JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 4503–4515, doi:10.1002/jgra.50379, 2013 Planetary wave-gravity wave interactions during mesospheric inversion layer events K. Ramesh,1 S. Sridharan,2 K. Raghunath,2 S. Vijaya Bhaskara Rao,1 and Y. Bhavani Kumar 2 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 few mesospheric inversion layer (MIL) events during 20–25 January 2007. The zonal mean removed SABER temperature shows warm anomalies around 50°E and 275°E indicating the presence of planetary wave of zonal wave number 2. The MIL amplitudes in SABER temperature averaged for 10°N–15°N and 70°E–90°E show a clear 2 day wave modulation during 20–28 January 2007. Prior to 20 January 2007, a strong 2day wave (zonal wave number 2) is observed in the height region of 80–90 km and it gets largely suppressed during 20–26 January 2007 as the condition for vertical propagation is not favorable, though it prevails 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 eastward and westward winds during the period of 20–26 January 2007. The two dimensional spectrum of Rayleigh lidar temperature observations available for the nights of 20, 22, and 24 January 2007 shows the presence of gravity wave activity with periods 18 min, 38 min, 38 min, and vertical wavelengths 6.4 km, 4.0 km, 6.4 km respectively. From the dispersion relation of gravity waves, it is inferred that these waves are internal gravity waves rather than inertia gravity waves with the horizontal phase speeds of ~40 m/s, ~37 m/s, and ~50 m/s respectively. Assuming the gravity waves are eastward propagating waves, they get absorbed only in the eastward local wind fields of the planetary wave thereby causing turbulence and eddy diffusion which can be inferred from the estimation of large drag force due to the breaking of gravity 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 to the gravity wave breaking and the inversion amplitude may get modulated by the interaction between gravity waves and planetary waves. The eddy diffusion associated with gravity wave drag 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), Planetary wave-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 kilometers thickness showing the positive lapse rate at the bottom and is superposed upon the characteristically decreasing temperature in the mesosphere is known as mesospheric inversion layer (MIL). There are various causative mechanisms suggested for the formation of these layers [Meriwether and Gardner, 2000; Meriwether and Gerrard, 2004] which 1 2 Department of Physics, Sri Venkateswara University, Tirupati, India. National Atmospheric Research Laboratory, DoS, Gadanki, India. Corresponding author: K. Ramesh, Department of Physics, Sri Venkateswara University, Tirupati, AP 517502, India. (karanamram@gmail.com) ©2013. American Geophysical Union. All Rights Reserved. 2169-9380/13/10.1002/jgra.50379 include the gravity wave breaking and the planetary wave critical level interaction. [3] According to the linear saturation theory, the amplitude of the gravity wave increases exponentially as it propagates vertically upward in response to the decreasing atmospheric density and breaks at a particular altitude where it becomes convectively unstable. The wave when breaks deposits a net momentum in the mean flow and accelerates the background wind in the direction of propagation of the wave and causes a downward heat flux, which results in cooling of the atmosphere at the breaking height [Walterscheid, 1981; Gardner and Yang, 1998; Ramesh and Sridharan, 2012]. This downward heat flux raises the heating at the bottom of the wave field which is maintained as an inversion layer. Though the downward heat flux due to gravity wave breaking is an important source of heat budget in the mesosphere, the resultant gravity wave induced cooling effects in the mean zonal flow could be due to the effect of wave drag. 4503 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS [4] Charney and Drazin [1961] explained about the vertical propagation of planetary scale disturbances from lower to upper atmosphere. The energy in the form of heat and momentum flux carried by the small scale disturbances modifies the zonal mean flow when they propagate from lower to upper atmosphere. They also suggested that, the planetary scale disturbances could propagate vertically only when the background winds are westerly relative to the phase speed and having lesser magnitude than a particular “critical velocity” which is inversely proportional to the zonal and meridional wave numbers. Lindzen [1981] proposed a simple theory which suggests that the drag forces due to the gravity wave breaking decelerates the mean zonal winds to balance the momentum budget in the mesosphere. He also suggested that the drag force peaks near the lowest level at which the gravity wave breaks. Holton [1983] discussed about the effect of gravity wave breaking on the general circulation of middle atmosphere. He suggested the vertical eddy diffusion generated by gravity wave breaking modifies the zonal mean flow and causes the planetary wave dissipation in the mesosphere. The momentum transferred by vertically propagating internal gravity waves could attenuate the amplitudes of planetary waves 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 mesosphere. In the absence of dissipation, the wave amplitude increases as ez/2H while propagating vertically upward and greatly reduces by the drag forces due to breaking of internal gravity waves. Salby et al. [2002] described about the relationship between the mesospheric inversion layers and the planetary wave activity from UARS/Microwave Limb Sounder. They suggested that the strong absorption of the planetary wave in the mesospheric inversion region is due to the turbulent mixing associated with gravity wave breaking. They also described how the phase shift of the wave geopotential related to the planetary wave activity during MIL event. Sassi et al. [2002] discussed about the contribution of planetary waves in causing MILs using Whole Atmosphere Community Climate Model (WACCM). They suggested that the existence of the critical level for the planetary waves in the mesosphere is due to the deposition of easterly momentum by small scale gravity waves [Matsuno, 1982; Holton, 1983; Garcia and Solomon, 1985] so that the planetary 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 ~50 K and thickness of ~4.5 km observed in the nightly mean vertical temperature profile using Rayleigh lidar over Gadanki (13.5°N, 79.2°E) on 24 January 2007. This large inversion is due to the breaking of a small scale internal gravity wave (T = 33 min., λz = 6.4 km) in the height region of 80–84 km. The turbulent eddy diffusion coefficient largely increased from bottom to the top of the inversion layer due to the wave breaking. It is observed from the wavelet analysis performed on ThermosphereIonosphere-Mesosphere Energetics and Dynamics-Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED-SABER) temperature perturbations of January 2007, a vertically propagating 2 day planetary wave was suppressed 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 wave could 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 interaction between the 2 day planetary wave and the small scale internal gravity wave in the occurrence and modulation of MILs using Rayleigh Lidar temperatures, MF radar winds, TIMED Doppler Interferometer (TIDI) winds, and TIMEDSABER temperatures. 2. Instrumentation and Data Analysis 2.1. Rayleigh Lidar Temperature Measurements [8] The Rayleigh Lidar system with improved laser power is in continuous operational mode on all cloud free nights since mid-January 2007 installed at National Atmospheric Research Laboratory (NARL), Department of Space, Gadanki (13.5°N, 79.2°E), India. From this lidar, the vertical temperature profile can be derived using the method given by Hauchecorne and Chanin [1980]. This lidar gives the vertical atmospheric density profile which is proportional to the back scattered photon counts from atmospheric air molecules above 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 the measured density profile. Applying the ideal gas equation, the vertical temperature profiles T(z) can be calculated using the expression given by T ðzi Þ ¼ M gðzi Þ Δz R Logð1 þ X Þ where X ¼ ρðzi Þ gðzi Þ Δz Pðzi þ Δz=2Þ (1) and the uncertainty in the measurement of temperature is given by δT ðzi Þ δLogð1 þ X Þ δX ¼ ¼ T ðzi Þ Logð1 þ X Þ ð1 þ X ÞLogð1 þ X Þ (2) [9] More details on this data analysis and NARL new lidar system specifications can be obtained from Siva Kumar et al. [2003] and Ramesh and Sridharan [2012]. Here, the increased laser power (up to 30 W) made possible to derive the vertical temperatures up to ~90 km with relatively less uncertainties during the observational period. 2.2. MF Radar Wind Measurements Over Tirunelveli [10] The zonal and meridional winds are obtained from Medium Frequency (MF) radar at Tirunelveli (8.7°N,77.8° E) which is in operational mode with the frequency of 1.98 MHz maintained by Equatorial Geophysical Research Laboratory (EGRL), Indian Institute of Geomagnetism since November 1992. This is the only MF radar near to Gadanki which gives the wind information in the height range of 78–98 km with the height resolution of 2 km and time interval of 2 min. More details about this radar can be obtained from Rajaram and Gurubaran [1998]. The zonal and meridional winds obtained from this radar for January 2007 are used for the current study to verify the condition for vertical propagation of planetary waves from lower atmosphere to the mesospheric height regions to calculate the planetary wave eddy momentum flux and drag force due to gravity wave breaking. 4504 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 1. (a) Nightly mean (5 h) vertical temperature profiles (thick line) derived from Rayleigh lidar over Gadanki (13.5°N, 79.2°E) during 17–24 January 2007 (each shifted by 50 K). The MSIS-90 model temperature profile (thin line) also been shown for each corresponding Rayleigh lidar temperature profile (each shifted by 50 K). (b) The uncertainties in the calculation of Rayleigh lidar temperatures with respect to height 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 inversion amplitudes from Rayleigh lidar (line with triangles) and SABER (line with circles) temperatures for 17– 24 and 17–31 January 2007, respectively. 2.3. TIMED-SABER Temperature Data [11] The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) experiment on the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite measures the temperature in the tangent height of ~15 km to ~120 km with high vertical resolution of 2 km. The kinetic temperature is retrieved from two 15 μm and one 4.3 μm CO2 radiometer channel measurements. Dou et al. [2009] found good agreement between LIDAR temperature measurements and that of SABER. More details on SABER instrument can be obtained from Remsberg et al. [2003] and Gan et al. [2012]. The SABER temperatures 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. The SABER temperatures (available for 50.0°N–50.0°S) are also used to find the dominant meridional wave number of the 2 day planetary wave during January 2007. 2.4. TIDI Wind Data [12] The TIMED Doppler Interferometer (TIDI) is basically a Fabry-Perot interferometer with a CCD detector aboard the TIMED satellite measures the neutral winds in zonal and meridional directions with a vertical resolution of 2.5 km and an accuracy of ~3 m/s in the height region of ~60–300 km. Using limb scans of airglow emissions through four orthogonally oriented telescopes, the TIDI simultaneously measures the mesospheric neutral winds and views emissions from OI 557.7 nm and O2 (0–0) to determine Doppler wind in the TIMED altitude range. In the present study, the vertical profiles of zonal mean of zonal winds from TIDI (data downloaded from ftp://tidi.engin.umich.edu/; version: 10) are used to verify the vertical propagation of 2 day planetary wave during the large MIL events on 20, 22, and 24 January 2007. More details on TIDI instrument can be obtained from Killeen et al. [1999, 2006]. 3. Results 3.1. Lidar and SABER MILs [13] The Rayleigh Lidar was operated continuously from 17 to 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 temperature profiles derived from Rayleigh Lidar observations over Gadanki during 17–24 January 2007, and each profile is shifted by 50 K. From this figure, the temperature inversions are observed in the height region of ~80 km on 20, 22, 23, and 24 January 2007. Also, the temperature inversion is observed above ~84 km on 18 January 2007 and the observed inversions are not much clear on 17, 19, and 21 January 2007, and the corresponding MSIS-90 model temperature profiles are also shown over these lidar temperature profiles. It can also be observed from this figure, there is a large negative deviation in the lidar temperatures from the model temperatures which denotes the temperature cooling just below the inversion layer during these inversion events. The corresponding uncertainties 4505 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS 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 of SABER temperatures at 84 and 86 km for January 2007. (c) The vertical profiles of 2 day wave amplitudes for k = 1,2,3,4 (left) and the wave phase profile for k = 2,3 (right). in the measurement of lidar temperatures are shown in Figure 1b; and from this figure, it can be observed that the uncertainties at ~85 km are exceeding ~17 K on 18, 21, and 23 January 2007 and ~12 K on 17, 19, 20, 22, and 24 January 2007. The SABER vertical temperature profiles for 10.0°N– 15.0°N and 75.0°E–80.0°E near to Gadanki location each shifted by 50 K are shown in Figure 1c for 17–31 January 2007. From this figure, the inversions are observed at ~75–85 km during almost all the nights but with large amplitudes on 20, 22, 24, 26, 28, 29, and 30 January 2007. The inversion amplitudes are plotted in Figure 1d from both Rayleigh Lidar (17–24 January 2007) and SABER (17–31 January 2007) temperatures. It can be observed from this figure, the SABER temperatures show the inversions with large amplitudes (>35 K) on 20, 22, 24, 26, and 28 January 2007 which indicates the 2 day wave modulation in the inversion amplitudes and also the influence of quasi-2 day planetary wave in the inversion region [Gurubaran et al., 2001]. However, the lidar inversion amplitudes are larger than that of SABER; they are not showing any 2 day wave oscillation after 20 January 2007. This could be due to the large uncertainties (~30 K) in the Rayleigh lidar temperature measurements during 21 and 23 January 2007 in the inversion region. Hence, the 20, 22, and 24 January 2007 (which have large inversion amplitudes with less uncertainties in the temperature measurements) events have been selected for the verification of vertical propagation and dissipation of 2 day planetary wave in 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 of 2 day planetary wave for the month of January 2007. The temperature 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, the 2 day planetary wave propagates vertically upward from the lower atmosphere and dissipates at the stratopause (~50 km not shown) or in the lower mesosphere (~61 km). Although the wave period is varying between 2 and 3 days in the upper stratosphere (not shown) and lower mesosphere (~61 km), this 2 day wave is dominant at all height regions up to ~80 km during 20–26 January, 2007. While propagating vertically upward, the wave amplitude becomes maximum at ~80 km which is the bottom of the temperature inversions during this observational period. Above this height, the amplitude decreases gradually, and the wave dissipates at ~84 km which is the top of the temperature inversion. The breaking altitude of small scale gravity wave (T = 33 min., λz = 6.4 km) in the MIL region for the case of 24 January 2007 was determined as zbreak = ~84 km (for details, refer to Ramesh and Sridharan [2012]). The 2 day planetary wave dissipates around the same heights during all the observational events including 24 January 2007 as shown in Figure 2a. Here, the dissipation of 2 day planetary wave in the MIL height region could be due to the large eddy diffusion and turbulent mixing generated by breaking of small scale gravity wave. [15] The two dimensional Fast Fourier Transform (FFT) analysis is performed on SABER temperatures to find the dominant period and wave numbers of the 2 day planetary wave at two different heights for January 2007. Figure 2b shows the two dimensional FFT power spectrum at the heights of 84 and 86 km. From this figure, it can be observed that the 2 day wave (T = 2.3 days) of zonal wave number 2 (k = 2) is dominant at these two height regions in January 2007 over Gadanki location. Figure 2c (left) shows the amplitude of the wave for different spherical zonal wave numbers (k = 1,2,3,4) above 60 km derived from SABER temperatures of January 2007. From this figure, it can be observed that the amplitude for k = 3 decreases above ~83 km as 4506 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 2. (continued) 4507 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 3. (a, c, and e) The zonal temperature anomaly and (b, d, and f) the corresponding wave geopotential anomaly for 20, 22, and 24 January 2007, respectively. it propagates upward and for k = 2, the amplitude increases with height above ~80 km and peaks at around 86 km and again decreases with height. Hence, it is clear that the 2 day wave of k = 2 is dominant with larger amplitude while the wave with k = 3 was suppressed in the inversion region (~80–86 km) during this observational period. The phase profiles of the wave for k = 2,3 are shown in the right panel of this figure. The phase profiles shown in Figure 2c (right) indicate the upward propagation of zonal wave number 2 and the dissipative nature of zonal wave number 3 above 80 km which can be inferred from the corresponding downward and upward phase progressions respectively. 3.3. Temperature and Wave Geopotential Anomalies [16] The temperature anomalies and their respective geopotential anomalies are presented in Figure 3 to show the wave phenomenon and the wave phase shift during these inversion events. The temperature anomalies (%) estimated from zonal mean removed SABER temperatures for 20, 22, and 24 January 2007 are shown in Figures 3a, 3c, and 3e, respectively. The variation of temperature anomaly largely represents the 2 day wave as it is dominant during this period at 80–85 km. It is observed that there are warm anomalies near 50°E and 250°E–275°E indicating the presence of planetary wave of zonal wave number 2. On 24 January 2007, the warm anomalies progresses downward with longitude. The planetary waves propagate from lower atmosphere to mesospheric heights with increasing amplitudes in the winter hemisphere, and the wave signatures can be identified by the calculation of wave geopotential anomaly so that the abrupt phase shift in the wave field implies the reduction in the wave amplitude above the inversion region [Salby, 1996]. Figures 3b, 3d, and 3f show the corresponding wave geopotential anomaly (difference in Φ' from equation (3)) with longitude versus altitude for 20, 22, and 24 January 2007. In Figure 3 (left), the temperature anomaly represents the wave structure for the mesospheric inversion layers between 80 and 85 km for all the three events. In Figures 3a and 3c, the wave extends over 40°E–50°E on 20 January 2007 and 40°E–60°E on 22 January 2007 with maximum amplitude at ~84 km over 50°E. But, from Figure 3e, the wave extends over 40°E–100°E with peak amplitude between 60°E and 80°E in the height range of 82–85 km on 24 January 2007. Thus, the wave is tilting westward and its amplitude became maximum on 24 January 2007 over Gadanki (79.2°E) region when compared to 20 and 22 January 2007. From this figure, it can also be observed that the wave (inversion) descends downward up to 70 km over 225°E with decreasing amplitude westward. For all the three events, there is a cold temperature anomaly just below the MIL(~80 km) which is capped overhead by warm anomaly. The cold temperature anomaly replaced by warm anomaly overhead and to its east represents an abrupt phase shift of wave temperature [Salby et al., 2002]. [17] The geopotential is the direct consequence of the planetary wave activity and the anomalies can be calculated using the expression given by Salby et al. [2002]: From the hydrostatic equation; ϕ z ¼ dϕ R ¼ T ðzÞ dz H [18] The above expression gives the perturbation in geopotential anomaly, 4508 ϕ′ z ¼ dϕ ′ R ′ ¼ T ðzÞ dz H RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 4. The latitudinal (60°N–50°S) structure of the 2 day planetary wave amplitudes for k = 2,3 between 80 and 86 km. [19] Vertical integration of the above equation gives the following equation: z2 ∫z1 dϕ ′ ¼ ϕ ′ ðz2 Þ ϕ ′ ðz1 Þ ¼ R z2 ′ ∫ T ðzÞ dz H z1 (3) where T′(z) represents the relative temperature perturbations, R is the universal gas constant for dry air (287.14 J kg 1K 1), and H ¼ RTg 0 (To = zonal mean temperature) is the scale height and z is the respective altitude. [20] Using equation (3), the altitude profiles of wave geopotential anomalies [ϕ′(z2) ϕ′(z1)] have been calculated for the above mentioned temperature anomalies and shown in Figures 3b, 3d, and 3f corresponding to 20, 22, and 24 January 2007. From these figures, it can be observed that the amplitude of wave geopotential anomalies are correlated with that of corresponding temperature anomalies and the mesospheric inversions are observed just above the negative maximum of the wave geopotential anomalies at ~80 km. The abrupt phase shift in wave geopotential from negative anomaly (westward tilt) to positive anomaly (eastward tilt) between 80 and 85 km over 50°E–80°E indicates that the wave could not propagate upward, and the wave has been dissipated above this height region. Thus, compared to 20 and 22 events, the 24 January 2007 event clearly shows the phase shift in the wave field (from negative to positive geopotential anomalies) in the inversion region (~80– 85 km) above which the wave could not propagate upward over Gadanki region (60°E–80°E). 3.4. Condition for Vertical Propagation [21] The condition for vertical propagation of planetary wave field can be verified by the equations given by Charney and Drazin [1961] and Holton [2004]. The vertically propagating modes of the planetary wave can exists only when m2 > 0 (4) with m2 ≡  N2 β 2 u c f0
k 2 þ l2   1 4H 2 (5) and 0<u c < Uc (6) where 
 U c ¼ β k 2 þ l2 þ f 20 4N 2 H 2  1 (7) [22] Here, the condition for vertical propagation of the wave is verified using the equations (6) and (7) for 20, 22, and 24 January 2007. In these equations, N2 is the buoyancy frequency squared calculated from Rayleigh lidar temperature perturbations over Gadanki, f0 is the Coriolis parameter for Gadanki location (3.40 × 10 5 rad/s), k is the zonal wave number, l is the meridional wave number, Uc is the Rossby critical velocity, H is the scale height, c is the wave phase speed, and β is the variation of the Coriolis parameter with latitude (Rossby parameter) which is given by β ¼ 2ω cosϕ a (β = 2.2158 × 10 11 rad/sec/m for Gadanki location). It has been considered that, if the condition for vertical propagation of the wave is not satisfied from equation (6) (u c > U c ), the wave could not propagate upward and is dissipated at that particular height region. The TIDI zonal mean of zonal winds are used for u to verify the condition for vertical propagation of the planetary wave for 20, 22, and 24 January 2007 MIL events. The available SABER temperatures are taken for 60°N–50°S for January 2007 are used to find the dominant spherical meridional wave number (l). Figure 4 shows the meridional distribution of 2 day planetary wave amplitudes for k = 2,3 at 80–86 km. From this figure, the dominant spherical meridional wave number is found to be l = 2 for k = 2 if the wave amplitudes are further extended in the southern hemisphere. Taking l = 2π/(20000 km), the westward phase speeds (c) of the wave are calculated to be 231.48 m/s, 115.74 m/ s, 77.16 m/s, and 57.87 m/s corresponding to the spherical zonal wave numbers, k = 1,2,3,4, and the condition for vertical propagation of the planetary wave has been verified for 20, 22, and 24 January 2007 as shown in Figures 5a, 5b, and 5c, respectively. From these figures, it can be observed that the vertical propagation condition is not favorable ( u c > U c ) above ~80 km for k = 1 on 20, 22, and 24 January 2007 where as the condition is favorable (u c < U c ) up to ~81 km and not favorable (u c > U c) above ~81 km for k = 2,3,4 during the three MIL events. Thus, the 2 day planetary wave of zonal wave number 1 is dissipating in the inversion region (~80 km), and the other wave numbers 2,3,4 are propagating up to ~81 km and dissipated above this height. The quasi 2 day planetary wave is a westward propagating wave with zonal wave number k = 2 or 3 or 4 (Meyer, 1999). Thus, it is clear for all the three cases, the 2 day planetary wave with k = 2,3,4 has been 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 from MF radar over Tirunelveli (8.7°N, 77.8°E) for January 2007. From this figure, it can be observed that the zonal winds show the presence of alternating eastward and westward winds during the period of 20–26 January 2007. These alternate eastward and westward zonal winds could be due to the modulation of background winds by 2 day planetary wave. It can also be observed that the amplitudes of eastward winds are decreasing after 18 January 2007 in alternative nights. Figure 6b shows the 10 day running average of zonal mean winds for January and February 2007 showing the background wind condition during this observational period. It can be observed from this figure, there are strong eastward winds above 80 km up to 17 January 2007 which is the favorable condition for vertical propagation of planetary waves in the mesosphere and after that the magnitudes of the eastward winds are weaken and became westward which is not 4509 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 5. The vertical profiles of Uc and ðu 2007, and (c) for 24 January 2007. cÞ for k = 1,2,3,4 (a) for 20 January 2007, (b) for 22 January 4510 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS 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 Figure 6. (a) The nightly mean MF radar zonal winds for January 2007 over Tirunelveli (8.7°N,77.8°E), (b) 10 day running average of MF radar zonal winds for January–February 2007 over Tirunelveli (8.7°N,77.8°E). favorable for vertical propagation of the wave up to end of January 2007. Thus, the magnitude of eastward winds are weaken by 20 and 22 January 2007 and the winds became strong and westward on 24 January 2007. According to Charney and Drazin [1961], transient waves interact with background flow and during this inversion period, the 2 day planetary wave may have induced westward acceleration, which brings the background winds toward the phase speed of the wave. 3.6. Drag Force and Eddy Momentum Diffusion [24] Miyahara [1985] explained about the effect of internal gravity waves on planetary wave suppression in the mesosphere. It is suggested that not only the Newtonian cooling effect but also the drag forces due to internal gravity wave breaking largely reduces the planetary wave amplitudes in the mesosphere. The momentum flux transport by upward propagating internal gravity waves acts like a Rayleigh friction on the upward propagating planetary waves so that their amplitudes are largely suppressed by the gravity wave breaking in the mesosphere. The drag forces due to the eddy diffusion deposited by the gravity wave breaking will affect largely the planetary wave amplitudes in the mesosphere while propagating vertically upward. Here, the drag force due to gravity wave breaking and the eddy momentum diffusion of planetary waves have been calculated for 20, 22, and 24 January 2007 using the equations given by Lindzen [1981], Holton [1983], and Miyahara [1985]. Dgw N 2 ðu cx Þ (8) where Dgw is the eddy diffusion coefficient due to gravity wave breaking, N2 is the buoyancy frequency squared, u is the mean zonal wind speed, and cx is the horizontal phase speed 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 gravity wave periods and vertical wavelengths are found to be 18 min, 38 min, 33 min, and 6.4 km, 4.0 km, and 6.4 km, respectively on 20, 22, and 24 January 2007 in the mesospheric height region as shown in Figures 7a–7c. The respective horizontal phase speeds (cx) of the gravity wave are calculated by the gravity wave dispersion relation using MF radar winds over Tirunelveli, and the Dgw values calculated from the equation given by Lindzen [1981]. Figure 8 shows the vertical profiles of eddy diffusion coefficients (Dgw) of gravity wave for 20, 22, and 24 January 2007. The eddy diffusion coefficient is decreasing with height above 80 km on 20 and 22 January 2007, and it is increasing up to 84 km and decreasing above this height on 24 January 2007. By substituting N2 values obtained from Rayleigh lidar temperatures over Gadanki, the 5 h mean zonal winds (u) over Tirunelveli, cx and Dgw values in equation (8), the drag force (Fx) due to gravity 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]:  2 ′ d V  Eddy momentum diffusion ¼ Dpw  2  dz (9) where Dpw is the vertical eddy diffusion coefficient corresponding to planetary wave dissipation calculated from the same equation given by Lindzen [1981]. While calculating Dpw, the TIDI zonal mean of zonal winds for 20, 22, and 24 January 2007 arep substituted ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for u. The horizontal wind perturbations V ′ ¼ u′ 2 þ v′ 2 were obtained from 40 to 60 h band-pass filtered zonal mean of zonal (u′) and meridional (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 estimated using (8) and (9) between 80 and ~87 km for 20, 22, and 24 January 2007 as shown in Figure 9. From this figure, it can be observed that, above 80 km, the drag force (Fx) dominates the eddy momentum diffusion for all the wave numbers (k = 2,3,4) almost at all the height regions on 20 and 22 January 2007. But, on 24 January 2007, the drag force is larger than the eddy momentum diffusion up to 84 km and it became lesser than the eddy momentum diffusion of spherical zonal wave numbers k = 2,3,4 between 84 and 85 km. Above this height region, the drag force again dominates the eddy momentum diffusion. However, the planetary wave eddy momentum diffusion of all the wave numbers dominates the force drag due to gravity waves, the eddy momentum diffusion 4511 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 7. The power spectral density from 2-dimensional FFT analysis to find dominant gravity wave period and vertical wavelengths in mesospheric height region: (a) for 20 January 2007, (b) for 22 January 2007, and (c) for 24 January 2007. 4512 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 8. The vertical profiles of eddy diffusion coefficient (Dgw) of gravity waves for 20, 22, and 24 January 2007. for k = 2 is larger than that of k = 3,4 at 84–85 km. The breaking altitude of the gravity wave is ~84 km in the inversion region (79–84 km) for the case of 24 January 2007 [Ramesh and Sridharan, 2012] above which the 2 day planetary wave of wave number 2 is dissipated and deposited larger eddy momentum diffusion in the background. Thus, the planetary wave suppression above 84–85 km could be due to the large planetary wave drag forces and the large eddy diffusion by the gravity wave breaking just below this height. It can also be observed from this figure that the drag force and eddy momentum diffusions for 24 January 2007 are ~100 times larger than that of 20 and 22 January 2007. Thus, when compared for the cases of 20 and 22 January 2007, the large MIL event on 24 January 2007 clearly shows that the 2 day planetary wave suppression above the inversion height could be due to the breaking of small scale gravity wave. 4. Discussion and Conclusion [29] Rayleigh lidar temperature observations over Gadanki show a few mesospheric inversion layer (MIL) events during 20–25 January 2007. The zonal mean removed SABER temperature shows warm anomalies around 50°E and 275°E indicating the presence of planetary wave of zonal wave number 2 above ~80 km. The two dimensional spectrum also confirms the dominant presence of 2 day planetary wave with zonal wave number 2. The MIL amplitudes in SABER temperature averaged for 10°N–15°N and 70°E–90°E show a clear 2 day wave modulation during 20–28 January 2007. Prior to 20 January 2007, the 2 day wave with large amplitudes is observed in the height region 80–90 km and it gets largely suppressed during 20–26 January 2007, as condition for the vertical propagation is not favorable, though it prevails at lower heights. The amplitude and phase profiles clearly show the 2 day planetary wave of spherical zonal wave number k = 2 is dominant while k = 3 was dissipated in the inversion region. [30] The planetary wave activity is inferred from the longitude-height cross section of geopotential anomalies estimated from the corresponding temperature anomalies [Salby et al., 2002]. It is observed that the temperature amplitudes are correlated with the wave amplitudes from wave geopotential anomalies in the inversion regions. The eastward tilt (positive geopotential anomaly) of the wave indicates the wave dissipation above the inversion heights, and the turbulence generated by the gravity wave breaking could modify the vertical structure of the planetary waves above the inversion layer [Salby et al., 2002]. The 10 day mean zonal wind over Tirunelveli shows deceleration of eastward winds indicating the westward drag due to wave dissipation. Charney and Drazin [1961] suggested that transient waves can interact with background flow and the interaction can bring the background winds toward the phase speed of the wave. The nightly mean MF radar zonal winds show the presence of alternating eastward and westward winds with larger amplitudes just before 20 January 2007 and with less amplitudes during the period 20–26 January 2007. The wave suppression in winds is consistent with the same observed in temperature. The alternating two day variation in the local winds could influence the propagation of gravity waves. [31] The two dimensional spectrum of Rayleigh lidar temperature observations, available for the nights 20, 22, and 24 January 2007, shows the presence of gravity wave activity with periods 18 min, 38 min, and 33 min with vertical wavelengths 6.4 km, 4.0 km, and 6.4 km, respectively. From the dispersion relation of gravity waves, it is inferred that these waves are internal gravity waves. Assuming that the gravity waves are eastward propagating waves, they get absorbed only in the eastward local wind fields of the planetary wave, thereby causing turbulence and eddy diffusion, inferred from the estimation of large drag force due to the gravity wave 4513 RAMESH ET AL.: PLANETARY WAVE-GRAVITY WAVE INTERACTIONS Figure 9. The vertical profiles of eddy momentum diffusion of planetary wave for k = 2,3,4 (in blue triangles, green squares, black asterisks, respectively) and the drag force (Fx) due to gravity waves (in red circles) for 20, 22, and 24 January 2007. breaking, leading to the formation of large amplitude inversion events in alternate nights. [32] The internal gravity waves in the eastward winds carry westward momentum upward and decelerate the mesospheric mean zonal eastward winds, and the drag forces due to the gravity wave breaking suppress the planetary wave components in the mesosphere [Miyahara et al., 1986]. The breaking gravity waves generate vertical eddy diffusion and this eddy diffusion decelerates the background wind and reverses the mesospheric wind shears [Lindzen, 1981]. Miyahara [1985] studied about the planetary wave suppression due to internal gravity waves in the mesosphere. The amplitudes of planetary waves are strongly reduced by the drag forces due to small scale internal gravity wave breaking in the mesosphere. Along with the Newtonian cooling effect, the wave drag forces and the effect of induced eddy diffusion are the suggested reasons for planetary wave suppression in the mesosphere. The calculated drag forces due to gravity wave breaking and eddy momentum fluxes of planetary waves suggest that the drag forces of gravity wave are dominant in the inversion height regions, and the eddy momentum diffusions of planetary wave are larger just above the inversion heights. On 24 January 2007, the large drag force and eddy diffusion deposited by the breaking of small scale gravity waves caused the larger eddy momentum diffusion of planetary wave just above the inversion 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 deposit more eddy diffusion in the background and strongly modify the background conditions than the wave near the critical level. Since the stratospheric and lower mesospheric horizontal phase speeds of gravity waves are ~41 m/s, ~37 m/s, and ~50 m/s, respectively (calculated from rocketsonde winds of 24 January 2007 since these winds are not available for 20 and 22 January 2007) and assuming these phase speeds are propagating upward with decreasing zonal wind amplitudes on 20, 22, and 24 January 2007; the critical levels (u cx ¼ 0 ) are very far; the breaking gravity wave deposits larger momentum flux in the background on 24 January 2007 compared to 20 and 22 January 2007. He also suggested that the group velocity of the gravity wave plays an important role in wave saturation so that waves of larger group velocities (faster waves) deposit greater momentum flux in the background to maintain the constant amplitude after dissipation. The typical values of ðu cx Þ are 20–30 m/s for the breaking gravity wave to deposit large drag force and  eddy diffusion in the mesosphere. Since the group veloc2 ity cgz ¼ k ðu Ncx Þ of the gravity wave is proportional to ðu cx Þ2 , the eddy diffusion coefficient should be larger in the breaking region of internal gravity wave. On 24 January 2007, the eddy diffusion coefficient increases in the inversion region from 80 to 84 km and again, it decreases whereas the eddy diffusion coefficient decreases above 80 km on 20 and 22 January 2007. [34] In the present study, it is shown that mesospheric temperature inversion is caused mainly due to gravity wave breaking and the inversion amplitudes got modulated by the interaction of gravity waves and planetary waves. The eddy diffusion associated with the gravity wave force drag caused the suppression of 2 day planetary wave in the mesospheric inversion region. [35] Acknowledgments. The authors are thankful to the technical staff for operating and maintaining the Rayleigh lidar system at NARL, Gadanki. They are thankful to EGRL, Indian Institute of Geomagnetism, Tirunelveli for 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 authors would like to acknowledge J.M. Russell and T.L. Killeen, the principal investigators of the SABER and TIDI projects, respectively. 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