig. 2 in the revised manuscript.) 𝒉\nWhy are R1, R2, R3 chosen to be slightly different from M1, M2, and M3?\nResponse: We thank the reviewer for the comment. The key regions were identified based on an EOF-based reconstruction of the QBO-induced tropospheric zonal-wind pattern. The R regions were derived from the ERA5 reanalysis and are used to assess zonal-wind changes across multiple models, whereas the M regions were defined using CESM1-WACCM only. To better present the sensitivity-experiment results, the M regions differ slightly from the R regions, although their core locations are consistent. We have clarified this in the revised manuscript.\n“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.” (Page 21, lines 489– 492 in the revised manuscript.)\n6. Fig. 4 Please include descriptions of shading and purple contours.\nResponse: Thanks for the reviewer’s comment. We have added the following description to the figure caption:\n“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.” (Caption for Fig. 4 in the revised manuscript.)\n7. Discussion following l272: The result in Fig. RA4 (panels a and i) shows that the QBO amplifies from 1 to 2x CO2, which may be in 2050. Perhaps this is worthy of mentioning? It would be in the opposite direction of the trend that you mentioned in the abstract.\nResponse: Thanks for the reviewer’s suggestion. We acknowledge that our previous wording may indeed have led to a misunderstanding by readers. We have added this discussion to the revised manuscript:\n“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.” (Page 5, lines 106–113 in the revised manuscript.)\n8. Equation 8: It is highly likely that the changes in the wave forcing which led to changes in the QBO would also change the properties of the SAO. It is also likely that the annual cycle would not be fixed in an increasing loading scenario. Perhaps these aspects should be mentioned. This is in the same spirit as comment 4 above. If you discuss such future scenarios, then it seems reasonable to try to imagine other aspects of strong changes that would occur. I think it’s fine to show the 1D model results as they are – it is too hard to parameterize changes in the SAO and annual cycle. But perhaps mention whatever caveats you think should be pointed out along these lines.\nResponse: We thank the reviewer for this helpful suggestion. We have therefore added a clarification in the Methods section. Specifically, we now state:\n“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.” (Page 16, lines 370–372 in the revised manuscript.)\n6"}]

Decision letter