Investigation of saturated gravity waves in the tropical lower atmosphere using radiosonde observations



[1] Characteristics of saturated gravity waves (GWs) in the tropical lower atmosphere, i.e., troposphere and lower stratosphere, have been investigated by utilizing ground-based radiosonde data over Gadanki (13.5°N, 79.2°E), India. The mean background structure has been examined before carrying out wave analysis, which indicates conducive conditions for ample wave activity. Derived energy components exhibit relatively higher magnitude in the lower stratosphere in comparison with the troposphere. The ratio of kinetic to potential energy shows significantly higher values in comparison with the theoretical estimates. Saturated GW spectra of the zonal wind, meridional wind, and temperature evince seasonal variability in the observed logarithmic slope, which reveals considerable variability about the modeled spectral slope. The order of the characteristic wavenumber deduced from our observations implies dominant vertical scale of the saturated GWs to be less than 3 km. Important factors responsible for variation in the globally observed saturated wavenumber spectra are discussed in the light of available literatures. Probable sources responsible for driving GWs are also mentioned.

1. Introduction

[2] A sound knowledge of atmospheric gravity waves (GWs) is indispensable for understanding dynamical processes transpiring in the atmosphere in course of space and time. These waves carry significant energy and momentum from one region to the other region and modify the energetics and dynamics of the ambient atmosphere [Lindzen, 1981; Fritts and Alexander, 2003]. Most of the GWs are generated in the lower atmosphere, i.e., troposphere and propagate through middle atmosphere (stratosphere and mesosphere) which can reach up to the thermosphere depending on surrounding atmospheric conditions (critical level interaction, wave filtering, wave dissipation, wave breaking, etc.). GWs can be generated by a number of excitation sources, e.g., orography, jet stream, fronts, convection, etc. [Fritts and Nastrom, 1992]. Near jets and fronts, the mesoscale fluctuation in the horizontal wind and temperature can enhance by an order of magnitude [Li and Yi, 2007]. Because of their myriad contribution to the energy budget of the atmosphere, they have been studied in extensive manner in several regions of the atmosphere for the last couple of decades by remote sensing and in situ measurement techniques [e.g., VanZandt, 1982; Tsuda et al., 1994; Kumar et al., 2007; Guharay et al., 2008].

[3] Equatorial troposphere is very important for generating a number of GWs due to persistent convective processes throughout the globe. Here mean background wind is very small in comparison with the mid latitude to produce significant wave activities [Tsuda et al., 1994]. Convective cumulous clouds can trigger significant nonstationary GW activities in both tropical [Sato and Dunkerton, 1997] and extratropical latitudes [Dhaka et al., 2003] during summer due to high convective processes driven by enhanced solar radiation. Strong interaction of GWs with mean wind can give rise to quasi-biennial oscillation (QBO) and semiannual oscillation (SAO) in the zonal wind and temperature in the tropics [Sato and Dunkerton, 1997; Ratnam et al., 2008; Guharay et al., 2009].

[4] For the last couple of years, significant investigations have been carried out to characterize the GW energy and momentum flux all around the globe using ground-based lidar, radar, and satellite-based instruments. Nevertheless, these instruments lack in providing complete information, as radar is inefficient in middle and upper stratosphere due to poor signal-to-noise ratio caused by absence of turbulence, Rayleigh lidar is operated above 25 km and satellite-based measurements contain poor vertical and temporal resolutions. Using radiosonde very high resolution regular study of GWs up to middle stratosphere (∼35 km) has been achieved. It has enabled the investigators to find out the smaller scale variability associated with GWs. The advantage of the radiosonde instrument is it can measure temperature, pressure, relative humidity, horizontal wind, and wind direction simultaneously, which are important tracers of GW activities in the troposphere and lower stratosphere (TLS). One demerit of the instrument is finite uncertainty at the upper limit of altitude due to unpredictable burst of the balloon.

[5] Recently, radiosonde has achieved immense importance for studying several scales of GW with horizontal wavelength in the order of few hundred kilometers and vertical wavelength in the order of few kilometers. Allen and Vincent [1995] performed GW climatological study over a large latitude range (12°S–68°S) in the Southern Hemisphere utilizing radiosonde data and they discerned agreement and disagreement in energy with the modeled values at various latitudes and altitudes as well as seasonal variability. Zhang and Yi [2007] carried out extensive statistical analysis of GWs with radiosonde data from 5 stations over China (10°N–40°N) and they concluded that the main source of their generation in the TLS is the strong tropospheric jet which also revealed significant seasonal and latitudinal variability. Characteristics of Brunt Väisälä frequency and temperature over Japan was studied by Tsuda et al. [1991] by utilizing radiosonde obtained vertical profiles in the range 0–30 km with resolution of 150 m. Past observations from Indian equatorial regions by Venkat Ratnam et al. [2008] revealed the characteristics of the source mechanisms (convection, wind shear, orography) for driving GWs in the TLS and its variability with season. The most recent work by Nath et al. [2009] (hereafter referred to as DN09) from the same station, Gadanki, India (13.5°N, 79.2°E) of the present study has shown GW activities in terms of vertical wavelength, energy and propagation direction. They also observed clear semiannual variability in the energy spectrum.

2. Database

2.1. GPS Radiosonde

[6] GPS radiosonde launched over Gadanki, India (13.5°N, 79.2°E) around 1200 UT (1730 LT) regularly is the base of the present study. We have used Meisei (Japan made) radiosonde to obtain the vertical profiles of temperature, pressure, horizontal wind components and relative humidity, which has an accuracy of 0.5 K, 0.5 hPa, 0.15 m s−1, and 2%, respectively. All the variables are measured with a height resolution of ∼5 m and later on interpolated to achieve a final height resolution of ∼100 m after reducing outlier noise due to random balloon motion. The obtained data are quality checked again to remove other noises. Details of the instrument and quality checks can be found in the DN09.

[7] We have utilized high vertical resolution (∼100 m) radiosonde data for the year 2008 as most of the time (about 56% of the total observation span), the balloon reaches up to 30 km, hence a higher vertical coverage is obtained unlike DN09 (maximum altitude ∼25 km). In this context, it should be mentioned that DN09 presented the statistical analysis of GW intrinsic parameters (horizontal and vertical wavelength, phase speed, propagation direction) and height average energy in the TLS region. In the present study, we have investigated the vertical energy (kinetic and potential) distribution and vertical wavenumber spectra in the saturated region of GW obtained through the dynamical parameters, e.g., zonal wind, meridional wind, and temperature in a detailed manner, which remained untouched so far for this tropical site. The balloon burst heights are shown in Figure 1. A total of 321 days profiles are utilized for the present work, where 76%, 89%, and 98% of the balloons reach a height of 25 km, 20 km, and 15 km, respectively.

Figure 1.

Balloon burst heights of the radiosonde launched during the year 2008.

2.2. NOAA Interpolated Outgoing Longwave Radiation

[8] Other than the radiosonde, we have utilized National Oceanic and Atmospheric Administration (NOAA)–provided outgoing longwave radiation (OLR) data corresponding to the day of the year, available at website, within a horizontal interpolation grid of 2.5° × 2.5° for a proxy of tropical convective clouds over the observational station. OLR value below ∼200 W m−2 has been considered as a representative of deep convective clouds for the present observation.

3. Mean Background Structure of the Atmosphere

[9] Monthly mean background structure of the atmosphere obtained by averaging the whole month daily vertical profiles of zonal wind (u), meridional wind (v), temperature (T), and Brunt Väisälä frequency squared (N2) has been plotted in Figures 2a, 2b, 2c, and 2d, respectively. The daily mean value of OLR for the year 2008 is shown in Figure 2e. The N2 is defined as

equation image

where g and T are acceleration due to gravity and temperature, respectively. The overbar denotes mean background value; dT/dz and Γ (∼9.8 K/km) are the lapse rate and dry adiabatic lapse rate, respectively.

Figure 2.

Monthly mean background structures of (a) zonal wind (m s−1), (b) meridional wind (m s−1), (c) temperature (K), and (d) Brunt Väisälä frequency squared (s−2) and (e) daily variation of daily mean outgoing longwave radiation (OLR) (W m−2) for the year 2008.

[10] Mean zonal wind profile reveals significant variability with respect to month and altitude. Most of the time, variability is limited within the range ∼−15 to +15 m s−1, except near tropopause height around monsoon season (June–September), when a strong tropical easterly jet (TEJ) is observed. The dominant jet present during the monsoon season modify the mean dynamical structure by a significant amount (up to 40 m s−1) probably due to high tropical convection geared up by higher solar incident radiation. Associated strong wind shear during this period is suspected to be an important source mechanism for the generation of GWs in the TLS [Venkat Ratnam et al., 2008; DN09]. Both (easterly and westerly) layers are well spread in space and time as evident from the contour. Mostly, westerly wind is prevalent at the lower altitude (<10 km) level. There is a high possibility of influence of SAO and QBO [Sato and Dunkerton, 1997; Vincent and Alexander, 2000] to the mean zonal background wind in the tropical TLS, but here it is difficult to conclude due to small data set.

[11] Mean meridional wind is found to be weak with compared to the zonal wind which evince less range of variability (−6 to12 m s−1) throughout the observational span and height. During most of the time of the year, meridional wind varies within −5 to +5 m s−1 with dominance of northerly component. Relatively strong southerly wind is observed during initial period (January–April) and end period (November and December) of the year around 10–15 km with a maximum magnitude of ∼12 m s−1. During monsoon (July–September) higher northerly wind (up to 6 m s−1) exists around 13–16 km region. Previous studies [Venkat Ratnam et al., 2008; DN09] from this site have found that the meridional wind component plays a dominant role over total GW energy during winter.

[12] Temperature contours exhibits highly stratified thermal structure in the TLS throughout the year. A well-defined cold point tropopause is observed at ∼17 km altitude. Tropopause temperature reaches a minimum at 180 K. Stratification reduces as it goes from the troposphere to the stratosphere possibly due to differential heating by the species, e.g., ozone (responsible for maintaining the heat budget of the stratosphere region) with respect to altitude and season. Tropopause temperature varies in the range 180–193 K throughout the year, and the corresponding tropopause height varies within the limit ∼16–18 km.

[13] Brunt Väisälä frequency squared profile reveals two level (troposphere and stratosphere) structure very prominently with very small variability. The transition region is evident at ∼17 km (tropopause). Lower value (within 2 × 10−4 s−2) below tropopause indicates higher instability in the troposphere. On the other hand, maximum value of N2 (10−3 s−2) near tropopause implies highly stable region. The stability decreases above the tropopause, but it attains almost constant magnitude assuring significant convective and possible dynamical stability in the stratosphere. Observed values are quite comparable with the previous observations from the tropical regions [Vincent and Alexander, 2000; DN09].

[14] Daily mean OLR values also show significant seasonal variation in their pattern. Deep convection (OLR < 200 W/m2) is observed during summer-monsoon season (May–September). Significant convective activity is also observed at certain times other than this period during the year as evident from several sharp troughs in the time series over the observational site. Following this convention we have found a total of 63 days in the whole year with high convective activity in our present study. Probable effect of OLR (convection) on GW activities has been discussed in section 5.2.

4. Method of Wave Extraction

[15] From Figure 2a, it is evident that there exists a strong jet near tropopause, which may contaminate in extracting the fluctuation components by applying polynomial fit as carried out by usual processes. To eliminate the influence of the strong jet on the derived GW parameters, we have divided the total region (0–30 km) into two separate regions, troposphere (0–14 km) and lower stratosphere (18–30 km). After that we have removed the mean background contribution of the observed variables by subtracting a second-order polynomial fit from the existing data separately for the two regions similar to the earlier investigators [e.g., Allen and Vincent, 1995; Zhang et al., 2006; Narendra Babu et al., 2008; DN09] to obtain GW fluctuation profiles (u′ in zonal wind, v′ in meridional wind, T′ in temperature data). Further, the wave parameters are estimated by using the derived fluctuation profiles in sections 5 and 6.

5. Gravity Wave Energy

[16] Derived fluctuation profiles of wind and temperature as described in section 4 undergo a high pass filter of cutoff ∼3 km similar to that of Tsuda et al. [2004], as higher wavelength components can contaminate the saturated region of the GW spectrum significantly. Hereafter, we have calculated kinetic energy (EK), potential energy (EP), total energy (ET = EK + EP) per unit mass and the ratio of the kinetic to the potential energy for the troposphere and lower stratosphere separately. The formulae for energy calculation are given below.

equation image
equation image

where N is the Brunt Väisälä frequency described in section 3 (equation (1)), T is the temperature and the overbar denotes ensemble average. The vertical component of the velocity is neglected here, as contribution of this component to the total EK is significantly smaller with compared to the other two horizontal components. The parameters EK, EP, ET, and EK/EP are shown in Figures 3a3d for troposphere and Figures 3e3h for lower stratosphere.

Figure 3.

Energy contours of (a) kinetic energy (J kg−1), (b) potential energy (J kg−1), (c) total energy (J kg−1), and (d) ratio of kinetic to potential energy in the troposphere and (e) kinetic energy (J kg−1), (f) potential energy (J kg−1), (g) total energy (J kg−1), and (h) ratio of kinetic to potential energy in the lower stratosphere for the year 2008.

5.1. Kinetic Energy

[17] Kinetic energy (EK) is normally below 1 J kg−1 in the troposphere. Relatively higher EK (>2 J kg−1) is observed at higher altitude (>14 km) during whole span of the year, probably due to presence of nearby jet streams which is also evident from the zonal and meridional wind shown in Figures 2a and 2b. Higher EK is observed during March, May, and November near surface, possibly due to local wind activity. The lower stratosphere EK is significantly larger with comparatively higher variability in comparison with the troposphere one. Here EK shows dominant magnitude within the order of ∼ 1–4 J kg−1. Energy is quite high (∼6–8 J kg−1) in the range 18–24 km during the wet season (May–August). Vincent and Alexander [2000] showed the mean value of EK over a 6 year period over Cocos Island (12°S, 97°E) ∼9.2 J kg−1 for dominant waves with a vertical scale ∼2 km in radiosonde wind data at a 18–25 km region. This observation shows slightly higher values in comparison with our obtained ones. Tsuda et al. [2004] obtained autumn-wintertime characteristics of GW EK with vertical wavelength less than 3.1 km within the range ∼4–15 J kg−1 at altitude 20–30 km using radiosonde observations from 3 equatorial sites, which partially overlaps with our results at lower limit of EK. Earlier investigation carried out by Venkat Ratnam et al. [2008], showed latitudinal variability characteristics of GW kinetic energy of total 12 stations scattered over India starting from equatorial to extra tropical latitudes using radiosonde data. They observed the EK variability within the limit ∼8 J kg−1 for all the stations in the troposphere which matches closely with our observed values and implies dominance of small vertical-scale waves. The most recent study by DN09 revealed EK variability over Gadanki with the same radiosonde data during the period April, 2006 to April, 2008 within 15 and 30 J kg−1 for the troposphere (0–14 km) and lower stratosphere (18–25 km), respectively. Observed considerable discrepancy between our results and DN09 indicates that higher vertical wavelength (>3 km) inertial GWs are significant contributors to the lower stratosphere dynamics over Gadanki, which are not incorporated in the present study.

5.2. Potential Energy

[18] Potential energy (EP) exhibits comparatively lower value (<1.8 J kg−1) in the troposphere. Relatively higher EP is observed during dry seasons (August–February) evident from several higher-order patches in contours at all altitudes implying presence of instability layers to produce thermally driven GW activity. The lower stratospheric EP mostly lies within the limit ∼2.4 J kg−1. Relatively less number of high-energy patches are visible in this region in comparison with the troposphere scenario. Abrupt high EP at 26–28 km during February and July–August and at 18–19 km during June–July is probably due to frontal activity [Eckermann and Vincent, 1993]. Using radiosonde observations over 18 stations in Australia and Antarctica, Allen and Vincent [1995] showed that EP can vary up to 14 J kg−1 and 11 J kg−1 in the tropical troposphere and lower stratosphere, respectively, which is less than our observed higher limit of EP. Utilizing 6 years of data of radiosonde derived temperature, Vincent and Alexander [2000] calculated the mean EP to be 5.6 J kg−1 over an equatorial station, Cocos Island, in the lower stratosphere which is higher in comparison with our observed results, as we have only considered smaller vertical-scale waves. In this context, it should be mentioned that Tsuda et al. [2000] carried out global morphological study of GWs with 2–5 km vertical wavelength using GPS meteorology (GPS/MET) data and their estimated EP over our observation site came to be below 3 J kg−1 at 20–30 km region. They also observed significant latitudinal and longitudinal variation of GW EP with higher value over land than ocean. Later on, Tsuda et al. [2004] showed with the help of Challenging Minisatellite Payload (CHAMP) GPS satellite and Darwin Area Wave Experiment (DAWEX) radiosonde data that the derived EP of the GWs with vertical wavelength less than 3.1 km remains in the range 2–7 J kg−1 at 20–30 km within 10°S–15°S latitude band over the globe and it maximizes near equator. Our obtained value of EP in the lower stratosphere region is generally lower than the above mentioned observations, may be due to geophysical difference between observational sites. Namboothiri et al. [2008] carried out global-scale feature of GWs of vertical scale within 10 km in the TLS region and they found relatively higher EP at 10–20 km region of maximum ∼15 J kg−1 than at 20–30 km region of maximum ∼6 J kg−1 with the help of CHAMP satellite observation over 20°N–20°S latitude region. Significantly higher EP for their observations at 10–20 km altitude range is possibly due to the tropical jet contribution to the total budget. Recent observation by DN09 revealed radiosonde derived EP within ∼15 and 10 J kg−1 in the troposphere and lower stratosphere, respectively, where they considered the full spectrum of the GW energy.

5.3. Total Energy

[19] The pattern of the total energy (ET) contours in the troposphere resembles with corresponding EP during dry seasons (August–February) and the same for the lower stratosphere reveals similarity with corresponding EK contour during whole year except in magnitude which implies EK is dominating to contribute to ET in the lower stratosphere. Prevalent energy lies within the order of 1.5 and 3 J kg−1 in the troposphere and lower stratosphere, respectively. Maximum values for ET are observed to be ∼4 and 9 J kg−1 in the troposphere and lower stratosphere, respectively. Significantly higher ET in the lower stratosphere altitudes (18–23 km) during May–August is predominately contributed by the zonal component of EK due to magnification of GW energy while passing through the TEJ region which may be closely associated with enhanced convection activity as evident from the OLR data. Our estimated correlation coefficient of OLR with mean troposphere ET and lower stratosphere ET comes out to be 0.78 and 0.28, respectively. Hence GWs are mainly driven by the convective activities in the troposphere, while stratospheric GWs are comparatively less affected by convection. Previously, Allen and Vincent [1995] observed average energy density of 6–11 J kg−1 within 10°S–15°S at 17–24 km altitude with radiosonde data from several stations, which matches well with our observations for lower stratosphere. Earlier investigators Vincent and Alexander [2000] showed the variability range of the mean ET ∼ 11–18 J kg−1 over 6 years of radiosonde data over Cocos Island at a 18–25 km region considering contribution of total GW spectrum. Past observation by Wang and Geller [2003] using high-resolution radiosonde data set of the lower stratosphere from low-latitude (12°N–15°N) stations revealed variability of ET ∼ 10–16 J kg−1 during 1998–2001 span for full GW spectrum. Tsuda et al. [2004] obtained ET within the range 8–19 J kg−1 in the lower stratosphere with radiosonde observations from 3 tropical stations for smaller-scale GWs. These findings exhibit obvious higher values in comparison with our observed values of ET. This discrepancy is possibly because of longitudinal difference of the observational stations. With the help of radiosonde observations over Haikou, China (20°N, 110°E), Zhang and Yi [2007] found the average ET variability throughout the season in the range ∼3–9 J kg−1 and 2–4 J kg−1 in the troposphere and lower stratosphere, respectively, which overlaps well with our observations, although the troposphere energy is higher than the lower stratosphere one unlike ours.

5.4. Ratio

[20] The ratio of the kinetic to the potential energy varies predominately within the order of ∼3 and 8 for the troposphere and lower stratosphere, respectively, which implies dominant role of EK to the total GW associated energy. The value of the ratio is significantly higher in the lower stratosphere in comparison with the troposphere. The calculated mean ratio comes out to be ∼1.8 and 5.1 for the troposphere and lower stratosphere, respectively. Earlier, Tsuda et al. [2004] observed the ratio within ∼8 using radiosonde observations from 3 equatorial sites below 35 km. Of late, Zhang and Yi [2007] observed mean value of the ratio over Haikou ∼1.31. Linear theory of GWs says that the ratio should be in the range 5/3 (∼1.67) to 2 [Tsuda et al., 2000]. Our observed ratio is generally higher than the theoretical estimate for lower stratosphere. In this context, it should be mentioned that Nastrom and VanZandt [2001] found the ratio ∼3 in the troposphere and ∼6 in the stratosphere. Less frequent extremely higher value of the ratio indicated by narrow patches in the contours implies the possibility of different wave characteristics at some regions [Tsuda et al., 2004].

6. Saturated GW Spectra

[21] The linear theory of GW saturation indicates that power spectral density and its slope of velocity fluctuations (due to GWs) with respect to the vertical wavenumber remains almost constant with altitude at larger value of wavenumber [Smith et al., 1987]. We will present here the observational results of vertical wavenumber (m) spectra of saturated GWs in term of horizontal wind (zonal and meridional) and temperature in the troposphere and lower stratosphere separately. In the saturation region, where m > m* (m* is the characteristic wavenumber where energy density maximizes), theoretically the saturated spectral density according to Smith et al. [1987] and Fritts and Alexander [2003] can be expressed as

equation image

where N is the Brunt Väisälä frequency described before. Equation (4) implies that energy density is highly dependent on N.

[22] The daily fluctuation profiles (u′, v′ and T′) are subjected to prewhitening process by first difference before performing any spectral analysis. Hereafter, we have carried out Lomb-Scargle transform [Lomb, 1976] with Hanning window for minimizing erroneous outcomes due to spectral leakage and finally, the spectra undergo a postdarkening process to compensate first difference effect [Dewan and Grossbard, 2000; Nastrom and VanZandt, 2001]. At last, we obtain the normalized power spectral density (PSD) with respect to the vertical wavenumber of the concerned parameters. Additionally, the lower stratosphere temperature spectra are corrected for temperature sensor's finite response time similar to the method given by Allen and Vincent [1995]. Obtained vertical wavenumber spectra of all the days for a particular month are averaged hereafter to minimize uncertainty in estimates. Thus 12 normalized spectra (for 12 months of the year 2008) for each of the parameter are obtained and finally, the mean zonal wind, meridional wind, and temperature wavenumber spectra are shown in Figures 4, 5, and 6, respectively, along with the theoretical estimated one (equation (4)). We have utilized monthly and vertically mean N2 profiles to calculate the theoretical spectra of the respective months and regions.

Figure 4.

Normalized power spectral density (PSD) of the vertical wavenumber spectra of zonal wind for the respective months of the year 2008. The dashed curves represent the theoretical estimate of the same. Red curves denote the troposphere; black curves denote the lower stratosphere.

Figure 5.

Same as Figure 4, but it is derived from meridional wind.

Figure 6.

Same as Figure 4, but it is derived from temperature.

[23] From these spectra (zonal, meridional, and temperature) it is conspicuous that generally, there is no significant difference in the PSD of the troposphere and lower stratosphere and latter usually possesses higher energy except few instances. Relatively large difference during certain times between the troposphere and lower stratosphere PSD implies that wave characteristics are different in these two regions, may be due to disparate source mechanisms for the generation of such waves. In general, there is good agreement between the observational and the model results, although details are different. At lower wavenumber region, troposphere spectral slope is higher than the model value and the opposite behavior is observed in the lower stratosphere. However, at higher wavenumber region, agreement between model and observation is better throughout the year. Observed small difference between the zonal and meridional PSD is possibly due to azimuthal asymmetry of the wavefield [Tsuda et al., 1989]. Observed smaller amplitude oscillations scattered in all the spectra are probably due to various scale irregularities in the atmosphere caused by turbulence associated instability.

[24] The characteristic wavenumber (m*), i.e., the knee of the vertical wavenumber spectra is found to vary in the order of ∼≤3 × 10−4 cycle/m in the spectra of all 3 parameters and hence the dominant vertical scale of the observed unsaturated GWs is in the order of ∼≥3 km, consistent with the previous observations [Tsuda et al., 1989, 1991; Allen and Vincent, 1995] and theoretical estimates [Smith et al., 1987]. Earlier, Tsuda et al. [1989] found the value 3.8 × 10−4 ≤ m* ≤ 5.6 × 10−4 cycle/m in the stratosphere and ≤3.8 × 10−4 cycle/m in the troposphere for zonal and meridional spectra using MU radar data from a midlatitude station in Japan, which are slightly higher than our obtained ones. This difference can be attributed to latitudinal difference of the observational sites. Obtained value of m* by Allen and Vincent [1995] from 6 equatorial sites in the Southern Hemisphere was found to be in the range 4.1 × 10−4 to 4.6 × 10−4 cycle/m and 3.3 × 10−4 to 4.2 × 10−4 cycle/m in the troposphere and lower stratosphere, respectively, which is a bit higher than our result. Zhang et al. [2006] observed the m* within the variability range ∼4.7 × 10−4 to 5.7 × 10−4 cycle/m from the site Haikou which is somewhat higher than our observed value, may be due to geophysical difference between two sites. Tropospheric jet has an important role for difference in behavior of the vertical wavenumber spectra in the troposphere and lower stratosphere and also at various latitudes [Zhang et al., 2006].

[25] Logarithmic slope of the vertical wavenumber spectra as shown in Figures 4, 5, and 6 has been calculated and plotted for the troposphere and lower stratosphere in Figure 7. Vertical bars in the plot represent respective error of the slope. The value of the slope varies within the range ∼−1.85 ± 0.14 to −3.67 ± 0.04, which are distributed around the modeled value (∼−3). Significant month to month variability throughout the year in the wavenumber spectra is evident from the estimated values of the slope. The yearly mean value of the slope for troposphere is −3.05 ± 0.02 and for lower stratosphere it comes out to be −2.83 ± 0.01. In general, steepness of the troposphere slope is higher than the lower stratosphere one, which differentiates the characteristic features of the GWs in these two regions. Significantly lower temperature spectral slope during February in the lower stratosphere is possibly due to unresolved temporary problem of the instrument. Abrupt change in the slope of few spectra at higher wavenumber region may be due to limitation of the instrument resolution at smaller oscillation scale. Tsuda et al. [1989] observed the slope for vertical wavenumber spectra of zonal and meridional wind in the mesosphere, stratosphere and troposphere region over a midlatitude and equatorial site in the range ∼−3.00 ± 0.15, which resemble well with our observed ones. Later on, Tsuda et al. [1991] showed that the logarithmic slope of the vertical wavenumber spectra of normalized temperature (T′/T) lied in the range −2.9 to −3.3 and −2.1 to −3.1 in the troposphere and stratosphere, respectively, which compares reasonably well with our results. Radiosonde temperature observations by Allen and Vincent [1995], carried out from 6 equatorial stations (12°S–20°S) of Southern Hemisphere revealed that the average value of the logarithmic slope was ∼−3 and −2.5 in the troposphere and lower stratosphere, respectively. Nastrom et al. [1997] observed the mean slope of −3.0 and −2.6 in the stratosphere and troposphere, respectively, with radiosonde horizontal wind and temperature. Pfenninger et al. [1999] found the mean slope ∼−2.5 and −2.4 in the troposphere and stratosphere, respectively, with 4 years of high-resolution radisonde data. Using radiosonde observations from an equatorial site, Haikou, China, Zhang et al. [2006] obtained the range of seasonal variability of the concerned slope in the order of ∼−2.23 to −3.02, which is in close agreement with the present work. Previous observation from the same place of the present study by Narendra Babu et al. [2008] showed that the logarithmic slope of the total kinetic energy (zonal, meridional, and vertical) varies in the range −2.0 to −2.8 in the troposphere (4–14 km) with the help of long-term (1995–2004) mesosphere-stratosphere-troposphere (MST) radar data, which is lower than our observed variability range.

Figure 7.

Spectral logarithmic slope of PSD for zonal wind, meridional wind, and temperature in the troposphere and lower stratosphere. Vertical bars represent corresponding errors.

[26] Application of prewhitening and postcoloring (PWPC) process before carrying out spectral analysis is essential for accurate calculation of the vertical saturated wavenumber spectra of GWs in case of steeper slope [Dewan and Grossbard, 2000]. Pfenninger et al. [1999] crosschecked the obtained vertical wavenumber spectra by using Hanning window followed by PW and only Hanning window independently and they found no remarkable difference between these two techniques in estimating power spectral slope (mean ∼−2.5 and −2.4 in the troposphere and stratosphere, respectively) and finally, they used only Hanning window method for computing the same. Nastrom and VanZandt [2001] reanalyzed their data by following PWPC before performing further spectral estimates and they concluded that PWPC is essential when the estimated spectral slope is more negative than −3. We have also verified the outcomes of the slope with PWPC and without PWPC and we found maximum difference ∼0.4 of mean value of the same.

[27] Universality of the vertical wavenumber spectrum of GWs raises some important issues, which needs to be discussed in perspective of the inferences of several investigators. Utilizing observational and theoretical estimations, VanZandt [1982] concluded that the respective spectra are considerably universal in the TLS, irrespective of geographical positions, ambient background conditions and source mechanisms. In fact, there are several factors which can cause more or less difference for comparison of the saturated wavenumber spectra among various studies carried out from different places on the globe. Derived wave parameters, i.e., zonal wind, meridional wind, temperature, etc. (from which the saturated spectrum is calculated) and also their spatial and temporal resolutions can differ for various observational techniques employed by different measuring instruments, e.g., radar, radiosonde, etc. for the same, which in turn may induce disparity in the behavior of the respective wavenumber spectra. Characteristics of variation of the spectral amplitude in the troposphere still lack sufficient understanding for complete explanation, since other than GW there are other factors, e.g., convection and temperature inversions, which may influence significantly to the nature of the spectral power variability and normally, the radiosonde slow response time in the stratosphere can associate further uncertainty in the derived spectra at that region [Allen and Vincent, 1995]. In addition to these, geographic location, type of waves, wave parameters, i.e., wavelength, period and the observed height range, etc. can induce subsequent difference in the intercomparison of various studies [Wang and Geller, 2003]. Another important reason for such ambiguity may be varying background wind shear, which can alter the spectral characteristics by considerable amount. In this regard, it is worthwhile to mention that Pulido and Caranti [2000] observed the spectral slope up to ∼−4 due to variable wind shear forcing in presence of spectral leakage. Also Doppler shifting of the frequency spectrum by the background wind may cause sufficient alteration of the intrinsic wave spectrum by different amount for different locations over the globe. Above all, lack of proper calibration of the instruments before starting the measurement can provide additional point of disagreement to the observed results and interpretations among various observers.

7. Sources of GWs

[28] It is well known that GWs are generated mainly by (1) convection, (2) wind shear, (3) topography, and (4) sudden disturbances (e.g., fronts). The observed GWs over Gadanki as experimented in the present study are also surmised to be caused by these factors, but their relative dominance over each other varies with seasons. Convection is the most important mechanism for the generation of GWs in the equatorial lower atmosphere, as we have seen from the correlation of GW energy and OLR in section 5.3. In Figure 2a, we have seen that there is a very strong TEJ existing during May–September, which in turn can cause very strong wind shear near tropopause (∼17 km), hence it is expected to be the most dominant stimulator for GW activity above tropopause during that period. After creation, these waves can propagate in both directions (upward and downward) vertically, i.e., troposphere and lower stratosphere and modify the dynamical condition of these regions [Li and Yi, 2007]. There is also a high possibility of strong wave filtering due to the TEJ. Westward components of the upward moving GWs through troposphere may encounter critical layer interaction and cease to propagate above the TEJ, whereas eastward GWs can pass through this region to lower stratosphere without any significant diminution of energy content. Previously, the effect of tropospheric jet on GW activity as a dominant exciting source was described by Zhang and Yi [2007], based on radiosonde observations carried out from several locations in equatorial and midlatitude. The wintertime GW activity over Gadanki is suspected because of dominant topographical effect. Generally, the wind direction during this time is northeasterly and there are mountains situated at a radial distance of ∼30 km with vertical extension nearly 1 km at northeast direction of the Gadanki [Venkat Ratnam et al., 2008]. In addition to these factors, fronts can provide sufficient input for the excitation of GWs [Eckermann and Vincent, 1993] in an intermittent manner throughout the year as discussed in section 5.2.

8. Summary and Conclusions

[29] In the present work, we have investigated characteristic features of saturated GWs of the tropical lower atmosphere using high-resolution radiosonde data. The GW activity in the troposphere and lower stratosphere has been shown separately. The main findings of our current study are summarized as follows.

[30] 1. The derived energy components show comparatively higher value in the lower stratosphere than the troposphere. The potential energy is significantly less in comparison with the kinetic energy and hence the total energy pattern is determined by the kinetic energy in the lower stratosphere. The results show appreciable resemblance as well as disagreement with other observations carried out by various investigators in the past. In general, our estimated ratio of kinetic to potential energy exhibits higher value when compared with the theoretical estimate.

[31] 2. Saturated spectra of GWs in terms of zonal wind, meridional wind, and temperature show normally good agreement with the modeled spectra of Smith et al. [1987]. Additionally, our obtained mean logarithmic slope remains close to the model estimate one. The characteristic wavenumber values are found to be lower than the results of the other observers with prevalent saturated GW vertical scale below ∼3 km. The notion of universality of the saturated wavenumber spectrum has been discussed in the light of the results obtained by several investigations carried out in the past.

[32] Present work has depicted GW activity in the saturation region of the spectrum over a low-latitude station in the TLS region with the help of radiosonde data. Simultaneous data from multi station observation network in the Indian subcontinent can give sufficient input to the knowledge of regional variability of such kind of waves which can be an excellent plan for future work.


[33] We would like to thank National Atmospheric Research Laboratory (NARL) for providing very good quality data. A. Guharay would like to thank P. Pant for his moral support. A. Guharay is grateful to Biman Jyoti Medhi, Orchid Medhi, and Manash Ranjan Samal for their constant support. Authors are thankful to Harish Chandra and three anonymous reviewers for their critical comments and suggestions, which have enriched the paper content.