JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 3139–3149, doi:10.1002/jgrd.50319, 2013

Stationary waves in the wintertime mesosphere: Evidence for gravitywave filtering by stratospheric planetary wavesR. S. Lieberman,1,2 D. M. Riggin,1,2 and D. E. Siskind3

Received 1 October 2012; revised 6 March 2013; accepted 6 March 2013; published 25 April 2013.

[1] Quasi-stationary planetary-scale waves in the wintertime mesosphere and lowerthermosphere (MLT) are thought to be forced in part by drag imparted by gravity wavesthat have been modulated by underlying stratospheric waves. Although this mechanismhas been demonstrated numerically, there have been very few observational studies thatexamine wave driving as a source of planetary waves in the MLT. This study uses datafrom EOS Aura and TIMED between 2005 and 2011 to examine the momentum budgetof MLT wintertime planetary waves. Monthly averages for January indicate that thedynamics of zonal wave number 1 are determined from a three-way balance among theCoriolis acceleration, the pressure gradient force, and a momentum residual term thatreflects wave drag. The MLT circulations in January 2005, 2006, 2009, and 2011 arequalitatively consistent with a simple model of wave forcing by drag from gravity wavesthat have been modulated by stratospheric planetary waves. MLT winds during theseyears are also consistent with analyses from a high-altitude operational prediction modelthat includes parameterized nonorographic gravity wave drag. The importance of wavedrag for the MLT momentum budget suggests that the gradient wind approximation isinadequate for deriving planetary-scale winds from global temperature measurements.Our results underscore the need for direct global wind measurements in the MLT.Citation: Lieberman, R. S., D. M. Riggin, and D. E. Siskind (2013), Stationary waves in the wintertime mesosphere: Evidencefor gravity wave filtering by stratospheric planetary waves, J. Geophys. Res. Atmos., 118, 3139–3149, doi:10.1002/jgrd.50319.

1. Introduction[2] Quasi-stationary planetary-scale waves are regular

features of the wintertime mesosphere and lower thermo-sphere (MLT) [Barnett and Labitzke, 1990; Wang et al.,2000]. Their relationships to stratospheric wintertime sta-tionary disturbances have been extensively examined bySmith [1996, 1997, 2003], who noted an almost universal180ı phase offset. MLT planetary wave (PW) signaturesare consistent with two mechanisms thought to link themwith the underlying stratospheric PW field. One is simplythe vertical propagation of the stratospheric Rossby wavesthat results in a half-cycle phase offset owing to their longvertical wavelengths.

[3] Another mechanism, first proposed by Holton [1984]and examined theoretically by Dunkerton and Butchart[1984], involves selective transmission of upward-propagating gravity waves through the stratospheric PWs.This process imparts longitudinal variability to the MLTgravity wave (GW) spectrum and to the drag that results

1Northwest Research Associates, Boulder, Colorado, USA.2GATS, Inc., Boulder, Colorado, USA.3Space Science Division, Naval Research Laboratory, Washington DC,

USA.

Corresponding author: R. S. Lieberman, GATS, Inc., 3360 Mitchell Ln.,Boulder, CO 80301, USA. (r.s.lieberman@gats-inc.com)

©2013. American Geophysical Union. All Rights Reserved.2169-897X/13/10.1002/jgrd.50319

from momentum flux convergence of dissipating GWs. Thelongitudinally variable drag in the MLT thus becomes an insitu source of PWs. The plausibility of this mechanism hasbeen confirmed in numerical experiments by Liu and Roble[2002], Smith [2003], and Oberheide et al. [2006]. Somedirect observational support for modulation of stratosphericGWs by the polar vortex has been presented by Ratnamet al. [2004], Duck et al. [1998], Thurairaja et al. [2010a,2010b], and Wang and Alexander [2009]. While numerousstudies have addressed the effects of dissipating PWs uponthe middle and upper atmosphere circulation [Lieberman,1999; Salby et al., 2002; Oberheide et al., 2006; Coy et al.,2011], there have been very few diagnostic studies of MLTPW generation by GW forcing.

[4] The purpose of this study is to examine the momen-tum budget and inferred wave driving of MLT wintertimePWs. The Thermosphere-Ionosphere-Mesosphere Energet-ics and Dynamics (TIMED) satellite has been monitoringthe MLT since late 2001. The microwave limb sounder(MLS) aboard EOS Aura was launched in late 2004 and isobserving stratospheric and mesospheric temperatures andconstituents. TIMED and Aura therefore provide simultane-ous and independent measurements of horizontal winds andgeopotential that are required for the horizontal PW momen-tum budgets. We also compare our results with analysesfrom the Advanced Level Physics High Altitude (ALPHA)Navy Operational Global Atmospheric Prediction System(NOGAPS) that includes nonorographic GW drag.

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[5] We examine PWs in both winds and geopotential andcompute the relative contributions of terms in the zonal andmeridional PW momentum budgets. The net forcing uponthe PWs, which we shall refer to as the “wave drag,” isdeduced as the momentum residual. Our findings indicatethat during January, the dynamics of the PW with zonal wavenumber 1 (hereafter referred to as PW 1) in the NorthernHemisphere MLT are controlled by a three-way balanceamong the Coriolis, pressure gradient, and drag. Compar-ison of the circulations of stratospheric and mesosphericPW 1 indicates that the MLT wave drag is consistent withbreaking GWs that have been filtered by the underlyingstratospheric PWs. This interpretation is supported by com-parisons with NOGAPS ALPHA analyses. The importanceof the wave drag term in the MLT momentum budget sug-gests that the gradient wind approximation is inadequatefor deriving planetary-scale winds from global temperaturemeasurements.

2. Data[6] The TIMED satellite was launched in December 2001

with the mission of studying the influences of the Sun andclimate change on the MLT and the ionosphere. TIMEDorbits the Earth about 15 times per day on the ascendingand descending portions of the orbit. The TIMED Dopplerinterferometer (TIDI) performs high spectral resolution limbscans with 2.5 km vertical resolution through the terrestrialairglow layers in the MLT [Killeen et al., 2006]. The hor-izontal wind vector is derived from the Doppler shifts andline shapes of the spectral features of the airglow emissions.TIDI obtains these scans simultaneously in four orthogonaldirections: two at angles 45ı forward, but on either side ofthe satellite’s velocity vector, and two at 45ı rearward of thesatellite. These four views provide the measurements neces-sary to construct the horizontal vector winds as a functionof altitude along two parallel tracks corresponding to the“warm” (sunward) and the “cold” (anti-sunward) sides of thespacecraft. Between 52ıS and 52ıN, TIDI views both thewarm and the cold sides. Poleward of these latitudes, TIDIviews only one side (warm in one hemisphere and cold in theother). The difference between the ascending and descend-ing local times varies from 8 to 12 h between 20ıN and20ıS. The warmside and coldside winds are separated onaverage by about 3 h in local time.

[7] Wind retrievals are reported every 2.5 km, althoughthe effective vertical resolution is half a scale height. Usefuldaytime winds are reported between 70 and 110 km, whilenighttime winds are retrieved only between 85 and 100 km.Although the nominal horizontal spacing between profilesis approximately 750 km along the orbit track, the effectivemeridional resolution of vector winds is about 6ı. Detailsabout instrument design, performance, wind retrievals, andproduct hierarchy appear in Skinner et al. [2003], Killeenet al. [2006], and Niciejewski et al. [2006]. We have optedto analyze inverted line-of-sight winds from the “PRF”files, since these data can be easily clustered by viewingangle, and by ascending and descending nodes. This studyuses version 10 PRF files distributed by the University ofMichigan (http://tidi.engin.umich.edu).

[8] The Earth Observing System (EOS) MLS waslaunched in July 2004 on the NASA Aura satellite andstarted full-up science operations on 13 August. The

EOS/MLS sampling

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Figure 1. (top) Local times sampled by EOS MLS duringJanuary 2006. Ascending node times (blue) and descend-ing node times (red). (bottom) Local times sampled byTIMED TIDI during January 2006. Warmside ascendingnode (black), warmside descending node (green), coldsideascending node (blue), and coldside descending node (red).

instrument measures temperature as well as various chemi-cal constituents during day and night [Waters et al., 2006].The Aura orbit is sun-synchronous with an ascending (north-going) equator-crossing time near 1:30 P.M., a 98.8 minperiod, and a descending node crossing time near 1:30 A.M.The data coverage spans 82ıS–82ıN on every orbit. EOSMLS retrieves useful temperatures from the troposphere upto about 0.001 hPa (�94 km). Geopotential height is com-puted from integration of the hydrostatic equation above the100 hPa reference level [Schwartz et al., 2008]. The pre-cision of an individual profile is about 35 m at 10 hPa,increasing to 110 m at .001 hPa. The EOS MLS geophysicalparameter data products are available at the NASA GoddardEarth Sciences Distributed Active Archive Center.

3. Wave Analyses[9] We have carried out zonal wave number decomposi-

tions of zonal wind (u0), meridional wind (v0), and geopo-tential (ˆ0) averaged over the month of January in theyears 2005–2011. Wave analyses begin with mapping TIDIwinds onto log-pressure surfaces and gridding the winds andgeopotential in 6ı latitude and 30ı longitude bins. Withineach grid box, we form averages of daily ascending anddescending node measurements. At Northern Hemispheremidlatitudes, ascending and descending node observation

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Table 1. Uncertainties Averaged Between 12.6 and 13.6 Scale Heights of PW 1 Variables Averaged Between 30ıNand 60ıN and Momentum Budget Terms at 54ıN (in m s–1 d–1)

u0 (m s–1) v0 (m s–1) ˆ0 (m2 s–2) fv0 and fu0 (a cos�)–1@ˆ/@� @ˆ/@y X0res Y0res

1.5 1.5 2.7 25. .8 3.6 25.8 24.3

times are separated by 11 h for MLS (see Figure 1, top) and8 h in the case of TIDI. Data are collected over monthlyintervals, during which TIDI daytime and nighttime mea-surements drift about 6 h. Our analysis mitigates the effectsof diurnal tides, but does not fully filter the semidiurnal tides.The effects of tidal residues upon the analysis are exploredin the discussion pertaining to Figure 5.

[10] At mesospheric altitudes, the uncertainties associatedwith the PW determinations (also listed in Table 1) are 1.5m s–1 for winds and 2.7 m for geopotential height. The errorestimates were obtained by iterating the analysis method 100times upon a known stationary wavefield perturbed by ran-dom fluctuations scaled by the measurement uncertaintiesassociated with individual profiles (25 m s–1 for winds and110 m for geopotential).

[11] Figure 2 shows the MLS PW 1 geopotential heightaveraged over January 2006. The stratopause is indicated bya thick dashed line, in order to demarcate the regions of thestratospheric and mesosphere PW. The behavior in Figure 2is typical of all the January averages considered in thisstudy, except 2009. PW 1 geopotential attains a maximumamplitude of 1025 m near 6 scale heights, decays to about300 m at 9 scale heights, and acquires a secondary maxi-mum of 400 m in the mesosphere (near 12 scale heights).The associated longitude-height structure at 60ıN is shownin Figure 3. Lines of constant phase tilt westward withheight, indicating upward transfer of wave energy. Whilethe secondary maximum in the mesosphere suggests possi-ble in situ PW 1 sources, the vertical phase tilt indicates thatstratospheric PW 1 is also a source of the mesospheric wave.

[12] Figure 4 shows the MLS 2006 January PW 1 geopo-tential height as a function of latitude and longitude at13 scale heights, together with the corresponding TIDIwinds (top). Gradient winds have been computed from thegeopotential and are shown for reference in the bottompanel. The gradient wind approximation represents a bal-ance between the pressure gradient, Coriolis, and centrifugalforces [Holton, 1992]. Thus, comparison of the gradient withthe actual winds provides an indicator of the influence ofdrag in the MLT.

[13] We begin by noting that gradient winds are virtu-ally nondivergent. They are oriented parallel to contoursof geopotential, streaming clockwise (anticyclonic) aroundgeopotential maxima and counterclockwise (cyclonic)around geopotential minima. Wind speeds are proportionalto the pressure gradient (indicated by the “packing” of thegeopotential contours). Thus, gradient winds are weakest atthe locations of the geopotential maxima and minima. Thebehavior of the actual TIDI winds differs from the gradi-ent winds insofar that they exhibit considerable divergence,manifested as cross-isobaric flow (i.e., flow across geopo-tential contours). In particular, the sites where geopotentialmaximizes and minimizes (at 60ıN) are the locations of thestrongest and most divergent TIDI winds. We conclude thatTIDI winds in January 2006 are not in gradient wind balanceat 13 scale heights.

[14] The patterns shown in Figure 4 for January 2006appear in January 2005, 2009, and 2011. Of the remain-ing years, we examine PW 1 in January 2007 in Figure 5.During this month, the TIDI wind pattern is character-ized by northward (southward) flow across the geopotentialminimum (maximum). In order to interpret this anoma-lous behavior, we must consider the effects of tides on thePW analysis.

[15] It was noted earlier in this section that tidal effectsare not fully removed from PW analyses. Diurnal tides withzonal wave numbers 0 and 2 westward (DS0 and DW2) aliasto satellite zonal wave number 1 spectra, along with west-ward traveling semidiurnal tides with zonal wave numbers1 and 3 (SW1 and SW3), and westward traveling terdiur-nal tides with zonal wave numbers 2 and 4 (TW2 and TW4)[Salby, 1982]. Tides are highly divergent motions that canpotentially contribute to the departures from gradient windsnoted in Figures 4 and 5. If full 24 h local time cover-age were available over the month-long analysis periods,tidal contributions that are steady in amplitude and phasewould average out, leaving only the stationary PW 1. How-ever, as seen from the bottom panel of Figure 1, there arelengthy gaps in TIDI local time coverage in the NorthernHemisphere midlatitudes, most notably between 4–9 LTand 15–20 LT. Moreover, tidal amplitudes and phases havebeen shown to vary on time scales shorter than 1 month[Smith et al., 2007].

[16] To assess the effects of tides upon the PW windretrievals, we computed the spectrum of diurnal, semid-iurnal, and terdiurnal tides in winds and geopotential.TIDI winds and SABER geopotential were collected forthe first yaw period (generally spanning January 13 toMarch 13) between 2002 and 2010, sorted into hourlybins at all longitudes, and Fourier transformed with

Wave 1 Stationary PHI JAN 2006

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Figure 2. MLS geopotential height amplitude (in m) ofPW 1 averaged over January 2006. Dashed curve indicatesstratopause level.

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Wave 1 Stationary PHI JAN 2006

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Figure 3. Longitude-altitude structure of MLS PW 1geopotential during January 2006 at 60ıN. Dashed curveindicates stratopause level.

respect to longitude and universal time. In the regionsof interest for the present study (13 scale heights in the40ıN–60ıN range), all of the relevant tidal harmonics haveamplitudes between 3 and 5 m s–1. The multiyear aver-age was required in order to obtain sufficient local timecoverage at middle and high latitudes. However, nonmi-grating tides are known to exhibit substantial interannualvariability [Wu et al., 2008; Fuller-Rowell et al., 2011],and our analysis strategy unfortunately deprives us of infor-mation about the tides within a particular year.

[17] The composite tidal fields are then sampled and pro-cessed identically to the actual January winds. The bottompanel of Figure 5 represents the PW 1 vector wind fieldat 13.1 scale heights obtained from sampling DS0, DW2,SW1, SW3, TW2, and TW4. Tidal aliasing clearly makesa significant contribution to the PW 1 pattern. Compar-ison of the top and bottom panels of Figure 5 showsimportant similarities, namely, the presence of northward(southward) flow across the geopotential minimum (max-imum). This behavior leads us to the conclusion thatin January 2007, our PW 1 analyses are dominated bytidal aliasing.

4. Momentum Budget of MLT PW 1[18] In the previous section, we examined PW 1 geopo-

tential and winds in the MLT and noted significant depar-tures from gradient wind balance. The effects of incompletefiltering of tides were also assessed. In this section, weseek to quantify the wave drag upon the PW and clarify itssources.

[19] The momentum budget of quasi-stationary plane-tary waves is given by the equations of horizontal motionlinearized with respect to a two-dimensional basic state:

(a cos�)–1Uu0� +h(a cos�)–1 �U cos�

��

– fi

v0

+ (a cos�)–1ˆ0� = X0res (1)

(a cos�)–1Uv0� +�

f + 2Ua–1 tan��

u0 + a–1ˆ� = Y 0res (2)

Aside from the designations of X ’res and Y ’res, (1) and (2)are stationary, quasi-geostrophic (QG) versions of equations3.4.2a and 3.4.2b in Andrews et al. [1987]. U is the TIDImonthly mean zonal mean zonal wind, f is the Coriolisparameter, a is the radius of Earth, and � is the latitude.The vertical coordinate z is the log-pressure. X ’res and Y ’res,hereafter referred to as the zonal and meridional momentumresiduals, represent the combined effects of friction, advec-tion by the mean meridional circulation, and nonlinear eddyforcing; see Lieberman et al. [2010] for a full expansion.The terms on the left side of (1) and (2) can be computed orinferred from measurements; these are hereafter collectivelyreferred to as the “momentum budget” terms. X ’res and Y ’resare unknown and estimated as residuals of the momentumbudget.

[20] In order to minimize tidal aliasing of X ’res and Y ’res,we filter the tidal contributions from U, u0, v0, and ˆ0 priorto calculating the terms on the left side of (1) and (2).This is accomplished by mapping the composite diurnal,semidiurnal, and terdiurnal harmonics to the coordinates anduniversal times of TIDI and MLS measurements, and sub-tracting the tidal estimate from the actual measurements.This strategy mitigates but does not fully eliminate tidalaliasing, because tides are known to vary on sub-yaw andinterannual time scales [Smith et al., 2007; Lieberman et al.,2007; Oberheide et al., 2009].

Stationary JAN 2006 13.1 sc ht

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Figure 4. Latitude versus longitude patterns of PW 1geopotential at 13.1 scale heights (approximately 85 km)for January 2006. (top) TIDI vector winds overplotted and(bottom) gradient winds overplotted.

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TIDI wind JAN 2007 13.1 sc ht

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Figure 5. (top) As in Figure 4, for 2007. (bottom)Vector wind patterns corresponding to the contributions ofDS0, DW2, SW1, SW3, TW2, and TW4 to PW 1 signature.

[21] The leading terms in equations (1) and (2) are theCoriolis force, pressure gradient, and momentum residuals.The remaining terms are advection and radial accelerationterms that are an order of magnitude weaker. Amplitudesof the leading terms are displayed in Figure 6, computedfrom composite January u0, v0, and ˆ0 values spanning2005–2011, from which the estimated tidal contributionshave been subtracted. Uncertainty estimates are tabulatedin Table 1. These are computed as standard deviations ofmomentum budget terms from the 100 sets of variables usedfor the calculation of the PW 1 uncertainties, described insection 3.

[22] The zonal Coriolis force and pressure gradient termsare generally in antiphase, nearly compensating each otherequatorward of 50ıN. Poleward of 50ıN, the imbalancebetween these two forces increases sharply, resulting inresiduals exceeding 100 m s–1 d–1. In the meridional direc-tion, a situation close to geostrophic balance is observedbetween 40ıN and 50ıN. However, the momentum residu-als increase between 30ıN and 45ıN, and poleward of 50ıN,attaining values of 100–150 m s–1 d–1. In the discussions ofFigures 8–10, we will argue that the momentum residuals atthe higher latitudes are associated with wave driving. How-ever, the cause of the secondary maximum between 35ıNand 45ıN is unclear.

[23] Midlatitude January momentum residuals for indi-vidual years are shown at 13.2 scale heights in Figure 7.

These have been derived from wind and geopotential valuesfiltered of tides. We also plot the estimates of the spuri-ous momentum residuals induced by unresolved tides. Theseare found by forming the difference between X ’res andY ’res computed from observed u0, v0, U, and ˆ0 and com-puted from the same suite of variables from which the tidalcontributions have been subtracted.

[24] A good deal of interannual variability is observedin the momentum residuals. In the meridional direction,momentum residuals significantly exceed the tidal aliasingequatorward of 40ıN and poleward of 50ıN. The strongestY0res values are observed in 2006, 2007, 2009, and 2011.Midlatitude zonal momentum residuals exhibit their high-est values in 2005, 2006, 2007, and 2009. The causes ofinterannual variability in X ’res and Y ’res cannot be fullyexplained on the basis of the data used in this study. Oneof the mechanisms contributing to the momentum residualis GW filtering, which is sensitive to the magnitude anddirection of the total (zonal mean plus perturbation) under-lying mean winds. Stratospheric January zonal mean zonalwinds vary substantially between 2005 and 2011 [Manneyet al., 2008; Wang and Alexander, 2009; Siskin et al., 2010].For example, winds were predominantly easterly at 60ıN inconnection with the major stratospheric sudden warming ofJanuary 2006, compared to a brief period of easterlies dur-ing a minor warming in January 2008, and westerly windsduring all of January 2005 (a non-warming year, not shown).The spectrum of GWs impinging upon the mesosphere in2006 might therefore be expected to differ significantly fromthose of 2005 and 2008 [Ern et al., 2011], yet the amplitudesof X0res in 2005 and 2006 are quite similar. Without specificknowledge of GW forcing, advection by the mean circu-lation (v, w), and year-to-year variations in tides and theiraliasing, the interannual behavior of the momentum residualcannot be explained at this time.

[25] In the following section, we attempt to understandthe relationship between the mesospheric PW 1 circulationsexamined here and the underlying stratospheric PW 1 cir-culation. To that end, we simplify equations (1) and (2) byretaining only the leading terms, to obtain

–fv0 + (a cos�)–1ˆ0� = X ’res (3)

fu0 + a–1ˆ� = Y ’res (4)

[26] The geostrophic wind (u0g, v0g) is defined from thebalance between the pressure gradient and Coriolis forces.The ageostrophic wind is defined as the difference betweenthe actual wind and the geostrophic wind. Using thesedefinitions, (3) and (4) simplify to

–fv0ag = X ’res (5)

fu0ag = Y ’res (6)

[27] Thus, a net eastward (westward) wave forcinginduces a southward (northward) ageostrophic wind(denoted v0ag), while a net northward (southward) wave forc-ing induces an eastward (westward) ageostrophic wind (oru0ag). These simple diagnostics will be applied in the follow-ing section to predict the mesospheric flow in the presenceof GW drag with a zonal wave number 1 structure.

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Wave 1 FV AMP JAN

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Figure 6. Latitude versus altitude plots of amplitudes of the leading terms of the (left column) zonal and(right column) meridional momentum budgets. Estimates of the tidal contamination of u0, v0, and �0 havebeen removed prior to the calculations. (top row) Coriolis acceleration, (middle row) pressure gradientforce, and (bottom row) momentum residuals. Units are m s–1 day–1.

4.1. Relationship to Stratospheric PW 1[28] The simple relationships contained in (5)–(6) are

used to schematically illustrate the mesospheric circulationinduced by breaking gravity waves filtered in longitude byan underlying stratospheric PW. Figure 8 shows the gradientwinds associated with a zonal wave number 1 geopoten-tial wave in the lower part of the diagram. The thickarrows in the top panel of the figure qualitatively illus-trate the wind patterns in the mesosphere induced by GWmomentum forcing.

[29] The basic assumptions used to create Figure 8 are(1) stratospheric winds absorb GWs propagating with thesame zonal phase speeds, while transmitting waves propa-gating opposite to the wind [Lindzen, 1981], and (2) the GWfield is quasi-stationary within a uniform background windover the extent of the stratospheric PW. The momentumdeposited to the mesosphere by the breakdown of transmit-ted GWs creates drag upon the PW, denoted in the top partof Figure 8 by Fx and Fy. The ageostrophic winds inducedby mesospheric Fx and Fy in accordance with equations

(5) and (6) are denoted by the thick arrows. Thus, forexample, westward stratospheric perturbations winds (redarrow in stratosphere) filter out westward propagating GWs,resulting in a net eastward GW momentum flux in the lowermesosphere, which when deposited yields an eastward force(Fx > 0), which from (5) causes a southward ageostrophicwind (thick red arrow) in the mesosphere. According tothis simple model, GW forcing induces divergent (con-vergent) airflow above a positive (negative) stratosphericgeopotential perturbation.

[30] Figure9 shows TIDI PW 1 winds (minus the tidalcontribution) overlying stratospheric gradient winds forJanuary 2006. The southern flank of the stratospheric “ridge”(positive geopotential perturbation) indicates westward flowbetween 100ıE and 200ıE. In the mesosphere, a distinctlysouthward component is observed within the geopotentialminimum that lies about 50ı to the west of the strato-spheric ridge. Similarly, the east flank of the stratosphericridge (spanning 180ıE–230ıE) is characterized by south-ward flow that extends from 190ıE to 310ıE. In the

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FILTERED XMOMRES AMP 13.2

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Figure 7. January (top) zonal and (bottom) meridionalmomentum residuals at 13.2 scale heights (with error bars)for individual years. Black solid curves are 2005, and blackdashed curves are 2011. Black dotted curves are the momen-tum residuals associated with tidal aliasing.

mesosphere, there is an eastward component to the windsobserved at 60ıN between 150ıE and 200ıE. Away fromthe maxima and minima of the mesospheric geopotentialperturbation, the circulations are consistent with a gradientwind associated with the geopotential perturbation: cyclonic(counterclockwise) flow within the negative perturbation,and anticyclonic flow within the ridge.

[31] The mesospheric circulation thus exhibits a com-bination of gradient and divergent winds. The divergenceis observed primarily within the geopotential maxima andminima and is qualitatively consistent with the patterns dia-grammed in Figure 8, shifted about 40ı–50ı to the west.This departure from the simple model of GW-PW interplaymay arise from more realistic conditions such as change-able (nonstationary or spatially nonuniform) GW sources,refraction of GWs by background wind gradients, and vor-ticity of the stratospheric PW itself. These effects can leadto significant lateral deflection of GW energy between thestratosphere and the mesosphere [Senf and Achatz, 2011].

[32] Similar PW 1 patterns prevail in January 2005, 2009,and 2011 (not shown), although PW 1 amplitudes in 2009are very weak. Of the remaining years, the circulation duringJanuary 2007 appears to be strongly influenced by incom-plete sampling of tides (see Figure 5). In January 2010, themonthly averaged mesospheric circulation exhibits a higherdegree of geostrophy and therefore does not conform to thesimple GW filtering model shown in Figure 8:

4.2. Comparison With NOGAPS ALPHA[33] The MLT circulations observed in January 2005,

2006, 2009, and 2011 are consistent to varying degreeswith a simple model of GW-driven circulations. We nowcompare the observations with MLT winds predicted byNOGAPS. NOGAPS-ALPHA represents a developmentalprototype of the vertical extension of the Navy’s operationalforecast model. This vertical extension required inclusionof additional stratospheric and mesospheric physical param-eterizations, including radiative heating and cooling ratesthat account for nonlocal thermodynamic equilibrium, ozoneand water vapor transport and photochemistry, and nonoro-graphic gravity wave drag [Garcia et al., 2007; Eckermannet al., 2009]. The data assimilation system for NOGAPS cur-rently assimilates MLT temperatures from TIMED/SABERand EOS MLS. Six-hourly analyses are generated byNOGAPS-ALPHA production runs. These analyses realis-tically describe the large-scale circulation below 100 kmdown to periods near 12 h [Eckermann et al., 2009; Coyet al., 2009; Siskind et al., 2011; McCormack et al., 2009,2010; Nielson et al., 2010; Stevens et al., 2010].

[34] Figure 10 is analogous to Figure 9, generatedfrom six-hourly NOGAPS ALPHA analyses, averaged overJanuary 2006. Both figures show important similaritiesbetween 50ıN and 60ıN in the MLT. The MLT geopo-tential perturbations lead the stratospheric perturbations byapproximately one-fourth cycle in longitude. Whereas thestratospheric circulations are nearly geostrophic, the MLTflows are highly divergent. Between 50ıN and 60ıN, bothNOGAPS ALPHA and TIDI winds indicate a southward(northward) wind component co-located with the geopo-tential minimum (maximum). Both the NOGAPS modeland the observations indicate maximum southward (north-ward) MLT winds occurring roughly 60ı to the west ofthe westward (eastward) winds on the equatorward flankof the stratospheric “high.” At MLT geopotential nodes,NOGAPS meridional winds are consistent with gradient

Figure 8. (top) Ageostrophic wind in the latitude-longitudeplane induced by breaking of mesospheric GWs whosevertical transmission has been filtered by the stratosphericcirculation. (bottom) Stratospheric PW 1 geopotential heightand gradient winds, plotted as a function of latitudeand longitude.

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Tidal wind and geop aliasing removed

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Figure 9. (top) As in Figure 4, with estimated tidal contri-bution removed. (bottom) Geopotential and gradient windscomputed from MLS, at 6.1 scale heights (approximately40 km) for January 2006.

winds. At higher latitudes where TIDI observations arenot available, NOGAPS ALPHA exhibits some essentialfeatures of the simple model of GW-driven PW 1 in themesosphere: northward (southward) flow across the easternflank of the geopotential minimum (maximum) overlyingeastward (westward) winds on the poleward flank of thestratospheric perturbation. Thus, the NOGAPS ALPHA cir-culation in the mesosphere includes a divergent componentthat is consistent with the patterns in the simple model ofFigure 8.

[35] In summary, both NOGAPS and TIDI winds indicatethe combined effects of gradient winds and divergent flowthat are consistent with an idealized GW-driving scenariooffset to the west of the stratospheric PW. The divergentflow seen in NOGAPS is largely meridional, whereas TIDIwinds exhibit a zonal wind component within the MLTgeopotential maxima and minima. These differences and thedepartures of TIDI and NOGAPS ALPHA divergence fromthe simple model of Figure 8 could reflect more realistic GWsources and the effects of background conditions on GWpropagation, as mentioned in section 4.1.

5. Discussion and Summary[36] We have analyzed MLS geopotential and TIDI winds

in the Northern Hemisphere for the months of January of

the years 2005–2011. PW 1 exhibited strong amplitudes inthe stratosphere during a significant part of these months.We focus on mesospheric PW 1 in January 2006, whosebehavior was fairly representative of the years in which tidalaliasing does not obscure the planetary wave dynamics. Onaverage, MLT PW 1 during January is controlled by athree-way balance among the Coriolis acceleration, the pres-sure gradient force, and wave drag. Maximum southward(northward) winds are generally co-located with the geopo-tential minima (maxima). Thus, at high latitudes duringJanuary, gradient wind balance is not observed in climato-logical planetary-scale MLT winds. Our results underscorethe need for direct global wind measurements in the MLT.

[37] Comparison of the stratospheric and MLT PW 1 cir-culations indicates regions of cross-isobaric, or ageostrophicflow in the MLT overlying stratospheric geopotential max-ima and minima. The MLT circulations in January 2005,2006, and 2011 are qualitatively consistent with a simplemodel of MLT PW 1 forcing by drag associated with dissi-pating GWs that have been modulated by stratospheric PW1. MLT PW 1 circulations have been examined in NOGAPS-ALPHA, which includes parameterized nonorographic GWdrag. The agreement between TIDI and NOGAPS-ALPHAwinds during January 2006 provides an important validationof TIDI perturbation winds and supports our interpretationof GW drag as a source of PW 1 in the MLT.

[38] The purpose of this paper was to present observa-tional support for GW driving of MLT PW. However, other

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Figure 10. As in Figure 9, computed from NOGAPS-ALPHA six-hourly analyses averaged over January 2006.

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Figure 11. Daily amplitude of PW 1 geopotential (m) at 60ıN during January 2006. Thick dashed curveindicates stratopause level.

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Figure 12. EP flux vectors and PW 1 geopotential ampli-tude (m) on (top) 9 January and (bottom) 20 January 2006.The vector magnitude has been divided by density and Earthradius, giving units of m2 s–2. The z component has beenmultiplied by 100 for greater visibility. Red dashed curveindicates the stratopause level.

sources for MLT PW 1 must be considered. GWs excitedby orography vary significantly in longitude, and the dragassociated with these waves has been shown by McLandressand McFarlane [1993] to significantly enhance PW ampli-tudes in the mesosphere. There is also evidence for directvertical propagation of stratospheric PW 1 into the meso-sphere. This is indicated by the phase tilt in the monthlymean longitude-height structure shown in Figure 3 and thepresence of a gradient wind component to the mesosphericflow (Figure 9). To further investigate the pathways of PW1 propagation into the mesosphere, we compute the QGEliassen-Palm (EP) flux in spherical coordinates, defined as

F =�

0, –�0a cos�v0u0, �0a cos�f0v0� 0/‚0z

�(7)

F is a diagnostic of wave action with the useful property ofbeing oriented parallel to the wave group velocity [Andrewset al., 1987]. Daily values of the EP flux were calculatedusing MLS temperature, geopotential, and gradient winds.In view of the evidence for wave drag at 13 scale heights, Fis therefore only determined up to 12 scale heights.

[39] Figure 11 shows the evolution of PW 1 at 60ıN asseen in MLS geopotential. In the MLT, the wave exhibitsamplitude maxima on 4, 20, and 29 January. The top panelof Figure 12 shows F on 9 January, corresponding to the“second” MLT PW 1 amplitude peak. Stratospheric PW 1propagates to about 10 scale heights and is then deflected lat-erally. The PW 1 circulation observed in NOGAPS ALPHAat 13 scale heights for this day (not shown) is similar to thatseen in Figure 10 and supports the interpretation of a GWdrag source. The situation on 20 January, illustrated in thebottom panel of Figure 12, is quite different. On this day, theEP flux vectors have a prominent upward component in thehigh latitude upper stratosphere, indicating that the strato-spheric wave is a direct source of the MLT PW 1, as opposedto the indirect source from GW filtering.

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[40] The behavior of mesospheric PW 1 between 20January and 7 February 2006 has been investigated bySiskind et al. [2010]. Numerical experiments conducted withthe NOGAPS-ALPHA indicated that GW drag did not playa significant role in the PW 1 enhancements during thisinterval. However, regions of negative QG potential vor-ticity were identified in the high latitude stratopause inthe NOGAPS analysis, together with PW 1 EP flux diver-gence. These indicate the possibility of QG instability as anadditional MLT PW 1 source.

[41] Acknowledgments. The authors wish to thank the SABER andMLS science and data processing teams for their careful study, validation,and processing of these data sets. We thank W. Skinner and the TIDI team atthe University of Michigan for their processing and dissemination of TIDIwind products. We would like to express our appreciation to our AssociateEditor and our anonymous referees for their comprehensive reviews. Thisresearch was supported by NASA contract NNH09CF47C to NWRA and aNASA Heliophysics Theory grant to NRL.

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