Revisiting the Quasi Biennial Oscillation as Seen in ERA5.Part II: Evaluation of Waves and Wave Forcing
Hamid A. Pahlavan, John M. Wallace, Qiang Fu, George N. Kiladis
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Revisiting the Quasi Biennial Oscillation as Seen in ERA5.Part II: Evaluation of Waves and Wave Forcing
Hamid A. Pahlavan ∗ , John M. Wallace, Qiang Fu Department of Atmospheric Sciences, University of Washington, Seattle, Washington
George N. Kiladis
Earth System Research Laboratory, NOAA, Boulder, Colorado
ABSTRACTThis paper describes stratospheric waves in ERA5 reanalysis and evaluates the contributions of different types of waves to the driving ofthe quasi-biennial oscillation (QBO). Because of its higher spatial resolution compared to its predecessors, ERA5 is capable of resolving abroader spectrum of waves. It is shown that the resolved waves contribute to both eastward and westward accelerations near the equator,mainly by the way of the vertical flux of zonal momentum. The eastward accelerations by the resolved waves are mainly due to Kelvinwaves and small-scale gravity (SSG) waves with zonal wavelengths smaller than 2000 km, whereas the westward accelerations are forcedmainly by SSG waves, with smaller contributions from inertio-gravity and mixed-Rossby-gravity waves. Extratropical Rossby wavespropagate into the tropical region and impart a westward acceleration to the zonal flow. They appear to be responsible for at least some ofthe irregularities in the QBO cycle.
1. Introduction
The Quasi-Biennial Oscillation (QBO) is the dominantmode of interannual variability in the tropical stratosphere.It is characterized by alternating, downward propagatingwesterly and easterly zonal wind regimes, with a periodof about 28 months. For reviews of the QBO literature,see Baldwin et al. 2001, Anstey et al. (2020), and ref-erences therein. The QBO is driven primarily by equato-rial synoptic scale and gravity waves propagating from thetroposphere into the stratosphere and interacting with thestratospheric mean flow (e.g., Lindzen and Holton 1968;Holton and Lindzen 1972; Dunkerton 1997). Latent heatrelease in precipitating clouds is the primary source ofvertically propagating stratospheric equatorial waves (e.g.,Salby and Garcia 1987; Stephan and Alexander 2015) thatrange in periods from days to minutes and include Kelvin,mixed Rossby-gravity (MRG), inertio-gravity (IG), andsmall-scale gravity (SSG) waves. Extratropical Rossbywaves also propagate from the winter hemisphere into thetropical region and interact with the QBO (Kawatani et al.2010a). Determining the roles and the precise partitioningbetween these various waves in the forcing of the QBO isstill an active area of research (Holt et al. 2020).The number of Coupled Model Intercomparison Project(CMIP) models that are able to simulate the QBO has in-creased from none in CMIP3 conducted ten years ago, to5 in CMIP5 seven years ago, to 15 in the current CMIP6(Richter et al. 2020). Most of these models simulate the ∗ Corresponding author : Hamid A. Pahlavan, [email protected] period of the QBO well but underestimate its amplitude atall levels below 20 hPa. Most of the models have robustKelvin and MRG waves in the lower stratosphere, but theforcing varies from model to model and is generally tooweak and does not extend high enough (Giorgetta et al.2002; Lott et al. 2014; Holt et al. 2020). Alexander andOrtland (2010), Ern et al. (2014), Vincent and Alexan-der (2020), and others have advocated that observationalstudies be conducted to help quantify QBO wave forcings.Global high-resolution modeling and observationalstudies suggest that in the westerly shear zones of the QBO,Kelvin waves provide about half of the eastward forcing,while the rest of forcing is provided by SSG waves. Inthe easterly shear zones, the SSG waves provide most ofthe westward forcing (Kawatani et al. 2010a; Holt et al.2020).Given the uncertainties in the contribution of the var-ious equatorial waves to the driving of the QBO in themodels, and the unavailability of direct measurements ofwave forcings, arguably the best way to proceed is touse global datasets derived from reanalyses in which allavailable radiosonde observations are assimilated, alongwith satellite-observed temperature data from 1979 on-ward. The ECMWF ERA-Interim (ERA-I) reanalysis hasbeen used extensively for this purpose (e.g., Ern et al.2014; Kim and Chun 2015) and found to be quite reliablein the tropical lower and middle stratosphere, with a goodrepresentation of planetary waves (e.g., Ern and Preusse2009a,b; Anstey et al. 2020). However, in Part I of thisstudy we showed that the forcing due to SSG waves in1 a r X i v : . [ phy s i c s . a o - ph ] A ug JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 1. Equatorial time-longitude sections of daily mean temperature(top), and meridional wind (bottom), in westerly (left) and easterly (right)shear zones of the QBO at 50 hPa. The zonal mean has been removed.The year is 2015 in the left panels and 2014 in the right panels.
ERA-I to be negligible, in particular in the easterly shearzones, consistent with the results of Ern et al. (2014).Here we revisit the QBO using ERA5, the fifth genera-tion of ECMWF atmospheric reanalyses (Hersbach et al.2020). The higher spatial resolution in ERA5 comparedto ERA-I, and in particular the higher vertical resolutionmakes it possible to resolve a broader spectrum of atmo-spheric waves and allows for a more realistic representa-tion of wave-mean flow interaction, all of which are ofcrucial importance for QBO studies. For a more detaileddescription of ERA5 and its representation of the QBO ascompared with ERA-I, we refer the reader to the Part I ofthis study.In Part I, we investigated the dynamics and momentumbudget of the QBO. It was shown that in ERA5, mostof the QBO wave forcing is provided by resolved wavesduring the descent of both westerly and easterly regimes.Here in Part II, we focus on the various atmospheric wavemodes and their roles in driving the QBO. Consistent withprevious modeling and observational studies, we find thatthe eastward accelerations are mainly due to Kelvin wavesand SSG waves, whereas the westward accelerations are
Fig. 2. As in Fig. 1, but for a shorter time span of 6-hourly zonalwind over the equator. In the top panels the data have been high-passfiltered to retain frequencies higher than 0.4 cycle day − . In the bottompanels they are not time-filtered, but they are Fourier filtered in longitudeto retain zonal wavenumbers higher than 20. forced mainly by SSG waves, with smaller contributionsfrom IG and MRG waves.This paper is organized as follows. In section 2 we an-alyze the equatorial winds and temperatures to reveal thevarious wave modes and to investigate how their distribu-tion is mediated by the background flow in association withthe QBO cycle. Section 2 also documents the two-sidedwavenumber-frequency spectra of the equatorial winds andtemperature in ERA5. Section 3 documents the contribu-tions of the momentum and heat fluxes to the forcing ofthe QBO, as estimated by decomposing the EP flux di-vergence. In section 4, by making use of the two-sidedspectra shown in section 2, the resolved waves are classi-fied into Kelvin, inertio-gravity (IG), mixed Rossby-gravity(MRG), small-scale gravity (SSG, here defined as waveswith zonal wavenumbers larger than 20), and extratropi-cal Rossby waves. Then the role of each wave mode indriving the QBO is evaluated. The paper concludes with asummary and a brief discussion in section 5. Fig. 3. Power spectral density of the symmetric (top) and antisymmetric (bottom) modes of the zonal (left) and meridional (right) windperturbations at the 50 hPa level, averaged over 15°N/S, plotted as the ratio of the computed spectrum to the background spectrum and indicated byshading. The theoretical dispersion curves for equatorial wave modes with equivalent depths of 25, 50, and 100 are superimposed.
2. Identification of equatorial wave modes a. Time-longitude sections
Figure 1 (top panels) shows time-longitude sections ofdaily mean temperature ( T (cid:48) ), where prime denotes devia-tion from the zonal mean, over the equator at the 50 hPa(20 km) level in a westerly shear zone (left) and in aneasterly shear zone (right). Both sections are dominatedby fluctuations that tilt upward toward the right, indicativeof eastward propagating Kelvin waves with periods of 15days, zonal wavenumber k = ,
2, and a phase speed around +
30 m s − . As expected on the basis of theory (Andrewset al. 1987), the waves in the westerly shear zone are muchstronger. The bottom panels show analogous sections formeridional wind ( v (cid:48) ). The waves in the westerly shearzone (left) at times appear to be standing oscillations, andoverall do not have a well-defined direction of phase prop-agation, whereas those in the easterly shear zone (right)are clearly westward propagating disturbances with peri-ods on the order of 4-5 days, zonal wavenumber k ∼
4, anda phase speed of ∼ −
20 to ∼ −
30 m s − , consistent withMRG waves (Andrews et al. 1987; Kiladis et al. 2016).They tend to be concentrated within eastward propagat-ing wave packets, indicative of an eastward group velocity,which is also characteristic of MRG waves.Figure 1 is based on unfiltered daily mean data, and so isdominated by low frequency, planetary scale waves. To be able to see the waves with higher frequency and/or smallerzonal wavelength, the data need to be temporally and/orspatially filtered. The top panels of Fig. 2 show sectionsbased on 6-hourly data that have been high-pass filteredto retain frequencies higher than 0.4 cycle day − : zonalwind ( u ) over the equator at the 50 hPa level in a west-erly shear zone (left) and in an easterly shear zone (right).Although they are noisy, these sections are dominated byeastward and westward propagating IG waves, respectively.Filtering 6-hourly u to retain zonal wavenumbers | k | > b. Wavenumber-frequency spectrum Figure 3 shows the power spectra of u (cid:48) and v (cid:48) at 50hPa, averaged over 15°N/S, plotted as a function of zonalwavenumber and frequency after removing the backgroundspectrum following Wheeler and Kiladis (1999). The vari-ables are split into symmetric and antisymmetric compo-nents with respect to the equator. The analysis is based on40 years (1979-2018) of 6-hourly data with a 96-day win-dow and 65-day overlap. The theoretical dispersion curvesof the equatorial wave modes (Matsuno 1966; Andrews JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 4. Time-height section of 6-hourly EP flux divergence (colored shading), and zonally averaged zonal wind (contours), averaged within 5°ofthe equator. Contour interval 5 m s − , westerlies solid, easterlies dashed, zero contour omitted. Based on 6-hourly data, smoothed by a 30-dayrunning mean.Fig. 5. Composite fields of EP flux divergence (colored shading), EPflux (vectors), and zonally averaged zonal wind (contours) for descend-ing westerly (left) and easterly (right) shear zones of the QBO. In thewesterly shear zone (left), the longest vertical components of the arrowscorrespond to 5 . × kg s − , while the longest horizontal compo-nents correspond to 1 . × kg s − . In the easterly shear zone (right),the arrows are scaled to be twice as long. Contour interval 7.5 m s − ,westerlies solid, easterlies dashed, zero contour bolded. et al. 1987) are superimposed on the spectra, for severaldifferent equivalent depths (h).Most of the spectral power in the symmetric zonal windspectrum appears along the Kelvin wave dispersion curvesat h ∼ ∼
30 ms − . The dominant features in the antisymmetric spectraof both the zonal and meridional wind components are as-sociated with MRG waves. The band of enhanced powerfollows the dispersion curve for n = . < ω < . − , and its peak has periods in the2.5-5 day range. Enhanced power associated with equato-rial westward IG waves is evident in the symmetric spectraof the zonal wind. The corresponding power spectra oftemperature and vertical velocity shown in Fig. S2 areconsistent with Fig. 3.These results are generally consistent with the findings ofprevious observational and modeling studies. For example,Kim et al. (2019) showed that the spectrum of zonal and meridional winds at 50 hPa is very similar among severalreanalysis products.
3. Term-by-term breakdown of the wave forcing
In Part I of this study we evaluate the QBO momentumbudget and show the total forcing by the resolved wavesbased on the transformed Eulerian mean (TEM) framework(Andrews et al. 1987), in which the wave forcing of themean flow is proportional to the divergence of the EliassenPalm (EP) flux vector. For reference, Fig. 4 shows a time-height section of the total wave forcing near the equatorduring a 10-yr interval superimposed upon the distributionof zonal wind itself and Fig. 5 shows the correspondingmeridional cross sections at the times of descending west-erly (left) and easterly (right) shear zones in the QBO, bothrepeated from Part I. The composites were constructedby averaging the months in which the zero-wind line ofzonally-averaged zonal wind over the equator in descend-ing westerly or easterly shear zones reaches a prescribedreference level, here taken to be 25 hPa ( ∼
25 km). Thezonal-mean forcing due to EP flux divergence is seen to begenerally concentrated near the zero-wind line in the areasof highest vertical shear of the zonal winds, especially theeastward forcing in the westerly shear zone. We refer thereader to the Part I for a more detailed description of thesefigures.The forcing due to EP flux divergence can be decom-posed into the contributions of the momentum fluxes( F M = F ( z ) M + F ( φ ) M ), and heat fluxes ( F H = F ( z ) H + F ( φ ) H ),where: F ( z ) M = ρ − ∂∂ z [ ρ (− w (cid:48) u (cid:48) )] ( ) F ( φ ) M = ( a cos φ ) − ∂∂φ [ cos φ (− v (cid:48) u (cid:48) )] ( ) F ( z ) H = ρ − ∂∂ z [ ρ ({ f − ( a cos φ ) − ( ¯ u cos φ ) φ } v (cid:48) θ (cid:48) / ¯ θ z )] ( ) F ( φ ) H = ( a cos φ ) − ∂∂φ [ cos φ ( ¯ u z v (cid:48) θ (cid:48) / ¯ θ z )] ( ) The notation follows the conventions described in Part I.We will refer to F M as the direct forcing by way of the wavefluxes of zonal momentum and to F H as the indirect forcing Fig. 6. As in Fig. 4, but the total forcing is decomposed into the contributions of the momentum fluxes (top) and heat fluxes (bottom).Fig. 7. As in Fig. 5, but the total EP flux is decomposed into thecontributions of the momentum fluxes (top) and heat fluxes (bottom). by way of the mean meridional circulations induced by thepoleward heat transports.Figure 6 shows time-height sections of F M and F H andFig. 7 shows their meridional distributions in descendingwesterly and easterly shear zones. Also shown in Fig. 7is the transport of westerly momentum in the meridionalplane, which is in the opposite direction of the EP flux vec-tors. Note that the directions of the EP flux and wave prop-agation in the meridional cross sections are the same for waves with westward (intrinsic) phase velocities, whereasthey are in opposite directions for waves with eastwardphase velocities (Andrews et al. 1983). Hence, duringthe descent of both westerly and easterly phases, the wavesare dispersing upward near the equator, but the EP flux isdownward during descending westerly phase, as they aredominated by eastward propagating waves.It is evident that F M is the dominant contributor to theEP flux forcing and that it plays an essential role in drivingthe QBO. It is strongest in the shear zones, where it reachesvalues as high as ± − d − at times of peak accel-erations. The top panels of Fig. 7 show that the eastwardaccelerations are concentrated within descending westerlyshear zones, with off-equatorial maxima. In contrast, weakwestward accelerations extend throughout much of the ofeasterly wind regimes, maintaining them in the presence ofpoleward flow induced by radiative damping of the QBO-related temperature perturbations, as described in Part I.The main purpose of including F H in Figs, 6 and 7 isto demonstrate that it is only of minor importance in theforcing of the QBO. However, its structure in the vicinityof descending westerly shear zones, with eastward forcingover the equator flanked by westward accelerations, renderthe meridional structure of the total forcing smoother thanthat of the F M forcing, with a maximum over the equator,as shown in Fig. 5.The corresponding four-term decomposition based onEqns. (1)-(4) is shown in Figs. 8 and 9. The term F ( z ) M involving the vertical fluxes of zonal momentum is by farthe largest of the four terms (note that the contour intervalis doubled relative to that of the other terms) and is also thedominant contributor to F M in Figs. 6 and 7. The heat flux JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 8. As in Fig. 4, but the total flux is decomposed into the contributions of each term of the EP flux in Eqns. (1-4), as indicated. term F ( z ) H , is zero on the equator, where the Coriolis forcevanishes, but it exhibits highly structured off-equatorialfeatures, with dipoles of accelerations in the vicinity of thewesterly shear zone with maxima ∼ F ( φ ) M is dominated by the westward acceleration inducedby the poleward transport of westerly momentum ( v (cid:48) u (cid:48) ) bythe extratropical waves in the winter hemisphere, whichis evidently modulated by the QBO. The westward accel-erations protrude deeper into the tropics in the westerlyregimes, thereby weakening them. The flux divergence ex-hibits distinct equatorial maxima, which also act to weaken the westerly regimes. It also exhibits a rather intricate pat-tern within and just below the westerly shear zones con-sisting of a westward forcing on the equator, flanked byeastward forcing centered ∼ F ( φ ) H displays a similar patternin the westerly shear zone that is of roughly comparablemagnitude but opposing sign.
4. Wave-by-wave breakdown of the forcing
The forcing attributable to each type of wave is cal-culated after splitting the perturbation variables in Eqns.
Fig. 9. As in Fig. 5, but the total flux is decomposed into the contributions of each term of the EP flux in Eqns. (1-4), as indicated. (1)-(4) within the domain 12.5°N/S into equatorially sym-metric and anti-symmetric components. Each componentis then spectrally transformed into the zonal wavenumber-frequency ( k − ω ) domain and filtered to retain eastwardand westward propagating waves in prescribed domains.Following conventions used in previous studies such asKim and Chun (2015a), and based on the spectral anal-ysis above (Figs. 3 and S2), the perturbations for theKelvin waves are restricted to 1 ≤ k ≤
20 and ω < . − in the symmetric spectrum, and those for theMRG waves are restricted to | k | ≤
20 and 0 . ≤ ω ≤ . − in the anti-symmetric spectrum. Hence in thispaper, the MRG waves refer to both the westward and east-ward propagating (EIG) n = | k | ≤
20 and ω < . − , and IG waves if | k | ≤
20 and ω ≥ . − .Perturbations with | k | >
20 (i.e., wavelengths shorter than2000 km) are classified as SSG waves regardless of theirfrequency and direction of propagation.The equatorial time-height section and the meridionalcross section for the forcing by each of the five wave modesare shown in Figs. 10 and 11, respectively and the con-tributions of the heat and momentum fluxes to the totalforcing of each wave mode in the westerly and easterlyshear zones are shown in Figs. 12 and 13, respectively.The eastward acceleration attributable to the Kelvinwave is concentrated in the westerly shear zones (Fig. 10).It exhibits a nearly Gaussian shape in latitude centered on the equator (Fig. 11), and mainly results from the verti-cal flux of zonal momentum (Fig 12). The Kelvin waveforcing dominates the eastward acceleration in the middleand lower stratosphere, reaching values as high as +0.5 ms − d − in strong shear zones, consistent with previous es-timates. For example, Alexander and Ortland (2010) usedtemperature measurements from the High Resolution Dy-namics Limb Sounder (HIRDLS), and estimated that abouthalf of the acceleration in the eastward shear zone is dueto Kelvin waves, with a typical magnitude of about +0.5 ms − d − . Similarly, Kim and Chun (2015b), using ERA-Imodel level data at 30 hPa, found that the Kelvin wave dom-inates the resolved forcing in the westerly shear zone, withaccelerations of about 7-13 m s − month − ( ∼ . − . − d − ).Also shown in Fig. 11 are the EP fluxes. As it is men-tioned earlier, the direction of the EP flux and wave prop-agation are opposed to each other for waves with eastwardphase velocity such as Kelvin waves, and eastward prop-agating SSG and IG waves. Hence the corresponding EPfluxes are downward in the westerly shear zone compositesbecause the waves are dispersing upward (Fig .11). Notethat the easterly jet in the lower stratosphere provides a fa-vorable environment for the upward dispersion of eastwardpropagating waves originating in the troposphere.It is evident from Fig. 11 that during the descent of thewesterly regimes (left), the Kelvin waves disperse upwardthrough the easterly regime in the lower stratosphere andinto the middle stratosphere. Note that Kelvin waves candisperse upward through an easterly background flow with-out appreciable dissipation. Kelvin waves are absorbedwhen they encounter a westerly shear zone, imparting a JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 10. As in Fig. 4, but the total flux is decomposed into the contributions of each term of the EP flux in Eqns. (1-4), as indicated. strong eastward acceleration. When the westerly jet is lo-cated in the lower stratosphere (right panel), the Kelvinwaves dissipate in the lower stratosphere, and thus, theiramplitudes in the middle and upper stratosphere are verysmall. It is also evident from Fig. 11 that as the Kelvinwaves dissipate within the westerly shear zone, their EPfluxes tend to diverge outward from the equatorial belt, consistent with results from Kawatani et al. (2010) andKim and Chun (2015b).The SSG waves produce eastward accelerations in thewesterly shear zones and westward accelerations in easterlyshear zones of comparable magnitude, and appear to beprimarily responsible for the episodes of rapid descent ofeasterly shear zones (Fig. 10) (Part I). It is evident from Fig.11 that during the descent of the westerly shear zones, the
Fig. 11. As in Fig. 5, but the total flux is decomposed into the contributions of each type of wave, as indicated. The longest vertical componentsof the arrows correspond to 9 × kg s − , while the longest horizontal components correspond to 1 . × kg s − . For the Rossby waves, thearrows are scaled to be twice as short. waves propagate upward through the easterly regime overa broad range of latitudes and converge into the westerlyshear zone, inducing an eastward acceleration over a broadarc in the meridional plane. During the descent of theeasterly shear zones, the SSG waves propagate through thenarrow westerly jet and dissipate in the easterly shear zoneabove it, inducing a westward acceleration.The accelerations due to SSG waves range as high as ± − d − ( ± − d − ) in strong shear zonesaround 30 hPa (10 hPa) pressure level (Fig. 10), and arealmost entirely a result of the vertical flux of zonal mo-mentum (Figs. 12 and 13). These values are generallyconsistent with the results from (Kawatani et al. 2010a,b),who used a high-resolution atmospheric general circulationmodel (60 km horizontal and 300 m vertical resolution), inwhich waves with short horizontal wavelengths were mod-eled explicitly and no gravity wave parameterization wasrequired. They estimated accelerations of about ± − d − due to the gravity waves with k >
11 (wavelengthssmaller than ∼ ≤ JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 12. As in Fig. 11, but the forcing of each wave is decomposed into the contributions of each term of the EP flux in the composite for thedescending westerly shear zone.
Decomposing the EP flux also reveals another contribut-ing factor to the weak eastward forcing by the IG waves(Figs. 12 and 13): during the descent of westerly shearzones, the accelerations due to F ( φ ) M and F ( z ) H oppose thatof the F ( z ) M , leading to an overall weak eastward accelera-tion along the westerly shear zone (Fig. 11). In contrast, indescending easterly shear zones, F ( z ) M induces a westwardacceleration, strongest within the easterly regimes, whichis reinforced by F ( φ ) M in the easterly shear zone, close tothe equator (Fig. 13). The combined forcing results in arelatively strong westward acceleration, particularly closeto the equator (Fig. 11).The MRG waves induce only a weak westward acceler-ation near the equator in both westerly and easterly shearzones with comparable magnitude (Figs. 10 and 11), sug-gestive of in situ generation owing to the instability of theQBO westerly jet as discussed (e.g., Maury and Lott 2014;Kim and Chun 2015b; Garcia and Richter 2019). In agree- ment, it was also shown by Giorgetta et al. (2002, 2006)and Kawatani et al. (2010a,b) that MRG waves play a mi-nor role in the descent of the easterly shear zones in generalcirculation models.During the descent of the westerly shear zones, the MRGwaves induce eastward accelerations at around 10°N/S andwestward accelerations near the equator. In descendingeasterly shear zones, the MRG waves converge near theequator, while the vertical component of the EP flux is quitesmall, suggesting the stratospheric generation of the MRGwaves rather than upward dispersion from the troposphere,consistent with results of Kim and Chun (2015b) basedon numerical experiments with the Hadley Centre GlobalEnvironment Model version 2 (HadGEM2).It is evident from Figs. 12 and 13 that MRG westwardforcing is due to F ( φ ) M in the westerly shear zone, whileit is mostly resulted from F ( φ ) H in the easterly shear zone.Figure 13 shows that the ratio of F ( z ) M to F ( z ) H in MRG1 Fig. 13. As in Fig. 12, but for composite for the descending easterly shear zone. waves is approximately 1 to -2 which is consistent with thetheoretical estimation (Andrews et al. 1987).Figure 10 shows that the Rossby wave forcing is strongin the upper stratosphere, where it tends to occur in phasewith easterly accelerations in the semiannual oscillation,but not always. The corresponding meridional cross sec-tion shown in Fig. 11 shows extratropical Rossby wavesdispersing into the tropical stratosphere and dissipating,inducing a westward acceleration. We have confirmed thatthe dispersion is almost exclusively from the winter hemi-sphere, where the waves are able to disperse upward andequatorward from their tropospheric sources through thewesterly waveguide (not shown). It is evident from Fig.11 that the latitude to which the Rossby waves are able topenetrate is modulated by the QBO. They penetrate deeperinto westerly wind regimes, and dissipate along the outeredges of easterly regimes, broadening them by extracting westerly momentum. Therefore, although they are not es-sential to the mechanisms that give rise to the QBO, Rossbywaves evidently influence the QBO, as suggested by Dick-inson (1968). On the basis of results of experiments witha simple numerical model Dunkerton (1983) argued thatRossby waves can indeed provide part of the forcing of theeasterly phase of QBO.A significant westward forcing is discernible in F ( φ ) M panel of Fig. 8 and Rossby waves panel of Fig. 10 justbefore the disruption of the QBO in early 2016 when aneasterly jet unexpectedly formed in the lower stratosphere at ∼
40 hPa during an westerly phase. Newman et al. (2016),Osprey et al. (2016), and Coy et al. (2017) have suggestedthat this disruption was due to the propagation of Rossbywaves from the Northern Hemisphere (NH) midlatitudesinto the tropical region. Barton and McCormack (2017)argued that NH subtropical easterly jet was anomalously2
JOURNAL OF THE ATMOSPHERIC SCIENCES weak during this event due to the timing of the QBO relativeto the annual cycle and an exceptionally strong El Nino,which allowed Rossby waves from the NH midlatitudes topenetrate all the way to the equator near the 40 hPa level.Lin et al. (2019) argued that MRG waves also made anappreciable contribution to the disruption.A second, similar QBO disruption, which began inSeptember 2019 (not shown) has also been attributed tothe westward forcing by dissipating Rossby waves fromthe winter hemisphere, but this time from the SouthernHemisphere (Anstey et al. 2020). These two disruptionssuggest that extratropical Rossby waves may be responsiblefor at least some of the irregularities in the QBO cycle.
5. Discussion and conclusion
In this paper we have documented QBO-related wave-mean flow interactions in ERA5. ERA5, which has highspatial and particularly vertical resolution, makes it pos-sible to resolve a broader spectrum of atmospheric wavesand to better capture their interaction with the mean flow.Filtering the resolved waves based on frequency andzonal wavelengths, we have documented the contributionof various types of waves to the forcing of the QBO. Thedescent of the westerly shear zones is mainly attributableto the Kelvin waves, with a significant contribution of SSGwaves, both of which contribute mainly by way of the ver-tical flux of zonal momentum ( F ( z ) M ). That the eastwardacceleration by the eastward propagating IG waves is weakbelow 10 hPa (Fig. 10), is attributable to the fact that theircontributions by F ( z ) M tend to cancel by way of the verti-cal flux of heat ( F ( z ) H ) and by way of the meridional fluxof zonal momentum ( F ( φ ) M ). The westward acceleration ismainly due to the SSG waves, with smaller contributionsfrom IG and MRG waves (Figs. 10 and 11). These resultsare in agreement with those of other studies based on gen-eral circulation models (e.g., Giorgetta et al. 2006; Evan etal. 2012; Krismer et al. 2013) and also with observationalstudies (e.g., Ern and Preusse 2009a; Alexander and Ort-land 2010; Ern et al. 2014), which indicate that small-scalegravity waves are just as important in forcing the descentof QBO westerly wind regimes as Kelvin waves, and thatthey dominate the wave forcing of easterly regimes.Somewhat different results were obtained by Garcia andRichter (2019) (GR) based on experiments with the WholeAtmosphere Community Climate Model (WACCM). Theirresults suggest that the westward acceleration near theequator is due mainly to westward propagating MRG waveswith zonal wavenumbers in the range k = −
12 which aregenerated in situ due to barotropic instability of the QBOwesterly jet. The MRG waves in WACCM produce a pat-tern of EP flux divergence that includes strong westwardacceleration close to the equator and eastward accelerationfarther from the equator (their Fig. 9), similar to our MRG acceleration pattern in the westerly shear zones (our Fig.11). As a possible explanation of the difference betweentheir results and those of Kawatani et al. (2010a,b), theysuggested that averaging accelerations over more than 5°oflatitude might have obscured the forcing due to the MRGwaves in the previous studies. However, this is not the casein the present study, because, like them, we meridionallyaverage over only 5°of latitude, yet we still find that thewestward acceleration due to the MRG waves is negligi-ble, even though we include the eastward portion of the n = Acknowledgments.
This research is supported by theNASA grant 80NSSC18K1031 and NSF grant AGS-1821437. The authors declare no conflicts of interest.
Data availability statement.
ERA5 data were down-loaded from ECMWF’s MARS archive. Aura MLSobservations were obtained from NASA Goddard EarthSciences (GES) Data and Information Services Cen-ter (DISC). CALIPSO data were downloaded us-ing NASA Search and Subsetting Web Application(https://subset.larc.nasa.gov/calipso/).
References