the 6.5-day wave in the mesosphere and lower thermosphere: evidence for baroclinic/barotropic...

The 6.5-day wave in the mesosphere and lower thermosphere:

Evidence for baroclinic////barotropic instability

R. S. Lieberman,1 D. M. Riggin,1 S. J. Franke,2 A. H. Manson,3 C. Meek,3 T. Nakamura,4

T. Tsuda,4 R. A. Vincent,5 and I. Reid5

Received 21 December 2002; revised 11 May 2003; accepted 19 June 2003; published 24 October 2003.

[1] Awestward propagating zonal wave number 1 wave with a period near 6.5 days was aprominent feature in the mesosphere and lower thermosphere (MLT) during the 1994equinoxes. The meridional structure of the wave in the upper stratosphere and the MLT isconsistent with the 5-day wave structure predicted by normal mode theory. However, theamplitude increases sharply above 80 km, where the wave exhibits a highly organizedbaroclinic circulation. The eddy fluxes and the background state suggest that the wave isamplified by instability of the mesospheric winds. INDEX TERMS: 3332 Meteorology

and Atmospheric Dynamics: Mesospheric dynamics; 3334 Meteorology and Atmospheric Dynamics: Middle

atmosphere dynamics (0341, 0342); 3384 Meteorology and Atmospheric Dynamics: Waves and tides; 0342

Atmospheric Composition and Structure: Middle atmosphere—energy deposition; KEYWORDS: 6.5-day wave,

5-day wave, mesosphere

Citation: Lieberman, R. S., D. M. Riggin, S. J. Franke, A. H. Manson, C. Meek, T. Nakamura, T. Tsuda, R. A. Vincent, and I. Reid,

The 6.5-day wave in the mesosphere and lower thermosphere: Evidence for baroclinic/barotropic instability, J. Geophys. Res.,

108(D20), 4640, doi:10.1029/2002JD003349, 2003.

1. Introduction

[2] Atmospheric wave theory indicates the existence of afree oscillation with a zonal wave number 1 and a period ofapproximately 5 days [Longuett-Higgins, 1967]. This waveis the gravest symmetric meridional mode of westward-propagating wave number 1, and is generally known as the‘‘5-day’’ wave. The 5-day wave is an example of an atmo-spheric normal mode, or an oscillation that is not maintainedby systematic forcing. In the absence of continuous forcing,energy densities of normal modes decay with altitude awayfrom their sources [Andrews et al., 1987]. Consequently,normal modes exhibit no phase variation (or ‘‘tilt’’) withaltitude. Using the polarization relations developed byChapman and Lindzen [1970] for tides, it can be shown thatthe normal modes of a frictionless, isothermal resting atmo-sphere do not transport heat, momentum, or energy.[3] Numerical models have shown that the spatial structure

of the 5-day wave is fairly robust, although the wave issubject to localized modification by mean winds and dissi-pation. Specifically, Geisler and Dickinson [1976] and Salby[1981] found that wave amplitudes are magnified within

regions of westward zonal mean winds. The 5-day wavehas been identified in surface pressure, and in troposphericand middle atmosphere observations of temperature andgeopotential [Eliassen and Machenhauer, 1965; Maddenand Julian, 1972; Rodgers, 1976; Mechoso and Hartmann,1982; Hirota and Hirooka, 1984; Lawrence and Randel,1996; Hirooka, 2000]. A 5-day wave has also been detectedin lower mesospheric ozone by Rosenlof and Thomas [1990].[4] Mesospheric and lower thermospheric (MLT) obser-

vations indicate the presence of waves whose meridionalstructure is highly consistent with the 5-day wave [Wu et al.,1994; Riggin et al., 1997; Kovalam et al., 1999; Clark et al.,2002; Talaat et al., 2001, 2002]. However, many of thesestudies report periods closer to 6.5 days, and vertical phasetilt that is more pronounced than the solutions of normalmode theory. One possible interpretation of the observed6.5-day wave is that it is a 5-day wave whose period isDoppler-shifted to 6.5 days by the background zonal wind[Wu et al., 1994; Meyer and Forbes, 1997]. The enhancedvertical phase tilt results from local modification of thevertical wave number by the variable background wind.Talaat et al. [2001, 2002], on the other hand, interpretedthe 6.5-day wave as an internal, forced oscillation that isdynamically distinct from the 5-day wave. Their observa-tions indicated oscillatory vertical structure, and amplitudegrowth with altitude that exceeded the theoretical growthrates of normal modes below 80 km. Talaat et al. sug-gested that the vertically propagating wave transportedenergy and momentum upward from a presumed tropo-spheric source region, and that the growth of the wavewith height was merely that to be expected from thedecrease in atmospheric mass density.[5] An alternate interpretation of the 6.5-day wave is that

it is an unstable perturbation, that is, a wave whose

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D20, 4640, doi:10.1029/2002JD003349, 2003

1Colorado Research Associates Division, Northwest Research Associ-ates, Boulder, Colorado, USA.

2Department of Electrical and Computer Engineering, University ofIllinois, Urbana, Illinois, USA.

3Institute of Space and Atmospheric Studies, University of Saskatch-ewan, Saskatoon, Saskatchewan, Canada.

4Radio Atmospheric Science Center, Kyoto, Japan.5Department of Physics and Mathematical Physics, University of

Adelaide, Adelaide, South Australia, Australia.

Copyright 2003 by the American Geophysical Union.0148-0227/03/2002JD003349

ACL 9 - 1

amplitude grows in time. A westward propagating zonalwave number 1 with a period between 6.5–8 days has beenidentified as an unstable response in quasigeostrophic (QG)and primitive equation models [Pfister, 1985; Elson, 1990;Meyer and Forbes, 1997]. Observational support for insta-bility was provided in a study by Elson [1990] thatdocumented a prominent peak near 8 days in a zonal wavenumber 1 temperature spectrum from the Limb InfraredMonitor of the Stratosphere (LIMS) satellite instrument.The wave variance maximized in a region of the middleatmosphere where the background QG potential vorticityexhibited a negative meridional gradient: a necessary con-dition for instability.[6] The goal of the present study is to provide further

observational support for the 6.5-day wave as an unstablewave. We examine spectral decompositions of westwardpropagating waves observed in stratospheric gridded anal-yses, and in mesospheric satellite and ground-based dataduring March–April 1994, and September–October 1994.Section 2 describes the data sets and analysis methods usedin this study. Both winds and temperatures are available,enabling us to diagnose eddy heat and momentum fluxes,and their relationship to the background state. These resultsare presented in section 3. Our findings suggest that the6.5-day wave is a normal mode (i.e., a 5-day wave) that isstrongly modified by an unstable background state. Thisinterpretation suggests an analogy between the 6.5-daywave, and the unstable 2-day wave studied by Salby and

Callaghan [2001]. These points are further discussed insection 4.

2. Data and Analysis

2.1. MLT Satellite Data

[7] MLT satellite temperature and winds are provided bythe Upper Atmosphere Research Satellite (UARS) HighResolution Doppler Imager (HRDI). HRDI infers daytimewinds and temperatures between 60–110 km from the offsetand shapes of O2 band emission lines [Abreu et al., 1989;Hays et al., 1993; Ortland et al., 1998]. This study usesversion 11 HRDI L2B vector wind profiles, archived at theUniversity of Michigan. We focus on two monthlongsequences: Period 1 spanning 19 March to 17 April 1994and period 2 spanning 15 September to 12 October 1994.These intervals are chosen because they were identified inprevious studies as periods of strong 5–7-day wave activity[Wu et al., 1994; Riggin et al., 1997; Talaat et al., 2001].HRDI sampled the daytime MLT daily during both periods,alternating between warm side and cold side viewing eachday. This sampling pattern ensured sufficient continuityduring both nearly monthlong sequences to perform high-resolution space-time Fourier analyses. However, the rangeof latitudes thus sampled was confined between 40�S–30�Nduring period 1, and 20�S–40�N during period 2.[8] HRDI vector winds are derived from information

provided by upward and downward scanned pairs of line-

Figure 1. S-transform amplitudes of the zonal wind field for six radar sites. S-transforms werecomputed for each height between 84 and 94 km, and the absolute values were averaged. Horizontaldashed lines show a 6.5-day period for reference. See color version of this figure in the HTML.

ACL 9 - 2 LIEBERMAN ET AL.: THE 6.5-DAY WAVE AS AN INSTABILITY

of-sight (LOS) radiance profiles, viewed from two nearlyorthogonal directions. The effective latitudinal separationbetween two successive independent vector wind determi-nations is about 10–12� along the satellite track (generallyoriented north-south). Although temperature retrievals arecarried out independently for forward and backward-scanned LOS radiances, we average the forward and back-ward temperatures in order to make them volumetricallyconsistent with the winds. At latitudes where only forward-or backward-scanned profiles are available, we retain theunpaired temperature data for analysis, but not the winds.(As a result, it will be noted in Figures 3 and 7 that thelatitudinal coverage of HRDI temperature exceeds that ofthe vector winds.)[9] Space-time spectral analysis of HRDI data is carried

out using the asynoptic mapping method of Salby [1982].Wind and temperature profiles are sorted into 10-degreewide latitude bins, organized sequentially by orbit, andinterpolated linearly in longitude (l) and universal time (t)to equispaced positions on a satellite-relative coordinateaxis (s) defined by [Salby, 1982]

s ¼ c0j jl� t

1þ c20� �1=2 : ð1Þ

The parameter c0 is the rate at which measurements on anindividual node (e.g., ascending or descending) precess inlongitude at a fixed latitude. Because of the multiplicity ofdirections associated with HRDI’s scanning, an averagevalue of c0 over the time series is computed explicitly at

each latitude, which turns out to range within ±2% of �6.37radians day�1. At each latitude the mean is removed, andthe perturbation series are reversed, tapered, and fast Fouriertransformed with respect to the orbital coordinate s. Theresulting spectra, denoted ks, are related to the zonal wavenumber m and frequency (s) according to [Salby, 1982]

ks ¼c0j jm� s

1þ c2ð Þ1=2: ð2Þ

The Nyquist period is approximately 2 days, while theNyquist zonal wave number is 4.

2.2. MLT Radar Winds

[10] The radar data analyzed in this paper were obtainedfrom five medium frequency (MF) radars, and from ameteor scatter radar. The MF radars are located at Saska-toon, Canada (52�N,107�W), Urbana, Illinois (40�N,88�W),Kauai, Hawaii (22�N,159�W), Christmas Island, Republicof Kiribati (2�N,157�W), and Adelaide, Australia(35�S,138�E). The meteor scatter radar is located at Jakarta,Indonesia (6�S,108�E). Both MF and meteor-scatter radarsmake continuous measurements of the winds with �4 kmheight resolution.[11] MF radars operate at frequencies near 2 MHz

and obtain partial reflection returns from mesosphericionization. The echoes are received by spatially separatedantennas and analyzed using full-correlation analysis (theso-called spaced antenna drift technique) [Holdsworth andReid, 1995]. The MF radars measure winds from 78 to

Figure 2. As in Figure 1, but for the meridional wind. See color version of this figure in the HTML.

LIEBERMAN ET AL.: THE 6.5-DAY WAVE AS AN INSTABILITY ACL 9 - 3

98 km with the highest data rate around 90 km. Morecomplete descriptions of the MF radar systems at Hawaiiand Christmas Island are given by Fritts and Isler [1992]and Vincent and Lessicar [1991].[12] The Jakarta meteor wind radar operates at a frequency

near 32MHz. It measures winds over an altitude range of 70–120 km with a maximum data rate also around 90 km. TheJakarta radar uses the Doppler technique with spatiallyseparated antennas and an algorithm for determining thelocation of meteor echoes. The use of echolocation providesmore accurate wind estimates, and makes it possible to use awide beam which captures more meteor echoes. Even withthis enhancement, meteor scatter radars typically have alower data rate than partial reflection radars over the heightswhere both types of systems provide data. A more completedescription of the Jakarta radar system is provided by Tsudaet al. [1995]. For these studies, the radar velocity estimateswere averaged into 1-hour time bins and we restricted the

analyses to heights between 84 and 94 km where the qualityof data from both types of radars was best.

2.3. Stratospheric Analyses

[13] Stratospheric temperatures were monitored during1994 by the UARS Halogen Occultation Experiment(HALOE) and the Microwave Limb Sounder (MLS). How-ever, HALOE’s sunrise-sunset sampling pattern providesrelatively little spatiotemporal overlap with HRDI’s mea-surements. Moreover, MLS O2 63 GHz band temperatureswere unavailable for lengthy segments of both the equinoxperiods examined in with HRDI MLT data. Thereforestratospheric temperatures and winds are obtained fromdaily gridded analyses.[14] The U.K. Meteorological Office (hereafter the Met

Office, or METO) produces daily sets of stratosphericdata assimilations at 12Z beginning in October 1991, andextending to the present-day. The assimilation model data

Figure 3. Latitude-longitude mappings of HRDI westward zonal wave number 1 T 0 contours andhorizontal wind vectors reconstructed with periods of approximately 5.5 and 7.2 days on 23 March 1994(top) and 26 September 1994 (bottom). Contour interval is 1 K. See color version of this figure in theHTML.


sets are described by Swinbank and O’Neill [1994]. METO‘‘data’’ are composed of 3-dimensional fields of tempera-ture, geopotential height, and wind component. The hori-zontal resolution is 2.5� latitude by 3.75� longitude, anddata are reported on 22 pressure levels ranging from1000 hPa to 0.3 hPa (�0–56 km).[15] METO data were constructed mainly from NOAA

polar orbiting meteorological satellite observations of tem-perature, and from radiosonde measurements. The data setswere derived independently of any observations made byUARS instruments. It should be borne in mind that thevertical resolution of METO data in the upper stratosphereis limited by the deep vertical weighting functions of theinstruments comprising the TIROS Operational VerticalSounder (TOVS) package on the NOAA operationalsatellites. These include the Microwave Sounding Unit(MSU), the Stratospheric Sounding Unit (SSU), and HighResolution Infrared Radiation Sounder/2 (HIRS/2). In the

upper stratosphere, the satellite data were assimilated invertical layers at 1–0.4 hPa (�48–55 km) and 2–1 hPa(�42–48 km).[16] The METO fields were interpolated from pressure

surfaces to geometric height surfaces using the geopotentialheight field. The 6.5-day wave was then extracted from thefields using a 2-dimensional frequency domain filter. Ateach time step during 1994, the zonal mean of u, v, and Twas subtracted to yield perturbation quantities u0, v0, and T 0.Space-time spectral analyses are carried out on the pertur-bation fields by applying a fast Fourier transform (FFT) inlongitude at each time step, followed by an FFTwith respectto time of the zonal wave number coefficients. A windowwas applied to the frequency domain representations withthe desired zonal wave number (1 or 2) and a taperedpassband in the frequency domain with unattenuatedperiods between 5 and 8 days (or 3–5 days in the case ofthe s = 2 wave component). The resulting 1-D filtered field

Figure 4. Latitude-longitude mappings of METO westward zonal wave number 1 temperature andhorizontal wind vectors reconstructed with periods of 5–8 days on 23 March at 100 hPa (bottom,�16 km), 14.687 hPa (center, �30 km), and 1 hPa (top, �48 km). Length of the longest wind vectorcorresponds to 1.6 m s�1 at 100 hPa, 2.3 m s�1 at 14.687 hPa, and 4.5 m s�1 at 1 hPa. Contour interval is0.2 K. The zero contour is not plotted.


was then inverse FFT’ed back to the time domain. Thismethodology was applied to produce both the METOmappings and vertical phase-amplitude slices.

3. Wave Analyses

[17] Temporal variations in radar winds are examinedusing the S-transform method. This is a technique fortemporal localization of the Fourier transform which isconceptually similar to wavelets, but which has severalunique advantages [Stockwell et al., 1996; Stockwell andLowe, 2001]. The S-transform has an absolute phase refer-ence and collapses in the time domain to give the Fourierspectrum exactly. The amplitudes are easily interpretedsince they are the same as would be derived from least

squares fits of sinusoids over Gaussian windows. TheGaussian localizing function length is proportional to waveperiod with a standard deviation equal to the wave period.The standard deviation of a Gaussian is where the peakvalue falls to �61% of the maximum, and the window fallsto half its peak value at �1.18 standard deviations. TheS-transform is conceptually similar to the Morlet wavelet,but in a simple implementation it provides better frequencyresolution, since the natural units are linear in frequency asopposed to logarithmic in frequency for the Morlet wavelet.[18] Figures 1 and 2 show S-transform time-frequency

representations (TFR) of zonal and meridional winds,respectively, for 1994 obtained at the six radar sites whosecoordinates are given in the previous section. Each of theTFRs was generated by averaging S-transform amplitudes

Figure 5. Latitude-longitude mappings of METO westward zonal wave number 1 temperature andhorizontal wind vectors reconstructed with periods of 5–8 days on 26 September at 100 hPa (bottom,�16 km), 14.687 hPa (center, �30 km), and 1 hPa (top, �48 km). Length of the longest wind vectorcorresponds to 1.6 m s�1 at 100 hPa, 3.6 m s�1 at 14.687 hPa, and 5.2 m s�1 at 1 hPa. Contour interval is0.2 K. The zero contour is not plotted.


over heights from 84 to 94 km. For the 6.5-day wave, thehalf-amplitude width of the Gaussian localizing functionturns out to be about 16.5 days, so the S-transform is onlysensitive to variability on this timescale or longer.[19] Figure 1 indicates power in the zonal wind compo-

nent at both 5- and 6.5-day periods. The zonal windresponses are most prominent at Hawaii, Christmas Island,and Jakarta. The strongest zonal activity is observed at thesesites between August and November, with additionalresponses at Jakarta between March and May. The6.5-day wave generally occurs in brief bursts of activity,and has a duration which is comparable to the timeresolution of the S-transform itself. Bursts of 6.5-day zonalwind activity are often preceded by activity at a period ofaround 4 days, and accompanied by 5-day activity. The 5-and 6.5-day zonal wind responses at Urbana and Adelaideare more limited, confined to June and October at Urbana,and in August at Adelaide. Responses at the 4-day periodare more prominent in the meridional winds (Figure 2),particularly at Urbana and Saskatoon.[20] Space-time spectral analyses of satellite and METO

time series indicate that the power in 6.5-day MLT zonalwinds is associated with zonal wave number 1. Figure 3shows representative latitude-longitude HRDI zonal wavenumber 1 wind and temperatures mappings, referenced to23 March 1994 and 26 September 1994. Only the HRDIspectral coefficients corresponding to westward periodsbetween 5 and 8 days are used for the mappings in Figure 3.For the remainder of this paper, the terms ‘‘5-day wave’’and ‘‘6.5-day wave’’ shall be used interchangeably whenreferring to westward zonal wave number 1 variabilitybetween 5–8 days. The meridional structures of u0, v0, and

T 0 are consistent with the theoretical predictions of the so-called 5-day wave [Longuett-Higgins, 1967]. The wavefields form a single rotational circulation in each hemi-sphere, with a global pattern that suggests symmetry aboutthe equator. However, instead of exhibiting a quadraturephase relationship for normal modes [Chapman andLindzen, 1970], warm anomalies are collocated with pole-ward flows, and cold anomalies with equatorward flow.These correlations tend to be highest between 80 and100 km. Such patterns of poleward heat flux are associatedwith baroclinic conversions between zonal mean and eddyavailable potential energy [Lorenz, 1967; Holton, 1992].[21] METO gridded fields have been used to extend our

analyses of the 5–8-day variability beyond HRDI’s altitudeand latitude coverage. Figures 4 and 5 show representativelatitude-longitude METO zonal wave number 1 mappingsreconstructed with westward periods between 5 and 8 daysat approximately 1, 14.7 and 100 hPa on 23 March 1994and 26 September 1994, respectively. The mappings con-firm the findings of Talaat et al. [2001, 2002] that the 6.5-day wave is a global-scale feature with origins below theMLT. However, the mappings also suggest that the waveundergoes considerable variation as it traverses the strato-sphere and the mesosphere. The circulation on 23 March at1 hPa (Figure 4) is stronger in the Northern Hemisphere,and is consistent with a developing baroclinic wave. Thishemispheric asymmetry is present at 14.7 and 100 hPa aswell, but with the baroclinic region at 14.7 hPa confinedpoleward of 60�N. On 26 September (Figure 5), the 6.5-daywave exhibits neutral structure in the Northern Hemisphere,but is slightly stronger and highly distorted in the SouthernHemisphere. As on 23 March, the hemispheric asymmetry

Figure 6. Phase (top) and amplitude (bottom) versus height of u0 (left), v0 (center), and T 0 (right) on26 September 1994.


is very pronounced at 14.7 and 100 hPa, where the wave issignificantly stronger at the southern polar latitudes. Theconfinement of the 6.5-day wave to polar regions in thelower and mid-stratosphere on 26 September is consistentwith the findings of Cheong and Kimura [1997]. Theyanalyzed European Centre for Medium-Range WeatherForecasting (ECMWF) data between 1984–1991, and spec-ulated on a possible Antarctic excitation source.[22] The transitions between neutral and developing wave

structure indicated in Figures 3–5 suggest that the verticalstructure of the 6.5-day may be quite variable. Figure 6depicts the vertical structure of zonal wave number 1between 5–8 days in u0, v0 and T 0 at 10�N on 26 September.METO data are used to construct the plot below 55 km, andHRDI data are used above 55 km. The amplitude of u0

increases monotonically in the stratosphere, and between 70and �90 km. The variations in v0 and T 0 amplitudes are notas smooth in altitude, but increase overall with altitude in

the MLT. The phase of u0 is steady between 40 and 55 km,and decreases systematically above 60 km, sweepingthrough 360� between 60 and 110 km. Similar behavior isnoted on 23 March at 10�S (not shown).[23] Space-time analyses of HRDI data indicate that the

variance near 4 days is associated with a westward-propa-gating zonal wave number 2 wave. This finding is consis-tent with reports of 4-day variance in METO analyses byPogoreltsev et al. [2002] and by Talaat et al. [2002].However, the zonal wave number 2 patterns are morevariable than wave number 1 in amplitude and phase overintervals 1 and 2, and are not always consistent with normalmode structures. For example, Figure 7 shows HRDIlatitude-longitude mappings reconstructed in the mannerdescribed for Figure 3. In this case, the zonal wave number2 fields are referenced to 30 March 1994 and 19 September1994, using spectral coefficients corresponding to westwardperiods between 3 and 5 days. Analyses for both days

Figure 7. Latitude-longitude mappings of westward zonal wave number 2 T 0 contours and horizontalwind vectors reconstructed with periods of approximately 3.2, 3.6, 4.3, and 5.3 days on 30 March 1994(top) and periods 3.2, 3.6, 4.1, and 4.9 days on 19 September 1994 (bottom). Contour interval is 1 K. Theperiods for the March and September mappings are not identical because of the different lengths (andspectral resolution) between HRDI data intervals 1 and 2 (see section 2.1). See color version of this figurein the HTML.


exhibit rotational circulations at 95 km, but with substantialamplitude near or at the equator. We note that the circulationsat 95 km are consistent with developing baroclinic waves inthe Northern, but not the Southern Hemisphere. The strato-spheric patterns (Figures 8 and 9), on the other hand, arecharacterized by midlatitude circulations that are symmetricabout the equator. Whereas v0 and T0 exhibit in-phase or out-of-phase relationships at 95 km and near 50 km on 30March,the two fields are in quadrature near 30 km. Thus thestratospheric patterns are more consistent with theoreticalpredictions for the neutral, second symmetric mode of zonalwave number 2 [Salby, 1981]; moreover, they do not appearto be structurally linked with the MLT waves. The primarysignificance of the perturbations with zonal wave number 2 istheir angular phase speed s/s (here s is the zonal wavenumber), which is close to that of the 6.5-day wave with azonal wave number 1. The presence of organized barocliniccirculations in zonal wave numbers 1 and 2 with uniformphase speeds suggests that the two perturbations may have

been excited within an unstable wind layer as members of aquasi-nondispersive wave ‘‘packet.’’ This interpretation ismotivated in part by the findings of Manney and Randel[1993], who speculated on barotropic instability as the sourceof an eastward-traveling, quasi-nondispersive ‘‘blob’’ thatcircles the winter pole every 4 days.[24] The vertical structure of the 6.5-day wave and the

circulations associated with zonal wave numbers 1 and 2suggest that the waves may transport heat and momentumvertically and meridionally, and interact with the mean flow.The effects of eddy heat and momentum fluxes are repre-sented in a compact form by making use of the Eliassen-Palm, or E-P flux vector (F), defined by

Ff ¼ r0a cosf �Uzv0q0=�qz � u0v0� �

ð3Þ

Fz ¼ r0a cosf f � a cosfð Þ�1U cosf� �

f

h iv0q0=�qz � u0w0

n o

ð4Þ

Figure 8. Latitude-longitude mappings of METO westward zonal wave number 2 T 0 contours andhorizontal wind vectors reconstructed with periods between 3 and 5 days on 30 March 1994 at 1 hPa(top, �48 km) and 14.7 hPa (bottom, �30 km). Length of maximum vector is 2.1 m s�1 at 1 hPa, and1.7 m s�1 at 14.7 hPa. Contour interval is 0.2 K. The zero contour is not plotted.


in spherical coordinates. We compute w0 from T 0, u0 and v0

using the thermodynamic energy equation in sphericalcoordinates [Andrews et al., 1987]. In the MLT, advectiveterms are computed from HRDI zonal mean winds.However, CIRA-86 zonal mean temperatures �Tð Þ [Fleminget al., 1990] are used for our calculations, because ofcontamination of HRDI �T by unresolved migrating tidesat equatorial latitudes [Yudin et al., 1998; Lieberman,1999].[25] The divergence of F per unit mass is an indicator of

wave driving [Andrews, 1987]. Figures 10 and 11 show thedirection of F, and contours of (r0a cos f)�1r F forperiods 1 and 2. The calculations are performed on pertur-bations consisting of the sum of zonal wave number 1filtered between 5–8 days and zonal wave number 2 filteredbetween 3–5 days. We note that separate data sets are usedfor the stratospheric (METO) and mesospheric (HRDI)analyses, which we have made no attempt to blend. (Notethat the E-P fluxes and their divergence per unit mass are

plotted on scaled log-pressure levels, as opposed to geo-metric altitude surfaces.)[26] Inspection of Figures 10 and 11 readily shows that the

strongest wave driving generally occurs in the MLT, and isdirected westward with peak values between 6 and 10 m s�1

day�1. Centers of eastward wave driving (or E-P fluxdivergence per unit mass) are layered between the conver-gent regions, and are usually associated with increases in thewind and temperature perturbation amplitudes. A prominentdivergent region is observed during period 1 (Figure 10),centered at 60 km between the equator and 20�S. In thestratosphere, the strongest values of E-P flux divergence arefound at high northern latitudes during period I and highsouthern latitudes during period 2.[27] The mechanisms for the westward driving in the

MLT are the convergence of meridional transports of heatand zonal momentum. The heat transport process is illus-trated by the in-phase and antiphase relationships betweenT 0 and v0 (Figures 3–5 and 7–8). Meridional transport of

Figure 9. Latitude-longitude mappings of METO westward zonal wave number 2 T 0 contours andhorizontal wind vectors reconstructed with periods between 3 and 5 days on 19 September 1994 at 1 hPa(top, �48 km) and 14.7 hPa (bottom, �30 km). Length of maximum vector is 2.9 m s�1 at 1 hPa, and1.5 m s�1 at 14.7 hPa. Contour interval is 0.2 K. The zero contour is not plotted.


Figure 10. Direction of E-P flux vectors and divergence of E-P flux per unit mass (contours), averagedbetween 22 March and 14 April 1994. The vertical component of the plotted vectors is scaled by 100, andthe vectors are subsequently normalized to unit length. Contour levels are 1 m s�1 day�1 in thestratospheric plot (bottom) and 2 m s�1 day�1 in the MLT plot (top). Negative values are shaded.

Figure 11. Direction of E-P flux vectors and divergence of E-P flux per unit mass (contours), averagedbetween 18 September and 9 October 1994. Contour intervals and vector scalings as in Figure 10.


zonal momentum is evidenced in Figures 3–5 and 7–8 byslanted (as opposed to a strictly horizontal or vertical) windvectors in the latitude-longitude plane. Inspection of thehorizontal eddy momentum flux divergence (not shown)indicates that this process is strongest above 80 km within20� of the equator. This process is associated with abarotropic conversion between eddy and mean wind kineticenergy [Holton, 1992]. The vertical divergence of meridio-nal heat flux (not shown) exhibits a broad structure inlatitude, maximizing between 30� and 40� above 90 km.This process is associated with a baroclinic conversionbetween eddy and mean wind available potential energy[Holton, 1992].[28] The centers of divergent E-P flux per unit mass are

indicative of wave sources. The baroclinic and barotropicenergy transitions implied by the perturbation heat andmomentum fluxes motivate an examination of instabilityof the mean state as a possible source for the 6.5-day wave.Figures 12 and 13 show zonal mean winds �Uð Þ, alongwith regions of negative meridional gradient of zonallyaveraged QG potential vorticity �qð Þ. In order to increasethe latitudinal coverage in the MLT, HRDI winds arecomposited using data from 1992, 1993, and 1994 for thefull two-month periods of March–April (Figure 12) andSeptember–October (Figure 13). In the stratosphere,METO winds from March–April 1994 (Figure 12) and

September– October 1994 (Figure 13) are used. CIRA-86zonal mean temperatures are used for the calculations of �qyin the mesosphere.[29] Westward winds dominate the tropical latitudes in

the stratosphere, and the tropical MLTwinds below 100 km.Above 95 km, westward winds prevail at middle and highlatitudes during period 1. Negative values of �qy occur inzones of shear and curvature of the westward MLT wind.During period 1, these are seen near 70 km at 20�S, andbetween 90 and 105 km centered at 45�S and 50�N. Duringperiod 2, these areas are observed around 70 km at 25�N,and at 90 km centered at 50�N. These pockets of negative �qycan be matched with divergent E-P fluxes. Such colloca-tions support the interpretation of wave enhancement in theMLT by instability of the zonal mean wind.

4. Summary

[30] A westward-traveling 6.5-day wave has been docu-mented in METO and HRDI winds and temperatures, and inradar winds during equinox periods in 1994. The waveappears to emanate from the polar region in the troposphere,and develop as a neutral normal mode (i.e., a 5-day wave) inthe stratosphere. This behavior is consistent with the clima-tological findings of Cheong and Kimura [1997] in theSouthern Hemisphere. In the upper stratosphere and the

Figure 12. Zonal mean zonal winds. Stratospheric winds are computed from METO analyses for Marchand April 1994. MLT winds are computed from HRDI composited from March and April values during1992, 1993, and 1994, in order to increase latitudinal coverage. Contour interval is 10 m s�1. Shadedareas denote negative d�q=dy.


MLT, the wave propagates vertically, and exhibits wind-temperature phase relationships suggesting growth due tobaroclinic and barotropic instability. The background windand temperature fields during equinox exhibit unstablestructures within the MLT westward jets. Our interpretationof the 6.5-day wave as an neutral normal mode thatamplifies in an unstable background state is supported bytheoretical studies of Salby and Callaghan [2001]. Theymodeled the 2-day wave as a normal mode whose eigen-frequency is allowed to be complex. The wave was shownto amplify rapidly by extracting energy from an unstablemean flow. Our results suggest an analogy between the6.5-day wave and the 2-day wave in this regard.[31] Additional variability was also detected in zonal wave

number 2 between 3 and 4 days. The 4-day wave exhibitsneutral normal mode structure in the stratosphere, and atransition to non-neutral behavior in the MLT. The 6.5-dayand the 4-day waves propagate zonally with a similar angularphase speed. These properties suggest a common origin ofthe waves within an unstable background wind.[32] Our case for instability is largely predicated upon the

application of QG instability theory to HRDI and METOdata diagnostics. However, the 6.5-day wave is a global-scale phenomenon, and some assumptions of QG theorybecome problematic near the equator. HRDI MLT �T and �Uare vulnerable to contamination by partially filtered diurnal

tides, because of the daytime-only nature of the measure-ments [Hays et al., 1994; Lieberman, 1999]. A definitivestudy of the 6.5-day wave and its connections to instabilityrequires two key elements: a data set allowing a fairlyprecise definition of the MLT background state, and a time-dependent primitive equation model with which to diagnosewave evolution and mean flow interaction. Numericalexperiments with the NCAR Thermosphere-Ionosphere-Mesosphere General Circulation Model (TIME-GCM) havefound that the structure and stability of the mean wind, andthe location of the critical layers of the 6.5-day wave allaffect the wave response in the MLT region. The peak waveresponses in the TIME-GCM MLT correspond to periodswhen regions with negative �qy are present in the MLTregion [Liu et al., 2002].

[33] Acknowledgments. We thank Richard Swinbank, Walter Rob-inson, Chris Meyer, and Han-Li Liu for helpful discussions and sugges-tions. Tim Dunkerton provided valuable assistance in using the METOgridded analyses. This research was supported by the Division of Atmo-spheric Sciences of the National Science Foundation under grants ATM-9813774 and ATM-0002656 and by NASA contract NASW-0040.

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Figure 13. Zonal mean zonal winds. Stratospheric winds are computed from METO analysis forSeptember and October 1994. MLT winds are computed from HRDI composited from September andOctober values during 1992, 1993, and 1994, in order to increase latitudinal coverage. Contour interval is10 m s�1. Shaded areas denote negative d�q=dy.


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��S. J. Franke, Department of Electrical and Computer Engineering,

University of Illinois, 319 Space Science and Remote Sensing Laboratory,1308 W. Main Street, Urbana, IL 61801, USA. ([email protected])R. S. Lieberman and D. M. Riggin, Colorado Research Associates

Division, Northwest Research Associates, 3380 Mitchell Lane, Boulder, CO80303, USA. ([email protected]; [email protected])A. H. Manson and C. Meek, Institute of Space and Atmospheric Studies,

University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan,Canada S7N 5E2. ([email protected]; [email protected])T. Nakamura and T. Tsuda, Radio Atmospheric Science Center, Gokasho,

Uji, Kyoto 611-0011, Japan. ([email protected]; [email protected])I. Reid and R. A. Vincent, Department of Physics and Mathematical

Physics, University of Adelaide, GPO Box 498, Adelaide, SA 5001,Australia. ([email protected]; [email protected])


the 6.5-day wave in the mesosphere and lower thermosphere: evidence for baroclinic/barotropic...

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