Investigation of convectively generated gravity wave characteristics and generation mechanisms during the passage of thunderstorm and squall line over Gadanki ( 13 . 5 ◦ N , 79 . 2 ◦ E )

This study illustrates the convectively generated gravity wave generation mechanisms during the passage of thunderstorms and squall line using Indian MST radar. For the first time, it has been shown that all three generation mechanisms have been involved in the generation of gravity waves during the passage of squall line event. It is observed that the periodicities in the range of 8–80 min in the tropospheric and 8–32 min in the lower stratospheric regions and vertical wavelengths in the range of 3.2–4.8 km in the tropospheric and 1.2–1.92 km in the lower stratospheric regions are found to be dominant in the present study and are distinctly different during initial, mature and dissipative phases of convection. Amplitude of vertical wind has been weakened (from∼ 4–6 m s−1 to ∼ 1 m s−1) considerably after 10– 30 min of a convection event. It appears that the wind shear associated with the convective clouds acted like an obstacle to the mean background flow during the squall line passage generated gravity waves. The phase profiles corresponding to the dominant period show both downward and upward propagation of waves. The vertical extent of heating is found to be deeper during squall line event compared with thunderstorm event. From the phase profiles, during 27 September 2004, two peaks of constant phase region are observed. One is due to convective elements and the other is due to strong background wind shear; however, only one peak is observed on 29 September 2004, which is only due to convective processes.


Introduction
It is well known that gravity waves significantly affect various dynamical processes in the upper and middle atmosphere (Fritts and Alexander, 2003;Mohankumar, 2008). The convectively generated gravity waves (CGWs) play a key role in organizing convection and initiating new cells (Lin et al., 1998). Mapes and Houze Jr. (1995) suggested that vertical motions in a stably stratified atmosphere allied with buoyancy oscillations favor the triggering of the additional convection that is perceived to be the main initiating mechanism of gravity waves (GWs).
Convection plays a major role in generating GWs by releasing enormous amounts of latent heat and contributes to the wave mean flow interactions in the tropical middle atmosphere (Alexander, 1995;Pandya and Alexander, 1999). Upstream propagating waves will be produced when a convective cloud obstructs the mean flow (Clark et al., 1986;Pfister et al., 1993;Alexander and Vincent, 2000;Beres et al., 2002).
CGWs are quite important in tropics because of their efficient transport of surplus energy to sub-tropics by means of general circulation (Green, 1999). Hence, an appropriate parameterization scheme needs to be developed for application in the global climate models (Beres et al., 2002). There are several studies analyzing the structure and impact of CGWs in tropical regions (Dhaka et al., 2002(Dhaka et al., , 2003Kumar, 2006Kumar, , 2007Dutta et al., 2009). Although an attempt was made by Beres et al. (2002), a cross-sectional understanding of CGWs in the three phases of convection has not yet been gained.
The present study describes the characteristics of GWs in initial, mature and dissipative phases of convection. From Indian MST radar, the ECWF model and satellite data an attempt to find the dominant generation mechanism of CGWs during the passage of thunderstorms and squall lines over Gadanki is made.

MST radar data
Radar observations are provided by the National Atmospheric Research Laboratory, Gadanki (13.47 • N,79.18 • E), between 10:30 LT (Local Time) on 27 September 2004 and 10:18 LT on 30 September 2004. We analyze two events of thunderstorm and squall line that took place over the studied location during this period: Event 1 on 27 September 2004 and Event 2 on 29 September 2004. Wind information obtained from radar data, which operated the vertical (Zenith-X, i.e., Z x ) direction, in the six beam (viz., East (E), West (W), Zenith (E-W polarization, i.e., Z x ), Zenith (N-S polarization, i.e., Z y ), North (N), and South (S)) mode at an 8-12 h interval. May and September months are likely for the observation of deep convective events such as thunderstorms over this part of the tropical region (Dutta et al., 2009). VHF radar located at Gadanki operates at 53 MHz with an average power aperture product of ∼ 7 × 10 8 W m −2 and a narrow beam width of 3 • . The technical specifications of Indian MST radar operating at VHF ranges at Gadanki (13.47 • N, 79.18 • E) have been furnished in Rao et al. (1995). Continuous observations of vertical velocities with a vertical resolution of 150 m and temporal resolution of 48 s and 38 s during events 1 and 2 have been utilized for the present study.

Satellite observations of equivalent blackbody brightness temperature
We have used the hourly cloud-top equivalent blackbody temperature, called brightness temperature, from Multifunctional Transport Satellite (MTSAT-1R) data provided by the Japan Meteorological Agency (JMA) through Kochi University, Japan. Data was recorded in a latitude-longitude grid 11.55 • N/77.2 • E-15.5 • N/81.15 • E with 0.05 • resolution covering the location of Gadanki. The black body brightness temperature (TBB) data, averaged from the pixel data, is used to examine the characteristics of synoptic-scale and mesoscale cloud systems. The occurrence of tropical convection during the studied period is inferred from this last information.

ERA-Interim reanalysis data
ERA-Interim reanalysis temperature data sets (Simmons et al., 2007) at 37 vertical levels from 1000 hPa to 1 hPa over the study area with a 1.5 • × 1.5 • grid have been obtained for 00:00, 06:00, 12:00 and 18:00 UTC (Universal Time Coordinated (UTC) = LT − 5.5 h) from the portal http://www.esrl. noaa.gov. Figure 1 shows the cloud top brightness temperature (TBB) over Gadanki (13.47 • N,79.18 • E) and Chennai (13.00 • N, 80.18 • E) obtained from MTSAT-1R satellite measurements. We adopted the criteria from TBB of less than 235 K to demarcate deep convective clouds (Chen et al., 1996;Arkin and Meisner, 1987). It is noticed from Fig. 1 that there is deep convective activity over Gadanki and Chennai on the night of 27 September to the early morning of 28 September. 40 mm rainfall was also recorded by the rain gauge of IMD, Chennai observatory (Suresh, 2012), and 56 mm was recorded by the disdrometer at the MST radar site (Radhakrishna et al., 2009). Even though cumulonimbus (Cb) clouds were going through Gadanki (GDK) towards Chennai (MDS) on 29 September at 09:12 LT (03:42 UTC) and on 30 September at 17:42 LT (12:12 UTC, as in Fig. 2), no significant rainfall had been recorded at GDK. However, 3 to 5 mm was recorded at MDS. The rainfall information has been obtained from precipitation accumulation data retrieved from the Doppler Weather Radar (DWR) IMD, Chennai (Suresh, 2012).

Background meteorological conditions
The Doppler Weather Radar (DWR) reflectivity products of the India Meteorological Department (IMD), Chennai (Fig. 2) depict the existence of matured thunderstorm and squall line events over Gadanki. The maximum value of reflectivity (Max (Z)) product shows the value of reflectivity over each pixel of the cylindrical volume in its plane view.  The height corresponding to the maximum value of reflectivity through west to east can be found along the right-hand side display, and the height of maximum reflectivity when viewed from south to north is projected over the top. Cloud heights exceeding 6 km and reflectivity exceeding 45 dBZ have been considered as thunderstorm/cumulonimbus (Cb) cloud (Suresh and Bhatnagar, 2005). Based on these criteria, thunderstorm events were observed close to/around Gadanki during the observational period as follows: ii. On 29 September 2004 from 09:12 to 10:12 LT, squall line passage between MDS and GDK with cloud tops 15-16 km over/near GDK (Fig. 2b) and whose extreme tip was close to GDK (Fig. 2b).
Height-time intensity profile of signal to noise ratio (SNR), vertical wind velocity (m s −1 ), and spectral width (m s −1 ) derived from the vertical (MST) radar beam for 27-30 September 2004 are shown in Fig. 3a-c. The events of passing of thunderstorm and squall line over GDK are clearly depicted in encircled ellipses in the figure. Within this encircled region, the SNR is found to be minimum during Event 1 at which the vertical velocities show strong downdrafts (−6.4 m s −1 ) compared with updrafts (3.9 m s −1 ). Even though there are strong updrafts (4.5 m s −1 ) and downdrafts (−4.6 m s −1 ) in the vertical velocity, the SNR minimum is not observed during Event 2. During the observational period there exist strong stratified layers (∼ 0.5-2 km) of turbulence associated with shear near the tropopause even when the spectral width was found to be strong. It may be noticed that convective overshooting was noticed particularly during Event 2, which may be evident from SNR and spectral width (encircled with ellipse, in between 08:00-12:00 LT on 29 September 2004). Figure 4 shows the height-time contours of available background zonal wind (m s −1 ) (top), meridional (m s −1 ) wind (middle) and corresponding horizontal wind shear (s −1 ) (bottom) for the present studied period. It may be noticed that the zonal wind shows a maximum easterly wind speed of about ∼ 28 m s −1 from 27-30 September 2004 over the ∼ 15-17 km height region. The easterly wind is higher than 25 m s −1 near the tropopause height and the meridional component shows strong southerly winds in the same height region (∼ 15.5-16.5 km), with a strong northerly component above this region. However, the southerly component was somewhat weaker during Event 1 compared with the remaining days. The time evolution of the southerly meridional wind (of the order of 15 m s −1 ) is found to be similar to that of zonal winds during the entire observation period, indicating that the zonal and meridional winds are strong at 15-17 km. Figure 4 (bottom panel) shows a strong vertical shear greater than 0.02 s −1 in magnitude, with a maximum of ±0.06 s −1 around 15-17.5 km. The magnitude of vertical wind shear is found to be larger than the Brunt-Vaisala frequency (∼ 0.0070-0.0209 s −1 ) in the upper troposphere and lower stratospheric (UTLS) regions. This indicates, as in Ramkumar et al. (2010), that the unstable shear layers ( Fig. 4) were the important sources for the generation of GWs.

Convective gravity wave characteristics
In order to define the stages of convection we consider convective activity, minimum subcloud buoyancy and minimum value of tropospheric vertical velocity at a given time. Convective activity and minimum sub-cloud buoyancy were defined, following Beres et al. (2002), as: Convective activity (CA) as a function of time t: where w max is the maximum value of tropospheric vertical velocity at a given time.
Minimum subcloud buoyancy B min as a function of time, t: where min() refers to a value in the domain at a given time t. B min represents the strength of the cold pool and θ is the air mass, given by: where T , p are temperature and pressure and p 0 = 1000 hPa. This is calculated from ERA. The reason is that the temperature data from ERA have a bias of nearly ±2 K, with the GPS radiosonde observations available since August 2006 at GDK. 3. Dissipation phase: it is observed that the magnitude of maximum updrafts is weakened further (1.63 m s −1 ) compared with downdrafts (3.84 m s −1 ) for Event 1 (at 18:30 LT), and the corresponding values are 1.32 m s −1 and 3.56 m s −1 for Event 2 (at 10:00 LT), respectively, during this stage.

Wavelet analysis
CWT analysis is applied to localize the main modes of oscillation in restricted intervals of the data series Hierro et al., 2012). In order to observe dominant spectral components in vertical wind perturbations, a Morlet (mother wavelet) continuous wavelet transform (CWT) (Torrence and Compo, 1998) is employed. Because of refraction effects and the intense background wind shear in the UTLS region, the amplitude of the CGW may not be the same throughout the UTLS region. In order to determine the dominant modes of oscillation, the UTLS region is divided into three parts, namely the mid-tropospere (MT), upper troposphere (UT) and lower stratosphere (LS). Since the sources of short GWs are most likely found in the middle and upper tropospheres, their propagation direction is mostly upward. We apply the CWT analysis to the perturbed vertical velocity (as in Alexander et al., 2008;Schmidt et al., 2008;Llamedo et al., 2009;de la Torre et al., 2011de la Torre et al., , 2012Hierro et al., 2012) to obtain the dominant modes between 4 min and 120 min. In order to distinguish the CGWs from other oscillations such as GWs, which are generated by turbulent wind shear and buoyancy oscillations, the data are classified into three parts. They are (a) before convection, (b) during convection and (c) after convection (Fig. 6a, b and c, respectively). Time history of peak vertical velocities (only during convection) is obtained taking the average over a given height region, and corresponding periodicities are tabulated for both the events I and II in Table 1a.   Figure 6A.

Hodograph analysis
Hodograph analysis is carried out to determine the GW vertical wavelength and horizontal direction of propagation following Tsuda et al. (1990). Hodographs were obtained following Dutta et al. (2009) Table 1c. From Figs. 7 and 8, the hodographs show counterclockwise and clockwise rotation, in the troposphere (source region) and stratosphere, respectively, leading to upward energy propagation. As the upward and downward energy  propagation found, its source could be present between the two regions, i.e., the strong shear zones near the tropopause. Strong wind shear (Fig. 4) associated with convection may generate GWs near the tropopause that may influence the structure of CGWs, leading to the formation of complicated wave structures (Vekat Ratnam et al., 2008). In this case it is difficult to distinguish the CGWs from shear-generated GWs. The horizontal direction of propagation of GWs as revealed from Fig. 7 is NNE-NE on 27 September 2004 and is NE-E on 29 September 2004, respectively. It could be mentioned that the direction of propagation of GWs coincides with the direction of movement of storm. Dutta et al. (2009), in their study on characteristics of short-period GWs, made a similar analysis in order to find the energy direction of propagation and found that the directions inferred from hodograph analyses are not conclusive. They also found that interaction between CGWs and shear-generated waves (low-frequency waves) could lead to the formation of nonlinear wave structures, it being difficult to distinguish them. This could be one of the reasons for the rotation of hodographs in violating the linear theory of GWs. The other reason would be the geographical variation of the wave packet due to large-scale convective movement in the background (Zhang et al., 2004).

Phase profiles
To find the direction of vertical propagation we computed the phase profiles of gravity wave corresponding to the dominant period for both events 1 and 2 using a fast Fourier transform (FFT) analysis as shown in Fig. 9. It is very interesting to note that these profiles show both downward and upward wave propagation during Event 1 and only upward propagation during Event 2. The phase profile of Event 1 shows that there are regions with reasonably constant phases, one at 10-11 km and another at 13.5-15 km within the troposphere. The phase profile of Event 2 shows that the waves propagate upward above 14 km, downward below 10 km, and that the phase is nearly constant in the 10.5-13.5 km region. The downward propagation of waves is due to the existence of strong shear zones near the tropopause at which partial reflection of waves may take place. The upward propagation is due to the existence of strong vertical updrafts associated with convection as in Kumar (2006).

Vertical wavenumber spectrum
Vertical wavenumber spectra are computed from the fluctuation profiles of vertical velocities by removing background mean from the profiles. Then, the corresponding height profiles are subjected to FFT analysis. Figure  and −1.8 (dissipative) for Event 1 and −1.75 (mature) and −1.85 (dissipative) for Event 2. The slopes in the stratosphere are found to be −1.15 (initial); −1.5 (mature) and −1.5 (dissipative) for Event 1 and −1.6 (mature); −1.6 (dissipative) for Event 2.

Estimation of gravity wave parameters from dispersion relation
We now illustrate the wave parameters using linear wave theory (Eqs. 3-6) (Dewan et al., 1998;Dhaka et al., 2003;Sentman et al., 2003) during the initial and mature phases of convection for Event 1 and only during the mature phase of convection Event 2 (since the squall line reached GDK in its matured stage): Intrinsic group velocity : c gx = ∂ω/∂k x = (λ x /τ ) 1 − (τ B /τ ) 2 and c gz = ∂ω/∂k = (λ z /τ ) cos 2 ϕ (5) Horizontal direction of propagation : ϕ = c gz /c gx = k/m = λ z /λ x or Intrinsic phase velocity : c px = ω/k x and c pz = ω/k z , where ω: intrinsic frequency, N: Brunt-Väisälä frequency, m: vertical wave number, k: horizontal wave number, ϕ: elevation angle of group velocity vector, τ : wave period, τ B : Brunt-Väisälä period, λ x : horizontal wavelength, λ z : vertical wavelength; c gx , c gz , c px and c pz are: components of intrinsic group velocity and phase velocity, respectively. The gravity wave parameters from Eqs. (1)-(4) are given in tables 2 and 3 for events 1 and 2 in both tropospheric and stratospheric regions. The gravity wave parameters are found to be different from Event 1 to 2 and also from initial to mature phase. From tables 2 and 3, it can be noticed that λ x is a linear function of λ z and τ . The horizontal group and phase velocities (c gx and c px ) increase with an increase in periodicity (τ ) of the wave as well as the horizontal wavelength (λ x ), and which is converse. From the present (tables 2 and 3) short-period GW observations, those with periodicities 32 min and 80 min during Event 1 and 48 min and 80 min during Event 2 are found to be dominant for vertical propagation. The GWs with periodicities (namely, 8 min, 10 min, 16 min and 24 min on 27 September and 29 September 2004) and weak amplitudes are removed by critical level filtering due to the influence of strong horizontal wind shear associated with convection (as in Preusse et al., 2008).

Gravity wave generation mechanisms
Strong convective updrafts are commonly associated with the release of a significant amount of latent heat by the convective system. In the present study, the convective events associated with upward propagating GWs lead to enhanced echo power, thereby increasing SNR (Fig. 3). It is clear from the vertical wavenumber spectra and hodograph analysis that vertical wavelengths in the stratosphere are close to half of those estimated in the troposphere in both the events (Table 1b and c). As is evident from Salby and Garcia (1987), McLandress et al. (2000) and Beres et al. (2002), in the present GW events may be generated by the thermal forcing due to diabatic heating.
However, during the passage of squall line there is strong convective overshooting (as the storm is reached over GDK in its mature stage) associated with strong vertical updrafts and downdrafts, which can be easily noticed from SNR and spectral width (Fig. 3, encircled with ellipses). There was relatively strong shear (∼ 0.06 s −1 , Fig. 4) associated with the squall-line passage and it acted as an obstacle to non-zero background wind (∼ 25-28 m s −1 near tropopause). This led to the generation of GWs, even above clouds, the obstacle effect being the apparent prominent mechanism. Similar features were observed in the case of squall-line simulation of vertical shear of horizontal wind by Beres et al. (2002). The obstacle effect is not present when the wind shear layer is located strictly far above the heating region (during Event 1, Figs. 4 and 9) rather than near the top and above it (Lane and Reeder, 2001). Wavelet amplitude spectra for the different time intervals showed short-period (∼ 10 min to 80 min) oscillations during events 1 and 2, as explained in Sect. 3.2.1. Table 1a shows that there are harmonics of 16 min, 24 min, 32 min and 80 min in the MT region; 10 min, 16 min, 32 min and 80 min in the UT region; and 8 min and 32 min in the LS region during thunderstorm events. Similarly, 16 min, 24 min and 80 min in the MT region; 16 min and 48 min in the UT region; and 10 min in the LS region during squall-line events. If the mechanical oscillator mechanism is effective, one should notice the harmonics in the stratosphere similar to that of tropospheric oscillations, which is true for the present observation of CGWs. The results obtained from the current observational study reconfirm that the mechanical oscillator effect is also effective in generating the GWs, as reported in earlier studies (Lane and Reeder, 2001;Dhaka et al., 2002Dhaka et al., , 2003Beres et al., 2004;Kumar, 2006Kumar, , 2007Dutta et al., 2009).

Summary and concluding remarks
In this paper, from Indian MST radar data, an attempt to explain the convectively generated gravity wave propagation characteristics in initial, mature and dissipation stages of convection during the passage of thunderstorm and squall  line using the continuous observation high-resolution data sets is made. Maximum updrafts and downdrafts are found within the 4-10 km region during Event 1 and within the 8-16 km region during Event 2. From phase profiles and hodograph analysis, it can be noticed that the source might be present within the tropospheric region. Rotation of hodographs is found to be clockwise in the troposphere and anti-clockwise in the lower stratospheric region, and hence, the energy (momentum) transport is upward (downward) of the middle atmosphere. From phase profiles we have also found that there are two regions of constant phase (one at 10-11 km and the other at 13.5-15 km within the troposphere) during 27 September 2004. One is due to convective event and the other due to strong background wind shear. However, there is only one constant phase region (10.5-13.5 km) observed on 29 September 2004 that is only due to a convective process. Slopes of vertical wavenumber spectra vary between −1.75 and −2.5 in the tropospheric region (4-15 km) and −1.15 and −1.6 in the stratospheric region. The vertical wavelength (λ z ) is found to be maximum for Event 2 compared with Event 1 (Figs. 7, 8 and 10). Also, the vertical wavelengths in the stratosphere are found to be half of those estimated in the troposphere, which is indicative of the vertical extent of heating of the storm (Salby and Garcia, 1987). From tables 2 and 3, it is found that for short-period CGWs the vertical component of group and phase velocities would be maximum and the horizontal component of group and phase velocities would be minimum. Also, the horizontal wavelengths are found to be shorter in the stratosphere, leading to weak horizontal group and phase velocities. Hence we may state that the waves most probably propagate in the vertical direction rather than in the horizontal direction. The present observation of short-period GWs shows that the waves generated in the troposphere propagate up into the stratosphere due to the presence of strong turbulence mixing associated with shear near the tropopause. A distinct feature differentiating between thunderstorm and squall-line events is sudden enhancement in the SNR and spectral width due to convective overshooting during squall-line events. The mechanisms of CGWs associated with the present study are oscillating updrafts and downdrafts like a harmonic oscillator, deep convective cloud associated with strong wind shear acting like an obstacle to the background mean flow, and strong thermal forcing due to deep convective clouds associated with a significant amount of rainfall. It may be stated that GW generation during Event 1 may be partially due to the mechanical oscillator effect as well as thermal forcing. However, in the case of Event 2, GWs are generated by the mechanical oscillator effect and thermal forcing as well as the effect of obstacle mechanism.
Even though there are dominant wave periods in CWT of vertical velocity perturbation before and after convective events, they are not in agreement with the criteria of the mechanical oscillator effect followed by the earlier authors (Fovell et al., 1992;Lane and Reeder, 2001;Dhaka et al., 2002Dhaka et al., , 2003Beres et al., 2004;Kumar, 2006Kumar, , 2007Dutta et al., 2009). The tropopause is found to be stable enough before and after convective events, so the GWs with weak amplitudes in the tropospheric region during this period may not be able to propagate into the lower stratospheric region. The vertical velocity perturbations amplitude is also weaker and varies between −0.5 m s −1 to 0.5 m s −1 before and after convective events. There are GWs present before and after the convective event that may be generated due to the existence of strong turbulence associated with shear but not due to convection. It is important to note that the oscillations of ∼ 8-10 min in the tropical troposphere and of 4.9 min in the lower stratosphere correspond to the Brunt-Vaisala period. Hence any oscillations greater than these periods are only considered as convectively generated (Dhaka et al., 2003;Kumar, 2007).
Even though the present study reconfirms the earlier results, however, more efforts are needed put forth in differentiating the fractional contributions of these mechanisms in generating GWs during intense convective events with the help of high-resolution, ground-based and satellite-borne observations.