Planetary wave-gravity wave interactions during mesosphericinversion layer events

K. Ramesh,1 S. Sridharan,2 K. Raghunath,2 S. Vijaya Bhaskara Rao,1 andY. Bhavani Kumar2

Received 24 December 2012; revised 13 May 2013; accepted 3 June 2013; published 3 July 2013.

[1] Rayleigh lidar temperature observations over Gadanki (13.5°N, 79.2°E) show a fewmesospheric inversion layer (MIL) events during 20–25 January 2007. The zonal meanremoved SABER temperature shows warm anomalies around 50°E and 275°E indicating thepresence of planetary wave of zonal wave number 2. The MIL amplitudes in SABERtemperature averaged for 10°N–15°N and 70°E–90°E show a clear 2 day wave modulationduring 20–28 January 2007. Prior to 20 January 2007, a strong 2day wave (zonal wavenumber 2) is observed in the height region of 80–90 km and it gets largely suppressed during20–26 January 2007 as the condition for vertical propagation is not favorable, though itprevails at lower heights. The 10 day mean zonal wind over Tirunelveli (8.7°N, 77.8°E)shows deceleration of eastward winds indicating the westward drag due to wave dissipation.The nightly mean MF radar observed zonal winds show the presence of alternating eastwardand westward winds during the period of 20–26 January 2007. The two dimensional spectrumof Rayleigh lidar temperature observations available for the nights of 20, 22, and 24 January2007 shows the presence of gravity wave activity with periods 18min, 38min, 38min, andvertical wavelengths 6.4 km, 4.0 km, 6.4 km respectively. From the dispersion relation ofgravity waves, it is inferred that these waves are internal gravity waves rather than inertiagravity waves with the horizontal phase speeds of ~40m/s, ~37m/s, and ~50m/s respectively.Assuming the gravity waves are eastward propagating waves, they get absorbed only in theeastward local wind fields of the planetary wave thereby causing turbulence and eddydiffusion which can be inferred from the estimation of large drag force due to the breaking ofgravity wave leading to the formation of large amplitude inversion events in alternate nights.The present study shows that, the mesospheric temperature inversion is caused mainly due tothe gravity wave breaking and the inversion amplitude may get modulated by the interactionbetween gravity waves and planetary waves. The eddy diffusion associated with gravity wavedrag may also cause suppression in the planetary wave activity.

Citation: Ramesh, K., S. Sridharan, K. Raghunath, S. Vijaya Bhaskara Rao, and Y. Bhavani Kumar (2013), Planetarywave-gravity wave interactions during mesospheric inversion layer events, J. Geophys. Res. Space Physics, 118, 4503–4515,doi:10.1002/jgra.50379.

1. Introduction

[2] The layer of enhanced temperature with several kilo-meters thickness showing the positive lapse rate at the bottomand is superposed upon the characteristically decreasing tem-perature in the mesosphere is known as mesospheric inver-sion layer (MIL). There are various causative mechanismssuggested for the formation of these layers [Meriwether andGardner, 2000; Meriwether and Gerrard, 2004] which

include the gravity wave breaking and the planetary wavecritical level interaction.[3] According to the linear saturation theory, the amplitude

of the gravity wave increases exponentially as it propagatesvertically upward in response to the decreasing atmosphericdensity and breaks at a particular altitude where it becomesconvectively unstable. The wave when breaks deposits a netmomentum in the mean flow and accelerates the backgroundwind in the direction of propagation of the wave and causesa downward heat flux, which results in cooling of the atmo-sphere at the breaking height [Walterscheid, 1981; Gardnerand Yang, 1998; Ramesh and Sridharan, 2012]. This down-ward heat flux raises the heating at the bottom of the wave fieldwhich is maintained as an inversion layer. Though the down-ward heat flux due to gravity wave breaking is an importantsource of heat budget in the mesosphere, the resultant gravitywave induced cooling effects in the mean zonal flow could bedue to the effect of wave drag.

1Department of Physics, Sri Venkateswara University, Tirupati, India.2National Atmospheric Research Laboratory, DoS, Gadanki, India.

Corresponding author: K. Ramesh,Department of Physics, Sri VenkateswaraUniversity, Tirupati, AP 517502, India. (karanamram@gmail.com)

©2013. American Geophysical Union. All Rights Reserved.2169-9380/13/10.1002/jgra.50379

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JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 4503–4515, doi:10.1002/jgra.50379, 2013

[4] Charney and Drazin [1961] explained about the verti-cal propagation of planetary scale disturbances from lowerto upper atmosphere. The energy in the form of heat and mo-mentum flux carried by the small scale disturbances modifiesthe zonal mean flow when they propagate from lower to up-per atmosphere. They also suggested that, the planetary scaledisturbances could propagate vertically only when the back-ground winds are westerly relative to the phase speed andhaving lesser magnitude than a particular “critical velocity”which is inversely proportional to the zonal and meridionalwave numbers. Lindzen [1981] proposed a simple theorywhich suggests that the drag forces due to the gravity wavebreaking decelerates the mean zonal winds to balance themomentum budget in the mesosphere. He also suggested thatthe drag force peaks near the lowest level at which the gravitywave breaks. Holton [1983] discussed about the effect ofgravity wave breaking on the general circulation of middleatmosphere. He suggested the vertical eddy diffusion gener-ated by gravity wave breaking modifies the zonal mean flowand causes the planetary wave dissipation in the mesosphere.The momentum transferred by vertically propagating internalgravity waves could attenuate the amplitudes of planetarywaves when they interact with each other [Lindzen, 1984;Schoeberl and Strobel, 1984].[5] Miyahara [1985] explained about the suppression of

planetary wave by the internal gravity waves in the meso-sphere. In the absence of dissipation, the wave amplitudeincreases as ez/2H while propagating vertically upward andgreatly reduces by the drag forces due to breaking of internalgravity waves. Salby et al. [2002] described about the rela-tionship between the mesospheric inversion layers and theplanetary wave activity from UARS/Microwave LimbSounder. They suggested that the strong absorption of theplanetary wave in the mesospheric inversion region is dueto the turbulent mixing associated with gravity wave break-ing. They also described how the phase shift of the wavegeopotential related to the planetary wave activity duringMIL event. Sassi et al. [2002] discussed about the contribu-tion of planetary waves in causing MILs using WholeAtmosphere Community Climate Model (WACCM). Theysuggested that the existence of the critical level for the plan-etary waves in the mesosphere is due to the deposition ofeasterly momentum by small scale gravity waves [Matsuno,1982; Holton, 1983; Garcia and Solomon, 1985] so that theplanetary waves are dissipated at this level.[6] Recently, the work executed by Ramesh and Sridharan

[2012] discussed about a large mesospheric inversion layer(MIL) event with an amplitude of ~50K and thickness of~4.5 km observed in the nightly mean vertical temperatureprofile using Rayleigh lidar over Gadanki (13.5°N, 79.2°E)on 24 January 2007. This large inversion is due to the breakingof a small scale internal gravity wave (T= 33min., λz = 6.4 km)in the height region of 80–84 km. The turbulent eddy diffusioncoefficient largely increased from bottom to the top of theinversion layer due to the wave breaking. It is observedfrom the wavelet analysis performed on Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics-Soundingof the Atmosphere using Broadband Emission Radiometry(TIMED-SABER) temperature perturbations of January2007, a vertically propagating 2 day planetary wave wassuppressed in the same inversion height region just above~84 km. It is considered that the large eddy diffusion caused

by the breaking of above mentioned small scale gravity wavecould be the reason for this planetary wave dissipation.[7] Based on the several investigations mentioned above,

the present work tries to investigate the role of interactionbetween the 2 day planetary wave and the small scale internalgravity wave in the occurrence and modulation of MILsusing Rayleigh Lidar temperatures, MF radar winds,TIMED Doppler Interferometer (TIDI) winds, and TIMED-SABER temperatures.

2. Instrumentation and Data Analysis

2.1. Rayleigh Lidar Temperature Measurements

[8] The Rayleigh Lidar system with improved laser poweris in continuous operational mode on all cloud free nightssince mid-January 2007 installed at National AtmosphericResearch Laboratory (NARL), Department of Space,Gadanki (13.5°N, 79.2°E), India. From this lidar, the verticaltemperature profile can be derived using the method given byHauchecorne and Chanin [1980]. This lidar gives the verti-cal atmospheric density profile which is proportional to theback scattered photon counts from atmospheric air moleculesabove 30 km where the aerosol distribution is neglected.Taking the pressure at the top of the height range (90 km)from the model, the pressure profile is computed using themeasured density profile. Applying the ideal gas equation,the vertical temperature profiles T(z) can be calculated usingthe expression given by

T zið Þ ¼ M g zið Þ ΔzRLog 1þ Xð Þ where X ¼ ρ zið Þg zið Þ Δz

P zi þ Δz=2ð Þ (1)

and the uncertainty in the measurement of temperature isgiven by

δT zið ÞT zið Þ ¼ δLog 1þ Xð Þ

Log 1þ Xð Þ ¼ δX1þ Xð ÞLog 1þ Xð Þ (2)

[9] More details on this data analysis and NARL new lidarsystem specifications can be obtained from Siva Kumar et al.[2003] and Ramesh and Sridharan [2012]. Here, the in-creased laser power (up to 30W) made possible to derivethe vertical temperatures up to ~90 km with relatively lessuncertainties during the observational period.

2.2. MF Radar Wind Measurements Over Tirunelveli

[10] The zonal and meridional winds are obtained fromMedium Frequency (MF) radar at Tirunelveli (8.7°N,77.8°E) which is in operational mode with the frequency of1.98MHz maintained by Equatorial Geophysical ResearchLaboratory (EGRL), Indian Institute of Geomagnetism sinceNovember 1992. This is the only MF radar near to Gadankiwhich gives the wind information in the height range of78–98 km with the height resolution of 2 km and time inter-val of 2min. More details about this radar can be obtainedfrom Rajaram and Gurubaran [1998]. The zonal and merid-ional winds obtained from this radar for January 2007 areused for the current study to verify the condition for verticalpropagation of planetary waves from lower atmosphere to themesospheric height regions to calculate the planetary waveeddy momentum flux and drag force due to gravitywave breaking.

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2.3. TIMED-SABER Temperature Data

[11] The Sounding of the Atmosphere using BroadbandEmission Radiometry (SABER) experiment on theThermosphere-Ionosphere-Mesosphere Energetics andDynamics (TIMED) satellite measures the temperature inthe tangent height of ~15 km to ~120 km with high verticalresolution of 2 km. The kinetic temperature is retrieved fromtwo 15μm and one 4.3μmCO2 radiometer channel measure-ments. Dou et al. [2009] found good agreement betweenLIDAR temperature measurements and that of SABER.More details on SABER instrument can be obtained fromRemsberg et al. [2003] and Gan et al. [2012]. The SABERtemperatures are downloaded from http://saber.gats-inc.com/ for January 2007 in the latitude region of 5.0°N–15.0°N to obtain the spatial extent of wave geopotential. TheSABER temperatures (available for 50.0°N–50.0°S) are alsoused to find the dominant meridional wave number of the2 day planetary wave during January 2007.

2.4. TIDI Wind Data

[12] The TIMED Doppler Interferometer (TIDI) is basi-cally a Fabry-Perot interferometer with a CCD detectoraboard the TIMED satellite measures the neutral winds inzonal and meridional directions with a vertical resolution of2.5 km and an accuracy of ~3m/s in the height region of~60–300 km. Using limb scans of airglow emissions throughfour orthogonally oriented telescopes, the TIDI simulta-neously measures the mesospheric neutral winds and views

emissions from OI 557.7 nm and O2 (0–0) to determineDoppler wind in the TIMED altitude range. In the presentstudy, the vertical profiles of zonal mean of zonal winds fromTIDI (data downloaded from ftp://tidi.engin.umich.edu/; ver-sion: 10) are used to verify the vertical propagation of 2 dayplanetary wave during the large MIL events on 20, 22, and24 January 2007. More details on TIDI instrument can beobtained from Killeen et al. [1999, 2006].

3. Results

3.1. Lidar and SABER MILs

[13] The Rayleigh Lidar was operated continuously from 17to 24 of January 2007 at NARL, Gadanki and after this period,the continuous lidar data are not available in January 2007.Figure 1a shows the nightly mean (5 h) vertical temperatureprofiles derived from Rayleigh Lidar observations overGadanki during 17–24 January 2007, and each profile isshifted by 50K. From this figure, the temperature inversionsare observed in the height region of ~80 km on 20, 22, 23,and 24 January 2007. Also, the temperature inversion is ob-served above ~84 km on 18 January 2007 and the observed in-versions are not much clear on 17, 19, and 21 January 2007,and the corresponding MSIS-90 model temperature profilesare also shown over these lidar temperature profiles. It can alsobe observed from this figure, there is a large negative deviationin the lidar temperatures from the model temperatures whichdenotes the temperature cooling just below the inversion layerduring these inversion events. The corresponding uncertainties

Figure 1. (a) Nightly mean (5 h) vertical temperature profiles (thick line) derived from Rayleigh lidar overGadanki (13.5°N, 79.2°E) during 17–24 January 2007 (each shifted by 50K). The MSIS-90 model temper-ature profile (thin line) also been shown for each corresponding Rayleigh lidar temperature profile (eachshifted by 50K). (b) The uncertainties in the calculation of Rayleigh lidar temperatures with respect toheight for 17–24 January 2007. (c) The TIMED-SABER vertical temperature profiles for 10.0°N–15.0°N and 75.0°E–80.0°E during 17–31 January 2007 and each profile is shifted by 50 K. (d) The inversionamplitudes from Rayleigh lidar (line with triangles) and SABER (line with circles) temperatures for 17–24 and 17–31 January 2007, respectively.

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in the measurement of lidar temperatures are shown inFigure 1b; and from this figure, it can be observed that the un-certainties at ~85 km are exceeding ~17K on 18, 21, and 23January 2007 and ~12K on 17, 19, 20, 22, and 24 January2007. The SABER vertical temperature profiles for 10.0°N–15.0°N and 75.0°E–80.0°E near to Gadanki location eachshifted by 50K are shown in Figure 1c for 17–31 January2007. From this figure, the inversions are observed at~75–85 km during almost all the nights but with large ampli-tudes on 20, 22, 24, 26, 28, 29, and 30 January 2007. The in-version amplitudes are plotted in Figure 1d from bothRayleigh Lidar (17–24 January 2007) and SABER (17–31January 2007) temperatures. It can be observed from this fig-ure, the SABER temperatures show the inversions with largeamplitudes (>35K) on 20, 22, 24, 26, and 28 January 2007which indicates the 2 day wave modulation in the inversionamplitudes and also the influence of quasi-2 day planetarywave in the inversion region [Gurubaran et al., 2001].However, the lidar inversion amplitudes are larger than thatof SABER; they are not showing any 2 day wave oscillationafter 20 January 2007. This could be due to the large uncer-tainties (~30K) in the Rayleigh lidar temperature measure-ments during 21 and 23 January 2007 in the inversion region.Hence, the 20, 22, and 24 January 2007 (which have large in-version amplitudes with less uncertainties in the temperaturemeasurements) events have been selected for the verificationof vertical propagation and dissipation of 2 day planetary wavein the inversion region during these MIL events.

3.2. Spectrum of SABER Temperature

[14] The SABER temperature profiles averaged for 5.0°N–15.0°N and 60.0°E–90.0°E are used to find the signatures of2 day planetary wave for the month of January 2007. The tem-perature perturbations were subjected to wavelet (Morlet)analysis between 35 km and 86 km as shown in Figure 2a. It

is clear from this figure that, during 7–13 January 2007, the2 day planetary wave propagates vertically upward from thelower atmosphere and dissipates at the stratopause (~50 kmnot shown) or in the lower mesosphere (~61 km). Althoughthe wave period is varying between 2 and 3 days in the upperstratosphere (not shown) and lower mesosphere (~61 km), this2 day wave is dominant at all height regions up to ~80 km dur-ing 20–26 January, 2007. While propagating vertically up-ward, the wave amplitude becomes maximum at ~80 kmwhich is the bottom of the temperature inversions during thisobservational period. Above this height, the amplitude de-creases gradually, and the wave dissipates at ~84 km whichis the top of the temperature inversion. The breaking altitudeof small scale gravity wave (T=33min., λz = 6.4 km) in theMIL region for the case of 24 January 2007 was determinedas zbreak = ~84 km (for details, refer to Ramesh and Sridharan[2012]). The 2 day planetary wave dissipates around the sameheights during all the observational events including 24January 2007 as shown in Figure 2a. Here, the dissipation of2 day planetary wave in the MIL height region could be dueto the large eddy diffusion and turbulent mixing generatedby breaking of small scale gravity wave.[15] The two dimensional Fast Fourier Transform (FFT)

analysis is performed on SABER temperatures to find thedominant period and wave numbers of the 2 day planetarywave at two different heights for January 2007. Figure 2bshows the two dimensional FFT power spectrum at theheights of 84 and 86 km. From this figure, it can be observedthat the 2 day wave (T=�2.3 days) of zonal wave number 2(k = 2) is dominant at these two height regions in January2007 over Gadanki location. Figure 2c (left) shows the am-plitude of the wave for different spherical zonal wave num-bers (k = 1,2,3,4) above 60 km derived from SABERtemperatures of January 2007. From this figure, it can be ob-served that the amplitude for k=3 decreases above ~83 km as

Figure 2. (a) The wavelet (Morlet) spectrum of SABER temperatures for 5.0°N–15.0°N and 60.0°E–90.0°E between 35 and 86 km during 01–31 January 2007. (b) The two dimensional FFT power spectrum ofSABER temperatures at 84 and 86 km for January 2007. (c) The vertical profiles of 2 day wave amplitudesfor k=1,2,3,4 (left) and the wave phase profile for k=2,3 (right).

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Figure 2. (continued)

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it propagates upward and for k=2, the amplitude increaseswith height above ~80 km and peaks at around 86 km andagain decreases with height. Hence, it is clear that the 2 daywave of k=2 is dominant with larger amplitude while thewave with k=3 was suppressed in the inversion region(~80–86 km) during this observational period. The phase pro-files of the wave for k=2,3 are shown in the right panel of thisfigure. The phase profiles shown in Figure 2c (right) indicatethe upward propagation of zonal wave number 2 and the dissi-pative nature of zonal wave number 3 above 80 km which canbe inferred from the corresponding downward and upwardphase progressions respectively.

3.3. Temperature and Wave Geopotential Anomalies

[16] The temperature anomalies and their respectivegeopotential anomalies are presented in Figure 3 to showthe wave phenomenon and the wave phase shift during theseinversion events. The temperature anomalies (%) estimatedfrom zonal mean removed SABER temperatures for 20, 22,and 24 January 2007 are shown in Figures 3a, 3c, and 3e, re-spectively. The variation of temperature anomaly largely rep-resents the 2 day wave as it is dominant during this period at80–85 km. It is observed that there are warm anomalies near50°E and 250°E–275°E indicating the presence of planetarywave of zonal wave number 2. On 24 January 2007, thewarm anomalies progresses downward with longitude. Theplanetary waves propagate from lower atmosphere to meso-spheric heights with increasing amplitudes in the winterhemisphere, and the wave signatures can be identified bythe calculation of wave geopotential anomaly so that theabrupt phase shift in the wave field implies the reduction inthe wave amplitude above the inversion region [Salby,1996]. Figures 3b, 3d, and 3f show the corresponding wavegeopotential anomaly (difference inΦ' from equation (3)) with

longitude versus altitude for 20, 22, and 24 January 2007.In Figure 3 (left), the temperature anomaly represents the wavestructure for the mesospheric inversion layers between 80and 85 km for all the three events. In Figures 3a and 3c,the wave extends over 40°E–50°E on 20 January 2007and 40°E–60°E on 22 January 2007 with maximum ampli-tude at ~84 km over 50°E. But, from Figure 3e, the wave ex-tends over 40°E–100°E with peak amplitude between 60°Eand 80°E in the height range of 82–85 km on 24 January2007. Thus, the wave is tilting westward and its amplitudebecame maximum on 24 January 2007 over Gadanki(79.2°E) region when compared to 20 and 22 January2007. From this figure, it can also be observed that the wave(inversion) descends downward up to 70 km over 225°Ewith decreasing amplitude westward. For all the threeevents, there is a cold temperature anomaly just below theMIL(~80 km) which is capped overhead by warm anomaly.The cold temperature anomaly replaced by warm anomalyoverhead and to its east represents an abrupt phase shift ofwave temperature [Salby et al., 2002].[17] The geopotential is the direct consequence of the plan-

etary wave activity and the anomalies can be calculated usingthe expression given by Salby et al. [2002]:

From the hydrostatic equation; ϕz ¼dϕdz

¼ R

HT zð Þ

[18] The above expression gives the perturbation ingeopotential anomaly,

ϕ′z ¼

dϕ′

dz¼ R

HT ′ zð Þ

Figure 3. (a, c, and e) The zonal temperature anomaly and (b, d, and f) the corresponding wavegeopotential anomaly for 20, 22, and 24 January 2007, respectively.

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[19] Vertical integration of the above equation gives thefollowing equation:

∫z2z1dϕ′ ¼ ϕ′ z2ð Þ � ϕ′ z1ð Þ ¼ R

H∫z2z1T

′ zð Þdz (3)

where T′(z) represents the relative temperature perturbations,R is the universal gas constant for dry air (287.14 J kg�1K�1),andH ¼ RT0

g (To = zonal mean temperature) is the scale heightand z is the respective altitude.[20] Using equation (3), the altitude profiles of wave

geopotential anomalies [ϕ′(z2)�ϕ′(z1)] have been calcu-lated for the above mentioned temperature anomalies andshown in Figures 3b, 3d, and 3f corresponding to 20, 22,and 24 January 2007. From these figures, it can be observedthat the amplitude of wave geopotential anomalies are corre-lated with that of corresponding temperature anomalies andthe mesospheric inversions are observed just above the neg-ative maximum of the wave geopotential anomalies at~80 km. The abrupt phase shift in wave geopotential fromnegative anomaly (westward tilt) to positive anomaly (east-ward tilt) between 80 and 85 km over 50°E–80°E indicatesthat the wave could not propagate upward, and the wavehas been dissipated above this height region. Thus, comparedto 20 and 22 events, the 24 January 2007 event clearly showsthe phase shift in the wave field (from negative to positivegeopotential anomalies) in the inversion region (~80–85 km) above which the wave could not propagate upwardover Gadanki region (60°E–80°E).

3.4. Condition for Vertical Propagation

[21] The condition for vertical propagation of planetarywave field can be verified by the equations given byCharney and Drazin [1961] and Holton [2004]. The verti-cally propagating modes of the planetary wave can existsonly when

m2 > 0 (4)

with

m2 ≡N2

f 20

βu� c

� k2 þ l2� �� �

� 1

4H2 (5)

and

0 < u� c < Uc (6)

where

Uc ¼ β k2 þ l2� �þ f 20

4N2H2

� ��1

(7)

[22] Here, the condition for vertical propagation of thewave is verified using the equations (6) and (7) for 20, 22,

and 24 January 2007. In these equations, N2 is the buoyancyfrequency squared calculated from Rayleigh lidar tempera-ture perturbations over Gadanki, f0 is the Coriolis parameterfor Gadanki location (3.40 × 10�5 rad/s), k is the zonal wavenumber, l is the meridional wave number, Uc is the Rossbycritical velocity, H is the scale height, c is the wave phasespeed, and β is the variation of the Coriolis parameter withlatitude (Rossby parameter) which is given by β ¼ 2ω cosϕ

a(β = 2.2158 × 10�11 rad/sec/m for Gadanki location). It hasbeen considered that, if the condition for vertical propagationof the wave is not satisfied from equation (6) (u� c > Uc),the wave could not propagate upward and is dissipated at thatparticular height region. The TIDI zonal mean of zonal windsare used for u to verify the condition for vertical propagationof the planetary wave for 20, 22, and 24 January 2007 MILevents. The available SABER temperatures are taken for60°N–50°S for January 2007 are used to find the dominantspherical meridional wave number (l). Figure 4 shows the me-ridional distribution of 2 day planetary wave amplitudes fork=2,3 at 80–86 km. From this figure, the dominant sphericalmeridional wave number is found to be l = 2 for k=2 if thewave amplitudes are further extended in the southern hemi-sphere. Taking l=2π/(20000 km), the westward phase speeds(c) of the wave are calculated to be�231.48m/s,�115.74m/s,�77.16m/s, and �57.87m/s corresponding to the sphericalzonal wave numbers, k=1,2,3,4, and the condition for verticalpropagation of the planetary wave has been verified for 20, 22,and 24 January 2007 as shown in Figures 5a, 5b, and 5c, re-spectively. From these figures, it can be observed that the ver-tical propagation condition is not favorable ( u� c > Uc )above ~80 km for k=1 on 20, 22, and 24 January 2007 whereas the condition is favorable (u� c < Uc) up to ~81 km andnot favorable (u� c > Uc) above ~81 km for k=2,3,4 duringthe three MIL events. Thus, the 2 day planetary wave of zonalwave number 1 is dissipating in the inversion region (~80km),and the other wave numbers 2,3,4 are propagating up to~81 km and dissipated above this height. The quasi 2 day plan-etary wave is a westward propagating wave with zonal wavenumber k=2 or 3 or 4 (Meyer, 1999). Thus, it is clear for allthe three cases, the 2 day planetary wave with k=2,3,4 hasbeen dissipated in the temperature inversion region above~81 km during 20, 22, and 24 January 2007.

3.5. Zonal Wind Reversal due to Planetary Wave Drag

[23] Figure 6a shows the nightly mean of zonal winds fromMF radar over Tirunelveli (8.7°N, 77.8°E) for January 2007.From this figure, it can be observed that the zonal winds showthe presence of alternating eastward and westward windsduring the period of 20–26 January 2007. These alternateeastward and westward zonal winds could be due to the mod-ulation of background winds by 2 day planetary wave. It canalso be observed that the amplitudes of eastward winds aredecreasing after 18 January 2007 in alternative nights.Figure 6b shows the 10 day running average of zonal meanwinds for January and February 2007 showing the back-ground wind condition during this observational period. Itcan be observed from this figure, there are strong eastwardwinds above 80 km up to 17 January 2007 which is the favor-able condition for vertical propagation of planetary waves inthe mesosphere and after that the magnitudes of the eastwardwinds are weaken and became westward which is not

Figure 4. The latitudinal (60°N–50°S) structure of the2 day planetary wave amplitudes for k= 2,3 between 80 and86 km.

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Figure 5. The vertical profiles ofUc and u� cð Þ for k = 1,2,3,4 (a) for 20 January 2007, (b) for 22 January2007, and (c) for 24 January 2007.

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favorable for vertical propagation of the wave up to end ofJanuary 2007. Thus, the magnitude of eastward winds areweaken by 20 and 22 January 2007 and the winds becamestrong and westward on 24 January 2007. According toCharney and Drazin [1961], transient waves interact withbackground flow and during this inversion period, the 2 dayplanetary wave may have induced westward acceleration,which brings the background winds toward the phase speedof the wave.

3.6. Drag Force and Eddy Momentum Diffusion

[24] Miyahara [1985] explained about the effect of internalgravity waves on planetary wave suppression in the meso-sphere. It is suggested that not only the Newtonian coolingeffect but also the drag forces due to internal gravity wavebreaking largely reduces the planetary wave amplitudes inthe mesosphere. The momentum flux transport by upwardpropagating internal gravity waves acts like a Rayleigh fric-tion on the upward propagating planetary waves so that theiramplitudes are largely suppressed by the gravity wave break-ing in the mesosphere. The drag forces due to the eddy diffu-sion deposited by the gravity wave breaking will affectlargely the planetary wave amplitudes in the mesospherewhile propagating vertically upward. Here, the drag forcedue to gravity wave breaking and the eddy momentum diffu-sion of planetary waves have been calculated for 20, 22, and24 January 2007 using the equations given by Lindzen[1981], Holton [1983], and Miyahara [1985].

3.6.1. Drag Force Due to Gravity Wave Breaking[25] The drag force due to gravity wave breaking is given

by the equation [Holton, 1983]:

Fx ¼ � DgwN2

u� cxð Þ (8)

where Dgw is the eddy diffusion coefficient due to gravitywave breaking, N2 is the buoyancy frequency squared, u isthe mean zonal wind speed, and cx is the horizontal phasespeed of gravity wave in the mesosphere.[26] From the 2-dimensional FFT analysis on the Rayleigh

lidar temperature perturbations (time resolution is 250sec,range resolution is 300m) over Gadanki, the dominant grav-ity wave periods and vertical wavelengths are found to be18min, 38min, 33min, and 6.4 km, 4.0 km, and 6.4 km, re-spectively on 20, 22, and 24 January 2007 in the mesosphericheight region as shown in Figures 7a–7c. The respective hor-izontal phase speeds (cx) of the gravity wave are calculatedby the gravity wave dispersion relation using MF radar windsover Tirunelveli, and the Dgw values calculated from theequation given by Lindzen [1981]. Figure 8 shows the verti-cal profiles of eddy diffusion coefficients (Dgw) of gravitywave for 20, 22, and 24 January 2007. The eddy diffusion co-efficient is decreasing with height above 80 km on 20 and 22January 2007, and it is increasing up to 84 km and decreasingabove this height on 24 January 2007. By substituting N2

values obtained from Rayleigh lidar temperatures overGadanki, the 5 h mean zonal winds (u) over Tirunelveli, cxand Dgw values in equation (8), the drag force (Fx) due togravity waves is calculated in the mesospheric height region(80–89 km).3.6.2. Eddy Momentum Diffusion of Planetary Waves[27] The eddy momentum diffusion of planetary wave is

calculated by the equation [Miyahara, 1985]:

Eddy momentum diffusion ¼ Dpwd2V ′

dz2

�������� (9)

where Dpw is the vertical eddy diffusion coefficient corre-sponding to planetary wave dissipation calculated from thesame equation given by Lindzen [1981]. While calculatingDpw, the TIDI zonal mean of zonal winds for 20, 22, and24 January 2007 are substituted for u. The horizontal windperturbations V ′ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu′2 þ v′2

pwere obtained from 40 to

60 h band-pass filtered zonal mean of zonal (u′) and meridio-nal (v′) winds from TIDI instrument during this period.[28] The drag force due to the gravity waves and the eddy

momentum diffusion of planetary waves for k=2,3,4 are esti-mated using (8) and (9) between 80 and ~87 km for 20, 22, and24 January 2007 as shown in Figure 9. From this figure, it canbe observed that, above 80 km, the drag force (Fx) dominatesthe eddy momentum diffusion for all the wave numbers(k=2,3,4) almost at all the height regions on 20 and 22January 2007. But, on 24 January 2007, the drag force is largerthan the eddy momentum diffusion up to 84 km and it becamelesser than the eddy momentum diffusion of spherical zonalwave numbers k=2,3,4 between 84 and 85 km. Above thisheight region, the drag force again dominates the eddy mo-mentum diffusion. However, the planetary wave eddy mo-mentum diffusion of all the wave numbers dominates theforce drag due to gravity waves, the eddymomentum diffusion

Figure 6. (a) The nightly mean MF radar zonal winds forJanuary 2007 over Tirunelveli (8.7°N,77.8°E), (b) 10 day run-ning average of MF radar zonal winds for January–February2007 over Tirunelveli (8.7°N,77.8°E).

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Figure 7. The power spectral density from 2-dimensional FFT analysis to find dominant gravity waveperiod and vertical wavelengths in mesospheric height region: (a) for 20 January 2007, (b) for 22January 2007, and (c) for 24 January 2007.

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for k=2 is larger than that of k=3,4 at 84–85 km. The break-ing altitude of the gravity wave is ~84 km in the inversion re-gion (79–84 km) for the case of 24 January 2007 [Ramesh andSridharan, 2012] above which the 2 day planetary wave ofwave number 2 is dissipated and deposited larger eddy mo-mentum diffusion in the background. Thus, the planetarywavesuppression above 84–85 km could be due to the large plane-tary wave drag forces and the large eddy diffusion by the grav-ity wave breaking just below this height. It can also beobserved from this figure that the drag force and eddy momen-tum diffusions for 24 January 2007 are ~100 times larger thanthat of 20 and 22 January 2007. Thus, when compared for thecases of 20 and 22 January 2007, the large MIL event on 24January 2007 clearly shows that the 2 day planetary wave sup-pression above the inversion height could be due to the break-ing of small scale gravity wave.

4. Discussion and Conclusion

[29] Rayleigh lidar temperature observations over Gadankishow a few mesospheric inversion layer (MIL) events during20–25 January 2007. The zonal mean removed SABERtemperature shows warm anomalies around 50°E and 275°Eindicating the presence of planetary wave of zonal wave num-ber 2 above ~80 km. The two dimensional spectrum also con-firms the dominant presence of 2 day planetary wave withzonal wave number 2. The MIL amplitudes in SABER tem-perature averaged for 10°N–15°N and 70°E–90°E show aclear 2 day wave modulation during 20–28 January 2007.Prior to 20 January 2007, the 2 day wavewith large amplitudesis observed in the height region 80–90 km and it gets largelysuppressed during 20–26 January 2007, as condition for thevertical propagation is not favorable, though it prevails atlower heights. The amplitude and phase profiles clearly showthe 2 day planetary wave of spherical zonal wave number

k=2 is dominant while k=3 was dissipated in theinversion region.[30] The planetary wave activity is inferred from the longi-

tude-height cross section of geopotential anomalies esti-mated from the corresponding temperature anomalies[Salby et al., 2002]. It is observed that the temperature ampli-tudes are correlated with the wave amplitudes from wavegeopotential anomalies in the inversion regions. The east-ward tilt (positive geopotential anomaly) of the wave indi-cates the wave dissipation above the inversion heights, andthe turbulence generated by the gravity wave breaking couldmodify the vertical structure of the planetary waves above theinversion layer [Salby et al., 2002]. The 10 day mean zonalwind over Tirunelveli shows deceleration of eastward windsindicating the westward drag due to wave dissipation.Charney and Drazin [1961] suggested that transient wavescan interact with background flow and the interaction canbring the background winds toward the phase speed of thewave. The nightly mean MF radar zonal winds show thepresence of alternating eastward and westward winds withlarger amplitudes just before 20 January 2007 and with lessamplitudes during the period 20–26 January 2007. The wavesuppression in winds is consistent with the same observed intemperature. The alternating two day variation in the localwinds could influence the propagation of gravity waves.[31] The two dimensional spectrum of Rayleigh lidar tem-

perature observations, available for the nights 20, 22, and 24January 2007, shows the presence of gravity wave activitywith periods 18min, 38min, and 33min with vertical wave-lengths 6.4 km, 4.0 km, and 6.4 km, respectively. From thedispersion relation of gravity waves, it is inferred that thesewaves are internal gravity waves. Assuming that the gravitywaves are eastward propagating waves, they get absorbedonly in the eastward local wind fields of the planetary wave,thereby causing turbulence and eddy diffusion, inferred fromthe estimation of large drag force due to the gravity wave

Figure 8. The vertical profiles of eddy diffusion coefficient (Dgw) of gravity waves for 20, 22, and24 January 2007.

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breaking, leading to the formation of large amplitude inver-sion events in alternate nights.[32] The internal gravity waves in the eastward winds carry

westward momentum upward and decelerate the mesosphericmean zonal eastward winds, and the drag forces due to thegravity wave breaking suppress the planetary wave compo-nents in the mesosphere [Miyahara et al., 1986]. The breakinggravity waves generate vertical eddy diffusion and this eddydiffusion decelerates the background wind and reverses themesospheric wind shears [Lindzen, 1981]. Miyahara [1985]studied about the planetary wave suppression due to internalgravity waves in the mesosphere. The amplitudes of planetarywaves are strongly reduced by the drag forces due to smallscale internal gravity wave breaking in the mesosphere.Alongwith the Newtonian cooling effect, the wave drag forcesand the effect of induced eddy diffusion are the suggested rea-sons for planetary wave suppression in the mesosphere. Thecalculated drag forces due to gravity wave breaking and eddymomentum fluxes of planetary waves suggest that the dragforces of gravity wave are dominant in the inversion height re-gions, and the eddy momentum diffusions of planetary waveare larger just above the inversion heights. On 24 January2007, the large drag force and eddy diffusion deposited bythe breaking of small scale gravity waves caused the largereddymomentum diffusion of planetary wave just above the in-version height regions (84–85 km).[33] Garcia [1991] suggested that the wave breaking far

away from the critical level (u� cx ¼ 0; ωi= 0) will depositmore eddy diffusion in the background and strongly modifythe background conditions than the wave near the criticallevel. Since the stratospheric and lower mesospheric horizon-tal phase speeds of gravity waves are ~41m/s, ~37m/s, and~50m/s, respectively (calculated from rocketsonde windsof 24 January 2007 since these winds are not available for20 and 22 January 2007) and assuming these phase speeds

are propagating upward with decreasing zonal wind ampli-tudes on 20, 22, and 24 January 2007; the critical levels (u�cx ¼ 0 ) are very far; the breaking gravity wave depositslarger momentum flux in the background on 24 January2007 compared to 20 and 22 January 2007. He alsosuggested that the group velocity of the gravity wave playsan important role in wave saturation so that waves of largergroup velocities (faster waves) deposit greater momentumflux in the background to maintain the constant amplitude af-ter dissipation. The typical values of u� cxð Þ are 20–30m/sfor the breaking gravity wave to deposit large drag forceand eddy diffusion in the mesosphere. Since the group veloc-

ity cgz ¼ k u�cxð Þ2N

� of the gravity wave is proportional to

u� cxð Þ2 , the eddy diffusion coefficient should be larger inthe breaking region of internal gravity wave. On 24 January2007, the eddy diffusion coefficient increases in the inversionregion from 80 to 84 km and again, it decreases whereas theeddy diffusion coefficient decreases above 80 km on 20 and22 January 2007.[34] In the present study, it is shown that mesospheric temper-

ature inversion is caused mainly due to gravity wave breakingand the inversion amplitudes got modulated by the interactionof gravity waves and planetary waves. The eddy diffusion asso-ciatedwith the gravitywave force drag caused the suppression of2 day planetary wave in the mesospheric inversion region.

[35] Acknowledgments. The authors are thankful to the technical stafffor operating and maintaining the Rayleigh lidar system at NARL, Gadanki.They are thankful to EGRL, Indian Institute of Geomagnetism, Tirunelvelifor providing the necessary wind data which is very important for this study.The SABER temperatures and TIDI winds are obtained from the websites:http://saber.gats-inc.com/ and ftp://tidi.engin.umich.edu/ and the authorswould like to acknowledge J.M. Russell and T.L. Killeen, the principal in-vestigators of the SABER and TIDI projects, respectively.[36] Robert Lysak thanks the reviewers for their assistance in evaluating

this paper.

Figure 9. The vertical profiles of eddy momentum diffusion of planetary wave for k = 2,3,4 (in bluetriangles, green squares, black asterisks, respectively) and the drag force (Fx) due to gravity waves(in red circles) for 20, 22, and 24 January 2007.

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