1. Introduction
Seasonal and longer-term variability of the zonally averaged tropical middle atmosphere is dominated by two cycles that are roughly periodic: the quasi-biennial oscillation (QBO), which is strongest in the lower to middle stratosphere, and the semiannual oscillation (SAO), which has one peak in the upper stratosphere to middle mesosphere and another in the upper mesosphere. Both the QBO and SAO are most clearly seen in zonal wind near the equator but also have signals in meridional wind, wave activity, temperature, ozone, and other trace species. In this introduction and in the following analysis, we address only the lower segment of the SAO, sometimes called the stratopause SAO (SSAO) in zonal wind. Limitations in wind observations preclude a similar analysis of the upper segment of the oscillation.
The existence of the QBO and its periodicity are driven by the interaction of vertically propagating waves with the background zonal mean atmosphere, as shown in a hierarchy of numerical models (e.g., Holton and Lindzen 1972; Kawatani et al. 2010; Bushell et al. 2022). The impact of the QBO on higher latitudes during Northern Hemisphere winter is well-documented (Holton and Tan 1980; Baldwin et al. 2001; Anstey and Shepherd 2014; Elsbury et al. 2021; Anstey et al. 2022). Observations show that the polar vortex in the winter stratosphere is more disturbed when the QBO in the lower stratosphere is in the easterly phase. Recent work by Gray et al. (2020, 2022) has shown observational evidence that variations in the timing of the SAO easterly wind transition after the autumnal equinox are also linked to dynamical developments in the NH winter polar atmosphere.
The accepted mechanism for the existence of the SAO involves the global-scale circulation and localized wave–mean flow interactions. Holton and Wehrbein (1980) proposed that the easterly phase of the SAO near the stratopause during solstice seasons is the result of advection of zonal mean momentum across the equator associated with the transformed Eulerian mean circulation, which is often referred to as the upper branch of the Brewer–Dobson circulation. The circulation is driven by wave activity, primarily in the extratropics of the winter hemisphere. This explanation has found additional support as new observations and more comprehensive models have become available (e.g., Tomikawa et al. 2008).
Holton and Wehrbein (1980) also suggested that the westerly phase of the SAO near the stratopause may be driven by dissipation of Kelvin waves generated in the troposphere. Using satellite data, Hitchman and Leovy (1988) found that dissipation of resolved Kelvin waves did contribute to the westerly winds. However, it was not sufficient to account for the wind acceleration from the easterly SAO maxima seen around solstices to the westerly winds seen a few months later at equinoxes. They suggested that the remaining eastward momentum forcing came from gravity waves, which were not resolved in the observations they analyzed.
Antonita et al. (2007) used Rayleigh lidar observations of middle atmospheric temperature (13.5°N) and rocketsonde observations of wind (8.5°N) to determine the variations of gravity wave momentum fluxes in the stratopause region. They found westerly fluxes for the altitude range 30–60 km (about 14–1.9 hPa) that maximize at the equinoxes; they also note a high degree of variability in the gravity wave forcing during the periods they analyzed.
Ern et al. (2015, 2021) used observations from several sources to show that gravity wave amplitudes and derived momentum flux convergences vary seasonally. They found that gravity waves contribute primarily to the westerly driving of the winds in the tropics near and above the stratopause. Even so, they found that waves that can be detected in available observations are not sufficient to supply all the momentum forcing needed to drive the development of westerly winds in the SAO. The shortfall in analyses of observations is most likely due to the inability of available instrumentation to detect all of the waves that contribute to the forcing. A model comparison study presented by Smith et al. (2022) supports the conclusion that forcing by gravity waves is an important component of the SAO eastward forcing. However, even though most of the models contributing to that study included a parameterization of nonorographic gravity waves, the winds they simulated generally have substantial easterly biases in the stratopause region, indicating an underestimate of the westerly forcing.
The high-resolution GCM used by Tomikawa et al. (2008) simulates a realistic SAO and background wind without including parameterized gravity waves. The model resolution allows for generation, propagation, and dissipation of a broad range of gravity waves in addition to larger-scale planetary waves. Their detailed analyses of these simulations allow them to quantify the balance of processes associated with all stages of the SAO evolution. They found that the impact of the cross-equatorial advection of easterly momentum by the mean circulation varies depending on the timing within the SAO cycle. Advection of momentum is the primary contributor to the easterly acceleration during the period when the easterly winds are developing before solstices. Even though the cross-equatorial flow continues, the advection of momentum then decreases because the meridional gradient in momentum is reduced. At the times of the SAO peak easterlies near and after solstices, these model results show that the advection of momentum by the large-scale circulation and the forcing by wave dissipation nearly cancel one another.
High-resolution models are valuable for understanding physical processes but usually are only run for a limited number of years. Climate models with standard resolution still require parameterization of gravity waves to simulate realistic middle atmosphere winds and temperatures. The inability of climate models to adequately simulate the winds in the tropical stratopause region poses an impediment to investigations of the multiyear variability of the SAO. An additional problem is that the representation of this oscillation in reanalysis datasets also has deficiencies (Baldwin and Gray 2005; Kawatani et al. 2016, 2020) and there is substantial interreanalysis variation (see chapter 11 of Fujiwara et al. 2022).
Observational evidence presented by Burrage et al. (1996), Dunkerton and Delisi (1997), Garcia et al. (1997), Ray et al. (1998), Smith et al. (2017), and others shows that the SAO varies depending on the phase of the QBO. The impact of the QBO on the SAO has been simulated in mechanistic numerical models (Garcia and Sassi 1999; Richter and Garcia 2006) and general circulation models with a self-generated QBO (Peña-Ortiz et al. 2010; Smith et al. 2022). While the general impact has been convincingly shown, there are many aspects of the relationship between the SAO and QBO that have not been described up to now. A potential explanation for the SAO–QBO relationship is that equatorial winds and wind shears associated with the QBO filter or otherwise affect the spectrum of vertically propagating waves that contribute to driving the SAO. Other mechanisms that involve the impact of the QBO on midlatitude wave processes and, consequently, on the forcing of the Brewer–Dobson circulation and the seasonal advection of momentum across the equator could also possibly contribute.
In the present study, we use zonally averaged zonal winds derived from satellite observations to look at the relationships between the QBO and the interannual variability of the SAO. We focus on characteristics of the relationships that can be directly observed and thus form the basis for validation of model simulations of the middle atmosphere tropics. To characterize interactions, we primarily investigate interannual variations of the monthly averaged winds, including the SAO and annual oscillation. This work describes the timing and the vertical and latitudinal structure of the responses of the SAO to QBO winds. These details have not been presented previously and are valuable for investigating mechanisms and for validating numerical models.
The data used are from two NASA instruments: the Microwave Limb Sounder (MLS) instrument on the Aura satellite and the Sounding of the Atmosphere by Broadband Emission Radiometry (SABER). Both datasets use limb observations of emissions to derive temperature profiles extending from the lower stratosphere or below through the depth of the mesosphere. Standard level 2 data products include vertical profiles of geopotential height, which are used here to derive zonal winds, as described by Smith et al. (2017). The reason for two different datasets is to provide more confidence in the results. In what follows, we emphasize only those results that are seen convincingly in both.
2. Data
This study uses geopotential height data from two satellite instruments. Low-latitude winds are derived from the satellite geopotential height data, as described in section 2c.
a. SABER geopotential height
SABER, which is on the Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED) satellite, has been recording data since January 2002. Temperature profiles are retrieved from about 20 to 110 km. Remsberg et al. (2008) discuss validation of temperatures for an earlier version of the SABER level 2 data. Validation of the more recent (version 2) temperature retrieval is provided by Dawkins et al. (2018). The geopotential height is determined by integrating vertically and tying onto a reference height at 10 hPa (Remsberg et al. 2008). In this study, version 2.07 level 2 data are used up to 14 December 2019 and version 2.08 for dates on and after 15 December 2019. The switch in version number occurs where the retrieval was modified to correct for some inconsistencies in the temporal behavior (Mlynczak et al. 2022).
TIMED precesses and must perform a yaw maneuver about every 60–65 days to prevent SABER from looking directly at the sun. Over each of these yaw periods, SABER accumulates observations over almost all local times in the latitude band between 53°S and 53°N. The effective resolution is about 15° in longitude, 4° in latitude, and 2 km in altitude. Geopotential heights for all results used here are interpolated in pressure and then sorted into 4° latitude bins. Profiles are averaged over longitude and calendar month to generate zonal and monthly averages. Local time variations are minimized by averaging ascending and descending parts of the orbit.
b. MLS geopotential height
The MLS instrument on the Aura satellite has been recording data since August 2004. Temperature profiles are retrieved from below the tropopause to 110 km. The geopotential height is determined by integrating vertically and tying onto a reference height at 100 hPa.
Aura does not precess; at a given latitude, all observations are taken at the same two local times, about 12 h apart. The effective resolution is about 15° in longitude and 1.5° in latitude. Vertical resolution is 3–4 km below 10 hPa, 7–8 km for 1–0.1 hPa, and 11 km above 0.1 hPa (Livesey et al. 2020). Geopotential heights used here are averaged over longitude and calendar month to generate zonal averages using latitude bins with width of 4°.
c. Calculation of winds
Smith et al. (2017) presented monthly average equatorial zonally averaged zonal winds derived from the SABER and MLS satellite data described here. They showed that the winds compare well with each other and with radiosonde observations (available at pressures of 10 hPa and higher) and meteor radar (available at altitudes at and above 81 km). The SABER and MLS datasets are updated for use in the present analysis; these data are invaluable because of the long data records, currently 20 and 18 years for SABER and MLS, respectively.
The derivations of zonal winds in this study differ from those used by Smith et al. (2017). In this study, the monthly mean values of geopotential height are obtained by averaging over all profiles within a calendar month, whereas Smith et al. (2017) processed the entire time series using the asynoptic mapping method of Salby (1982) and then computed longitudinal monthly averages from the coefficients. This change does not affect the calculated monthly mean winds.
We use the term QBO to refer to the net winds, which include the background time mean and the deviations at all periods longer than a month. These therefore include the asymmetry in the duration and magnitude of westerly and easterly QBO phases or, equivalently, the offset of the time-mean wind from zero. Smith et al. (2017) used radiosonde wind data compiled by Frei Universität Berlin (Naujokat 1986) to define the monthly QBO wind. In the present study, we define a QBO index using the equatorial winds at 10 hPa derived from the respective satellite dataset. Consistent with the modest differences in the winds from SABER and MLS, the QBO index for an individual month is occasionally different between the two analyses. There are 9 out of 217 cases, or about 4% of months with both SABER and MLS winds, for which the QBO index is different in the two analyses. For both datasets, the index indicates that the QBO is in the easterly phase at 10 hPa during 70% of the total months.
Previous analyses of QBO impacts have used several different pressure levels or winds from a combination of levels to define a QBO index. If the QBO influences the SAO by filtering upward-propagating gravity waves, then the levels at which this filtering is most effective will likely vary. There is also a strong east–west asymmetry in the QBO at different levels; QBO easterlies persist for longer than QBO westerlies at 10 hPa and vice versa at 30 hPa. To test for any dependency to the selected pressure level of the index, we completed comprehensive sensitivity tests using different pressure levels for the QBO index. These indicate that a major impact of using different levels for the analyses in this paper is to shift the relationship vertically but not to alter the essential nature of the relationship. Another aspect to consider is that the magnitude of the responses of the SAO to the QBO is larger when the QBO index itself shows the greatest range between maximum easterly and westerly values. This is interpreted to be because the QBO amplitude directly affects any mechanism that depends on the magnitude of the wind shifts, such as filtering of gravity waves. Taking these factors into account, we have used 10 hPa throughout because this level is near the altitude of the peak QBO wind amplitude (Schenzinger et al. 2017) but is below the altitude where the SAO becomes important.
d. Limitations of available observations
Analysis of the tropical wave activity is not presented in this study because an important class of waves, the internal gravity waves, are not adequately resolved in observations of the middle atmosphere (e.g., Ern et al. 2017). The wave-driven Brewer–Dobson circulation is also not resolved and we do not attempt to calculate it. Even though these limitations mean that mechanisms cannot be definitively identified, we are able to determine many aspects of the QBO–SAO relationship from analyses using the latitude, pressure, and temporal structure of the zonally averaged zonal wind.
3. Climatology of the SAO in zonal wind
a. Mean characteristics of the SAO zonal wind
Figure 1 shows the monthly average zonal mean zonal wind climatology at the equator in the stratosphere and lower mesosphere derived from SABER and MLS observations. Results from all available years are included. Since the MLS data record starts approximately 31 months later than the SABER record, the periods covered are not identical but include more than 17 years overlap. It is evident from this figure that the SABER and MLS observations give qualitatively similar results although many differences in detail are evident. These differences do not disappear when identical periods are compared. The SAO can be seen by inspection as a prominent variation with maximum westerly winds near the equinoxes and maximum easterly winds at the solstices. The wind variations seen in Fig. 1 will be referred to as the SAO. While the wind variations are dominated by the 6-month harmonic, other periods also contribute.
Monthly mean climatology of zonal wind (m s−1) at the equator for (top) SABER from February 2002 through July 2022 and (bottom) MLS from September 2004 through July 2022. The contour interval is 10 m s−1; the zero contour is dashed.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
The latitude structure can be seen in Fig. 2, which shows the time-mean wind and the amplitudes of the 12- and 6-month variations. The 6-month harmonic in zonal wind peaks at 1 hPa. The latitude of the maximum is offset toward the Southern Hemisphere by 10°–15° as reported from other observations (Hopkins 1975; Ray et al. 1998). The maximum of ∼25 m s−1 occurs in April (see Fig. 1). Holton and Wehrbein (1980) found that the region of easterly winds in the stratopause SAO was extended in latitude toward the winter hemisphere by interactions with planetary waves. As a result, the latitudinal width of the 6-month oscillation extends beyond the tropics as seen in Fig. 2.
Time-mean (top) zonal wind and amplitudes of the (middle) 12- and (bottom) 6-month variations of the monthly mean zonal wind for (left) SABER and (right) MLS. Contour intervals are (top) 5, (middle) 10, and (bottom) 4 m s−1. The dashed line in the middle row gives the 5 m s−1 contour.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
As has been pointed out in several studies (Delisi and Dunkerton 1988; Garcia et al. 1997; Ray et al. 1998; Smith et al. 2022) and is clearly seen in Fig. 1, the wind variations in the cycle that begins at the onset of NH winter (i.e., the half year extending from November to April) are larger than those during the half-year cycle beginning in May. The increased month-to-month variation is due both to stronger easterlies around the January solstice and stronger westerlies around the March/April equinox. The stronger easterlies during NH winter are consistent with the stronger cross-equatorial flow driven by more active winter dynamical activity. Stronger easterlies then lead to stronger westerlies above (around 0.1 hPa) due to filtering of upward-propagating waves. The westerly winds propagate down to 1 hPa over a period of several months and lead to the stronger westerlies seen during March/April than during September/October.
The asymmetry in the two SAO cycles is captured as the 12-month oscillation in Fig. 2, which has two local maxima at the equator: one at around 0.1 hPa with amplitude of ∼10 m s−1 and a second peak just below that of the semiannual peak, near 1 hPa. Finally, we note a strong time-mean westerly wind that has a maximum at 0.1 hPa of 20–30 m s−1 near the equator. As emphasized by Smith et al. (2022), the time-mean wind is poorly simulated in many current global models.
A view of the temporal evolution of the latitudinal structure of the SAO is given in Fig. 3, which shows month by latitude plots of zonal wind at three pressure levels. This projection clearly shows the relation between the SAO at the equator and the extension of easterlies from the summer hemisphere toward the winter hemisphere during the solstices. The equatorial westerly maxima during the equinox seasons also show seamless continuity with westerly winds in midlatitude winters. The strong easterly (January) and westerly (March) winds at 1 hPa that extend toward the tropics from the Southern Hemisphere midlatitudes project onto the 6-month amplitude (Fig. 2) and account for the offset of the amplitude maximum from the equator.
Month-by-latitude cross section of SABER and MLS winds at three pressure levels. The contour interval is 10 m s−1; the zero contour is dashed.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Figure 4 shows the amplitude of the 6-month harmonic at 1 hPa along with Gaussian fits centered at the equator. The shape is approximately Gaussian except for the offset in the maximum toward the SH. Haynes (1998) showed that periodic momentum forcing will drive an oscillation of zonal wind that decreases with distance from the equator, as shown in his mechanistic model of the QBO. Note, however, that Figs. 2 and 4 indicate that the semiannual amplitude does not drop to zero even at latitudes beyond the tropical belt. The presence of a semiannual periodicity in midlatitudes has long been recognized (e.g., Hirota 1980). However, there is no evidence that the tropical and midlatitude periodicities have similar origins. A semiannual period is likely to be apparent wherever the seasonal cycle is not captured completely by an annual sinusoid.
Amplitude of the 6-month harmonic of zonal wind for SABER (solid lines) and MLS (dashed lines) at 1 hPa (black). Red curves show Gaussian fits centered at the equator.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
b. The annual cycle of winds in the upper stratosphere
Figure 5 isolates the 12- and 6-month variations of winds at the equator. Consistent with Fig. 1, it is clear that the magnitude of the annual harmonic is not negligible when compared with the semiannual harmonic. The sum of these two periodicities accounts for almost all of the seasonal variation in climatological monthly winds. The easterly peak of the 12-month harmonic at 1 hPa is at the end of November or beginning of December, about one month earlier than the easterly peaks of the 6-month harmonic at the same pressure. This timing difference can be seen more clearly in Fig. 6, which shows the phases of these harmonics at the equator, plotted as the months of minimum zonal wind components shown in Fig. 5. Above about 0.5 hPa, the phase of the 6-month component is nearly constant and indicates that wind minima occur in December (and June, not shown). Below that level, there is a slow but steady downward phase propagation of about 8 km month−1. The 12-month component also shows clear signs of a downward propagation with time. The rate is not steady; rather, the progression is fastest during the period between September and December (or, equivalently, when the minimum winds are in the pressure range ∼0.4–1 hPa) and then slows considerably during December (1–3 hPa).
Reconstructed winds to show the month-by-pressure behavior of the climatological annual and semiannual oscillations at the equator from (left) SABER and (right) MLS. The contour interval is 5 m s−1.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Phase (month of minimum) of the 12-month (black) and 6-month (red; only one of the two minima is shown) components of the wind at the equator. Solid is from SABER; dashed is from MLS. Month axis extends from July to June.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Lindzen and Holton (1968) linked the downward propagation of tropical zonal wind perturbations to dissipation of upward-propagating waves. While they specifically focused on the QBO, the same physical processes act at higher altitudes. Clear downward phase progression of both the 6- and 12-month harmonics suggests that wave processes play a role in these two oscillations as well. Figure 6 suggests that the scenario at play for the annual cycle is similar to those of the QBO and SAO. Vertical shears in the time-mean zonal wind, which are appreciable at and above the tropical stratopause (Fig. 2), also contribute to wave interactions. An annual maximum in the easterlies appears near the stratopause during northern winter, as seen in Fig. 1, associated with the extension of the midlatitude SH (summer) easterly winds across the equator (see Fig. 3). Annual variations in the generation of waves in the tropical troposphere also contribute to forcing of an annual cycle in the equatorial middle atmosphere (e.g., Hampson and Haynes 2004; Rajendran et al. 2018; Coy et al. 2020). Regardless of what generates them, the annually varying winds and the accompanying shear zones can then propagate downward due to wave interactions; the rate of downward propagation is controlled by variations in the vertical shear of the background zonal wind and the available wave fluxes.
The rates of downward propagation of the 12- and 6-month wind periodicities are determined by the combined effects of forcing by dissipating tropical waves and by the seasonal global circulation. Without comprehensive observations of the waves contributing to the wind changes, we cannot assess which of these factors is dominant.
The dissipation of waves and their interaction with the zonal wind drive changes in the wind. These wind changes are not specific to any one of the oscillations described here or to the annual mean wind; rather, they can contribute to any one or more of the observed cycles—SAO, AO, and QBO—or to the mean.
4. Impact of the QBO on variability of the SAO
The results and discussion presented here use winds that include the time-mean wind, the annual and semiannual cycles, the QBO winds, and other interannual variations.
a. Transition between the QBO and SAO
The amplitude of the QBO in zonal wind peaks around 10–20 hPa in the middle stratosphere (Schenzinger et al. 2017). The layer from 10 to 1 hPa is characterized by decreasing amplitude of the QBO and increasing amplitude of the SAO. The time-mean easterly wind below 1 hPa, seen in Fig. 2, illustrates the tendency of the easterly winds of the QBO at 10 hPa to have higher speeds and to persist for longer than the westerly QBO winds.
Figure 7 shows wavelet spectrum plots of SABER monthly winds for several pressure levels in the mid- to upper stratosphere. At the lowest level shown (10 hPa, about 31 km), the largest signals are seen in the range of periods between 24 and 30 months associated with the QBO. This pressure level approximately coincides with the level where the QBO reaches peak amplitude. At levels above 10 hPa (6.8 hPa and above), there is evidence of intermittent power at the 6-month period. At 4.6 and 2.2 hPa, the QBO signal has become weaker and the intermittent SAO signals are stronger and more regular; they show maxima in the time variation of the wavelet power at roughly a biennial period. At 1 hPa, the QBO and biennial signals have virtually disappeared and the spectrum is dominated by the SAO period. However, although the SAO power is less intermittent at this level it is nevertheless not continuous and still displays a roughly biennial periodicity in its signal strength. At 1–2 hPa (top panels of Fig. 7) there is no visible power at QBO periods. This indicates the absence of simple (linear) interference, where two independent (QBO and SAO) signals lead to constructive or destructive interference. Instead, the amplitude of the SAO power shows QBO-like variations in time, an indication of amplitude modulation by the QBO. The most likely mechanism for this modulation is the effect that the underlying QBO winds have in altering the flux of vertically propagating waves by filtering or other interaction. Such an interaction will also contribute to the generation of oscillations with periods that are higher and lower than 6 months, at approximately 7.6 and 4.9 months (derived from the sum and difference frequencies). Note also that the annual cycles at 2.2 and 1 hPa are strong for intervals of several years but that these are not the same intervals at the two levels.
Wavelet analysis of SABER monthly averaged equatorial zonal wind at five pressure levels. The dashed white lines indicate periods of 6, 12, and 28 months. The solid white line shows the cone of influence; results outside of this are not shown. Units are m2 s−2. Color scales are at right.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Figure 8 shows the power from Fig. 7 at periods of 6 and 12 months at 4.6 hPa using both SABER and MLS datasets. At this level, the QBO is still the dominant component of variability although the SAO appears intermittently (Fig. 7). There are some differences between the analyses using SABER and MLS winds; here we focus on aspects that are similar in the two datasets. The variations in the 6-month power are quite strong, especially in the early and later parts of the record. They exhibit a roughly biennial variation with amplitude modulation on longer time scales. Comparison with the middle and bottom panels shows that peaks in the 6-month power correspond to periods when there is a deep layer of easterly winds associated with the QBO. In particular, the local maxima in power for the 6-month period at the beginning and end of the time interval align with intervals when easterlies overlie a shallow layer of westerlies. During the intervening years 2010–16, the semiannual signal is weak and shows less interannual variability, while the annual signal is as large as or larger than the semiannual signal. In contrast, the annual signal does not show any consistent variation with the phase of the QBO.
(top) The wavelet power of equatorial zonal winds at 6 months (red) and 12 months (black) for SABER (solid lines) and MLS (dashed lines) at 4.6 hPa from Fig. 7. Units are m2 s−2. (middle) SABER and (bottom) MLS zonal winds at the equator (green is positive and black is negative). The dashed white lines are aligned with the local maxima for the 6-month periodicity in the top panel.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
This correspondence between the amplitude of the 6-month power at 4.6 hPa and the underlying QBO winds indicates that the SAO extends to lower altitudes (i.e., down to at least 4.6 hPa) when there is a deep layer of easterly winds below. In the following section, we look at composites of the winds in the height region dominated by the SAO for easterly and westerly phases of the QBO, to document differences in the seasonal cycle of winds for the different QBO phases. One aspect of the behavior that cannot be determined solely from the wavelet analyses is whether it is the SAO easterlies, westerlies, or both that respond to the QBO phase.
b. Winds separated by phase of the QBO
To quantify the QBO impact on the SAO, we define a monthly index for the QBO. We use the wind at 10 hPa for the respective dataset; i.e., the SABER derived QBO wind is used for analyzing the SABER results and likewise for MLS. Due to its rapid evolution in altitude, the phase of the QBO will vary depending on the pressure used for defining it. Since 10 hPa is near the peak QBO amplitude, its phase is likely to be well-captured in the satellite-derived winds. Results are qualitatively similar if monthly mean radiosonde or reanalysis winds are used to determine the QBO index. All months are included in the composites, even those where the wind speed of the QBO index is small.
Figure 9 shows the differences in the monthly mean winds in the height region dominated by the SAO (0.1–10 hPa) between the east and west phases of the QBO, composited according to the sign of the zonal wind at 10 hPa. The QBO index is applied for each month independently. As a result, the pattern does not represent an actual time sequence during any given year. The differences in the figure suggest that some or all of the processes that drive the SAO (tropical waves, midlatitude waves, momentum advection by the mean circulation) are responding to the QBO. The difference patterns and magnitudes are very similar if only months with QBO winds with magnitudes greater than 5 m s−1 are used in the sorting (not shown).
Average difference (m s−1) of monthly mean equatorial zonal wind for months with easterly winds at 10 hPa and those with westerly zonal winds there. Panels show data from (top) SABER and (bottom) MLS. The 10 hPa wind is taken from the respective dataset. The stippling indicates months and pressures for which the signal is not significant at the 90% level according to a t test.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Above 3 hPa the wind differences between the E and W phases of the QBO are almost exclusively positive or near zero. In other words, the wind in the upper stratosphere and lower mesosphere is more westerly when the QBO is easterly at 10 hPa, as expected from filtering of waves by the underlying winds (e.g., Dunkerton and Delisi 1997; Ern et al. 2021). The wind anomaly propagates downward with a period of about 6 months. There are a few months for which the composite winds over a limited pressure range are somewhat more easterly during periods when the QBO at 10 hPa is in the westerly phase but these are the exception; in most cases the differences are positive where they diverge from zero. Note also that the apparent response to the QBO in the region 5–0.5 hPa is roughly even between the two cycles of the SAO, i.e., that these differences project strongly onto the 6-month period. However, we can identify asymmetries between the two cycles of the SAO; for example, the positive difference (stronger winds during the easterly phase of the QBO) descends lower in altitude in May–June (∼5–6 hPa) than during November–December (∼3–4 hPa). This and other asymmetries indicate that the QBO affects the 12-month as well as the 6-month oscillation at the equator.
In the layer around 1–3 hPa, there are two periods with enhanced difference, occurring February–May and August–November. The magnitudes of the differences are similar during the two equinox periods: about 20 m s−1 (SABER) and 10–15 m s−1 (MLS). Higher up in the mesosphere, there is a difference peaking in April–May that has only a weak counterpart during October–November.
Figure 10 shows the differences in the time-mean wind and amplitude of the annual and semiannual harmonics between the E and W phase of the QBO. There are differences peaking near the equator for both the time-mean wind and the semiannual amplitude. The easterly phase of the QBO is associated with more westerly time-mean wind at altitudes above 3 hPa, weaker amplitude of the 6-month harmonic above the region of the maximum (which is at 1 hPa; see Fig. 2), and stronger 6-month amplitude below that level. The enhanced 6-month amplitude around 4 hPa during the easterly phase of the QBO is consistent with the patterns seen in Fig. 8. Figure 9 indicates that the differences are almost exclusively due to enhanced westerly winds during the equinox seasons when the SAO is in its westerly phase. In other words, during the easterly QBO, the westerly phase of the SAO is enhanced above its normal westerly winds. This implies that the QBO winds affect primarily the westerly (wave-driven) phase of the SAO rather than the easterly phase, which, near the equatorial stratopause, is driven by momentum advection. Figure 10 confirms that the semiannual amplitude at 4 hPa is larger during the easterly phase of the QBO.
Colors show differences of the (top) time-mean zonal wind and amplitudes of the (middle) 12- and (bottom) 6-month variations of the monthly mean zonal wind for months when the wind at 10 hPa is easterly minus those when it is westerly. Columns show data from (left) SABER and (right) MLS. Black lines show the means of these variables from Fig. 2.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Differences in the equatorial time-mean winds in Fig. 10 are easily seen to be consistent with the monthly differences from Fig. 9. To interpret the differences in the winds near the stratopause, it is helpful to overlay the climatological monthly average winds and the differences due to the QBO. This is shown in Fig. 11. During the easterly phase of the QBO, the maximum westerly winds that normally occur near and above the stratopause around April and October extend downward to lower altitude (higher pressure). At the higher levels near 0.1 hPa, the easterly QBO also delays the peak climatological westerlies, especially during the NH spring equinox (April–May). The differences indicate that the westerly wind peaks during the easterly phase of the QBO occur earlier at 3–1 hPa and occur later at 0.3–0.1 hPa.
Climatological monthly average winds (color) and difference of monthly mean equatorial zonal wind for months with easterly winds at 10 hPa and those with westerly zonal winds there (black contours; dashed lines indicate negative values). Panels show data from (top) SABER and (bottom) MLS.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Figures 9–11 together show how the equatorial winds in the layers above 10 hPa respond to the QBO. Under QBO easterly conditions, the stronger westerlies in the upper stratosphere and lower mesosphere (10–0.3 hPa) occur predominantly in areas where there is already a westerly shear zone. This is not confined to a single altitude region. For example, in Fig. 9, there are layers where differences are pronounced separated by other layers that show little response to the QBO, most prominent in March and April.
These results are consistent with the interpretation that the differences in winds in the stratopause region due to the QBO are the direct result of impacts from vertically propagating waves. For this to occur, the wind oscillations are driven by waves that are not eliminated by filtering or other dissipation mechanisms in the range where QBO winds are prominent. This could happen if the waves do not encounter a critical layer, are generated locally within the stratosphere (rather than propagating from the troposphere), or have relatively small amplitude and do not break as they propagate through the layers below.
c. Latitude structure of QBO differences
Figure 12 shows month by latitude cross sections of the QBO differences at three pressures: 3, 1, and 0.3 hPa (Figs. 12a,d,g for SABER; Figs. 12b,e,h for MLS). The right column (Figs. 12c,f,i) shows the amplitudes of the 6-month periodicity and the amplitude of the difference due to the phase of the QBO. In the Northern Hemisphere, the amplitude of the oscillation persists into midlatitudes but the amplitude of the difference drops to near-zero around 20°–25°N. Even though the 6-month harmonic persists well into midlatitudes, its variation due to the QBO is largely confined to the tropics. It is also evident from Figs. 12c, 12f, and 12i (right column) that the Southern Hemisphere situation is not as simple. The amplitudes of the differences drop to near-zero at a comparable latitude away from the equator (20°–25°S) but then grow again toward higher southern latitudes.
Differences of the monthly mean zonal wind for months when the wind at 10 hPa is easterly minus those when it is westerly from (a),(d),(g) SABER and (b),(e),(h) MLS. Results are shown for (a)–(c) 0.3, (d)–(f) 1, and (g)–(i) 3 hPa. The contour interval is 2 m s−1; the zero contour is not shown. (c),(f),(i) Amplitude of the 6-month periodicity (black) and the amplitude of the difference due to the sign of the QBO wind (red) at the same three pressure levels. Solid is SABER; dashed is MLS.
Citation: Journal of the Atmospheric Sciences 80, 7; 10.1175/JAS-D-22-0255.1
Schenzinger et al. (2017) present estimates of the width of the QBO, defined as the full width at half maximum, from observational data. The estimates cluster around 20°–22°. Figure 12 indicates that the change in the SAO at 3 and 1 hPa due to the phase of the QBO resembles the QBO width. From Fig. 12, the widths are 23°, 21°, and 37° for pressures of 3, 1, and 0.3 hPa. Note also that, in the tropics, the amplitude of the difference is more tightly symmetric about the equator than is the SAO itself. This is not surprising since it would be expected that the QBO is affecting the SAO winds only over the latitude range where the QBO itself has appreciable amplitude. This latitudinal confinement suggests that the QBO influence on the tropical SAO acts exclusively in the vertical direction. This notion is supported by the relative magnitudes of the vertical (cgz) to horizontal (cgx) group velocities of the gravity waves that presumably mediate the QBO–SAO connection. For mesoscale gravity waves in the midfrequency approximation, cgz/cgx = k(U − c)/N, where k is horizontal wavenumber, U is background horizontal wind, c is wave phase speed, and N is buoyancy frequency (e.g., Andrews et al. 1987). Using typical values, k ∼ 2π/100 km−1, (U − c) ∼ 30 m s−1, and N ∼ 0.02 gives cgz/cgx ≈ 0.1. On the other hand, the vertical extent of the QBO is at most 30 km, such that gravity wave groups will propagate vertically through the entire QBO while remaining within 300 km (∼3°) of their original latitude.
From the left and center columns of Fig. 12, it is evident that differences at 0.3 hPa extend toward higher latitudes during the months when they are large at the equator. The extension to higher latitudes occurs in the hemisphere that is transitioning toward winter: the extension into the SH peaks in May and that into the NH peaks in December. The differences are present between ∼20°S and 20°N in both equinoxes but also extend into the subtropics of the respective winter hemisphere (to 40°S in May and to 40°N in December), suggesting an interaction or overlap of the QBO signal and the annual cycle at these heights.
5. Conclusions
This investigation used zonally averaged monthly mean zonal winds derived from satellite geopotential height data to quantify aspects of the SAO and its relation to the QBO. The structure of the annual cycle in the equatorial middle atmosphere is also presented. We present ample evidence that the phase of the QBO is affecting both the SAO and the annual mean wind over the range from the middle stratosphere to the middle mesosphere.
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Both the SAO and the annual mean winds are more westerly during months when the zonal wind at 10 hPa is in the easterly phase. This is consistent with filtering of vertically propagating waves by the easterly wind, such that the spectrum of waves reaching the stratopause region is skewed toward eastward waves.
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The altitude to which the SAO descends is lower when the QBO is characterized by a deep layer of easterly wind.
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Differences in the SAO winds in the upper stratosphere due to the phase of the QBO are confined to low latitudes. This implies that the influence of the QBO on the SAO at and below the stratopause is primarily a response to vertical coupling. If coupling to midlatitudes through the Holton–Tan relation and its impact on the mean circulation were an important contributor, we would not see a disappearance of the signal at latitudes poleward of the tropical QBO. However, differences in the westerly winds in the mesosphere due to the phase of the QBO extend well into midlatitudes of the winter hemisphere, indicating that interactions with midlatitudes may be occurring.
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The amplitude of the 12-month harmonic is not negligible at the equator. This is apparent in the difference in the wind variations during the first and second halves of the year. Over the normal pressure range of the SAO from the middle mesosphere to the middle stratosphere, amplitudes of the annual harmonic are in the range of 5–10 m s−1. The phase of the annual harmonic propagates downward; months of maximum easterlies shift monotonically from September at 0.5 hPa to March at 10 hPa. Wavelet diagnostics indicate that there are periods of several year’s duration when the annual and semiannual cycles have comparable amplitudes in the upper stratosphere.
Acknowledgments.
The National Center for Atmospheric Research is sponsored by the U.S. National Science Foundation. Additional support was provided by the U.S. National Aeronautics and Space Administration (NASA) Grant 80NSSC18K0613. The authors thank Nicholas Davis and William Randel for comments on the manuscript.
Data availability statement.
NASA supports the TIMED and Aura satellites and their instruments; retrieved profile data are freely available. Version 2.07 and 2.08 geopotential height and pressure profile data from TIMED/SABER are available from http://saber.gats-inc.com. Version 5.2 geopotential height profile data from MLS are available from http://disc.sci.gsfc.nasa.gov/Aura/data-holdings/MLS/index.shtml.
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