# The equatorial stratospheric semiannual oscillation and time-mean winds in QBOi models

A. Smith, L. Holt, R. Garcia, J. Anstey, F. Serva, N. Butchart, S. Osprey, A.

Bushell, Y. Kawatani, Y.-h. Kim, et al.

► To cite this version:

A. Smith, L. Holt, R. Garcia, J. Anstey, F. Serva, et al. The equatorial stratospheric semiannual oscillation and time-mean winds in QBOi models. Quarterly Journal of the Royal Meteorological Society, 2020, 10.1002/qj.3690. hal-03049562

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Distributed under a Creative Commons Attribution 4.0 International License
DOI: 10.1002/qj.3690

Quarterly Journal of the
Royal Meteorological Society

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RMets

SPECIAL SECTION QBO MODELLING INTERCOMPARISON

# The equatorial stratospheric semiannual oscillation and time-mean winds in QBOi models

A. K. Smith<fnref n="1" /> ID | L. A. Holt<fnref n="2" /> ID | R. R. Garcia<fnref n="1" /> | J. A. Anstey<fnref n="3" /> | F. Serva<fnref n="4" /> ID | N. Butchart<fnref n="5" /> | S.

Osprey<fnref n="6" /> ID | A. C. Bushell<fnref n="7" /> ID | Y. Kawatani<fnref n="8" /> | Y.-H. Kim<fnref n="9" /> | F. Lott<fnref n="10" /> ID | P. Braesicke<fnref n="11" /> | C.

Cagnazzo<fnref n="4" /> | C.-C. Chen<fnref n="1" /> | H.-Y. Chun<fnref n="12" /> | L. Gray<fnref n="6" /> | T. Kerzenmacher<fnref n="11" /> ID | H. Naoe<fnref n="13" /> ID | J.

Richter<fnref n="1" /> ID | S. Versick<fnref n="11" /> | V. Schenzinger<fnref n="14" /> | S. Watanabe<fnref n="8" /> | K. Yoshida<fnref n="13" />

**Correspondence**

A. K. Smith, Atmospheric Chemistry Observations and Modeling, National Center for Atmospheric Research, 3450 Mitchell Lane, Boulder, CO 80301, USA.
Email: aksmith@ucar.edu

**Abstract**

The Quasi-Biennial Oscillation initiative (QBOi) is a model intercomparison programme that specifically targets simulation of the QBO in current global climate models. Eleven of the models or model versions that participated in a QBOi intercomparison study have upper boundaries in or above the mesosphere and therefore simulate the region where the stratopause semiannual oscillation (SAO) is the dominant mode of variability of zonal winds in the tropical upper stratosphere. Comparisons of the SAO simulations in these models are presented here. These show that the model simulations of the amplitudes and phases of the SAO in zonal-mean zonal wind near the stratopause agree well with the information derived from available observations. However, most of the models simulate time-average zonal winds that are more westward than determined from observations, in some cases by several tens of m·s⁻<fnref n="1" />. Validation of wave activity in the models is hampered by the limited observations of tropical waves in the upper stratosphere but suggests a deficit of eastward forcing either by large-scale waves, such as Kelvin waves, or by gravity waves.

**KEYWORDS**

equatorial wind, QBO, SAO, semiannual oscillation, stratosphere

<footnote n="1">¹Atmospheric Chemistry Observations and Modeling, National Center for Atmospheric Research, Boulder, Colorado</footnote>

<footnote n="2">²Northwest Research Associates, Boulder, Colorado</footnote>

<footnote n="3">³Canadian Centre for Climate Modelling and Analysis, Victoria, British Columbia Canada</footnote>

<footnote n="4">⁴Institute of Marine Sciences, National Research Council (ISMAR-CNR), Rome, Italy</footnote>

<footnote n="5">⁵Met Office Hadley Centre (MOHC), Exeter, UK</footnote>

<footnote n="6">⁶National Centre for Atmospheric Science (NCAS), University of Oxford, Oxford, UK</footnote>

<footnote n="7">⁷Met Office, Exeter, UK</footnote>

<footnote n="8">⁸Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokohama, Japan</footnote>

<footnote n="9">⁹Ewha Womans University, Seoul, South Korea</footnote>

<footnote n="10">¹⁰Laboratoire de Météorologie Dynamique (LMD), Paris, France</footnote>

<footnote n="11">¹¹Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany</footnote>

<footnote n="12">¹²Yonsei University, Seoul, South Korea</footnote>

<footnote n="13">¹³Meteorological Research Institute (MRI), Tsukuba, Japan</footnote>

<footnote n="14">¹⁴University of Vienna, Vienna, Austria</footnote>
# 1 | INTRODUCTION

Variations in the zonally averaged zonal winds and temperatures in the tropical middle atmosphere are dominated by cycles: the quasi-biennial oscillation (QBO) in the lower stratosphere and the semiannual oscillation (SAO) extending from the upper stratosphere to the upper mesosphere (Garcia et al., 1997; Baldwin et al., 2001). These cycles comprise the main variations of tropical winds on time-scales longer than a month. It is only recently that models have been able to simulate realistic winds in the tropical middle atmosphere through a combination of improved resolution and parametrization of the momentum forcing by unresolved waves. The model development efforts have been focused on simulation of the QBO, motivated by its important impacts on the global troposphere and stratosphere.

The QBO variations in wind and temperature are well resolved up to 10 hPa in radiosonde observations. A long-running time series of radiosonde data at Singapore (1°N) and other near-equatorial sites captures the historical record since the 1950s (Naujokat, 1986); assimilation of these and other data ensure that the QBO is seen in reanalysis datasets (Kawatani et al., 2016). The SAO winds, by contrast, are not regularly observed because they are beyond the range of radiosondes and difficult to measure remotely. The SAO was described by Garcia et al. (1997) based on various data available at that time. Updates to the description of the SAO include direct calculation of winds from satellite geopotential data available since 2002 (Smith et al., 2017) and evaluation of the SAO in the upper stratosphere as represented in several reanalysis products (Long et al., 2017). The portion of the SAO that reaches peak zonal wind amplitude near 1 hPa is normally referred to as the stratopause SAO. Semiannual periodicity in tropical wind variations continues into the mesosphere to 80 km or higher (Garcia et al., 1997).

The Quasi-Biennial Oscillation initiative (QBOi) is an international project sponsored by Stratosphere-troposphere Processes And their Role in Climate (SPARC) that focuses on assessing the simulation of the QBO in global climate models (Butchart et al., 2018). The participating models self-consistently generate realistic QBOs. The motivation for the initiative is described by Butchart et al. (2018). QBOi compares simulations under present-day conditions (Experiments 1 and 2, described by Bushell et al. (2019, in press)) as well as simulations for higher concentrations of atmospheric CO₂.

Many of the models participating in QBOi have upper boundaries in the mesosphere or thermosphere and therefore include part or all of the altitude range where the SAO dominates the variability of the zonally averaged zonal wind in the Tropics. The present study presents and

compares the SAO winds in those models using simulations completed as part of QBOi.

Unlike the QBO, the SAO has a period that is regular; by definition it is exactly one half-year. Westward wind maxima near the stratopause occur during both solstice periods when there is advection of westward momentum across the Equator by the upper branch of the Brewer-Dobson circulation (e.g. Ray et al., 1998; Peña-Ortiz et al., 2010). Observations indicate that the amplitude of the SAO signal varies within each year (on average it is stronger during the first half of the year) and also has appreciable interannual variability. SAO signals are seen above about 3 hPa (~40 km) to at least 0.01 hPa (~80 km). The QBOi protocol specifies the archiving of model results on pressure levels extending up to 0.4 hPa, approximately 55 km. This study therefore addresses the simulations of the SAO in the range 10–0.4 hPa.

# 2 | QBOI MODELS AND COMPARISON DATA

## 2.1 | Observations

Figure 1 summarizes equatorial zonal wind features determined from observations. The only long-running series of direct wind measurements in the tropical upper stratosphere and lower mesosphere is from rocket-borne instruments at two tropical wind stations (7.6°S, 8.7°N) made regularly over several decades beginning in the early 1960s (Dunkerton and Delisi, 1997). Other profiles shown are winds from the ERA-Interim reanalyses (Dee et al., 2011), averaged 5°S–5°N for the period 1979–2016, and winds derived from temperature profiles from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER; 2002–2018, averaged 8°S–8°N) and Aura Microwave Limb Sounder (MLS; 2004–2018, averaged 6°S–6°N) satellite instruments (Smith et al., 2017). The SABER and MLS winds were derived from geopotential height using the balance wind equation. The satellite-derived winds were calculated to 8°N and 8°S for SABER and to 6°N and 6°S for MLS; this difference is due to the different latitudinal resolution along the orbit track (Smith et al., 2017). The difference between the time-mean winds derived from SABER and MLS observations indicates the uncertainties in the observations and/or the technique used to derive winds in the Tropics. Long et al. (2017) give comparisons of mean and SAO winds from other reanalysis products. The time-mean rocket winds are more westward than the winds derived from satellite observations; this difference could be a result of the locations of the rocket sites at latitudes away from the Equator or from trends in the decades between the rocket and the other observations.
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**FIGURE 1** Observational determination or estimate of the time mean zonal-mean zonal wind and the amplitude and phase of the SAO. The phase is given as the calendar date of the first maximum [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

One feature that is seen in the rocketsonde and satellite-derived analyses in Figure 1 is a steady eastward shear of the time-mean zonal wind between the pressures of 4 and 0.4 hPa. The anomalous deviation of the wind in the ERA-Interim mean above 1 hPa appears to be a model artefact and is most likely due to insufficient observations to constrain the winds away from a sponge layer near the model upper boundary at 0.1 hPa. All of the profiles show that the SAO amplitude begins to grow just above 10 hPa and reaches a maximum of 20–30 m·s⁻¹ around 1 hPa. There is no appreciable SAO signal below 10 hPa (not shown). In the discussion of the SAO simulations that follows, comparisons will be made with the winds derived from SABER and MLS.

## 2.2 | QBOi models

The analysis presented here uses model output from the 11 participating models that have upper boundaries above 0.4 hPa; in all cases the upper boundaries are at or above 77 km. See Butchart *et al.* (2018) for descriptions of participating models. Butchart *et al.* (2018) give many details of the models such as the formulation of the dynamical core, diffusion, and sponge layer (see their table 7). A list of the models included, along with a general reference for each, is given in Table 1. Not all output products are available for every model so some comparisons will not include the full suite of participating models.

<table><caption>**TABLE 1** The names of the models whose simulations are used in this study and a key reference for each</caption><thead><tr><td>Model or version name</td><td>Reference</td></tr></thead><tbody><tr><td>AGCM3-CMAM</td><td>Anstey et al., 2016</td></tr><tr><td>CESM1(WACCM5-110 L)</td><td>Garcia and Richter, 2019</td></tr><tr><td>ECHAM5sh</td><td>Serva et al., 2018</td></tr><tr><td>EMAC</td><td>Jöckel et al., 2010</td></tr><tr><td>HadGEM2-A</td><td>Martin et al., 2011</td></tr><tr><td>HadGEM2-AC</td><td>Kim and Chun, 2015</td></tr><tr><td>LMDz6</td><td>Lott et al., 2012</td></tr><tr><td>MIROC-ESM</td><td>Watanabe et al., 2011</td></tr><tr><td>MRI-ESM2</td><td>Adachi et al., 2013</td></tr><tr><td>UMGA7</td><td>Walters et al., 2017</td></tr><tr><td>UMGA7gws</td><td>Walters et al., 2017</td></tr></tbody></table>

Simulation results are presented from QBOi Experiment 1, which uses prescribed monthly mean, time varying sea-surface temperatures from observations for the years 1979–2008 (Butchart *et al.*, 2018; Bushell *et al.*, 2019 in press). The SAO analysis presented here will focus on the zonally averaged zonal wind and on the zonal component of momentum forcing in the transformed Eulerian mean framework. There are also archived results for most of the models from Experiment 2, which had a model set-up similar to Experiment 1 except that the sea-surface
temperature was an annually repeating climatology representative of present conditions. The simulated SAO in Experiment 2 is quite similar to that in Experiment 1, so only results from Experiment 1 will be shown and discussed here. The response of the QBO in these models to changes in CO₂ are determined using additional experiments with increased atmospheric CO₂ and are described and analysed by Richter (personal communication).

Results from the first 30 years of each model simulation are used. For cases where results from more than one realization are available, analysis is applied to each and the results are averaged. Except where noted otherwise, the analysis uses results from the “monthly mean” archives. The definition of monthly mean for each model is based on the calendar used in the model. For those with years defined to be 360 days (UMGA7, UMGA7gws, LMDz6, HadGEM2-A, HadGEM2-AC), the months consist of periods of 30-day length. For the models with a standard calendar or with years of exactly 365 days, the periods archived as monthly mean conform to calendar months.

## 3 | SIMULATIONS OF MEAN AND VARIABLE ZONAL WINDS AT THE EQUATOR

An overview of the seasonally varying zonal wind for each of the participating models is given in Figure 2. Winds derived from SABER are shown for comparison. All of the simulations show a strong semiannual periodicity in the upper stratosphere whose extrema shift toward later times with increasing pressure (decreasing altitude), giving a sense of downward propagation. For most of the models, the westward winds have their apparent peaks within the plot domain (below 0.4 hPa) while the peaks in the eastward winds for most of the models appear to be at or above the 0.4 hPa level. The offset in the altitude of the eastward and westward wind peaks is also seen in the analysis based on SABER satellite observations; SABER westward maxima are at ~1 hPa while the eastward maxima (not shown; see Smith *et al.*, 2017) are at ~0.1 hPa.

Figure 3 shows the time-mean wind and the amplitude and phase of the semiannual harmonic from all the models considered. These profiles are computed from daily model output. The black lines indicate the corresponding mean winds derived from SABER and Aura MLS satellite measurements of temperature from Figure 1. The SAO amplitudes and phases are determined by fitting a half-year harmonic to 30 years of daily model output. Figure 3 and other figures presented below illustrate the long-term average of the winds and SAO behaviour. There is also a large degree of interannual variability but only the variability due to the QBO is shown (see Section 5).

All of the models are able to simulate an SAO; the peak amplitude is at 1 hPa for most of the models but is lower (2 hPa) for MRI-ESM2 and higher (at or above 0.4 hPa) for MIROC-ESM and LMDz6. The phases, as indicated by the date of the first maximum, cluster around mid-April at 1 hPa. The progressively later phase with decreasing altitude indicates a time of about 2 months to propagate downward from 1 to 10 hPa, or about -8 km per month. For most of the models, the phases indicate that the peak winds are earlier by up to half of a month than those deduced from monthly mean observations. For all of the models, the slope of the phase with pressure conforms well to the observations between 10 and 1 hPa but deviates between 1 and 0.4 hPa.

The comparisons of time-mean winds indicate that the simulated winds in the vicinity of the stratopause are more westward than observed. Without exception, the models fail to simulate the eastward shear between 5 and 1 hPa seen in the winds derived from MLS and SABER data and also the rocketsonde observations (Figure 1). The strongest westward winds in the models cluster around 1–2 hPa, which is about 10 km above the location of the strongest westward winds derived from satellite. At 1 hPa, differences between the model winds and those derived from observations can be as large as 30 m·s⁻¹. The simulated time-mean winds in the equatorial middle stratosphere (30–2 hPa) have the opposite bias and, for the majority of the models, are more eastward than observed.

Figure 4 shows the time-mean wind and SAO amplitude at 1 hPa as a function of latitude over the tropical belt. For the mean winds, some models indicate a pronounced peak (more eastward) at the Equator while others indicate a local minimum there. The overall offset from the satellite-derived winds, i.e. the more westward winds seen in the models, extends over the full range of latitudes shown. Note, however, that the satellite-derived winds are interpolated at the Equator (between 8°S and 8°N for SABER and 6.5°S and 6.5°N for MLS; see Section 2.1) and therefore cannot resolve a narrow local maximum or minimum there. As also seen in Figure 3, the models do a better job at simulating the SAO amplitude than they do the time-mean wind. All of the models capture the shift in the peak SAO amplitude off the Equator to about 10°S. The SAO amplitude does not fall off as rapidly away from the Equator as the QBO (Bushell *et al.*, 2019 in press).

One feature of the SAO that has been noted in many studies (e.g. Garcia *et al.*, 1997 and references therein) is that the half-year cycle that begins in Northern Hemisphere (NH) winter (January–June) is stronger than the one that begins in SH winter. To quantify this in the models, we calculate the amplitude of the sinusoidal component for two half-year periods. The analysis uses daily output; the beginning dates are varied by increments
<figure><img src="image_5.png" /><figcaption>**FIGURE 2** Climatological annual cycle of equatorial zonally averaged zonal wind for each calendar month from 11 models, as labelled. The lower-right panel shows winds derived from SABER observations. Dashed lines indicate negative (westward) winds. Units are m·s⁻¹ [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

of 1 day to identify which six-month periods have the largest differences. Figure 5 shows the ratios at 1 hPa between the amplitude during the first period, identified by its first day, and that during the second. The

observations, using monthly mean data, indicate that the largest asymmetry of almost a factor of two occurs between the six-month December–May period and the six-month June–November period. The asymmetry seen
<figure><img src="image_6.png" /><figcaption>**FIGURE 3** Coloured lines show the multi-year time average (left) and amplitude (centre) and phase (right) of the semiannual component of the equatorial zonally averaged zonal wind for 11 models. The dashed (SABER) and dotted (MLS) black lines are values derived from satellite geopotential height observations, repeated from Figure 1; month labels on the axis indicate the first day of the respective month [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 4** Variations of time-mean zonal winds (upper) and SAO amplitude (lower) versus latitude. Dashed and dotted black lines are from SABER and MLS, respectively. Units are m·s⁻¹ [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_8.png" /></figure>

in the models is in most cases weaker and peaks earlier. For example, for several of the simulations the largest differences are seen comparing the November–April period to May–October.

## 4 | PROCESSES THAT DRIVE THE SAO

The transformed Eulerian mean momentum equation (Andrews et al., 1987) can be used to diagnose the

processes that determine the acceleration of the zonally averaged zonal wind:

$$ \frac{\partial \bar{u}}{\partial t} = -\bar{v}^* \left[ \frac{1}{a \cos \phi} \frac{\partial \bar{u} \cos \phi}{\partial \phi} - f \right] - \bar{w}^* \frac{\partial \bar{u}}{\partial z} + \frac{1}{\rho_0 a \cos \phi} \nabla \cdot F + \bar{X}. \quad (1) $$

$\phi$ is latitude, $z$ is altitude, $u$ is zonal wind, $f$ is the Coriolis parameter, $v^*$ and $w^*$ are the transformed Eulerian mean meridional and vertical winds, $F$ is Eliassen-Palm
<figure><img src="image_9.png" /><figcaption>**FIGURE 5** Ratio of two half-year cycles of equatorial zonal wind at 1 hPa, indicating the asymmetry in the SAO for different times of the year. For example, a value of 2 indicates that a sinusoidal fit to the first cycle (beginning on the indicated day and month) has twice the amplitude of a fit to the second cycle, beginning 6 months later. The black symbols are for MLS (triangles) and SABER (squares) [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

(EP) flux, $X$ represents the zonal mean acceleration due to subgrid-scale processes and an overbar denotes the zonal mean. In the middle atmosphere of the global models considered here, the most important subgrid-scale momentum forcing is that from the parametrized gravity-wave drag, GWD. See Butchart *et al.* (2018) for descriptions and references for the GWD scheme used in each of the participating models. In the equatorial upper stratosphere, the orographic gravity-wave drag is smaller than the non-orographic gravity-wave drag by an order of magnitude or more, as also seen in the lower equatorial stratosphere (Holt, personal communication). Note that the non-orographic gravity-wave drag parametrizations typically involve free parameters that have been tuned in the tropical region to give a realistic simulation of the QBO.

To compare the magnitudes and phases of the processes that drive the SAO, we take the mean and semi-annual components of the forcing terms. The forcing terms can be referred to as advection by the residual meridional wind ($-\vec{v}^* \left[ \frac{1}{a \cos \phi} \frac{\partial \vec{u}}{\partial \phi} \cos \phi - f \right]$), advection by the residual vertical wind ($-\vec{w}^* \frac{\partial \vec{u}}{\partial z}$), forcing by resolved waves ($\frac{1}{\rho_0 a} \nabla \cdot F$), and parametrized forcing by unresolved waves ($\vec{X}$). Information to determine the mean and semi-annual components of these forcing processes for most of the models is available in the output supplied to the QBOi project.

As seen in Figure 3, the time-mean wind in most of the simulations is more westward than observed so we first compare the forcing terms averaged over the 30-year periods of the simulations. Figure 6 gives the time-mean balance of terms for each of the models averaged over the latitude band 5°S to 5°N based on monthly-mean archived model output. Notice that not all of the participating models are shown; for some of them one or more of the contributions was absent from the archive. The most notable feature of Figure 6 (see the dark blue lines) is that all of the models have a strong westward forcing from the advection of momentum by the meridional residual velocity that peaks near or above 1 hPa. This contribution is due to the meridional component of the seasonal Brewer-Dobson circulation from the summer to the winter hemisphere during the solstices. The westward forcing from advection of momentum by the meridional component of the residual velocity $v^*$ is partially balanced by eastward forcing from advection of momentum by the vertical component $w^*$ (cyan lines).

Time-mean forcing by resolved waves, denoted “divF” in Figure 6 (green lines), is weak compared to the residual advection terms. The sign is not consistent among models; at 0.4 hPa the forcing is eastward (positive) in UMGA7 and UMGA7gws; westward in AGCM3-CMAM, ECHAM5sh, EMAC, MRI-ESM2 and WACCM; and near zero in LMDz6. Positive (eastward) momentum forcing by large-scale waves in the Tropics is likely associated with the dissipation of Kelvin waves; a net westward forcing seen in some of the models indicates that Kelvin waves are not the dominant contributor to the forcing by resolved waves. Note that the time-mean forcing from non-orographic GWD (red lines) is in some cases larger than the net forcing of waves resolved in the models and has a more consistent sign between models. In most of the models, the forcing by parametrized non-orographic gravity waves is eastward and increases with height in the stratopause region; the exceptions are EMAC and LMDz6, which have very weak time-mean forcing. Using lidar and rocketsonde observations over two sites in India, Antonita *et al.* (2007) found that the net drag due to gravity waves was eastward although the vertical structure and magnitude varied over different SAO cycles.

Forcing by both the resolved waves and the parametrized gravity waves provided by the models may be affected by cancellation between waves carrying westward and eastward momentum. The “net” values shown are the sum of all the processes on the right side of Equation 1. Note that their sum does not equal the mean-wind change, which is near zero for the multi-year average. The sum is consistently negative, indicating that the net forcing probably includes a systematic omission or error. An omitted process is vertical diffusion, which is not available in the
<figure><img src="image_10.png" /><figcaption>**FIGURE 6** Multi-year time average of processes driving a tendency in the zonally averaged zonal wind (see text, Equation 1). The dashed line gives the net forcing from the advection and wave forcing terms, which should approximately equal the time tendency term (solid black line). Units are m·s⁻¹·day⁻¹ [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

archive but may be important in the models; see table 7 of Butchart *et al.* (2018). The time-mean wind (left column in Figure 3) has a sharp westward peak at 1 hPa in many of the models; vertical diffusion would tend to weaken that peak (i.e. increase the wind at 1 hPa). This indicates that vertical diffusion would give a momentum forcing that has a sign consistent with the missing forcing for several of the models. There also are likely to be errors or imbalances introduced in the interpolation from the model vertical grids to the pressure levels specified for the QBOi archive and in the use of monthly mean rather than daily

values for calculating the advection by the mean residual circulation in our analysis.

Figure 7 shows the annual cycle of the zonal momentum forcing terms at 1 hPa and 5°S–5°N based on monthly averages. From this figure, the strong westward forcing due to the advection by the meridional wind (−**v**\* [$\frac{1}{a \cos \phi} \frac{\partial \bar{u} \cos \phi}{\partial \phi} - f$]) that occurs during both solstice periods stands out. The temporal changes in the wind follow those in the net forcing but, for most of the models, there is not an exact balance for most months (compare the solid and dashed black lines). The imbalances (dashed
<figure><img src="image_11.png" /><figcaption>**FIGURE 7** Average seasonal variation at 1 hPa of processes driving a tendency in the zonally averaged zonal wind (see text, Equation 1). The dashed line gives the net forcing from the advection and wave forcing terms, which should approximately equal the time tendency term (solid black line). Units are m·s⁻¹·day⁻¹ [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

lines) are more westward than the actual changes in the zonal winds (solid lines), consistent with the net forcing imbalances in Figure 6. From Figure 7, it is evident that the largest contributions to the imbalance occur at solstices and closely follows $-\bar{v}^* \left[ \frac{1}{a \cos \phi} \frac{\partial \bar{u} \cos \phi}{\partial \phi} - f \right]$. This suggests that the imbalance in the budget may be related to this term, which was calculated using the monthly mean values of $\bar{v}^*$ and $\bar{u}$. $\bar{v}^*$ was supplied to the QBOI archive by the individual model groups and, in some cases, was calculated from wave forcing terms that had already been combined into monthly averages.

Note an overall lack of eastward forcing in Figure 7, which is consistent with the imbalance also seen in the time-mean forcing in the stratopause region (Figure 6). In all cases, the non-orographic gravity-wave drag is largest eastward (positive) during February–March and August–September, that is, during the months that mark the transition from solstice to equinox. This indicates that the forcing from these parametrized waves plays a

role in bringing the wind back towards zero from the large westward values seen during solstices. Ern et al. (2015) estimated the absolute value of gravity-wave drag in the tropical stratosphere from High-Resolution Dynamics Limb Sounder (HiRDLS) observations and inferred, based on considerations of filtering and dissipation, that the net forcing was eastward. The timing of the maximum amplitude of the drag, about 1 m·s⁻¹·day⁻¹, varied with altitude but occurred just after solstice at 48 km (~1 hPa). The magnitude of drag they found is roughly consistent with the drag seen in the models although the timing is shifted earlier than all of the models except for CESM1(WACCM-110L).

Neither the sign nor the magnitude of forcing from the resolved waves $\frac{1}{\rho_0 a \cos \phi} \nabla \cdot F$ is consistent among the models. In AGCM3-CMAM and ECHAM5sh, the seasonal magnitudes of the forcing by the resolved waves exceed those by the parametrized gravity-wave drag, whereas in the other models, the resolved wave forcing is comparable
<figure><img src="image_12.png" /></figure>

**FIGURE 8** Difference in equatorial zonal wind sorted by the direction of the monthly averaged wind at 10 hPa (westward QBO minus eastward QBO). The left panel shows differences in the time-mean wind and the right panel shows differences in the amplitude of the semiannual component of the wind. Black dashed and dotted lines show differences derived from SABER and MLS observations [Colour figure can be viewed at wileyonlinelibrary.com]

<figure><img src="image_13.png" /></figure>

to or weaker than that parametrized. Observational analysis of SABER by Ern and Preusse (2009) finds strong seasonally varying eastward forcing by Kelvin waves; however, they did not present westward forcing so the net wave forcing has not been constrained by these observations.

5 | VARIABILITY OF THE SAO AND ITS RELATIONSHIP TO THE QBO

Previous studies have found two relationships between the SAO and the QBO: (a) the strength and phase of the SAO varies depending on the phase of the QBO (Garcia *et al.*, 1997; Peña-Ortiz *et al.*, 2010; Smith *et al.*, 2017), and (b) the initial westward and eastward descending shear zones of the QBO appear to be seeded by the SAO winds (Dunkerton and Delisi, 1997; Scaife *et al.*, 2002; Kuai *et al.*, 2009; Read and Castrejón-Pita, 2012). There is some ambiguity about whether the QBO is affecting the SAO or vice versa; this will need targeted model simulations to disentangle (Dunkerton, 2017).

To investigate the first of these interactions in the QBOi models, we sort the winds in each model by the phase of

the model QBO, that is, by whether the equatorial zonal wind for each month at a particular pressure level is eastward or westward. The QBO index is defined to be eastward for any month in which the sign of the monthly average zonal wind at 10 hPa, averaged over the latitudes 5°S to 5°N, is positive and is westward when the sign is negative. We then average the model winds from all the months with an eastward QBO index and separately average all the months with a westward QBO index. If the QBO influences the SAO in the models, there will be a difference between these average winds. Figure 8 shows differences in the time-mean wind and the amplitude of the SAO, sorted by the effective QBO index in the respective model. Results are sorted month-by-month, so that subsequent months are not necessarily defined to have the same phase of the QBO. The SAO amplitude is calculated from harmonic fits of the separate climatologies for the two QBO phases. The models show agreement with the observational finding that the time-mean zonal winds are more eastward in the upper stratosphere when the winds at 10 hPa are westward (Figure 8; left panel), which is expected due to QBO winds acting to filter upward-propagating waves that force the SAO. The observations indicate that the SAO amplitude
<figure><img src="image_14.png" /><figcaption>**FIGURE 9** Difference in the equatorial wave forcing of zonal momentum sorted by the direction of the monthly averaged wind at 10 hPa. The left panel shows differences in the resolved wave EP flux divergence and the right panel shows differences in the zonal component of gravity-wave drag. Units are m·s⁻¹·day⁻¹. Note that the scales are different on the two panels [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

between 10 and 1 hPa is larger during months when the QBO phase at 10 hPa is westward. Note that the records for these satellite observations are fairly short, spanning approximately five or six cycles of the QBO. After sorting for the phase of the QBO, the number of months for each QBO phase is limited and therefore the results for strati-fying depending on QBO phase are somewhat uncertain. There is no systematic signal seen in the SAO amplitude in the models (Figure 8; right panel). Six of the models show enhanced SAO amplitude when QBO at 10 hPa is west-ward, in agreement with the observational analysis, while five models show little change or show a lower amplitude. Although a mechanism for the impact of the QBO phase on the amplitude of the SAO has not been definitively deter-mined, one possibility is that it is controlled or influenced by changes in the spectrum of waves that reaches the equa-torial upper stratosphere during different phases of the QBO (Garcia and Sassi, 1999; Ern and Preusse, 2009).

Figure 9 shows differences in the zonal component of wave forcing from resolved and parametrized waves, sorted by the sign of the monthly mean wind at 10 hPa. The wave driving of the QBO itself is clearly seen in forcing by both resolved and parametrized waves: westward forcing

below 10 hPa is leading to downward propagation of the QBO. At levels above 10 hPa, forcing by parametrized grav-ity waves is more positive when the QBO is westward at 10 hPa. The same is also true for forcing by the resolved waves, although the magnitudes are smaller. Differences in the forcing by resolved waves at altitudes above 3 hPa, including in the vicinity of the peak SAO amplitude, vary in sign among the different simulations.

It is evident from the seasonal cycle in winds (Figure 2) that the SAO in these simulations does not necessarily result in equal occurrences of westward and eastward winds at a pressure near the upper reaches of the QBO (around 3–5 hPa). For example, the climatological winds in HadGEM2-A at 3 hPa during every month are westward. Other models do simulate both eastward and westward winds but have balances that differ from observations due to the large simulated time-mean wind speed. Although the data length of 30 years for the models is longer than that available in satellite observations, it does not contain sufficient QBO west-to-east or east-to-west transitions for robust statistics.

Although all of the models have vertical shears of the zonal wind that vary seasonally, there are large differ-ences among the models in the magnitude and timing of these shear variations. The vertical resolution of the archived output in the upper stratosphere is not adequate for detailed description of the shear or the interactions of waves with the background flow. For these reasons, these simulations are not well suited for investigating the pos-sible seeding of the QBO by alternating westward and eastward winds above.

## 6 | WAVE FORCING OF THE ZONAL WIND

As noted above, one common feature of the QBOi models is a failure to simulate the eastward shear in the mean wind in the upper stratosphere. One possible cause of this is that the balance of wave forcing in the models due to equa-torially trapped waves is not sufficiently eastward due to inadequate forcing by Kelvin waves. While low-frequency Kelvin waves are likely to dissipate in the QBO region, faster Kelvin waves (periods less than a week) do not encounter critical levels and generally have longer vertical wavelengths so they are able to propagate into the upper stratosphere and beyond (e.g. Hirota, 1978; Salby *et al.*, 1984; Garcia *et al.*, 2005). These fast Kelvin waves may contribute to driving of the zonal winds of the SAO. We examine the planetary-scale equatorial waves with east-ward phase speeds in the QBOi models to assess whether there is a relation between momentum forcing by these waves and the simulated time-mean winds.
<figure><img src="image_15.png" /></figure>

Holt (personal communication) gives extensive information about the waves seen in the Tropics in the QBOi models. That study is focused on the troposphere and lower stratosphere in order to determine which resolved waves are generated in the troposphere and how they affect the evolution of the QBO. Here, we use the same wave analysis, based on model output at 6 h intervals, to look at the upward extension of the zonal mean wind forcing by large-scale eastward and westward waves and compare this with estimates from satellite observations. With this high output rate and full longitudinal coverage, the wave analysis can separate eastward and westward waves using spectral analysis; see Calvo and Garcia (2009) for details. The analysis in this section averages over an expanded latitude band of 10°S to 10°N in order to include equatorially trapped waves that have a broader structure in latitude. As seen in Figure 4, the SAO itself has a broad latitudinal range.

Figures 10 and 11 show the forcing from large-scale eastward and westward waves for a three-year period calculated using 6 h output. Large-scale is defined as those waves with zonal wave-numbers 1–12. This analysis follows that of Holt (personal communication). There is a large range in the magnitude of the different forcing components among models, as discussed for the lower stratosphere, but here also seen in the upper stratosphere. For both eastward and westward waves, the magnitude of the forcing in the vicinity of the upper levels shown (1 and 0.4 hPa) is largest around the solstices in regions of eastward background zonal wind. Since the eastward and westward waves force wind changes with opposite signs, there is considerable cancellation. This is consistent with the weak net forcing by resolved waves seen in Figures 6 and 7 for the narrower latitude band of 5°S to 5°N. The magnitude of both eastward and westward forcing is lowest for HadGEM2-A, HadGEM2-AC, MRI-ESM2, UMGA7 and UMGA7gws; also note that for these simulations, the background winds are strongly westward (Figure 3). The background zonal wind can both affect wave propagation and be affected by wave dissipation.

The spectral range of the waves included in the momentum forcing in Figures 10 and 11 is for periods from 2 to 30 days. A more detailed look indicates that there is also strong forcing at the diurnal period (not shown); at this period there is also an indication of strong cancellation between eastward and westward momentum forcing.

Unfortunately, there are limitations in determining the complete wave spectrum in the tropical middle atmosphere from current global observations. Two frequently used satellite measuring systems (SABER and MLS) have records of long duration but have low horizontal and temporal resolution that is not adequate to

determine the full range of large-scale and gravity waves. Furthermore, diagnosing wave properties from temperature profiles alone involves assumptions that reduce the accuracy of the analysis. Gravity-wave measurements from ground-based observations (e.g. Antonita et al., 2007) are limited to only a few locations. These limitations, along with the lack of global direct wind observations in the equatorial stratopause region, leave us unable to validate the SAO wave driving in the QBOi models.

7 | CONCLUSIONS

We have described simulations of the time-average and semiannual oscillation of the zonally averaged zonal wind near the equatorial stratopause in models that participated in the SPARC QBOi; it complements investigations describing the QBO in the same simulations (Bushell et al., 2019 in press). Results shown here are from QBOi Experiment 1. These are 30-year simulations using observed sea ice amounts and sea-surface temperatures from the years 1979–2009.

There are several successes shared by the participating models: all simulate seasonal variations of the zonal wind that have reasonable semiannual amplitude and phase and all show that the amplitude is larger during the half year beginning in early NH winter although the seasonal asymmetry is weaker in most of the models than in observations. The models also successfully simulate the offset of the SAO maximum amplitude toward the Southern Hemisphere. According to the simulations, large-scale eastward and westward waves contribute momentum forcing of the zonal wind, although, due to coincidence in timing of the strongest forcing, there is a considerable degree of cancellation between them. The monthly average net momentum forcing by resolved waves is smaller than that from parametrized gravity waves in most of the models.

There are also several shortcomings that are shared in the simulations: all fail to simulate the time-mean eastward shear at levels between 10 and 1 hPa and most of the models indicate a time-mean wind in the upper stratosphere that is more westward than observed, in some cases by 20–30 m·s⁻¹. The total wave forcing of the SAO in the models is difficult to validate with observations because the largest contribution is from parametrized non-orographic gravity waves.

These simulations, which were primarily focused on the QBO region in the lower stratosphere, illustrate both the successes and shortcomings in the SAO simulated by present-day models with self-generated QBOs. Further progress in reducing the SAO discrepancies is likely to require both realistic simulation of tropical waves, such as Kelvin waves with periods shorter than 10 days, and
<figure><img src="image_16.png" /><figcaption>**FIGURE 10** Three-year time series of momentum forcing (m·s⁻¹·day⁻¹) from waves with eastward phase speeds (periods 2–30 days) and zonal wave-numbers 1–12. The contours give zonally averaged zonal wind with contour interval of 5 m·s⁻¹; negative contours are dashed [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

observational validation of representation of the impact of subgrid-scale gravity waves.

The SAO has not received as much attention as the QBO, due in large part to the difficulty of measuring or deriving winds in the tropical upper stratosphere and

lower mesosphere. However, the influence of the SAO could, like that of the QBO, extend beyond the equatorial middle atmosphere. The impact of SAO variability on the dynamically active high-latitude winter was investigated in model simulations by Gray *et al.* (2001) but has not been
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>**FIGURE 11** As in Figure 10 except for waves with westward phase speeds [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
a focus of investigations using observations or present-day models. Possible links that could be explored using model simulations are the role of SAO variability in the response of middle and high latitudes to the QBO, the impact of SAO variability on the occurrence of sudden stratospheric warmings, and the impact of variations in the winter hemisphere on the interannual variations in the SAO winds and interhemispheric coupling.

## ACKNOWLEDGEMENTS

The National Center for Atmospheric Research is sponsored by the National Science Foundation. We thank the model groups that participated in QBOi for performing the simulations and providing output for analysis. The authors also acknowledge support for early career researchers from the World Climate Research Programme core project Stratosphere-troposphere Processes And their Role in Climate. The QBOi archive was hosted by the Centre for Environmental Data Analysis (CEDA), UK. L. Holt was supported by NASA's Atmospheric Composition Modeling and Analysis Program (ACMAP) Grant No. 80NSSC18K0069, and NASA's Modeling, Analysis and Prediction (MAP) programme Grant No. 80NSSC17K0169. C. Cagnazzo and F. Serva have been supported by the Copernicus Climate Change Service, funded by the EU and implemented by ECMWF. Y. H. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2015R1C1A1A02036449). F. Lott, L. Gray, S. Watanabe and S. Osprey acknowledge support from the JPI-Climate/Belmont Forum project GOTHAM (ANR-15-JCLI-0004-01, NE/P006779/1). P. Braesicke, T. Kerzenmacher and S. Versick acknowledge support by the state of Baden-Württemberg through bwHPC. Y. Kawatani was supported by Japan Society for Promotion of Science (JSPS) KAKENHI Grant Numbers JP15KK0178, JP16H04052, JP17K18816 and JP18H01286. A. K. Smith acknowledges comments from and discussion with W. J. Randel, I. R. Simpson and T.J. Dunkerton.

## ORCID

A. K. Smith https://orcid.org/0000-0003-2384-5033

L. A. Holt https://orcid.org/0000-0003-0211-053X

F. Serva https://orcid.org/0000-0002-7118-0817

S. Osprey https://orcid.org/0000-0002-8751-1211

A. C. Bushell https://orcid.org/0000-0001-5683-4387

F. Lott https://orcid.org/0000-0003-2126-5510

T. Kerzenmacher https://orcid.org/0000-0001-8413-0539

H. Naoe https://orcid.org/0000-0002-6261-0854

J. Richter https://orcid.org/0000-0001-7048-0781

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**How to cite this article:** Smith A. K, Holt LA, Garcia RR, Anstey JA, Serva F, Butchart N, Osprey S, Bushell AC, Kawatani Y, Kim Y-H, Lott F, Braesicke P, Cagnazzo C, Chen C-C, Chun H-Y, Gray L, Kerzenmacher T, Naoe H, Richter J, Versick S, Schenzinger V, Watanabe S, Yoshida K. The equatorial stratospheric semiannual oscillation and time-mean winds in QBOi models. *QJR Meteorol Soc*. 2022;148:1593–1609.
https://doi.org/10.1002/qj.3690