the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jun 2026
Analysis of systematic biases in equatorial resolved and parameterized wave forcing of the quasi-biennial oscillation in a multi-model ensemble
Abstract. The equatorial resolved and parameterized wave forcing of the quasi-biennial oscillation (QBO) in models participating in phase 2 of the Atmospheric Processes and their Role in Climate (APARC) Quasi-Biennial Oscillation initiative (QBOi) is analyzed. We compare two experiments performed by the multi-model ensemble, NoNudge and ObsQBO, covering the period from 1979 to 2020. In this study, NoNudge designates experiments where the QBO is generated internally without nudging, whereas ObsQBO represents experiments in which the QBO is bias-corrected by nudging stratospheric zonal-mean zonal winds toward ERA5, allowing investigation of modelling uncertainties originating from biases in the background winds. While the NoNudge simulations exhibit QBO biases typically seen in models, including eastward wind bias in the mid-stratosphere and underestimation of the QBO amplitude in the lower stratosphere, these discrepancies are effectively mitigated by nudging in ObsQBO simulations. In the NoNudge experiments, the models reveal weaker Kelvin and gravity wave forcing in the tropical lower stratosphere than ERA5, but these forcings are enhanced in the ObsQBO experiment, suggesting that weak wave forcing of internally generated QBOs results from reduced critical-level filtering of waves due to unrealistically weak vertical wind shear at these levels. However, in ObsQBO experiments, the models still exhibit insufficient Kelvin and gravity wave forcing in the lower stratosphere. This suggests that the weak QBO amplitude in the lower stratosphere may stem from the inherent deficit in wave forcing in the models. One notable feature of the ObsQBO experiments is the excessive eastward wave forcing in the mid-to-upper stratosphere during the easterly QBO phase in the lower tropical stratosphere. The correlation coefficient between the 10 hPa eastward wave forcing and westerly QBO amplitude is 0.8, indicating that excessive westerly QBO is associated with strong eastward wave forcing in the mid-to-upper stratosphere.
Competing interests: At least one of the (co-)authors serves as co-editor for the special issue to which this paper belongs.
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- RC1: 'Comment on egusphere-2026-2856', Anonymous Referee #1, 03 Aug 2026 reply
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- 1
Review of:
Analysis of systematic biases in equatorial resolved and parameterized wave forcing of the quasi-biennial oscillation in a multi-model ensemble
by:
Lee et al.
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General comments
This article analyzes the QBO forcing in simulations from the QBOi project. The analysis includes the “NoNudge” simulations, ie. the original simulations, as well as “ObsQBO” simulations, where a nudging scheme for the zonal wind in the equatorial stratosphere is used to effectively assimilate the QBO from ERA5. A set of diagnostics is applied to understand better how the wave mean-flow interaction works and how this can be split in contributions by different wave types. The article is mostly descriptive and is useful because it provides a general view on the problems in simulating the QBO in this class of models model. It extends the existing collection of publications on the QBOi simulations.
The article is generally well written and the structure leads from the broader features to the finer details. Figures should be produced in a better resolution or in a scalable vector format, because some figures, e.g. Fig. 5, contain a large number of panels, so that zooming in is necessary.
The minor comments given below should be considered to improve the details of the article.
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Minor comments
L34 and L112: “… NoNudge and ObsQBO …”
These names could be chosen better. As the focus is on the QBO, and one set of experiments simulates the QBO internally, as currently used for NoNudge, it seem straightforward to use the acronym “InternalQBO” or shorter “IntQBO”. The other experiments have a nudged QBO, which should resemble the observed QBO but still isn’t the real QBO. Anyway a natural acronym would be “NudgedQBO” or shorter “NdgQBO”. So “IntQBO” and “NdgQBO” would be a nice pair. Please consider to change the acronyms.
L37: maybe better: “… stratospheric zonal-mean zonal winds in the simulations toward that in ERA5 …”
L44: If it is the case, it would be worth to mention that the vertical momentum flux across a level near the tropopause is statistically the same, because the sources of waves in the NoNudge and ObsQBO are the same, and only the filtering and thus the momentum transfer to the QBO jets are different. If however the sources are systematically different between NoNudge and ObsQBO, than please mention this instead. (And of course, if the filtering at lower levels is inefficient, then the momentum will be transferred at higher levels, where conditions are favorable, as you know.)
L65: “… In phase 1 of the Atmospheric Processes And their Role in Climate (APARC) QBO initiative (QBOi), which provided the first comprehensive multi-model intercomparison of QBO resolving GCMs, including an analysis of QBO wave driving (Holt et al., 2022). …”
The article by Holt et al. is from 2020, not 2022 (also on L79). And their work was “… in phase 1 of the Stratosphere–troposphere Processes And their Role in Climate (SPARC) …”. SPARC became APARC only later. Please clarify this, for example in a footnote.
L69: Also Bushell et al. is from 2020, not 2022 (also L86). Please check the publication years in all references!
L85: “… the drag …”
Does “the drag” mean parameterized drag, then please write so. Very high resolution models may produce explicitly the gravity waves producing such drag, but Holt et al. probably analyzed CMIP-type model simulations, which do not simulate gravity waves explicitly, and instead depend on a parameterization for their drag.
L88: “…, or all of these.”
should be extended to make it clear that this concerns the resolved as well as the parameterized wave spectrum, for example: “…, or all of these, in the resolved and/or the parameterized waves.”
L105: “… In the Exp1-ObsQBO experiment, the zonal-mean zonal winds in the models are nudged toward the zonal-mean zonal winds of ERA5 in the equatorial stratosphere. Equatorial waves in the troposphere are not constrained by the nudging. However, because full-field nudging is applied to three models …”
The nudging of the QBO needs some latitude and pressure (or height?) structure for the nudging strength (or nudging time scale), and some times also a target QBO structure in latitude and pressure. As the nudging details are important for the result, it is worth to add here some description. Please also state that only the zonal wind is nudged, if this is true. And if this is not true, please add information on other fields which are nudged. (I hope nobody nudged temperature!)
L114: “Table 1: Summary of the QBOi phase-2 models used in this study.…”
Please add a brief explanation of the difference between “MIROC6.1, p1” and “MIROC6.2, p2”.
L115: “… H denotes that the model provided high-frequency data (6-hourly) …”
Please specify also the output data frequency of all other models.
L133: “… by subtracting the climatology from the monthly averaged zonal wind at 30 hPa …”
Which kind of climatology is subtracted, the climatology of the annual mean or the annual cycle? What is the range of the normalized zonal wind, and which original zonal mean wind strengths correspond to the threshold values of +0.5 and -0.5? Please clarify this.
L135: “Second, the descending westerly (DW) and descending easterly (DE) are defined …”
Do mean QBO phases? Like: “… and descending easterly (DE) phases are defined …”
L144: “… of the five-month smoothed zonal wind …”
You mean “… of the five-month smoothed zonal mean zonal wind …”?
L170: “A half level is identified at the altitude where …”
Does this mean: “ Then the highest half level below the upper level is identified where …”
L216: “… In the NoNudge experiments, none of the models reproduce the westward winds of ERA5 between 10 and 50 hPa (Fig. 1a). …”
This should be reformulated. All models produce westward winds between 10 and 50 hPa! The issue is that none of the model profiles of westward wind reaches or exceeds the westward wind profile of ERA5.
L217: “… At 10 hPa, the multi-model mean (MMM) …”
From here on the multi model mean is used to represent the “typical” model behavior. A multi model median would be another option, which is probably more “typical” if a few models are outliers. Please insert in this section or in the previous section a discussion on the statistics to be used to represent the typical model behavior, which currently is the mean, though a median would be another good choice.
Some of the following discussion about the influence of outliers on the MMM could be reduced if the median was used.
L252: “Metrics of the vertical and latitudinal extent of the QBO are shown in Table S1. …”
As these quantities are discussed here, it would be better to include this table in the main article.
L280: “… all models except BCC-CSM2-MR exhibit QBO periods of 28 months for the FFT method.”
Table 3 reports and FFT period of 25.4 months in ObsQBO of BCC-CSM2-MR. What is the reason for this “failure”? Fig. S1 shows the correct number of cycles (~17) and thus it is surprising that the FFT amplitude, which is also averaged over levels, and which is described as the more robust method, results in a substantially shorter period.
L293: Please combine Fig. 2 and Fig. S2 as two panels in a single Figure.
L315: already Horinouchi et al. (2003) observed this large variation between model (https://doi.org/10.1175/1520-0469(2003)060%3C2765:TCCAUW%3E2.0.CO;2)
L323: “The differences between the ObsQBO and NoNudge experiments are very small in both the symmetric and antisymmetric spectra. … Consequently, nudging applied in the equatorial stratosphere has a limited impact on the tropospheric source, allowing the stratospheric wave forcing to be examined with minimal influence from changes in tropospheric sources.”
This is an important though possibly unwanted finding of this analysis. This should be part of the abstract too, because it effectively makes the interpretation of the later results easier. (NoNudge to ObsQBO differences in the stratosphere are not related to differences in the tropospheric convectively coupled wave sources.)
L371: “Table 4 shows the modulation of instability in five models …”
For this discussion it would be helpful to have the same diagnostics also form ERA5, which provides the nudging target for the ObsQBO simulations, but which does not generate its QBO by means of a nudging procedure. First, this would provide a sense of what should be a realistic value. Is it closer to ca. 4 units as for example in the MIROC6.1 simulations, or less than 1 unit as in E3SM? Further this would provide information on the role of the QBO jet structure vs. the assimilation method. Therefore please add ERA5 to Table 4 and discuss the model results also with respect to this source.
L380: “… the increased frequency of 𝑞φ …” → “… the increased frequency of negative 𝑞φ …” ?
L381: “… Consequently, a realistic WQBO structure could be an important factor to accurately reproduce the MRG waves in the equatorial stratosphere. …”
Is there any simulation in which the nudging degrades the QBO jets? Or is this about the type of nudging: zonal mean nudging vs. full field nudging?
L399: “The momentum budget of the QBOi models is examined through the individual TEM components (Eq. 2). …”
In Eq.2, there exists also the imbalance term Ximbalance that should include effects by diffusion and in the case of nudging additionally the nudging tendency Fnudging. Please include Ximbalance in your discussion and in the related figures. It would clarify the importance of Ximbalance in comparison to the internal forcing by EPFD. (Alternatively, if available from the nudged simulations, show Fnudging.) The Ximbalance or Fnudging term could be discussed after that on Xparam.
L409: “… which corresponds to the slowdown of the downward propagation of the QBO induced by tropical upwelling. …”
There should be a hint to the role of the secondary meridional circulation of the QBO, which modifies the advection, and especially in the case of the westerly phase can reduce the advection effect of the general tropical upwelling to nearly zero. I think that is also what we can see in Fig. 8.
L589: “… the maxima and minima of the zonal wind between 200 and 85 hPa, averaged over 5°N and 5°S …”
Does this mean maxima and minima of u5N-5S over all levels in the range and all longitudes, or maxima and minima of the zonal mean of u: u5N-5S over all levels?
L612: “… When the onset of the easterly wind occurs, the TEM components of QBOi models in ObsQBO generally capture the characteristics of ERA5, although individual models diverge in their equatorial wave forcing (Figs. 16m–16p). …”
This is not entirely the case. A critical difference exists in the delayed forcing by XPW + XGW. (Fig. 16k). In ERA5 and MERRA2, this forcing peaks at month -1 and 0, but in the model simulations this forcing peaks later between months 0 to +2.
L637: “The correlations between WF30-50 in the ObsQBO and A50 in the NoNudge …”
Probably should be: “The correlations between WF30-50 and A50 in the ObsQBO …”
Data Availability
For the QBOi phase 2 model outputs it is mentioned that these are hosted by the NERC Centre for Environmental Data Analysis (CEDA), but no information is given on the accessibility. Are all these data accessible? How can the data be accessed and downloaded? This should be explained.