Short-period gravity waves associated with the passage of tropical cyclone using mesosphere-stratosphere-troposphere (MST) radar located at Gadanki (13.5°N, 79.2°E) has been discussed. The observed stratospheric gravity wave is found to have a periodicity of ∼42 min, vertical and horizontal wavelength of ∼3.5 km and 14 km, respectively. Maximum amplitude of gravity wave is observed in the upper troposphere and lower stratosphere (UTLS) region due to which periodic updrafts and downdrafts are observed. This weakens the stability of tropopause, which is observed in radar signal-to-noise ratio (SNR). The enhancement of vertical momentum flux of order ∼−0.6 m2/s2 observed in the lower stratosphere is attributed to the cyclone generated gravity waves. The obstacle effect is found to be the generative mechanism for the observed gravity waves associated with the tropical cyclone.
 The importance of gravity waves in controlling the dynamics of the atmosphere, their energy sources and generative mechanisms has been extensively studied since 1950s. Gravity waves play a vital role on transport of energy and momentum from lower to the middle and upper atmosphere due to which various ground based (radars and lidars), in situ, satellites, rockets and modeling studies have been carried out to improve our understanding on physical and dynamical processes involved in it. Most of the earlier studies have explained the major sources of gravity waves generation are viz., frontal systems, jet streams, wind shear, shear instability, wave-wave interaction, convections, cyclones and orography [Fritts and Alexander, 2003, and references therein]. In spite of various studies carried out in past, the convective and cyclone generated gravity waves over tropics have not been fully understood due to the lack of continuous high resolution measurements and the area is still a focus of increasing scientific interest.
 There are three proposed mechanisms for the generation of short-period gravity waves due to cumulus heating associated with convections and cyclones,viz., (1) thermal forcing or deep heating, (2) obstacle effect, and (3) mechanical oscillatory effect. In thermal forcing, the wave forcing is time dependent and the latent heat released within the convective storm is the main source of gravity wave [Holton et al., 2002]. Salby and Garcia  have shown that this mechanism results in peak wave excitation and the vertical wavelength is found to be 2–4 times more than that of vertical extent of heating (depth of heating). This also depends on horizontal and temporal scale of the heating. Another mechanism proposed by Clark et al.  is obstacle effect, which is analogous to mountain waves. In this mechanism, the hot cumulus towers acts as an obstacle (mountain) to the horizontal flow due to which the gravity waves will generate and initially propagate opposite to the direction of mean wind. Generally, in mountain waves the amplitude and propagation characteristics depends on the height of the mountain and direction of horizontal flow with respect to mountain. But in the present case (during convection/cyclone) the hot cumulus tower which acts as a mountain is not stationary. The third mechanism proposed by Fovell et al. is the mechanical oscillator, in which the air parcel rises to its level of neutral buoyancy and oscillates at that buoyancy frequency, which generates the propagating waves. The wave generated by this mechanism will have a localized momentum source. All these three mechanisms highly depend on the local wind shear, height profile and temporal dependence of the latent heat. It is still not well understood that which mechanism dominates the generation of gravity wave associated with convections and cyclones. Nevertheless, in most of the cases, it is the combination of all the three mechanisms or some other unknown mechanisms, through nonlinear forcing. In order to improve the parameterizations of these short-period gravity waves in the general circulation model (GCM), the generative mechanisms have to be significantly understood in detail.
 The state-of-the-art of MST radar located at Gadanki (13.5°N, 79.2°E) provides a better opportunity to study the short and long period gravity waves associated with tropical convection and cyclone.Das et al. have studied characteristics of gravity wave during the passage of tropical depression in detail using the Gadanki MST radar but their studies focused on the long-period gravity waves (inertia-gravity wave) of 55 h. The main intent of this paper is to discuss the characteristics of shorter-period gravity wavesviz., its plausible source mechanisms, horizontal and vertical wavelength, group and phase velocities associated with a tropical cyclone. An attempt has also been made to estimate the gravity wave momentum flux during the tropical cyclone. As there are very few observational evidences on the mechanisms involved in the cyclone generated short-period gravity waves, especially over tropics, the present results are of importance for gravity wave community and for the improvement of General Circulation model.Section 2 provides the experimental details. The results including the meteorological background are discussed in section 3 and summary is provided in section 4.
2. Experimental Details
 The MST radar located at the tropical station Gadanki is a high power, coherent, pulsed Doppler radar operating at 53 MHz, corresponding to the wavelength of 5.66 m. The detail system description is given by Jain et al.  and Rao et al.  and data processing by Anandan et al. . An experimental campaign was carried out to study the various aspects of atmospheric dynamical processes associated with tropical cyclone from 15 to 16 October 2001. During this experiment the MST radar was operated to obtain 3-dimensional winds and turbulence intensity with ∼4 min time resolution in two different operational modesviz.- mode-1: data were collected for 30 min with an interval of every 1 h on 15 October 2001, and mode-2: data were continuously collected for 4.5 h from 9:30–13:00 IST (= GMT+5:30 h) on 16 October 2001.The height resolution in both the modes of operation is 150 m. However, for the present study, continuous measurement of 4.5 h data obtained in mode-2 experiment is only used. In mode-2 experiment, there are data gaps of <2–4 min at ∼10:15 h and 11:55 h, which are filled with spline interpolation method. Detail experimental specifications are given inTable 1.
Table 1. Radar Parameters Used for the Experiment Using Gadanki MST Radar
E, W, N, S and Z represent east, west, north, south and zenith beam respectively. The numbers indicate the oblique angle in degree, y and x indicate the east-west and north-south plane, respectively.
 In the early morning of 15 October 2001, a low pressure system was formed in the west Bay of Bengal, which slowly distorted into deep-depression and finally converted into a tropical cyclone on early morning of 16 October 2001. The storm moved further toward west-northwest in the late evening of 16 October 2001. The cyclone dissipated in the early morning of 17 October 2001. The definition of depression and cyclone is provided by India Meteorological Department (IMD), which follows the guidelines of World Meteorological Organization (WMO).Figure 1shows the intensity plot of wind speed and direction (wind vectors) at 150 hPa pressure level derived from National Centre for Environmental Prediction (NCEP) re-analysis data at 6 GMT (IST = GMT-5:30 h) on 16 October 2001 [Kalnay et al., 1996]. Strong easterly jet is observed between 5 and 10°N, maximum wind speed is as high as 25 m s−1center around 70–80°E at 150 hPa. Upper tropospheric wind is also strong in and around radar site. The track of the cyclone provided by the IMD during 14–17 October 2001 is also shown in Figure 1. Dotted and solid lines indicate the depression and cyclonic path, respectively. The observational site Gadanki is shown with circle in Figure 1.
Figure 2shows the infrared (IR) satellite image of cloud activity obtained from METEOSAT-5 at 15:30 and 21:30 GMT of 15 October, and 3:30 and 9:30 GMT on 16 October 2001. The movement of the cyclone is clearly seen in the images. Satellite image at 3:30 GMT on 16 October 2001 is coincides with the mode-2 operation of the radar observations used for the present study. During the radar observation, the cyclone was well developed and the center was located close to the radar site, ∼60 km. To have a record on surface rainfall a histogram of hourly rain rate obtained from the Optical Rain Gauge (ORG-15) over the radar site from 15 to 17 October 2001 is plotted inFigure 3. This rain gauge measures surface rainfall rates in the range of 0.1 to 500 mm/hr with a time resolution of ∼1 min. The rainfall figure clearly shows heavy rain, as high as ∼9 mm/hr during late night of 15 October 2001. The rainfall rate on 16 October is very less and during the radar observation period (mode-2 experiment) used for the present study, no rain was observed.
3.2. Characteristics of Winds
Figures 4a–4c(left) show the height-time section of zonal, meridional and vertical wind velocities, respectively from 4 to 20 km from 9:30 to 13:00 IST on 16 October 2001. Strong jet stream of order −30 m s−1 is observed between 16 and 18 km in both zonal and meridional winds. All the three components of wind show strong variations and reversal of winds. Such strong jet stream wind in zonal component is usually observed during summer monsoon (June–September) over the Indian peninsular region, known as tropical easterly jet (TEJ) [Sathiyamoorthy et al., 2007; Das et al., 2011]. But interestingly, in the present case, such a strong jet is observed in the month of October in both the zonal and meridional wind components, suggesting that the occurrence of jet is associated with tropical cyclone [e.g., Das et al., 2010]. The jet stream developed during cyclone can give rise to strong wind shears in the upper troposphere and lower stratosphere (UTLS). The tropopause is considered to be statically stable layer and due to the presence of such strong wind shear near the tropopause, shear instability (Kelvin-Helmholtz instability) can be produce in this layer.Das et al. [2008a]have shown the presence of shear instability in many cases of tropical cyclones using Gadanki MST radar. This strong wind shears in UTLS region can also trigger long-period gravity waves,viz.inertia-gravity wave [e.g.,Fritts and Alexander, 2003; Das et al., 2010].
 The vertical velocity plot clearly shows strong updrafts >1 m s−1 between10–14 km from 9:30–10:30 IST and 8–12 km from 10:30–11:30 IST. Strong downdraft <−1 m s−1is observed between 6 and 12 km from 11:30–12:45 IST. In between time-dependent periodic updrafts and downdrafts are also been observed which is probably due to the presence of short period gravity waves associated with cumulus convection [Sato et al., 1995; Kumar, 2006]. Periodic updrafts and downdrafts have also been observed in the UTLS region. It is to be noted that the short period gravity waves are expected to be observed directly above the convection area [e.g., Beres et al., 2002; Alexander and Holton, 2004], which may also effect the stability of tropopause [Kumar, 2006]. From the past two decades, VHF radars are used to detect the tropopause height [e.g., Das et al., 2008b, and reference therein]. At the tropopause level, a sharp gradient in the temperature lapse rate gives rise to enhanced radar echo power. Also the air around the tropopause will have sharp change in refractive index, which gives rise to a persistent radar reflectivity layer at the tropopause level. This method of radar detecting tropopause height is also valid under different atmospheric weather conditions [Das et al., 2008b]. Thus, to detect the tropopause height, we have plotted the height-time intensity plot of radar signal-to-noise ratio (SNR) between 9:30–13:00 IST on 16 October 2001 as shown inFigure 5a. A sharp enhanced echo power (indicated by arrow) is observed at ∼17.5 km. The echo power at 17.5 km gets diminished between 10:45–11:15 IST, which indicates the weakening of the tropopause. This is because of the continuous impinging of air parcel on the tropopause due to the presence of updrafts and downdrafts produced by gravity waves. A slanting wise strong echo power of ∼1 km thickness is also observed below tropopause, which is attributed to the stratospheric intrusion into the troposphere (for details see Das ). Figure 5bshows the height-time intensity plot of half-power full spectral width, which is an indicator of turbulence. Strong turbulence is also observed below tropopause. Thus, any gravity waves produced by convection could produce mixing around the tropopause level [Pavelin et al., 2002] and enhance the stratosphere-troposphere exchange (STE) processes [Kumar, 2006; Das, 2009; Das et al., 2011].
3.3. Characteristics of Short-Period Gravity Wave at UTLS Region
 As mentioned in the introductory section, the obstacle effect explained by Clark et al.  is one of the plausible mechanisms for the generation of short period gravity waves during the passage of tropical cyclone. It well known that a matured tropical cyclone consist of warm core, which is calm, surrounded by hot cumulus tower associated with deep convection with extreme cyclonic wind. Details of the structure of matured tropical cyclone can be found elsewhere [Frank, 1977, and references therein]. These hot cumulus towers act as an obstacle, to the free flow of horizontal wind, due to which the gravity waves generate and initially propagates in a direction opposite to the mean wind. To examine the vertical extent of convective cloud in the vicinity of cyclone, the satellite observations of cloud brightness temperature (BT) obtained from the Terra MODIS satellite in the atmospheric window of thermal infrared band is used. Figure 6 shows the cloud BT corresponding to the cyclone event on 14–16 October 2001. The BT obtained from MODIS satellite is an average picture of day and night. Cloud BT clearly shows a notable low value of 185–190 K at the center and peripheral of the cyclone. Such low value of cloud BT suggests that the cloud has extended up to the tropopause height [Rao et al., 2004]. This indicates that the cumulus cloud tower which has reached the tropopause level may act as an obstacle for the background wind. It is also to be noticed that the existence of strong wind in the vicinity of tropopause shown in Figure 4 will be obstructed by these cumulus towers present at this height level, which could have become the possible source region for the generation of short period gravity waves. It is also true that the wave can also be generated in the lower troposphere due to convection itself by oscillatory motion, which can be observed in the vertical velocity [e.g., Kumar, 2006]. The convective tower is extended up to the tropopause height and at its proxy, strong easterly wind is also observed, which can further triggers gravity wave. So both the triggering mechanisms for the generation of wave may be valid in this case. However, one cannot say which one is exactly dominating in the present observation.
 In order to investigate the prominent periods that are associated with short period gravity wave, spectral analysis have been performed on the fluctuation of vertical wind time series during 9:30–13:00 IST on 16 October 2001 using least square harmonic analysis. The harmonic analysis is used to determine the spectra in which sinusoidal function with period of 8 to 200 min are successfully fitted in least squares with the time series of the vertical wind component. For present analysis, the vertical wind velocity is used rather than the horizontal wind components as the previous studies indicate that it is the best observational technique for extracting the convective generated shorter-period period gravity waves [e.g.,Choi et al., 2006, and references therein]. Figure 7 shows periodogram of vertical wind at 16.35 and 18.5 km (lower stratosphere). The peridiograms shows a first dominant periodicity of ∼42 min and second dominant peak of ∼70 min. The amplitude of the first dominant peak is twice than that of the secondary peak. This indicates that the observed gravity wave is not purely monochromatic wave. However, for the present study we have considered only the first dominant peak for further estimation of wave parameters.
 One of the typical behavior of gravity wave is its characteristic propagation. To gain further insight, we re-examine the time series of all the three components of winds, i.e., zonal, meridional and vertical. A band-pass Butterworth filter of third order is applied to the time series of winds. The lower and upper limits of the filter are 30 and 50 min, respectively.Figure 8shows the height-time section of filtered zonal, meridional and vertical wind velocities. Upward propagating waves are observed from 12 to 18 km in both the zonal and meridional winds. Above 18 km, the phase remain almost constant. In the vertical velocity, the phase tends to zero, which may be a signature of wave generated by obstacle effect (mountain wave).Réchou et al.  and Kirkwood et al. have shown the signature of mountain waves in the vertical velocity observed using ESRAD MST radar over Kiruna, Sweden. However, for their studies the mountain is stationary and thus they observed the phase speed is zero. But in the present case, the mountain, i.e., hot cumulus tower of cyclone (as obstacle) is non-stationary and thus the wave generated can propagates vertical with very low phase speed in the lower stratosphere as observed fromFigure 8. This shows that vertically extended deep cloud can act as an obstacle and has become the source of gravity wave.
 It is equally important to understand the forcing in the vertical direction. The filtered time series of vertical wind (bandwidth of 30–50 min) shown in Figure 8is then averaged between 12:30 to 13:00 IST of 16 October to obtain the half-hour averaged height profile of vertical velocity. This profile is then subjected to least square harmonic analysis in which sinusoidal function with wavelength of 0.3 to 15 km are fitted in least squares and the peridiogram is shown inFigure 9. The vertical wavelengths of 2, 3.5 and 4.5 km are observed in the peridiogram. However, for further calculation of wave parameters, we have averaged these three dominant vertical wavelengths (∼3.5 km). Dhaka et al.  have shown a periodicity of 40–60 min with 3 km vertical wavelength in the UTLS region during the passage of typhoon using Middle and Upper atmosphere (MU) radar at Shigaraki, Japan (midlatitude). The present observation also agrees with observation of midlatitude.
 To get further insight, we have also carried out hodograph analysis to verify whether the processes are gravity waves. The hodograph analysis gives an idea to trace the course of the deviation of the horizontal wind vector with respect to height. Figure 10 shows the results of hodograph analysis applied on the wind perturbation after band pass filtering with a bandwidth of 30–50 min in time and 2.5–4.5 km in height at 12 IST on 16 October 2001. The clockwise rotation of horizontal wind vectors above the jet stream indicates the upward propagation of energy. The ellipse is fitted (solid line in Figure 10) to the observed hodographs and the orientation of the major axis is shown by dotted arrow lines, which indicate the line of propagation of energy. Figure 10 shows the change of the wind vector with height in the range of 18–21 km.
 An attempt has also been made to estimate other waves parameters viz., horizontal wavelength, group and phase velocity using the well-established linear wave theory for gravity wave during the passage of cyclone. The wind velocity observed in the vicinity of tropopause is 20–30 m/s. Thus, the observed frequency (ωo) by radar near tropopause is Doppler shifted by background wind and the Doppler relation is given by
where, ωi is the intrinsic frequency, Ū is the mean horizontal wind parallel to the wave propagation and k is the horizontal wave number. However, the gravity waves interact very little with the background wind in the lower stratosphere >18 km, where the horizontal wind velocity decreases <5 m s−1. In this condition (present case), the Doppler shift by background wind is very less in the lower stratosphere and thus, the observed period by the radar is closed to the intrinsic period (ωo ∼ ωi) of the wave in the lower stratosphere (∼18.5 km). Thus, we have estimated the horizontal wavelength in the lower stratosphere, where the magnitude of the mean wind speed is quite low using the dispersion relation given below
where, ω, N, k, and m are the intrinsic frequency, Brunt-Vaisala frequency, horizontal and vertical wavelength, respectively. The horizontal wavelength of the wave for the observed wave period at lower stratosphere is approximately found to be 25 km by considering Brunt-Vaisala frequency as 2π/10 min−1 in the lower stratosphere using the above equation (2). The intrinsic horizontal (vphi) and vertical (vpzi) phase velocities are given by
 Also, the intrinsic horizontal (vghi) and vertical (vgzi) group velocities are given by
 The estimated horizontal and vertical intrinsic phase velocities are 5.7 m s−1 and 1.4 m s−1, and group velocities are 6 m s−1 and 1.5 m s−1, respectively. The observed characteristics of the wave is consistent with the earlier observations associated with cumulus convections over midlatitudes [Dhaka et al., 2003; Sato, 1993; Choi et al., 2006]. Details of wave parameters estimated are given in Table 2.
Table 2. Short-Period Gravity Wave Parameters During the Passage of Tropical Cyclone
Horizontal phase velocity
5.7 m s−1
Vertical phase velocity
1.4 m s−1
Horizontal group velocity
6 m s−1
Vertical group velocity
1.5 m s−1
3.4. Estimation of Momentum Flux
 It is known that the short period gravity waves from few minutes to few hours associated with cumulus convection are significant for the transport of momentum from troposphere to stratosphere [e.g., Alexander and Pfister, 1995; Worthington and Thomas, 1996]. It is to be noted that the deposition of momentum into the background wind system due to small scale disturbances associated with gravity wave takes place through wave breaking. As mentioned above the gravity wave observed in the present study will also play a significant role in exchange processes as discussed earlier. Thus, the vertical momentum flux associated with this short period gravity wave developed by Vincent and Reid  is estimated using symmetric beam method by MST radar as follows:
where, u, v, and w are the zonal, meridional and vertical wind, respectively. The vrE, vrW,vrN, and vrS represent the radial velocity perturbation in east, west, north and south direction, respectively. The θ indicates the zenith angle between two consecutive radar beams. Further details and accuracy regarding the estimation of vertical momentum flux using MST radar can be found elsewhere [Vincent and Reid, 1983; Worthington and Thomas, 1996; Dutta et al., 2005, and references therein]. Figure 11 shows the vertical profiles of zonal (Figure 11, left) and meridional (Figure 11, right) momentum flux. Enhanced momentum flux is observed above the tropopause and it is found to be as high as ∼−0.6 m2 s−2. It should be noted that during normal weather conditions, the momentum flux is found to be ∼−0.05 to −0.2 m2 s−2 in the vicinity of tropopause [Worthington and Thomas, 1996; Dutta et al., 2005, 2009]. Dhaka et al.  and Dutta et al.  have estimated the momentum flux of the order ∼−0.9 and ∼−2.5 m2 s−2, respectively during the passage of tropical mesoscale convective system. Thus, the enhanced momentum flux in the present case is associated with cyclone generated gravity waves.
 The present study has shown the generation of short-period gravity wave during the passage of tropical cyclone. The influence of cyclone generated gravity waves on STE processes has to be investigated in future with more data set of high resolution measurements of MST radar (especially vertical wind) along with background temperature, humidity and ozone.
 Short-period gravity waves generated by the tropical cyclone has been investigated in the present study. Analysis show that the short-period gravity waves detected during the passage of tropical cyclone have periodicity of ∼42 min with ∼3.5 km and 14 km vertical and horizontal wavelength, respectively. Such short-period with shorter vertical wavelength is found to be typical characteristics of gravity wave associated with the cyclone. The horizontal and vertical phase velocities are found to be 5.7 m s−1 and 1.4 m s−1, and group velocity of 6 m s−1 and 1.5 m s−1, respectively. It is envisaged that the obstacle effect may be one of the causative mechanisms in exciting the gravity waves during the passage of tropical cyclone. Upward propagating waves are clearly seen in the horizontal wind velocity as well as with hodograph analysis. An interesting feature observed in vertical velocity above tropopause height is the constant phase propagation, which is probably due to the fact that the gravity waves are generated by obstacle effect associated with cyclone. The momentum flux is observed to be very high (0.6 m2 s−2) in the upper troposphere and lower stratosphere during the passage of cyclone compared to that of normal weather conditions. The observations of short-period gravity wave during the passage of tropical cyclone using Gadanki MST radar reported is new and need to be studied further with large data set along with background atmospheric measurements to understand its impact on mixing process taking place in the vicinity of tropopause.
 The authors would like to thank many of their colleagues at the National Atmospheric Research Laboratory (NARL), Gadanki, who have contributed to the collection of the data reported in this paper. Thanks are also due to the former director of NARL, A. R. Jain, for conducting the experiment.