A case study on occurrence of an unusual structure in the sodium layer over Gadanki, India

The height-time-concentration map of neutral sodium (Na) atoms measured by a Na lidar during the night of 18 to 19 March 2007 over Gadanki, India (13.5° N, 79.2° E) reveals an unusual structure in the Na layer for around 30 min in the altitude range of 92 to 98 km which is similar to the usual ‘C’ type structures observed at other locations. In order to understand the physical mechanism behind the generation of this unusual event, an investigation is carried out combining the data from multiple instruments that include the meteor wind radar over Thiruvananthapuram, India (8.5° N, 77° E) and the SABER instrument onboard the TIMED satellite. The temperature and wind profiles from the data set provided by these instruments allow us to infer the Richardson number which is found to be noticeably less than the canonical threshold of 0.25 above 92 km over Thiruvananthapuram suggesting the plausible generation of Kelvin-Helmholtz (KH) billows over southwestern part of the Indian subcontinent. Based on the average wind speed and direction over Thiruvananthapuram, it is proposed that the KH-billow structure was modified due to the background wind and was advected with it in nearly ‘frozen-in’ condition (without significant decay) in the northeastward direction reaching the Na lidar location (Gadanki). This case study, therefore, presents a scenario wherein the initially deformed KH-billow structure survived for a few hours (instead of a few minutes or tens of minutes as reported in earlier works) in an apparently ‘frozen-in’ condition under favorable background conditions. In this communication, we suggest a hypothesis where this deformed KH-billow structure plays crucial role in creating the abovementioned unusual structure observed in the Na layer over Gadanki.


Background
Mesospheric Na was discovered via measurements of nighttime spectral emissions at the wavelength corresponding to the NaD 2 (589.0 nm) emission resonance line (Slipher 1929). The ablation of meteoroids and interplanetary dust in the mesosphere and lower thermosphere (MLT) (80 to 130 km) gives rise to the mesospheric Na layer. Mathews et al. (2001a) (and references therein) found the whole earth meteoroid mass flux in the meteor zone to be of the order 1.6 to 2.7 × 10 6 kg/year. Others find larger values (e.g. Hughes 1992) while Mathews et al. (2010) provide evidence of both direct ablation and fragmentation -suggestive of direct dust formation -of incoming meteoroids in the meteor zone. These processes, the meteoroid mass flux arriving in the meteor zone as both ablated atomic metals and as dust, are widely accepted to be the major source of atomic Na (and NaHCO 3 , Na + , etc.) in mesosphere (Plane 2004). While Plane (2003), in examining Na chemistry, suggests that the sporadic enhancements in Na + concentrations can be correlated with meteor shower events, Plane et al. (2007) find that meteor showers produce a negligible change in atomic Na. This suggests that the reservoir of Na in the MLT region is large compared to that represented in the diurnal meteoroid mass flux as well as in shower events thus suggesting that dynamics and chemistry are also important. Lidars with high time and range resolution have enabled direct observation of metals represented in short-lived meteor trails (Kane and Gardner 1993;von Zahn et al. 1999;Pfrommer et al. 2009). Bowman et al. (1969) first measured the vertical distribution of Na atoms using resonance lidar and, subsequently, systematic measurements were carried out over the globe. Lidar measurements of Na atom concentration over low latitude stations have been carried out for several decades (e.g. Clemesha et al. 1979;Taylor et al. 1995;Collins et al. 2002;Clemesha 2004;Sarkhel et al. 2009Sarkhel et al. , 2010Sarkhel et al. , 2012a. On occasion, the Na concentration profiles show enhancement by a factor of 2 or more over the usual background layer in a narrow altitude region of up to a few kilometer thickness. These layers are known as sporadic Na layer (Na S ) (e.g. Clemesha et al. 1978) and often appear to be related to the ion layers called sporadic E (E S ). The generation of Na S in this case is believed to be neutralization of metallic ions accumulated (concentrated) within a narrow altitude region (sporadic E) by the wind shear mechanism (e.g., Mathews 1998). Several observations of Na S have been reported (e.g. Kane et al. 1991;Fan et al. 2007;Dou et al. 2009) wherein they deal with the correlation of Na S events with E S events. In this context, it is also to be noted that high altitude sporadic metal layers (or high altitude metal layers) have been reported from several observational sites (e.g. Friedman et al. 2013, Höffner andFriedman 2004;Chu et al. 2011;Xue et al. 2013). Gao and Mathews (2014a,b) and references therein report on high altitude radar and optical meteors indicative of sputtering as a source of metal ions above the traditional meteor zone. Kane et al. (2001) observed a rare type of sporadic Na layer structure over Arecibo, Puerto Rico. They suggested that these structures could be related to the occurrence of field-aligned ionospheric irregularities detected by a nearby VHF radar pointed towards the k⊥B region to the magnetic north of Arecibo Observatory and concluded that Kelvin-Helmholtz (KH) billows were the cause. These structures are different from conventional Na S structures and often resemble the rare 'C-type' Na layer structures sometimes seen in lidargrams (e.g., Clemesha et al. 2004). KH billows are generally considered to occur due to dynamical instability with onset condition judged by the Richardson number (R i ) (Richardson 1920) given by where u(z) and v(z) are the zonal and meridional winds (in m/s) at an altitude z. N 2 is the square of the Brunt-Väisälä frequency where T(z) is temperature at height z (meters), g is the acceleration due to gravity (m/s 2 ), and C p is the molecular specific heat at constant pressure (1,004 J kg −1 K −1 for diatomic molecules like N 2 and O 2 ).
The dynamical instability may cause turbulence if the wind shear is sufficiently large. The canonical value of the Richardson number yielding dynamic instability is R i < 0.25. As is well accepted in the literature, wind shears in the MLT region play a critical role in sodium layer characteristics. For example, Pfrommer et al. (2009) found clear evidence for dynamic instability by direct observation of KH billows in the MLT region using a high resolution Na lidar. These dynamic instability processes are also responsible for generating various short-period structures (e.g. Sarkhel et al. 2012b). Clemesha et al. (2004) also observed 'C-type' structures in the Na layer. However, they suggest an alternative to direct instabilities in creating these structures. Based on nearby simultaneous meteor wind measurements, they suggest that these 'C-type' structures might be the result of direct wind-shear distortion of preexisting clouds of enhanced sodium concentration (Nas) and advection of those spatial structures over the lidar site. They also conclude that there is limited evidence for the relationship between these 'C-type' structures and E S . Hysell et al. (2004) shows an example of the complex structure of E S over Arecibo Observatory. This structure, sometimes associated with quasi-periodic echoes, may be the result of both horizontal and vertical convergence of ions (Mathews et al. 2001b). Mathews (1996) notes the interplay between E S and neutral Na layers and that the issue ultimately demands an instrument cluster to resolve. Sridharan et al. (2009) observed rare complex structures in the Na layer over Gadanki (India) characterized by rapid enhancements of Na concentration that are completely different from the usual sporadic Na structures. They concluded that these complex structures could be due to the KH instability occurring in a region of strong wind shear. Of late, Sarkhel et al. (2012a) observed a frozen-in billow-like structure in the Na layer over Arecibo and found that it was likely created via dynamical instability processes. As this topic remains open and with the prior observations of these unusual structures over Gadanki and Arecibo, we are motivated to carefully examine additional Na lidargrams, in this case from Gadanki on the night of 18 to 19 March 2007. It should be noted that the Na lidar data on this night was reported in a different context in Sarkhel et al. (2010). The theme of the earlier paper was entirely different wherein they investigated the sensitivity of Na airglow intensity to the altitude-dependent collisional quenching that ultimately affects the Na airglow emission intensity. Based on available meteor wind radar observations from Thiruvananthapuram, India and available satellite-borne measurements, the goal of this communication is to investigate the physical mechanism(s) behind the occurrence of the observed unusual structure in the Na layer that has not been reported so far to the best of our knowledge.

Methods
Na atom concentration in the altitude range of 80 to 105 km was derived using the Na resonance lidar at the National Atmospheric Research Laboratory (NARL), Gadanki, India (13.5°N, 79.2°E; dip lat 6.3°N). A tunable dye laser, pumped by a Nd:YAG laser, is used in the Na lidar system operating at 50-Hz pulsing rate with an output energy of 12 mJ per pulse at 589 nm. The first lidar observations of the nighttime Na layer over Gadanki and the specifications of this Na lidar system are available in the literature (Bhavani Kumar et al. 2007a,b). For the uses herein, the 18 to 19 March 2007 Na concentration profiles are derived with an altitude resolution of 300 m (bin width of 2 μs) and temporal resolution of 2 min.
In order to assess the effect of neutral atmosphere instability on the neutral Na layer, mesospheric horizontal wind profiles are also used in the present investigation. The wind measurements were carried out using the SKiYMET meteor wind radar (Hocking et al. 2001;Hocking 2005) situated at the Space Physics Laboratory (SPL), Thiruvananthapuram, India (8.5°N, 77°E). This radar operates at 35.25 MHz, with a peak power of 40 kW. The radar site is close to the magnetic equator. Hence, a special transmitting scheme has been worked out to avoid the echoes from the equatorial electrojet (EEJ). A detailed discussion of the transmitting scheme and the system specifications are given in Deepa et al. (2006). The horizontal wind structure was obtained by measuring the radial velocity with an accuracy of 5% or better for every acceptable meteor event and combining these measurements yielding an all-sky manner. The minimum elevation angle used was 20°. This corresponds to the radar volume of approximately 550-km diameter at 100-km altitude. The vector wind measurements were carried out in every 15 min with an altitude resolution of approximately 3 km within 82-to 97-km region.
The mesospheric temperature profiles needed for our neutral atmosphere instability calculations are obtained from the TIMED (Thermosphere Ionosphere Mesosphere Energetics and Dynamics) satellite. The altitude profiles of mesospheric kinetic temperature obtained by the SABER (Sounding of Atmosphere using Broadband Emission Radiometry) instrument onboard TIMED are additionally employed in this study (data source: http:// saber.gats-inc.com; v2.0). SABER uses the 15 μm CO 2 terrestrial emission to retrieve pressure, which is then utilized to derive temperature with a maximum uncertainty of 10 K in the altitude range of 80 to 105 km (Mertens et al. 2001). SABER measurement locations are chosen nearest to the meteor wind radar observational site (SPL, Thiruvananthapuram), which are depicted in Figure 1. The SABER measurement time used here was at about 01:30 IST (IST = UT + 5.5 h) on 18 to 19 March 2007. Figure 1 shows a map of the Indian subcontinent depicting the locations of NARL and SPL. The SABER measurement locations are also shown in same figure. These locations are chosen based on the SPL, Thiruvananthapuram meteor radar observing site. For this event case study, two SABER profiles at different measurement locations were used; these measurements were carried out almost simultaneously (at approximately 01:30 IST).

Data analysis
The mesospheric temperature profile is used to calculate N 2 , while Richardson number R i requires additional knowledge of wind shear. Altitude profiles of R i at different times during 18 to 19 March 2007 are calculated using the SABER temperature profiles and the SPL, Thiruvananthapuram meteor winds. It is to be noted that the SABER snapshot measurement of nocturnal mesospheric temperature is available only at around 01:30 IST. In this context, it is important to note that the average temporal variation in the nocturnal temperature over Gadanki (a low latitude station) during spring equinox (March) is only approximately 20 K in the altitude range of 80 to 105 km (Kishore Kumar et al. 2008). They present height-time contours of SABER-derived temperatures during the spring equinox (March and April) over the southern Indian subcontinent, which reveals that the average temperature during nighttime (16 to 24 UT) varies in over 180 to 200 K in the altitude range of 80 to 105 km. However, the nocturnal temporal variation in mesospheric temperature is taken to be small as just outlined. Hence, the single approximately 01:30 IST, location-averaged, temperature profile obtained from SABER is used as a representative value during the interval of interest. As Thiruvananthapuram is also a low latitude station, the same temperature profile is (necessarily) adopted for this location. From these two datasets -using SPL, Thiruvananthapuram meteor wind profiles and the average temperature profile of SABER 1 and 2 (shown in Figure 1) -a height-time R i map is developed. As shown in Figure 1, the SABER 1 and 2 locations are separated by around 500 km while the variation in temperature between the locations is only 5% to 7% in the altitude range of 800 to 100 km (presented in Figure 2, to be discussed in the 'Results' section). Thus, the spatial variability between SABER 1 and 2 is expected to be small. Since the SPL, Thiruvananthapuram meteor radar site is approximately 600 km from the SABER 1 and 2 locations, a similar argument is taken for the radar site. That is, the snapshot temperature profiles are measured approximately 600 km away from radar site at 01:30 IST, we thus (necessarily) assume that the temperature profile in the radar volume is that of the SABER locations. We again note that meteor radar provides average wind over approximately 275-km radius around the radar site. We thus used the average temperature profile for the calculation of Richardson number over Thiruvananthapuram.
The uncertainty in the meteor radar-derived horizontal wind is approximately 5 m/s in the altitude range of 91 to 97 km and over the approximately 275-km radius. Hence, when also considering the uncertainty in SABER temperatures of approximately 10 K, the maximum uncertainty in computing R i is approximately 0.02. Figure 3a displays the atomic Na height-timeconcentration map (or lidargram) for the night of 18 to 19 March 2007 over the 80-to 105-km altitude range above Gadanki. Figure 3b gives a detail of the 90-to 105-km altitude region Na distribution on that night. As previously noted, this paper is prompted by the unusual sodium concentration structure resembling a mirror image of λ (named as 'λ image ' henceforth) that is observed in the altitude range of 92 to 98 km over 21:30 to 22:00 IST. Of further interest is the net increase of the background Na atom concentration above 94 km after the occurrence of this structure. Figure 3c gives the sequence of individual Na concentration profiles on that night. There is no apparent downward phase progressionan acoustic gravity wave feature -after the structure appeared in the lidargram up to 00:00 IST and over the altitude range of 93 to 100 km. Figure 3d shows the integrated column content between the base and top of the λ image structure (93 to 100 km). The column content is observed to increase noticeably after the appearance of the structure until 22:30 IST. This increase is in addition to a steady column content increase through the whole observation period. Figure 2 gives the individual SABER temperature profiles, SABER 1 and 2, during the night of 18 to 19 March 2007 at approximately 1:30 IST. The measurement locations are shown in Figures 1 and 2, and they reveal that the variation in temperature between SABER 1 and 2 is only 5% to 7% in the altitude range of 80 to 100 km. Figure 4a,b gives the SPL, Thiruvananthapuram meteor radar-derived zonal and meridional wind profiles for the 18 to 19 March 2007 observing period. It is interesting to note that the zonal wind is eastward (positive) and meridional wind is northward (positive) over 17:00 to 00:00 IST above 91-km altitude. Figure 4c shows the altitude variation of R i at different times over Thiruvananthapuram. R i is calculated using total wind   shear and the average temperature profile obtained using SABER 1,2 data, which are the closest SABER passes to Thiruvananthapuram (shown in Figure 1). It can be noted that R i remains less than 0.25 during 18:00 to 19:00 IST above 92 km, which is likely to be an indication of KH billows. It has been also verified that the convective instability was absent on that night as the Brunt-Väisälä frequency (N 2 ) derived at both SABER 1 and 2 locations were found to be positive throughout the entire region (80 to 105 km). While Na lidar measurements over Thiruvananthapuram would have been ideal, we must address the lidar at Gadanki observational results per the generation of KH instabilities over this location using the Thiruvananthapuram meteor wind data. However, the R i < 0.25 altitude region inferred from the meteor radar winds and SABER winds reasonably matches the region over Gadanki where the 'λ image ' type structure was observed over 21:30 to 22:00 IST. While not proof, the R i < 0.25 region and the scale over which it is estimated together with the 'λ image ' structure suggests that the origin of the 'λ image ' type structure is in the generation (and the subsequent advection to the Gadanki area) of KH instabilities as we further address in the 'Discussion' section. Figure 4d gives the average zonal and meridional wind profiles. Importantly, the horizontal background wind above approximately 92 km is northeastward with a mean speed of approximately 58 m/s. Figure 5 highlights the zonal and meridional wind during 18:00 to 19:00 IST over Thiruvananthapuram when R i < 0.25. It can be noted that the zonal wind switches direction between eastward and westward above 95 km over the 18:15 to 18:45 IST period. In addition, it is predominantly westward at 18:30 IST except at 94-km altitude where it is observed to be eastward. The direction of the meridional wind is unaltered during this time period, and the net wind vector is observed to be northeastward. These facts support the idea that the instability region over Gadanki is indeed advected towards Thiruvananthapuram and that the 'λ image ' Na layer structure is arguably a result of a KH billow that occurs in the inferred -and likely mesoscale sized -dynamic instability region over the southwestern Indian subcontinent.

Discussion
This section explores and discusses the role of various physical mechanisms that can generate the 'λ image ' structure observed in the lidargram (Figure 3) presented in the above section.

Role of dynamical instability and advection
In order to understand the occurrence of the 'λ image ' structure in the lidargram shown in Figure 3, we assembled all available data to determine if we could identify a possible source of this structure. Atmospheric winds and temperatures in the MLT region are necessary to investigate the possible role of convective or dynamic instabilities. In the absence of wind measurement over/nearby Gadanki, zonal and meridional wind profiles over Thiruvananthapuram are used in the present investigation (location is shown in Figure 1). Based on the horizontal winds and SABER temperature profiles, the altitude variation of R i is derived at different times and found to be predominantly less than the canonical instability threshold of 0.25 during the 18:00 to 19:00 IST period ( Figure 4c) -a condition which is conducive for the generation of KH billows. It is important to note that the average background wind above 92 km is northeastward with magnitude of approximately 58 m/s. As Gadanki is northeast of Thiruvananthapuram, the atmospheric background condition is suitable not only for generation of KH-billow structures but also for the (in this case necessary) advection of these billows towards Gadanki. As the beam-width of SKiYMET meteor wind radar is several tens of degrees (Hocking 2005), the derivation of horizontal wind profiles is necessarily averaged over a vast horizontal area of the MLT region. Hence, these winds are taken to prevail over a wide region in southern part of India (as is the SABER temperature determination) and thus that the KH-billow structure we suspect to have developed during 18:00 to 19:00 IST over Thiruvananthapuram to have been advected to Gadanki (possibly) without further modification till 23:00 IST. The important point here is that conditions are conducive for KH-billow formation and for advective transport of these structures from southern India to Gadanki.
It is to be noted that the volume-averaged meteor radar wind data is dominated by large-scale temporal changes instead of spatial changes within the observing volume. The changes in the horizontal wind during 18:00 to 19:00 IST (shown in Figure 5) suggest that the generation and the temporal evolution of the proposed KH-billow structure occur during this interval (to be discussed later in detail in Figure 6a). However, in the absence of strong shear in the horizontal wind after this time, it is assumed that the structure, thus formed, remains temporally less affected and is spatially advected in the northeastward direction as a result of winds in the direction leading to its appearance over Gadanki. Additionally, it is to be noted that the meteor radar, given the volume averaging, does not reveal any information on the KH-billow structure and only provides the information on the wind, one of the parameters for determining dynamical instability. The generation and evolution of the KH-billow structure, as mapped into the Na profile, and its subsequent transport in nearly 'frozen-in' condition is only a proposition and not a proof. At the core of our argument, this hypothesis does appear to explain the Na lidar observation over Gadanki.
Given our hypothesis whether the KH billow will be transported by background wind to reach the Na lidar location can now be investigated further. Based on the horizontal background wind of approximately 58 m/s above 92 km averaged throughout the entire observational period (17:00 to 02:00 IST), the travel time for KH billow to reach Gadanki around -600 km away from Thiruvananthapuram -is 3 ± 1 h. The uncertainty involved in estimating travel time is calculated based on the standard deviation of horizontal wind of approximately 17 m/s during entire observational period above 92 km. Interestingly, this travel time nearly matches with the time difference between the conjectured occurrence of KH billow (dynamical instability conditions) over Thiruvananthapuram and the appearance of the 'λ image ' structure in the Na layer over Gadanki. Thus, based on these observations, it is reasonable to assume that the formation and advection of KH billows left a unique signature on the Na layer. It is also to be noted that λ image structure appeared in the Na layer during 21:30 to 22:00 IST (Figure 3) before the second wind reversal that occurred at 97 km during 23:30 to 00:00 IST (Figure 4), which would have no effect on the already formed λ image structure over Gadanki. A scenario for formation of the sodium 'λ image ' structure due to KH billows is addressed next.
It is important to note that Na lidar records horizontally narrow vertical profiles of Na atom concentration as a function of time. Thus, the lidargram represents a time history of the vertical distribution of Na atoms in a narrow cylindrical volume over the lidar location. The lidargram of course includes the effects of neutral Figure 6 Manifestation of a KH billow on the lidargram. Schematic diagram describing how a KH billow moving towards the Na lidar beam will manifest a 'C-type' structure on the lidargram.
atmosphere dynamics on the Na layer as these atoms have a long lifetime relative to the evolution of atmospheric dynamics and they are collisionally wellembedded in the atmosphere. Based on typical electron concentration (approximately 3,000 electrons cm −3 ), Sarkhel et al. (2012a) estimated the rate at which the Na atoms ionize would be approximately 3 × 10 −6 s −1 , which corresponds to a lifetime of neutral Na atoms of more than a day. This is supported by Xu and Smith (2003) wherein they have shown that the chemical lifetime of mesospheric Na atoms is more than a day in the MLT region, which is much larger than the transport time considered in our hypothesis. Hence, any Na-layer temporal variation on the scale of a few hours is predominantly due to dynamical effects in the Na layer where background horizontal wind and its shear play important roles. Thus, any horizontal structures, generated in the observed vertical Na profile by winds, will be translated into temporal variations of lidargram. Kane et al. (2001) describe 'C-type' structures observed in the Na layer on several occasions. They suggested this type of structure could be caused by wave breaking or KH billows and could be generated in the Na layer due to strong wind shear. However, Clemesha et al. (2004) argued that advection could possibly generate 'C-type' structures in the Na layer. They describe a scenario wherein any Na cloud advected with the horizontal wind can be elongated via the prevailing wind and will be manifested as a 'C-type' structure in the lidargram. The schematic diagram in Figure 7 explains how a KH-billow structure can imprint a 'C-type' structure in the lidargram. As described in the figure, the three points ' A, ' 'B, ' and 'C' on the billow whose curvature is facing towards the lidar beam will manifest as a 'C-type' structure. As discussed earlier, the lidargram represents a time history of vertical distribution of Na atoms over the lidar location. Hence, the point ' A' on the advecting billow will appear first on the observed 'C-type' structure relative to points 'B' and 'C' that occur later.
In the present investigation, R i remains less than 0.25 during 18:00 to 19:00 IST as a consequence of strong wind shear and hence indicates the possible generation of KH billow. The overturning shape of these billows also depends on the direction of winds. In order to test this hypothesis, we critically observe the direction of zonal and meridional wind profiles during the time of interest. The horizontal winds do reveal remarkable features. As shown in Figure 5, the zonal wind above 91 km is eastward and the meridional wind is northward during 18:00 to 18:15 IST and 18:45 to 19:00 IST. A significant wind reversal is observed at approximately 18:30 IST wherein the zonal wind is predominantly westward except for a altitude-narrow region near 94 km altitude where it is eastward (note again that the meteor radar winds are assembled over a relatively large volume). The meridional wind direction is unchanged during this time period. However, the meridional wind magnitude at 94 km is observed to increase to 68 m/s at approximately 18:30 IST -this is more than 1.5 times higher than that during 18:00 to 18:15 IST and 18:45 to 19:00 IST. Hence, the horizontal wind at 94 km is northeastward with higher magnitude and northwestward at other altitudes at 18:30 IST. This sudden wind reversal over a limited altitude region generates a strong wind shear. This interesting and perhaps unique phenomenon -that occurs over a significant volume -leads to the possible shape of the hypothesized evolving KH billow. Figure 6 represents our schematic depiction of how a KH billow generated and evolving in the observed strong wind shear might result in the observed 'λ image ' type structure. Again, note that the observed horizontal wind was northeastward above 93 km and northwestward below this altitude during the 18:00 to 18:15 IST period. That is, given the observed winds, the billowoverturning feature will face towards the northeastward as is sketched in Figure 6a. Then, the KH billows is subject to a wind reversal at approximately 18:30 IST that could produce an additional 'fold' in billow structure due to the net wind being northeastward at 94 km with a higher magnitude and northwestward elsewhere. As is well accepted in the literature that KH billows, generated within a particular altitude region, expand both horizontally and vertically. In the present case, we suggest that the KH billow is generated at approximately 93 km where we infer that R i < 0.25 -the wind reversal takes place just above the altitude region where the billows are likely generated. Additionally, the background winds during 18:00 to 18:15 IST period favor the evolution and expansion of this KH billow. In particular, when the extended portion of the billow encounters the wind reversal region, it -under our hypothesis -undergoes deformation due to the northwestward wind. This peculiar wind pattern at 94 km during 18:30 IST deforms the shape of the KH billow and creates a small bulge or outward notch at 94 km which is conceptually drawn in Figure 6a. This bulge will be eventually elongated outward due to strong wind shear experienced during 18:45 to 19:00 IST. The protruding notch will subsequently overturn as a consequence of shear and enhancement of the northeastward wind at the height region around the notch similar to the condition prevalent during 18:00 to 18:15 IST. The possible shape of the bifurcated KH billow at 18:45 to 19:00 IST is indicated in Figure 6a. The curvature of the elongated notch will be northeastward similar to the original curvature of the KH billow adjacent to the overturned notch. How this structure may be translated or mapped into a lidargram is indicated in Figure 6b. To summarize, we suggest that this deformed KH-billow structure, generated during 18:00 to 19:00 IST over Thiruvananthapuram region, was then advected in the northeastward direction having developed more folder that was revealed subsequently as it crossed the field-of-view of the Na lidar over Gadanki.
Given the observed wind structure, the deformed KHbillow traveling with mean speed of approximately 58 m/s will reach the lidar site after 3 ± 1 h. This study suggests that such conditions can last for a few hours, thus yielding an estimate of the lifetimes of the KH billow which is generated and deformed during 18:00 to 19:00 IST interval and can then be nearly 'frozen-in' and advected along with the mean wind in the absence of strong shears. Sarkhel et al. (2012a) observed similar billow-like structures in the Na layer over Arecibo, Puerto Rico. They concluded that strong wind shear made the region dynamically unstable and was likely responsible for the observed structure in the Na layer that were observed in the lidargram for about 3 h. This structure -while still evolving -would likely be transported some distance by the overall background wind.
Since the Na layer is embedded in the neutral atmosphere, any structure/instability created in the neutral atmosphere will also be mapped into the Na layer. As demonstrated in Figure 6, the KH billow whose curvature is faced towards the lidar beam will appear as 'C-type' structure in the lidargram. Since Gadanki is northeast of Thiruvananthapuram, a KH-billow structure, whose overturning shape is towards northeastward, will face towards the lidar beam. Hence, it will imprint a 'C-type' structure in the lidargram. As conceptually described in Figure 6a, the bifurcated KH billow that continues to 'fold' may develop a more complex structure facing towards lidar beam and may resemble the lidargram structure shown in Figure 6b. That is, these two adjoining 'C-type' structures, as a whole, then manifest a 'λ image ' structure in the lidargram.
The detection of any Na layer structures depends on the chemical lifetime of Na atoms, which must be large compared to the typical time scale of the dynamical events. Thus, once a KH-billow structure is generated due to favorable background conditions, it should be traceable using a Na lidar. This conducive atmospheric condition is achieved when R i < 0.25 which, in turn, depends on the altitude profiles of horizontal winds and temperature. It must be noted that the meteor wind radar, which measures altitude profiles of the horizontal wind, is not capable of detecting KH billow directly. The meteor wind radar only indicates the presence of wide-scale wind shears necessary for the generation of KH billow. In order to detect KH-billow structures in mesosphere, an instrument such as Na lidar is needed. Hence, the fact that R i > 0.25 after 19:00 IST over Thiruvananthapuram does not necessarily mean that the KH billow, generated during 18:00 to 19:00 IST, has vanished. Instead, it may indicate that the background condition is simply not conducive for further generation of KH billows. Our hypothesis is that the KH-billow structure (and its effect on the Na layer), once generated, remains more or less intact in the atmosphere for, perhaps, a few hours. This hypothesis is supported by the previous observations of billows in the Na lidar data over Arecibo that were seen for at least 3 h of observing period (Sarkhel et al. 2012b). Such structures can move with the mean wind and reaches the Na lidar location where it is detected.
In the next subsections, we will be exploring other plausible scenarios which could be responsible for modification of the Na layer and thus creating the 'λ image ' structure in the lidargram.

Role of gravity waves
The possible role of gravity waves in the generation of these structures is considered next. A steady increase in column density, between the base and top of the λ image structure (93 to 100 km) that continues to the end of the observation period is noted in Figure 3d. This feature might be related to long-period gravity waves with a dominant time period of fluctuation of approximately 88 min. However, the Na column density increases noticeably after the occurrence of the structure until 22:30 IST that may also indicate vertical overturning -due to the billows formation -whereby the Na content from the main layer is transported up into the region directly above. Whether this increase in Na abundance until 22:30 IST is due to gravity waves can be investigated. As revealed from Figure 3c, the sequence of Na concentration profiles on that night does not reveal any downward phase progression up to 23:30 IST in the altitude range of 93 to 100 km after the structure appeared. Hence, it seems unlikely that the increase in column abundance during 21:00 to 22:30 IST is due to the effect of gravity waves propagating through the main Na layer. It remains possible, or perhaps even likely, that this increased column content is associated with the creation of the KHbillow structure, a consequence of dynamical instability. Moreover, the main layer is centered around 90 km and shows the influence of wave activity during the entire observation. Thus, the λ image structure is not strongly related to the layer at 90 km and occurs only for short duration as compared to the main layer evolution. All these phenomena strengthen the hypothesis of the nearly 'frozen-in' KH-billow structure, which was created in the southwestern part of India due to appropriate atmospheric conditions and then transported along with the northeastward background wind which might have created the 'λ image ' structure in the lidargram over Gadanki.

Role of sporadic-E activity
While we conclude that dynamical instability led to the observed λ image structure, the possible relationship between the Na λ image structure and E S is examined next. Clemesha et al. (2004) found weak correlation between these 'C-type' structures and E S . Their conclusion is that the wind plays a major role creating the structure instead of conversion of Na + in E S to neutral Na. It is important to note that the region where the 'λ image ' structure appeared is aeronomically very complex. The effect of atmospheric dynamics and Na ion-molecular chemistry is necessarily coupled together. The false color background gradient in Figure 6a schematically underscores the complex chemical/dynamical interplay in producing the Na distribution in the MLT. As the lifetime of Na + ions below 90 km is a few seconds (Daire et al. 2002), the recombination of Na + ions and electrons produces neutral Na atoms which are then embedded into the background atmosphere. Thereafter, the neutral Na layer follows the background atmosphere wherein dynamics plays major role. On the contrary, recombination of Na + ions and electrons occurs slowly above 100 km. As a consequence, the lifetime of Na + ions increases to a few hours at this height region. Thus, the neutral Na layer produced by neutralization of Na + ions into Na atoms retains the memory of its ion layer and hence E S . That is, any structure related to Na + ions will map into the neutral Na layer on a few hour time scale. Sarkhel et al. (2012a) observed high altitude (>102 km) billows in the neutral Na layer wherein they discussed that such structures in the neutral Na layer can be associated with the underlying ion layer during strong E S events for which ion concentration often exceeds 10 4 ions.cm −3 . In the intermediate altitude region (90 to 100 km), we encounter the most complex interaction with both neutral Na and Na ions playing comparable roles. The lifetime of Na + ions ranges from a few minutes to tens of minutes (Daire et al. 2002). Therefore, the neutral Na layer will have a limited memory of E S where the presence of sufficient wind shear can generate E S layers (e.g. Mathews 1998). That is, since the Na + ions in the MLT region are partially collisionally coupled to neutral atmosphere, structures such as KH billows generated due to strong wind shear in the neutral atmosphere also may share features exhibited in E S layer structure. Thus, as the neutral Na layer and E S layers may share a common origin in the atmospheric wind system, it is difficult to exclude E S layer influence on the sodium distribution. In any case, with the absence of any ionosonde observations close to the lidar location during these observations, it is difficult to comment further on the occurrence/influence of E S layer over Gadanki region. Sporadic-E layers are related to the neutral enhancements via ion-neutral coupling (Raizada et al. 2011(Raizada et al. , 2012, any structure-like appearance of billow-like features are usually linked to dynamical instabilities (Sarkhel et al. 2012b). In order to address this aspect comprehensively, further investigations involving instrument clusters are needed (Mathews 1996).
The next subsections are dedicated to explain the valid assumptions that are used in the present investigation. The justifications behind such assumptions are also discussed in detail. We have also explored the limitations while formulating the hypothesis based on the available data set.

Assumptions and their justifications
We have necessarily calculated the time-resolved R i from temporally variable wind data and a snapshot temperature profile obtained approximately 600 km from the lidar site. We simply note the assumption that the temporal variation of temperature is not expected to be significant enough to alter the conclusion of the paper. As discussed earlier, the spatial variability between SABER 1 and 2 is not significant and this is taken as a proxy for changes, or rather the lack of change, in temperature with time. We have also verified the differences between the Richardson numbers derived using individual SABER 1, SABER 2, and average SABER 1,2 (which is already in Figure 4c) temperature profiles. We have observed that the R i 's are different for different temperature profile during 18:00 to 19:00 IST. However, they still remain less than 0.25 above 92 km during the abovementioned time. Therefore, the assumption that the spatial variation between SABER 1 and SABER 2 temperature profiles is not significant is fairly justified and we have thus used the average SABER 1,2 temperature profile to calculate the Richardson number.
The work of Kishore Kumar et al. (2008) indicates that the average nocturnal temporal variation of temperature in the altitude range of 80 to 105 km is approximately 20 K during spring equinox (March and April) over southern part of Indian subcontinent. Friedman and Chu (2007) also report that the standard deviation of temperature at a given upper mesosphere altitude is less than 20 K and is due to tides during March over Arecibo (a low latitude station) -this is also not very significant. Since R i is calculated based only on snapshot temperature profile, there can be an additional variability in R i due to variation in temperature during the night. Owing to the lack of measurement of the temporal variation of temperature at a given altitude over Thiruvananthapuram, it is not possible to comment on the variability of R i due to the temperature variation. The present work is based on the assumption that the temperature does not change significantly during the interval of generation of the KH billow over Thiruvananthapuram and subsequent propagation to Gadanki.

Limitations
In addition, the limitation of the available data set does not allow us to study the influence of small-scale horizontal/vertical variability -due largely to acoustic gravity waves -for this case. Short-scale, wave-related variability may change the local temperature and wind fields. However, the data provided in the manuscript is the best available data set that can be used to study possible mechanisms for generation of the observed λ image structure. While we cannot rule it out, there is no evidence that the temporal/horizontal variation of temperatures is not significant. However, the altitude variation of temperature is important, along with wind shears, in creating instabilities. Therefore, the vertical temperature gradient is an important parameter as it is used to calculate Brunt-Väisälä frequency and Richardson number. As discussed earlier, Friedman et al. (2003) reports that the nocturnal temperature variation at a given altitude in the MLT region is small over the low latitude site, Arecibo Observatory (latitude: 18.6°N). Hence, we assume that temporal variation of the vertical gradient of temperature will also be small. Therefore, ignoring the temporal variation of the vertical temperature gradient at a given altitude in the MLT region is reasonable.
There are two other limitations in the present paper that could not be addressed due to lack of supporting observations. These are the possible effects of 'fieldaligned irregularity' and 'gravity wave ducting'. In the absence of collocated HF/VHF radar measurements, it is difficult to explore the impact of the field-aligned irregularities on the structures in the Na layer. The lack of imaging observations also does not allow investigation of the role of acoustic gravity wave ducting as horizontal phase speed and wavelength are unknown. A vertically propagating gravity wave can be ducted in a region where m2 > 0 (m is the vertical wave number) and is bounded by regions of evanescence (m2 < 0) (e.g., Walterscheid et al. 2000). However, Sarkhel et al. (2012a) inferred that the ducted gravity waves are unlikely to generate a particular frozen-in billow-like structure in the Na layer reported in that work.
Despite the obvious limitations, the present investigation strongly suggests the importance of dynamical phenomena such as KH instabilities in the upper mesosphere and their likely role in the generation of complex structures, such as the 'λ image ' structure shown in Figure 3, in the Na layer. The multi-instrument observations reported here suggest how a bifurcated KH billow (and the embedded Na content) generated in the southwestern part of India due to wind shears -along with appropriate vertical temperature gradient -and advected by the background wind towards the northeast is consistent with the unusual structure observed in the Na layer. In the absence of measurements that are closely separated in space, the present explanation is only suggestive in nature.

Lifetime of the deformed KH billow
Despite the limitations due to the lack of cluster of instruments and coordinated measurements, our effort on the hypothesis of generation of the 'λ image ' structure in the lidargram brings out an important parameter that should be addressed: the lifetime of deformed KH billow. Our investigation poses a question: Can the deformed KH billow have a few hours lifetime? As already discussed, Pfrommer et al. (2009) found clear evidence of KH billows in the MLT region using a high resolution Na lidar. However, they observed KH billows in the lidargram only for a few minutes. As described by Hecht et al. (2005), the lifetime of such KH billows is a few tens of minutes. Theoretical studies by Fritts et al. (1996) and Palmer et al. (1996) show that the lifetime and evolution of such KH billows and their subsequent dissipation are complex and far less understood.
In recent times, the Na lidar observations and investigations on the manifestation of the KH billows in the Na layer brought the attention among the researchers. A few observations of 'C-type' structures in the lidargram from different locations bring out the existence of KH billows in the Na layer (Kane et al. 2001;Sridharan et al. 2009). All the observations reveal that the lifetime of the structures is 30 min to 2 h. As explained by Clemesha et al. (2004), the occurrence of the 'C-type' structure in the lidargram is a result of wind-shear distortion of preexisting clouds of enhanced Na concentration. Kane et al. (2001) and Sridharan et al. (2009) suggested that KH billows play important role in the formation of 'C-type' structures that appeared in the lidargram. These observations indicate that the background wind and atmospheric conditions play crucial role in the evolution and sustenance of the KH billows in the MLT region. In the present case study, the KH billow has been hypothesized to be generated and deformed during 18:00 to 19:00 IST over Thiruvananthapuram. Further evolution and deformation of this KH billow was probably ceased due to the absence of strong wind shears. As a consequence, this KH billow is believed to get nearly 'frozen-in' the background wind and advected to Gadanki. In absence of the Na lidar measurements, the formation of KH billow over Thiruvananthapuram cannot be unambiguously established. Nevertheless, the wind observations over Thiruvananthapuram and the Na lidar observations over Gadanki provide credence to the proposition made in the present study. However, it remains to be confirmed whether favorable background conditions in the MLT region can help to sustain the KH billows for a few hours without significant decay. This communication poses an open question on the lifetime of KH billows in the MLT region. Further investigations including theoretical work along with systematic and coordinated measurements using cluster of instruments possibly can answer this.

Conclusions
This investigation suggests the physical mechanism behind an unusual structure (resembling a mirror image of λ or 'λ image ') observed in the Na layer for around 30 min in the altitude range of 92 to 98 km over Gadanki. The meteor wind observation from Thiruvananthapuram and the TIMED satellite measurements of mesospheric temperature over nearby locations reveal the possibility of occurrence of KH billow in the southwestern part of Indian subcontinent. The horizontal wind direction and magnitude over Thiruvananthapuram indicate that the shape of the KH billow was modified initially. Later, it got 'frozen-in' the background medium and advected with the northeastward wind to the lidar location where it appeared as the λ image structure in the lidargram. This case study presents a scenario wherein the 'frozen-in' deformed KH-billow structure sustained for a few hours without significant decay in the mesosphere. It is, therefore, suggested that the lifetime of the KH billows in the mesosphere can be of the order of a few hours under favorable background conditions.