Revisiting the Quasi Biennial Oscillation as Seen in ERA5. Part I: Description and Momentum Budget
Hamid A. Pahlavan, Qiang Fu, John M. Wallace, George N. Kiladis
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Revisiting the Quasi Biennial Oscillation as Seen in ERA5.Part I: Description and Momentum Budget
Hamid A. Pahlavan ∗ , Qiang Fu, John M. Wallace Department of Atmospheric Sciences, University of Washington, Seattle, Washington
George N. Kiladis
Earth System Research Laboratory, NOAA, Boulder, Colorado
ABSTRACTThe dynamics and momentum budget of the quasi-biennial oscillation (QBO) are examined in the ERA5 reanalysis and compared withthose in ERA-I. Because of ERA5's higher spatial resolution it is capable of resolving a broader spectrum of atmospheric waves and allowsfor a better representation of the wave-mean flow interactions, both of which are of crucial importance for QBO studies. It is shown that theQBO-induced mean meridional circulation, which is mainly confined to the winter hemisphere, is strong enough to interrupt the tropicalupwelling during the descent of the westerly shear zones. Since the momentum advection tends to damp the QBO, the wave forcing isresponsible for both the downward propagation and for the maintenance of the QBO. It is shown that half the required wave forcing isprovided by resolved waves during the descent of both westerly and easterly regimes. Planetary-scale waves account for most of the resolvedwave forcing of the descent of westerly shear zones and small-scale gravity (SSG) waves with wavelengths shorter than 2000 km accountfor the remainder. SSG waves account for most of the resolved forcing of the descent of the easterly shear zones. The representation of themean fields in the QBO is very similar in ERA5 and ERA-I but the resolved wave forcing is shown to be substantially stronger in ERA5.The contributions of the various equatorially-trapped wave modes to the QBO forcing are documented in Part II.
1. Introduction
The quasi-biennial oscillation (QBO) is the primarymode of interannual variability in the tropical and sub-tropical stratosphere (e.g., Baldwin et al. 2001). It ischaracterized by the downward propagation of successivewesterly and easterly wind regimes with an average periodof about 28 months. It has come to be recognized as re-sulting from the interaction between the axisymmetric flowand a broad spectrum of waves dispersing upward from be-low (Lindzen and Holton 1968; Holton and Lindzen 1972;Dunkerton 1997; Giorgetta et al. 2002). Although theQBO is a tropical stratospheric phenomenon, it influencesthe circulation and the interannual variability of the globalstratosphere and lower mesosphere, and has a discernibleeffect on the weather and climate in the troposphere. Adetailed characterization of the QBO and its impact can befound in the review of Baldwin et al. (2001) and in Ansteyet al. (2020).Since their emergence in the mid- 1990's, global reanal-yses by the world's leading centers for operational numer-ical weather prediction have been among the most widelyused datasets in the geosciences. Swinbank and O'Neill(1994) and Randel et al. (1999) were able to obtain a dy-namically consistent QBO in the analyses produced at theU. K. Met. Office in support of the Upper Atmosphere ∗ Corresponding author : Hamid A. Pahlavan, [email protected]
Research Satellite (UARS) mission. Pawson and Fiorino(1998) investigated the QBO in National Centers for En-vironmental Prediction-National Center for AtmosphericResearch (NCEP-NCAR) reanalyses and European Centrefor Medium-Range Weather Forecasts (ECMWF) Reanal-ysis (ERA-15) and found the axisymmetric zonal windon the equator to be in good agreement with radiosondewinds at Singapore (1.8°N, 104.8°E) at 30 hPa and be-low, though the westerly regimes in the reanalysis weregenerally weaker than observations.Using singular vector decomposition, Ribera et al.(2004) were able to discern coherent QBO-induced meanmeridional circulations in the NCEP-NCAR reanalyses.Pascoe et al. (2005) examined the amplitude, period andvertical structure of the QBO in the ERA-40 data set andwere even able to resolve the cycle-to-cycle variability ofthe QBO seen in the station data. Coy et al. (2016) ex-amined the structure, dynamics, forcing, and ozone signalof the QBO in the NASA Modern-Era Retrospective Anal-ysis for Research and Applications (MERRA), and in itssecond version (MERRA-2) and found an improved rep-resentation of the QBO in MERRA-2, mainly due to theretuning of the gravity wave drag (GWD) parameterizationin the model, amplifying it in the tropics by nearly a factorof 8 compared to MERRA (Molod et al. 2015).The ECMWF ERA-Interim (ERA-I) reanalysis has alsobeen used extensively for assessing various aspects of the1 a r X i v : . [ phy s i c s . a o - ph ] A ug JOURNAL OF THE ATMOSPHERIC SCIENCES
QBO, including its momentum forcing by the equatorialwaves (e.g., Ern et al. 2014; Kim and Chun 2015; Schen-zinger et al. 2017). ERA-I has been found to be quite re-liable in the tropical lower and middle stratosphere and tohave a particularly good representation of planetary waves(e.g., Ern and Preusse 2009a,b).Recently, Anstey et al. (2020) examined the representa-tion of the QBO in various reanalyses and found that thereis a good agreement between the modern products on theevolution of the QBO-related zonal wind variations and therelative contributions of the various tropical waves to theforcing of the QBO. Here we revisit the QBO using ERA5,the fifth generation of ECMWF atmospheric reanalyses(Hersbach et al. 2020). This paper (Part I) provides a gen-eral overview of the structure and dynamics of the QBO,as represented in ERA5 and an indication of the ways inwhich the representation is improved in ERA5 relative toERA-I. The goal is to gain a deeper understanding of theQBO dynamics and momentum budget.ERA5 improves upon ERA-I in several respects. Its con-siderably higher spatial resolution in both the horizontaland vertical makes it possible to resolve a broader spectrumof atmospheric waves in ECMWF's Integrated ForecastingSystem (IFS). With its higher vertical resolution it is alsopossible to represent the process of wave-mean flow in-teraction more realistically (Dunkerton 1997). Numerousprevious modeling studies have shown that increasing theresolution increases the Eliassen-Palm flux (EP flux) diver-gence (i.e., the momentum forcing by the resolved waves)and that increasing the vertical resolution has a much largereffect than increasing the horizontal resolution (Holt et al.2016, 2020).More detailed descriptions of ERA5 and the methodsused in this study are presented in section 2. In section3, we document the structure of the QBO-related axisym-metric fields, and discuss the interactions of the QBO withsemiannual oscillation (SAO), and the Brewer-Dobson cir-culation (BDC). We also describe the seasonality of theQBO in this section. Section 4 presents an overview of themomentum budget of the QBO. It is shown that the advec-tion of westerly momentum acts to damp the QBO. Hence,the wave forcing is responsible, not only for the downwardpropagation, but also for maintaining its amplitude. Amore detailed documentation of the contributions of dif-ferent modes of atmospheric waves to driving the QBO ispresented in Part II. Section 5 of Part I compares the per-formance of ERA5 and ERA-I in representing the QBO.While the mean fields are very similar in the two reanaly-ses, the resolved wave forcing is shown to be substantiallystronger in ERA5 than in ERA-I. Section 6 presents a fewconcluding remarks.
2. Data and methodology
The ERA5 global reanalysis for 1979 to present is theprimary basis for this study. It is produced using the IFS cy-cle 41r2 with four-dimensional variational (4-DVar) dataassimilation. It has a horizontal resolution of ∼
31 km( ∼ × ∆ x , where ∆ x is the native resolution of the model (e.g., Skamarocket al. 2014), ERA5 should be capable of resolving equato-rial waves with zonal wavelengths as short as 1°longitude,equivalent to zonal wavenumber 360. Between 100 and 1hPa, the ERA5 has 41 vertical levels with a resolution of ∼
300 m at 100 hPa, decreasing gradually to ∼ ∼ ∼ u t = ¯ v ∗ [ f − ( a cos φ ) − ( ¯ u cos φ ) φ ] − ¯ w ∗ ¯ u z + ( ρ a cos φ ) − ∇ . F + ¯ X ( ) Here, ¯ u t is the tendency of the zonal mean zonal wind, f the Coriolis frequency, a is the radius of Earth, φ islatitude, and ρ ( z ) is the reference density. ¯ v ∗ and ¯ w ∗ are the meridional and vertical components of the residualcirculation, respectively, defined as¯ v ∗ = ¯ v − ρ − ( ρ o v (cid:48) θ (cid:48) / ¯ θ z ) z ( ) ¯ w ∗ = ¯ w + ( a cos φ ) − ( cos φ v (cid:48) θ (cid:48) / ¯ θ z ) φ ( ) F is the EP flux, whose meridional and vertical compo-nents are F ( φ ) = ρ a cos φ ( ¯ u z v (cid:48) θ (cid:48) / ¯ θ z − v (cid:48) u (cid:48) ) ( ) F ( z ) = ρ a cos φ {[ f − ( a cos φ ) − ( ¯ u cos φ ) φ ] v (cid:48) θ (cid:48) / ¯ θ z − w (cid:48) u (cid:48) } ( ) Fig. 1. Time-height section of monthly zonally averaged zonal wind averaged over 5°N/S. The tick marks on the x-axis represent January 15 foreach year.
In these expressions θ is potential temperature and thesubscripts ( φ ) and ( z ) indicate differentiation in the merid-ional and vertical directions, respectively. Overbars denotezonal means, and primes denote deviations from zonalmeans. Above 73 hPa ( ∼
18 km), model levels correspondto pressure levels. Hence, in effect, pressure is used as thevertical coordinate in evaluating the terms in Eq. (1).The divergence of the EP flux represents the momentumforcing by the waves that are explicitly resolved in the re-analysis. The residual zonal wind tendency ¯ X , representsthe zonal forcing associated with subgrid-scale waves inthe reanalysis, including mesoscale gravity waves forcedby dynamical processes such as convection, frontogene-sis, processes involving jet stream fine structure, and flowinstabilities. These waves have to be parametrized usingschemes that are subject to large uncertainties. One ofthe objectives of this paper is to assess how well they arerepresented.
3. Structure of the axisymmetric fields
The time-height section of the monthly mean zonallyaveraged zonal wind, averaged over 5°N/S, shown in Fig.1, reveals many of the essential dynamical properties of theQBO. A succession of westerly and easterly wind regimesdescends through the equatorial stratosphere from ∼
35 km( ∼ ∼ ∂ u / ∂ z ). As a result, the westerly regimes last noticeably longer than the easterly regimes at 50 hPaand below, while the reverse is true at 10 hPa and above.The peak winds in the easterly regimes are more than twiceas strong as those in the westerly regimes. This disparityis consistent with the fact that the stratospheric mean cli-matology is characterized by deep layers of off-equatorialeasterlies with peak values ∼
14 m s − centered ∼ ∼
28 months, consistent with the label"quasi-biennial oscillation", a term coined by Angell andKorshover (1964).In the season from July to February the QBO often stallsfor several months when it is in the phase of its cycle withthe peak easterly winds in the 30-50 hPa layer and wester-lies in the vicinity of the cold point tropopause ∼
100 hPa.These irregularities in the cycle have been attributed toseasonal variations in the wave forcing. During the borealsummer the tropical upper tropospheric zonal winds aremore easterly and less favorable for the upward dispersionof westward propagating waves (Maruyama 1991; Kris-mer et al. 2013), and during the boreal winter the strongerequatorial upwelling tends to slow the downward phasepropagation of the QBO (Kinnersley and Pawson 1996;Hampson and Haynes 2004; Dunkerton 2016).It is evident from Fig. 1 that the QBO vanishes asit approaches the tropical tropopause layer, even thoughthe vertically propagating waves that drive the QBO orig-inate in the troposphere several kilometers below. UsingMERRA-2 and ERA-I reanalysis, Match and Fueglistaler
JOURNAL OF THE ATMOSPHERIC SCIENCES (2019) showed that mean-flow damping due to horizontalmomentum flux divergence weakens the QBO amplitudein this region.The flow in the upper stratosphere and mesosphere ex-hibits a pronounced semiannual oscillation, characterizedby westward wind maxima a few weeks after the sol-stices and eastward wind maxima a few weeks after theequinoxes, as first documented by Reed (1962, 1966). Ithas been suggested that the westerly phase of the SAO isdue to eastward propagating waves, in particular shorter-period Kelvin waves with high phase speed, while the east-erly phase is driven by a combination of planetary waveforcing and the meridional advection of angular momen-tum in the upper branch of the Brewer-Dobson circulation(BDC), consisting of rising motions in the summer hemi-sphere, a cross-equatorial drift, and sinking in the winterhemisphere (Holton and Wehrbein 1980).It is evident from Fig. 1 that the QBO and SAO share thesame westerly shear zones at altitudes between about 35-40km (Smith et al. 2017). Once in every 4 to 6 semiannualcycles, the westerly wind shear zone at the base of the SAO( ∼
40 km) begins to propagate downward, initiating the de-scent of a new westerly shear zone of the QBO. Hence,the arrival of successive westerly QBO regimes at 30 kmtends to occur at multiples of 6 months, as hypothesized byLindzen and Holton (1968) and verified in observations byGarcia et al. (1997). Theoretical and idealized model stud-ies and laboratory experiments suggest that QBO westerlyshear zones can originate in the upper stratosphere in theabsence of preexisting SAO westerly shear zones (Holtonand Lindzen 1972; Plumb 1977; Plumb and McEwan 1978;Mayr et al. 2010). Yet, within the layer in which the SAO isactive, the deposition of eastward momentum by breakingwaves tends to be focused in its westerly shear zones, en-abling them to continue propagating downward far beyondthe layer in which the SAO is dominant. In effect, whatwas an SAO westerly shear zone becomes a QBO westerlyshear zone. These transitions occur in the phase of theQBO when westerly wind regimes are present in the lowerstratosphere (Wallace 1973; Dunkerton and Delisi 1997;Garcia et al. 1997). As the westerlies weaken, the lowerstratosphere becomes more permeable to the waves thatare producing an upward transport of eastward momen-tum, because fewer of them encounter their critical level(i.e., the level at which their wave phase speed is closeto the zonal wind speed) and break. With more eastwardmomentum reaching the upper stratosphere, the SAO west-erly shear zones are forced more strongly, enabling them topenetrate deeper into the lower stratosphere (e.g., Krismeret al. 2013).Figure 2 summarizes the characteristics of the QBO asthey appear in equatorial time-height sections for variousvariables. It shows time (lag) vs. height sections created byregressing monthly time series of zonally-averaged zonalwind and other variables at different levels and time lags upon a common reference time series of monthly equato-rial zonally-averaged zonal wind at the 29 km ( ∼
14 hPa)level, scaled by its one standard deviation. The results arenot sensitive to the choice of reference level. The annualcycle is removed by subtracting the 40-yr average of eachmonth. For reference, the patterns in all panels are super-imposed upon the corresponding QBO-related temperatureanomalies as inferred from linear regression. Consistentwith Fig. 1, the QBO signal in zonal wind propagatesdownward with a period of ∼
28 months. Consistent withthe scale analysis of Reed (1962), the zonal wind and tem-perature fields are seen to be in thermal wind balance, withpositive temperature anomalies in the westerly shear zonesand vice versa. The QBO-related temperature anomaliesare strongest near 30-50 hPa, with values ranging up to ± ± ∼
100 hPa) (Randel et al. 2000).In the absence of dynamically induced heating/cooling,radiative relaxation would damp these temperature anoma-lies on a time scale of weeks (Hartmann et al. 2001; Ran-del et al. 2002). They are maintained, as required forthermal wind balance, by the adiabatic warming and cool-ing associated with the axially symmetric vertical motions,downward in the relatively warm westerly shear zones andupward in the cold easterly shear zones, as indicated bythe black contoured field in Fig. 2b. For reference, theclimatological mean ascent rate in the BDC is ∼ − at the 60 hPa level and ∼ − at the 30 hPalevel (Lin et al. 2013). The descent in the westerly shearzones within 5 degrees of the equator is thus strong enoughto largely compensate and even temporarily interrupt theascent associated with the BDC. An anomalous upwardvertical motion in the troposphere is also evident in Fig.2b during the easterly phase of the QBO, implying deeperand/or more convection. Several studies have suggestedthat the QBO is able to modulate the tropical deep convec-tion by perturbing the state of the lower stratosphere andupper troposphere (see Nie and Sobel 2015 and referencetherein).Vestiges of the QBO-related temperature perturba-tions penetrate downward deep enough into the tropicaltropopause layer (TTL) to modulate the areal coverage ofhigh, thin cirrus clouds (Tseng and Fu 2017), here de-fined as clouds with bases higher than 14.5 km. Negativetemperature anomalies favor higher relative humidity andconsequently more extensive cloud cover and vice versa,as indicated by red and blue contours in Fig. 2b, based on12 years (2006 to 2018) of observations from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observa-tions (CALIPSO).The concentrations of many trace constituents are alsoaffected by the QBO. Schoeberl et al. (2008) documentedthe QBO signals in multiple trace gases based on HALOEand Aura MLS observations. Here, we consider only water Fig. 2. Time (lag)-height section created by regressing time series of zonally averaged variables (contours) and temperature (colored shading),averaged over 5°N/S, at different altitudes and time lags upon zonally averaged zonal wind at the 29 km ( ∼
14 hPa) level using monthly data. Thecontours are (a) zonal wind, contour interval 2.5 m s − , (b) vertical velocity (black), contour interval 0.075 mm s − , and cloud fraction (red andblue), contour interval 0.75%, (c) water vapor, contour interval 0.04 ppmv (not shown below 15 km), and (d) ozone, contour interval 0.075 ppmv.The zero contours are omitted, and negative contours are dashed. The top panels are based on a 40-year record (1979 to 2018), while the bottompanels are based on a 14-year record (2004 to 2018). vapor and ozone based on a 14-year record (August 2004to December 2018) of MLS observations.It is well recognized that the temperature of the tropicalcold point controls the amount of water vapor entering thelower stratosphere (Brewer 1949). The ascent of alternat-ing moist and dry layers formed during different phasesof the annual cycle in cold point temperature has come tobe referred to as "atmospheric tape recorder" (Mote et al.1996). It is evident from Fig. 2c that QBO-related tem-perature variations also modulate the tropical tropopausetemperatures and hence water vapor concentrations of airentering the stratosphere in a similar manner, with morewater vapor entering the stratosphere when QBO-relatedtemperature anomalies are warm near the cold point ataround 100 hPa. That the QBO-related anomalies in watervapor mixing ratio maintain their integrity as they ascendthrough the lower stratosphere from the cold point up to ∼
30 km at approximately the rate of the background meanupwelling in the BDC, is consistent with the tape recorderanalogy, as articulated, for example, by Fueglistaler andHaynes (2005). In the upper stratosphere, the QBO water vapor anomalies are approximate mirror images (with op-posite sign) of those in methane (not shown), because theoxidation of methane is the main source of the water vaporabove 35 km (Randel et al. 1998). Considering that therate of methane oxidation is temperature-dependent, QBO-related water vapor variations in the upper stratosphere arelikely due to QBO-induced perturbations in both temper-ature and advection. That the westerly and easterly windregimes of the QBO propagate downward through theseascending moist and dry layers proves that they must bepropelled by downward propagating sources of momen-tum, as discussed in the next section.The QBO signal in the equatorial ozone, shown in Fig.2d, reveals the existence of separate lower stratospheric(20-27 km) and middle stratospheric (30-37 km) regimes,with a transition at around 28 km (e.g., Schoeberl et al.2008 and references therein). Below 28 km, the chemicallifetime of ozone is relatively long compared with dynam-ical transport processes and hence it may be regarded as along-lived, passive tracer. Because the background ozonemixing ratio increases rapidly with height in this layer,
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Fig. 3. Composites of temperature anomalies (colored shading) and zonal wind (contours) in descending westerly (left) and easterly (right) shearzones of the QBO, as defined in the text. Note that the zonal wind represents the total field, not just the anomalies. Contour interval 7.5 m s − ,westerlies solid, easterlies dashed, zero contour bolded. the QBO-related ozone anomalies are positive in regionsof descent and vice versa. Above 28 km ozone chemi-cal lifetime is much shorter, limiting the direct impact ofadvection. At these altitudes, the key catalytic cycles con-trolling ozone loss are linked to reactive nitrogen in theform of nitrogen oxides (NOy) (Park et al. 2017). Hence,the QBO-induced perturbations in chemical loss rate due tovariations in temperature and NOy transport are the maincause of the QBO-related ozone variations above 28 km,where its concentration is largely controlled by the ambienttemperature (Fleming et al. 2002).Meridional cross sections of the total zonal wind andtemperature anomalies are shown in Fig. 3 for the QBOwesterly (left) and easterly (right) shear zone composites,constructed by averaging variables for the months whenthe zero-wind line of zonally averaged zonal wind over theequator in a descending westerly or easterly shear zonesreaches a prescribed reference level, here taken to be 25hPa ( ∼
25 km). The months used in constructing each com-posite are indicated in Fig. S1. Since linear regression isnot employed in creating the composites, the anomaly fieldsare not constrained to be equal and opposite in contrast-ing composites. In contrast to the zonal wind anomaliesshown in many previous studies (e.g., Randel et al. 1999),the easterly wind regimes in the total wind field are muchwider than the westerly regimes, consistent with the meanclimatology, as noted above. The disparity could simplybe a reflection of the background climatology, as suggestedby Randel and Wu (1996). But if the structure and the peakwind speeds in westerly and the easterly wind regimes areshaped by the spectrum of waves dispersing upward frombelow, the mean climatology might be shaped by the QBO.Another distinctive feature of the cross sections shown inFig. 3 is that the westerly regimes exhibit U-shaped bases,while the easterly regimes exhibit flatter bases, as pointedout by Hamilton (1984). This difference also appears to be
Fig. 4. Composites of temperature anomalies (colored shading),zonal wind (contours), and TEM mean meridional circulation (MMC)(arrows) for descending westerly (left) and easterly (right) shear zonesof the QBO. The QBO-induced MMC is shown in the top panels andthe total MMC, which includes the climatological mean, is shown in thebottom panels. Contour interval 7.5 m s − , westerlies solid, easterliesdashed, zero contour bolded. The longest horizontal components ofthe arrows ( ¯ v ∗ ) correspond to 0.3 m s − , while the longest verticalcomponents ( ¯ w ∗ ) correspond to 1 mm s − . a consequence of wave-mean flow interaction, as discussedin Section 4.b.Figure 4 documents the QBO-induced and total meanmeridional circulations (MMC). The QBO-induced MMCcomposite patterns shown in the top panels, with descentin the westerly shear zones and ascent in the easterly shearzones are in qualitative agreement with the circulationspostulated by Reed (1964) and Wallace (1967) on the basisof simple dynamical and thermodynamic arguments. Thevertical advection associated with QBO-induced MMCthus speeds the descent of westerly wind regimes whileit impedes the descent of easterly regimes. The tempera-ture field in the QBO is maintained against radiative relax-ation by the QBO-induced MMC. In this sense, the QBO-induced MMC can be viewed as a consequence of radiativerelaxation, which drives the wind and temperature fieldsout of thermal wind balance. In effect, the QBO-inducedMMC creates and sustains the QBO-related temperatureperturbations while it damps the QBO-related zonal windperturbations, as discussed in section 4.a.The total TEM MMC fields constructed by adding theperturbations in the top panels of Fig. 4 to the climato-logical annual mean BDC are shown in the bottom pan-els. Within 5°of the equator the descent in the westerlyshear zones is strong enough to cancel the BDC-relatedupwelling. The flow in the BDC is deflected around theirflanks. In the seasonally dependent composites, the flowis deflected preferentially into the winter hemisphere (notshown). In the easterly shear zones the upwelling is en-hanced. Hence, the collapse of westerly wind regimes asthey approach the tropopause is attended by a breakthroughof the BDC-related upwelling, increasing the concentra-tions of tropospheric trace constituents, and decreasing theconcentrations of ozone and other stratospheric trace con-stituents.From Figs. 3 and 4 it is readily apparent that theQBO-related temperature anomalies and the correspond-ing MMCs are nearly equatorially symmetric when esti-mated on the basis of year-round data. However, whenthe westerly and easterly shear zone composites are con-structed based on seasonal mean data, important equato-rial asymmetries emerge. The composites shown in Fig. 5are constructed separately for 3-month seasons December-February (DJF) and June-August (JJA). The criterion forselecting the months included in the easterly composite isthat zonally-averaged zonal wind at the 50 hPa level beeasterly and in excess of -5 m s − and the same criterionwith reversed sign is used for the westerly composite. Sincethe composites for westerly and easterly phases are simi-lar but with the sign reversed, only their difference (i.e.,easterly minus westerly) is shown in Fig. 5. The subtrop-ical/midlatitude centers of action in the QBO-related tem-perature and MMC fields are confined to the winter hemi-spheres. Concentrations of tracers transported by QBO-induced MMC, such as ozone, also exhibit an analogousseasonality, with much larger poleward transports in thewinter hemisphere (Randel and Wu 1996). The seasonalityof the QBO-induced MMC can be related to the seasonallyvarying hemispheric asymmetries in the BDC, whose pole-ward branch and associated planetary Rossby wave drivingis concentrated in the winter hemisphere (Holton 1989). Alikely explanation is that the QBO-induced mean merid-ional motions can extend into middle latitudes only in the Fig. 5. Meridional cross sections of temperature (colored shading),MMC (arrows) and zonal wind (contours) for easterly minus westerlycomposites as defined by the magnitude of zonally averaged zonal wind> 5 m s − at the 50 hPa level for DJF (top), and JJA (bottom). Contourinterval 7.5 m s − , westerlies solid, easterlies dashed, zero contour omit-ted. The longest horizontal components of the arrows ( ¯ v ∗ ) correspondto 0.4 m s − , while the longest vertical components ( ¯ w ∗ ) to 0.6 mm s − . presence of Rossby wave-breaking and as noted by Hitch-man and Huesmann (2007), at stratospheric levels Rossbywaves are present only in the winter hemisphere.
4. The momentum budget
The smoothness of the zonal wind field in Fig. 1 is dueto the zonal averaging, which effectively removes the fluc-tuations associated with the passage of atmospheric waves.The colored shading in Fig. 6 shows a time-height sectionof the resolved wave component (i.e. departures from thezonal mean) of temperature at an equatorial grid point onthe Date Line during a year-long interval in which a west-erly shear zone, indicated by the zonal wind contours, isdescending through the lower stratosphere. To simplifythe signature of the waves, the temperature perturbationsare smoothed by applying a 5-day running mean. They arewavelike with periods on the order of 10-15 days and down-ward propagating, and particularly well organized withinthe slowly descending westerly shear zone.Equatorially-trapped waves with a variety of vertical andhorizontal wavelengths and phase speeds, excited mainlyby convection in the tropical troposphere, disperse upwardinto the stratosphere, producing transports of momentum
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Fig. 6. Time-height section of the wave component of the temperature field (colored shading) for the equatorial grid point at the longitude of theDate Line (0°, 180°) in calendar year 2012-2013. The contours indicate equatorial zonally averaged zonal wind, contour interval 5 m s − , westerliessolid, easterlies dashed, zero contour omitted. The temperature perturbations are smoothed by a 5-day running mean. and heat. As the waves approach their critical levels,they either break or are radiatively damped (Holton andLindzen 1972) and deposit their zonal momentum to themean flow (Booker and Bretherton 1967). The absorp-tion of the waves induces a downward displacement of theshear zone and this, in turn, causes the waves to break anddeposit their momentum at progressively lower levels, sothat the shear zone continues to descend. In Fig. 6 thewesterly shear zone descends from ∼
27 km to below ∼ a. The role of advection Figure 7 shows time-height sections of the advectionterms in Eq. (1) averaged over 5°N/S for a 10-yr inter-val and Fig. 8 shows their distribution in the meridionalplane in composites for westerly and easterly shear zones,constructed in the same manner as Fig. 3. In both figuresthe zonal wind tendencies are superimposed upon the dis-tribution of zonal wind itself. The meridional advection,the first term on the right-hand side of Eq. (1), is smallin the equatorial time-height section. The most notablefeature is the westward acceleration that occurs regularlyat 6-month intervals above ∼
30 km. It peaks at the timesof the solstices, when air is flowing across the equatorfrom the summer hemisphere to the winter hemispherein the upper branch of the BDC (Delisi and Dunkerton1988). Holton and Wehrbein (1980) proposed that the seasonally reversing cross-equatorial flow at these levelsplays a prominent role in forcing the SAO. The meridionaladvection term in Fig. 7 also produces weak westward ac-celeration within the westerly shear zones. The strongestinfluence of meridional advection term is off the equator,where the f ¯ v ∗ term makes the dominant contribution, asshown in the top panel of Fig. 8. It tends to damp theQBO by weakening the easterly wind regimes along theirpoleward flanks and by eroding the westerly wind regimesalong their bottom edge.The vertical advection term, the second term on theright-hand side of Eq. (1), shown in the middle panels ofFigs. 7 and 8 also tends to weaken the easterly regimesalong the equator, but off the equator it is overshadowed bythe meridional advection term. The net effect of the twoterms, shown in the bottom panels, is to damp the QBO(e.g., as noted by Dunkerton 1997) without contributingappreciably to its downward propagation. That they shouldhave a net damping effect is consistent with the energeticsof the QBO and BDC, whose mean meridional motions areknown to be thermally indirect, converting kinetic energyto available potential energy, which is subject to radiativedamping (Wallace 1967).Figures 9 and 10 present an overview of the momentumbudget in the tropical stratosphere. The zonal wind ten-dency, shown in Figs. 9a and 10a, is arguably the mostrobust of the terms in the balance because it is large anddirectly related to the winds assimilated from observations,at least in the lower and middle stratosphere. Values rangeas high as ± − d − for brief periods within strongshear zones. The "adjusted tendency", shown in Figs. 9band 10b, which is the zonal wind tendency minus totaladvection, is the tendency that remains to be explained bythe wave forcing after the advection by the mean merid-ional motions is taken-into account. In the easterly shearzones, which are propagating downward in the presence ofstrong ambient ascent (Fig. 4), the adjusted tendency isappreciably larger than the observed tendency. The wave Fig. 7. Time-height sections of zonal wind tendency (colored shading) due to the advection terms in Eq. (1) as indicated, superimposed uponthe zonally averaged zonal wind (contours), averaged over 5°N/S. Contour interval 5 m s − , westerlies solid, easterlies dashed, zero contour omitted.Based on 6-hourly data, smoothed by a 30-day running mean.Fig. 8. Composites for descending westerly (left) and easterly (right)shear zones of the QBO. The colored shading shows the zonal wind ten-dency due to the advection terms in Eq. (1) as indicated, superimposedupon the zonally averaged zonal wind (contours). Contour interval 7.5m s − , westerlies solid, easterlies dashed, zero contour bolded. forcing needs to account for the downward propagation ofsuccessive westerly and easterly regimes and it also needsto account for the maintenance of the QBO in the presenceof damping (especially of the easterlies) by the advection.How the waves satisfy (or fail to satisfy) these balancerequirements, is the focus of the remainder of this section. b. Forcing by the resolved waves The adjusted zonal wind acceleration near the equatordue to the wave forcing is due to both resolved and unre-solved waves. The resolved forcing is proportional to thedivergence of the EP flux, shown in Figs. 9c. The EP fluxdivergence is concentrated within the shear zones, withvalues ranging as high as ± − d − over intervalsof a month or two. These values are generally consis-tent with results of general circulation models in whichwaves of short horizontal wavelength are modeled explic-itly and no gravity wave parameterization is required (e.g.,Kawatani et al. 2010a,b), and they are larger than thosebased on ERA-I, especially in the easterly shear zones thathave been documented in previous studies such as those ofErn et al. (2014) and Kim and Chun (2015). The strongcorrespondence between the strength of the shear and thestrength of the forcing in Fig. 9c is consistent with the-oretical expectations: the stronger the vertical shear, themore of the upward-dispersing waves encounter their crit-ical levels per unit height, the more zonal momentum theydeposit, and hence, the stronger the zonal acceleration. Itis evident from Fig. 9c that the waves also induce a more0 JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 9. As in Fig. 7 but the zonal wind tendency due to different terms in Eq. (1) indicated by colored shading. See the text for the definition of theadjusted and residual tendencies. widespread westward acceleration of a few tenths of a ms − d − throughout the lower halves of easterly regimes.Meridional cross-sections of wave forcing during thephases of the QBO cycle when westerly and easterly shearzones are descending through the 25 hPa level are shownin Fig. 10c. Also shown in these panels is the transport ofwesterly momentum in the meridional plane, which is inthe opposite direction of the EP flux vectors. In the west-erly shear zone composite (left), waves dispersing upward through the easterly regime in the lower stratosphere areabsorbed when they encounter the overlying westerly shearzone, inducing a strong eastward acceleration. In a simi-lar manner, in advance of the descending easterly regime(right), westward momentum converges to the shear zone.Weaker convergence is evident throughout most of the east-erly regime. In both Figs. 9 and 10, and during the decentof the easterly shear zones, the pattern of resolved wave1 Fig. 10. As in Fig. 8 but the zonal wind tendency (colored shading) due to different terms in Eq. (1) as indicated. Arrows in (c) indicate the EPfluxes. In the westerly shear zone (left), the longest vertical components of the arrows correspond to 5 . × kg s − , while the longest horizontalcomponents correspond to 1 . × kg s − . In the easterly shear zone (right), the arrows are scaled to be twice as long. See the text for thedefinition of the adjusted and residual tendencies. forcing (c) resembles the adjusted zonal wind tendency(b), but it is not as strong.To gain further insight to the relative contribution ofwaves with different scales to the forcing of the QBO, theresolved wave forcing in Figs. 9c and 10c are separated inFigs. 11 and 12 into contributions from waves with zonalwavenumbers less than and greater than 20, referred tohere as "planetary-scale" and "small-scale gravity" (SSG)waves. It is evident that the forcing due to planetary andSSG waves are of comparable importance. The planetary-scale waves make a stronger contribution to the descent ofwesterly shear zones, while the SSG waves appear to beprimarily responsible for the episodes of rapid descent ofeasterly shear zones, consistent with findings of Giorgettaet al. (2002).The patterns of wave forcing in the meridional planeby the two scales of waves shown in Fig. 12 are similarin many respects, but there are some distinctions betweenthem. That the EP flux vectors are quite different suggeststhat different kinds of equatorially-trapped waves domi-nate the transports at the different scales, as documentedin Part II. While both scales contribute to the eastward accelerations in the descending westerly shear zones, thecontribution from the planetary waves is focused in theequatorial belt, whereas the contribution from the SSGwaves spans a wider range of latitudes and conforms tothe "U" shape of the shear zone. The westward forcing bythe planetary-scale waves is broadly distributed within theeasterly regimes, whereas the contribution from the SSGwaves is more focused in the shear zones, where it playsthe dominant role in their descent.Earlier study also suggests the importance of the SSGwaves in the forcing of the QBO. Kawatani et al. (2010a,b)simulated the QBO using a high-resolution atmosphericgeneral circulation model with 60 km horizontal resolutionand 300 m vertical resolution, in which waves with shorthorizontal wavelengths were modeled explicitly so that nogravity wave parameterization was required. They alsoconcluded that the gravity waves with k > 36 are the maincontributors to producing the descent of the easterly shearzones in the simulated QBO.2 JOURNAL OF THE ATMOSPHERIC SCIENCES
Fig. 11. Time-height sections of the EP flux divergence (colored shading) due to planetary-scale waves (top) defined as waves with zonalwavenumbers | k | ≤
20, and small-scale gravity (SSG) waves (bottom) defined as waves with zonal wavenumbers | k | >
20, averaged over 5°N/S.Contours indicate the zonally averaged zonal wind. Contour interval 5 m s − , westerlies solid, easterlies dashed, zero contour omitted. Based on6-hourly data, smoothed by a 30-day running mean.Fig. 12. Composites for descending westerly (left) and easterly (right)shear zones of the QBO. The colored shading indicates the EP flux di-vergence due to planetary-scale waves (top) defined as waves with zonalwavenumbers | k | ≤
20, and SSG waves (bottom) defined as waves withzonal wavenumbers | k | >
20, superimposed upon the zonally averagedzonal wind (contours). Contour interval 7.5 m s − , westerlies solid, east-erlies dashed, zero contour bolded. Arrows indicate the EP fluxes. In thewesterly shear zone (left), the longest vertical components of the arrowscorrespond to 3 × kg s − , while the longest horizontal componentscorrespond to 1 . × kg s − . In the easterly shear zone (right), thearrows are scaled to be twice as long. c. Interpretation of the unresolved wave forcing The residual zonal wind tendency ¯ X in Eq. (1), thatremains after the contribution from the resolved waves issubtracted out from the adjusted tendency, is shown in Figs. 9d and 10d (i.e., d = b - c in Figs. 9 and 10). In studiesof Ern et al. (2014), Kim and Chun (2015) and others,the terms used in evaluating ¯ X are assumed to have beenestimated with sufficient accuracy to warrant interpreting¯ X as the contribution of unresolved gravity waves to thewave forcing. Here we make the same assumption. Thesimilarity between the resolved and the residual forcingduring the descent of the easterly shear zones suggests thatmuch of the residual can be explained simply by assumingthat the unresolved waves behave in the same manner asthe resolved waves. Indeed, by multiplying the resolvedwave forcing by a factor of ∼ ∼
40% ofthe total (i.e., resolved plus unresolved) wave forcing inthe easterly shear zones. The unresolved waves evidentlyproduce a strong westward forcing in the core of the easterlyshear zones, especially during intervals of rapid descent.Results of Giorgetta et al. (2006), Kawatani et al. (2010a),among others, based on numerical models with high spatialresolution also suggest that waves on scales too small to beresolved by ERA5 could play an important role in forcingthe descent of easterly regimes.The residual tendencies are also marked by eastwardforcing in a thin layer just above the peaks of the easterlywind regimes, accompanied westward forcing higher up,near the zero-wind line. The existence of this couplet in-dicates that the unresolved waves must be depositing east-ward momentum lower in the westerly shear zones thanthe resolved waves. Two different, but complementaryideas can be put forth to explain it: (1) that the verticalwind shear in westerly shear zones may become so strongthat it exceeds the criterion for Kelvin-Helmholtz (KH)instability, in which case the shear is maintained at the3critical value by the downward mixing of eastward mo-mentum in the unresolved waves, (2) that eastward propa-gating waves dispersing upward through the layer of peakeasterlies begin to amplify in inverse proportion to theirDoppler-shifted frequency and the waves with the short-est vertical wavelengths are the first to break as the shearwithin them becomes supercritical.Other notable features in the pattern of the residual ten-dency are the patches of eastward forcing along the flanksof the westerly wind regimes (Fig. 10d). Several studieshave investigated the possible role of barotropic instabil-ity of the westerly jet (e.g., Andrews and McIntyre 1976;Hamilton et al. 2001; Yao and Jablonowski 2015). Indeed,the presence of narrow westerly jets gives rise to a reversalof the zonal mean barotropic vorticity gradient, which is anecessary condition for barotropic instability (Garcia andRichter 2019). The distinct pattern around the westerly jet,with westward forcing near its nose and patches of east-ward forcing along its flanks, acts to decelerate the westerlyjet close to the equator and to accelerate it away from theequator. Its role would be to reduce the curvature of thewesterly jet by broadening its profile, thereby neutralizingthe instability inherent in the flow configuration.The residual wave forcing ¯ X can be partitioned intothe part that is captured by the gravity wave parameteri-zation scheme and the analysis correction, which can beinterpreted as the error in the model’s representation ofthe QBO momentum balance, prior to the data assimila-tion step in constructing the reanalysis. The parameterizedgravity wave drag (GWD) in ERA5 shown in Figs. 9eand 10e captures some of these unresolved features. Thatthere are differences between the patterns in panels (d) and(e) is indicative of systematic (and therefore potentiallycorrectable) biases in the GWD parameterization or in theevaluation of the terms in the balance. Near the equator(Fig. 9e), the GWD parameterization scheme overcompen-sates for the weakness of the resolved waves. If the GWDparameterization is tuned to fit ¯ X , the analysis correctionwould be reduced accordingly. In contrast, at latitudes ∼
5. The QBO in ERA5 vs. ERA-I
Here we document the results of a detailed comparisonof the representations of the QBO in ERA5 and in ERA-I.The difference in monthly mean zonally averaged zonalwind, averaged over 5°N/S, is shown in Fig. S2. Prior to1998, the SAO-related winds are systematically stronger inERA5, particularly during the westerly phase. The QBO-related winds are also stronger in ERA5 prior to 1998,particularly near the shear zones in the easterly regimes.The differences decrease with time during the 1999-2006period, and a good agreement can be seen thereafter. Itshould be borne in mind that throughout this period ofrecord, fewer data are assimilated in reanalysis datasets at the higher altitudes because it is difficult to measure windsat these heights based on satellite or ground-based remotesensing (Anstey et al. 2020). Satellite direct wind mea-surements have not been available above ∼
30 km (Smithet al. 2017) and nadir-viewing satellite observations havedifficulty resolving the temperature perturbations in thelayers of strong vertical wind shear in the SAO, creatinglarge uncertainties in the SAO winds (Coy et al. 2016).The analyses presented for ERA5 in the text were alsoperformed on ERA-I and the results are presented in thesupplemental material along with their ERA5 counterpartsto make the comparison easier. Overall, the differences inthe mean fields are subtle, as documented in Figs. S3 to S6.The patterns of adjusted zonal wind tendency and resolvedwave forcing in ERA-I and ERA5 are similar in manyrespects (Figs. S7 to S9). However, the resolved waveforcing in ERA5 is stronger, and accounts for a substantiallylarger fraction of the adjusted zonal wind tendency. Amore quantitative comparison between the resolved waveforcing in the two reanalysis is presented in Figs. 13 and 14in which EP flux divergence in ERA-I is subtracted fromthat in ERA5. For reference, ERA5 is capable of resolvingwaves with wavenumbers ranging up to 360, comparedto 120 in ERA-I. It is evident that forcing in ERA5 isstronger by up to 0.3 m s − d − during the descent of theeasterly shear zones and up to 0.2 m s − d − during thedescent of the westerly shear zones. Generally speaking,the forcing in ERA5 more faithfully captures the spikes inwave forcing that gives rise to short-lived episodes in whicheasterly regimes descend as rapidly as westerly regimes.The bottom panels reveal that this difference is mainlyattributable to forcing from SSG waves.Indeed, we find the forcing due to SSG waves in ERA-Ito be much reduced (Figs. S10 and S11), in particular in theeasterly shear zones, consistent with the results of Ern et al.(2014), who calculated the EP flux divergence by waves k = 1-20 in ERA-I and found the contribution from thewavenumbers higher than that to be relatively unimportant.The planetary-scale forcing is also slightly smaller in ERA-I than in ERA5 (Figs. S9 and S10), which is probably dueto lower vertical resolution of ERA-I, resulting in a poorerrepresentation of wave-mean flow interaction processes.
6. Discussion and conclusion
This study has documented several aspects of the QBOand provided deeper insights into its momentum budget. Itis shown that the QBO-induced MMC, while mainly con-fined to the winter hemisphere, is strong enough to modifythe BDC-related upwelling. Within 5°of the equator thedescent in the westerly shear zones interrupts the tropicalupwelling and deflects the flow around the flanks of thewesterly regimes. In the easterly shear zones the tropicalupwelling is enhanced. The QBO-induced MMC createsand sustains the QBO-related temperature perturbations4
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Fig. 13. Time-height sections of the difference between ERA5 and ERA-I in EP flux divergence (colored shading) due to all resolved waves(top), and SSG waves (bottom) defined as waves with zonal wavenumbers | k | >
20, averaged over 5°N/S. Contours indicate the zonally averagedzonal wind. Contour interval 5 m s − , westerlies solid, easterlies dashed, zero contour omitted. Based on 6-hourly data, smoothed by a 30-dayrunning mean.Fig. 14. Composites for descending westerly (left) and easterly (right)shear zones of the QBO. The colored shading indicates the difference be-tween ERA5 and ERA-I in EP flux divergence due to all resolved waves(top), and SSG waves (bottom) defined as waves with zonal wavenum-bers | k | >
20, superimposed upon the zonally averaged zonal wind (con-tours). Contour interval 7.5 m s − , westerlies solid, easterlies dashed,zero contour bolded. Arrows indicate the EP fluxes. In the westerly shearzone (left), the longest vertical components of the arrows correspond to2 . × kg s − , while the longest horizontal components correspondto 3 . × kg s − . against radiative damping, while it damps the QBO-relatedzonal wind perturbations. Consequently, the wave forcingis responsible for both the downward propagation and themaintenance of the QBO. The resolved waves in ERA5 produce roughly compa-rable contributions to the eastward and westward acceler-ations, which range as high as ± − d − during thedescent of the westerly and easterly shear zones of the QBO.Separating ERA5 resolved wave forcing into contributionsfrom SSG waves with zonal wavelengths less than 2000 kmand planetary-scale waves with wavelengths longer thanthat reveals that the planetary scale waves make a strongercontribution to the descent of westerly shear zones, whileSSG waves play the dominant role in the descent of easterlyshear zones.The time-height section for the analysis correctionshown in Fig. 9f exhibits a distinctive pattern during theextended intervals in which a westerly regime is temporar-ily stalled at the 20 km level while the core of the easterlyregime that will eventually replace it is stalled in the 27-30km layer. Under these conditions the model used in gener-ating the ERA5 reanalyses produces a spurious westwardacceleration in the lingering westerly regime and an east-ward acceleration in the stalled easterly shear zone centered ∼
23 km (Fig. 9e), both of which need to be corrected bythe analysis increment. It is evident from Fig. 9f that muchof the required analysis correction involves a cancellationof the spurious forcing imposed by the GWD parameteri-zation scheme.This problem is not apparent in the meridional crosssection for the easterly shear zone shown in Fig. 10f be-cause the composite upon which it is based includes onlyrapidly descending shear zones (see Fig. S1). To show theoff-equatorial structure during these intervals, we defined anew composite based on the 120 months of the 480-monthperiod of record when the easterly jet at 27-30 km levelwas strongest (Fig. S12). The results shown in Fig. 15 aregenerally consistent with the time-height sections in Fig.5
Table 1. Variance of tendencies [10 (m s − ) day − ], averaged over 5°N/S, integrated over time (1979 to 2018) and height (10-90 hPa), and theirratio with respect to the adjusted tendency (parentheses). See the text for explanation.zonal wind tendency adjusted tendency EP flux divergence residual tendency parametrized GWD analysis correctionERA5 5.1 11.3 5.6 (50%) 3.7 (33%) 6.4 4.4ERA-I 4.9 10.5 2.7 (26%) 4.9 (47%) - -Fig. 15. Composites for descending easterly shear zone of the QBO,as defined in the text. The colored shading shows the zonal wind ten-dency due to the indicated terms, superimposed upon the zonally av-eraged zonal wind (contours). Contour interval 7.5 m s − , westerliessolid, easterlies dashed, zero contour bolded.
9, including the analysis correction. The features in theequatorial time-height sections extend out to 15-20°N/S.As previously discussed, the terms used in evaluating theresidual tendency ¯ X (see Eq. (1)), are assumed to have beenestimated with sufficient accuracy to justify interpreting theresidual tendency as the contribution of unresolved gravitywaves to the wave forcing. While It is encouraging to seesome similarity in the parameterized GWD and residualtendency patterns (Figs. 9d,e, Figs. 10d,e, Figs. 15a,b),it is evident from the analysis correction that significantdiscrepancies remain. For example, the westward forcingin the parameterized GWD in the easterly shear zone is toostrong and too low, leading to a dipole of westward andeastward forcing in the lower stratosphere in the analysiscorrection (see Fig.15c and Fig. 9f). The representation of the mean fields in the QBO isfound to be very similar in ERA5 and ERA-I, but ERA5'shigher spatial resolution makes it possible to resolve abroader spectrum of atmospheric waves. With its highervertical resolution, it is also possible to represent the pro-cess of wave-mean flow interaction more realistically. Asshown in Table 1, the resolved waves in ERA5 (i.e., theEP flux divergence) explains half of the variance of the ad-justed tendency, indicating a significant improvement overERA-I. The variance attributable to unresolved waves (i.e.,the residual tendency) has decreased in ERA5 accordingly.That the sum of the variances of the EP flux divergence andthe residual tendency is smaller than the variance of the ad-justed tendency is indicative of their nonzero covariance inthe time-height domain. This is to be expected, since thepattern of the residual tendency projects positively uponthe pattern of the EP flux divergence, as shown in Fig. 9.If the covariance were eliminated by artificially inflatingthe amplitude of the EP flux divergence by a factor of 1.18,the fraction of the variance "explained" by the resolvedwaves would increase from 50% to 69% and the residual"unexplained" variance would drop to 31%. However, lo-cally large analysis corrections would still be required in thewesterly shear zones. The GWD parameterization schemeaccounts for much of the unresolved forcing in the westerlyshear zones, but in the present version it produces an exces-sively strong westward forcing in the rapidly descendingeasterly shear zones, and it prematurely damps the stalledwesterly regimes at 50 hPa and below. To further reducethe analysis correction, it will thus be necessary both to fur-ther increase the resolution of the model, especially in thevertical, and to further refine the GWD parameterizationsscheme. Acknowledgments.
The authors would like to thank M.Joan Alexander, Peter H. Haynes, and Pu Lin for the helpfuldiscussions and suggestions. This research is supported bythe NASA 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/).6
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