Seasonal variation of the turbulence parameters, refractivity structure constant Cn2, eddy dissipation rate ɛ, and eddy diffusivity K, is presented using 3 years (April 2006 to March 2009) of high vertical resolution GPS radiosonde measurements over the tropical station Gadanki (13.5°N, 79.2°E). First, a correlation analysis was done in order to study the relative contributions of temperature (T) and relative humidity (RH) to the refractive index gradient (M). A strong positive (negative) correlation between M and RH (T) gradients is noticed up to 10 km. Above 10 km, a strong positive correlation between M and T gradients is seen, except at altitudes near the tropopause. In the present study we flag the turbulent layers using the Thorpe sorting method and estimate the structure constant Cn2 for the turbulent layers. The probability of occurrence of Cn2 is derived from the cumulative distribution at each height and is found to decrease from 10−7 to 10−17 m−2/3 with height. The probability of the occurrence of Cn2 conditioned to the occurrence of turbulence as a function of height is derived, and it is found that only the mean and the 90th percentile profile reach an altitude of ∼27 km. The demarcation between the boundary layer and the free atmosphere as well as between the troposphere and the stratosphere are quite clear from the turbulence profile, which allows us to identify the boundary layer and tropopause heights from turbulence profiles. Thus, the present analysis introduces an alternative approach to identify the height of the boundary layer as well as the tropopause and also to characterize the probability of turbulence and thickness of turbulent eddies in the atmosphere with a finer scale size (down to 5 m) for the first time from a tropical latitude.
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 Turbulence in the atmosphere can be described as the dissipation of mechanical energy to internal energy occurring by an energy cascade process through a series of Fourier modes of the velocity field, in which large-scale eddies break up, subdividing into smaller eddies until they disappear by means of heat dissipation through molecular viscosity [Justus, 1969]. Turbulence can be generated by nonlinear breaking and critical level interactions of upward propagating gravity waves. Small-scale turbulence plays a crucial role in middle atmospheric dynamics, as it is the end product of many dynamical motions in the atmosphere. It not only heats the atmosphere but also causes diffusion of momentum, heat, and matter. It transports energy and momentum extracted from the wave, contributing to the eddy diffusion process. Energy loss is significant in the dissipation region, which is separated from the energy input region by the inertial subrange. Thus, all the energy is transmitted to the viscous subrange through the inertial subrange without any significant loss. Hence, turbulence plays a significant role in the energy budget and thermal structure of the atmosphere.
 Atmospheric turbulence depends largely on background atmospheric parameters such as wind, temperature, and humidity [VanZandt et al., 1981]. To quantify the turbulence from VHF radar measurements three methods are mainly used: the Doppler spectral width method, backscatter signal power method, and velocity variance method. With these methods characteristics of turbulence are estimated using mainly the turbulence refractivity structure constant Cn2, turbulent eddy dissipation rate ɛ, and turbulence or eddy diffusivity K. A few studies were carried out over this observational site using 53 MHz mesosphere-stratosphere-troposphere (MST) radar to quantify the turbulence parameters in the troposphere and lower stratosphere [Rao et al., 1997], and later these studies were extended to bring out the height structure of Cn2 for different seasons using 4 years of MST radar observations [Rao et al., 2001a] and the height structure of K in the troposphere, lower stratosphere, and mesosphere [Rao et al., 2001b]. Sasi and Vijayan  estimated the turbulent kinetic energy dissipation rate and eddy diffusion coefficient using MST radar data. Satheesan and Krishna Murthy  adopted the variance method and estimated the turbulence parameter ɛ and the eddy diffusivity for momentum Km in the upper troposphere and lower stratosphere. They also made a comparative study using all three techniques. Nastrom et al.  measured atmospheric turbulence using a dual-beam-width method.
 All these studies were made under the assumption of local homogeneity and stationarity of the refractive index fluctuations on the basis of Kolmogorov's  theory. However, a major difficulty in radar experiments is the assumption of homogeneity and stationarity of turbulence within the illuminated volume, which is hardly satisfied [e.g., see Dole et al., 2001; Wilson et al., 2005]. Atmospheric turbulence is known to occur in thin layers (say, 100 m depth or less) and is highly intermittent in time and space. Radar experiments also have limitation for the height region of 13–15 km owing to the poor signal-to-noise ratio and, further, are limited to an altitude of 20 km. Note that in the tropics, turbulence parameters show large seasonal variations because of extreme weather phenomena such as monsoons and associated tropical easterly jets.
 In situ measurements from radiosonde are also used to study the turbulence parameters. Using a small data set from these measurements, an attempt has been made to study Cn2 [Ghosh et al., 2001] over this site. Recent efforts by Clayson and Kantha  provided a new approach for retrieving turbulence properties in the free atmosphere from high-resolution soundings which was originally designed for oceanic mixing. In the present paper an attempt is made to characterize the seasonal variation of Cn2, ɛ, and K using 3 years of high-resolution GPS radiosonde measurements following Clayson and Kantha . Although the temporal resolution is poor, GPS radiosonde provides meteorological parameters with very high vertical resolution (5 m) and a height coverage of 30 km. In addition, temperature measurements using radiosonde allow us to derive the profiles of Brunt Väisälä (BV) frequency (N) and hence the Richardson number (Ri). Further, a totally different approach has been followed to estimate the profile of Cn2 for the tropical station. The purpose of this paper is threefold: first, to estimate the probability of turbulence, a method to derive Cn2 profiles from the high-resolution radiosonde data; second, to study the role of temperature and humidity gradients in the refractive index gradient; and, finally, to calculate the thickness of the turbulent layer and hence Cn2, ɛ, and K.
 High-resolution, ground-based GPS radiosonde (Väisälä RS-80, RS-92, and Meisei) balloons were launched almost regularly over Gadanki from April 2006 to March 2009 at about 1730 local time (LT; LT = UT + 0530). About 926 profiles of temperature (T), pressure (p), relative humidity (RH), and horizontal wind, reaching an average height of 30 km, were obtained in different seasons. All atmospheric parameters were collected with a height resolution of 25–30 m (sampled at 5 s intervals) from RS-80, 10 m (sampled at 2 s intervals) from RS-92, and 5 m (sampled at 1 s intervals) from Meisei. The resolutions provided by Meisei allow the identification of turbulent layers as small as 10 m. In the present paper the analysis is carried out with the 30 m data set for the whole length of the observations as well as with the 5 m data set for Meisei sondes (May 2007 onward) separately. Continuity and consensus average techniques [Rao et al., 1998] have been applied to remove spurious values. Note that there is no difference in the atmospheric parameters retrieved from RS-80, RS-92, and Meisei except for a better accuracy of humidity in the latter two cases. Horizontal winds, T, and RH were measured with an accuracy of 0.5 m s−1, 0.5 K, and 5% (2% in RS-92), respectively, for all types. Quality checks were then applied to remove outliers arising for various reasons following Tsuda et al.  to ensure high-quality data that would not contaminate the results. About 96.6% of the balloons reached the height of the tropical tropopause (∼16 km), and 86.4% and 65.5% reached heights of >20 and >25 km, respectively.
 In this section, we briefly introduce various turbulence parameters and methodology adopted to identify the turbulence layers. In order to quantify turbulence, Cn2, ɛ, and K can be calculated for individual radiosonde launches. The turbulent layers in the atmosphere can be identified from estimates of Ri. Generally, Ri < 0.25 is taken to be a condition for turbulence associated with the dynamical instability of the atmosphere. It is the ratio of the work done against gravity and the kinetic energy, i.e., the square of the BV frequency to the kinetic energy available in the shear flow. The smaller the value of Ri, the less the stability of the flow and the greater the likelihood of turbulence. Ri < 0.25 is generally considered as the critical condition (necessary but not sufficient) for the atmosphere to be unstable. If Ri is negative, then the region becomes convectively unstable. However, note that unstable does not necessarily mean turbulent, as turbulent regions are, strictly speaking, regions of overturning, meaning regions with Ri ≤ 0. Nevertheless, once turbulence is established within a shear layer, it can be sustained as long as Ri < 1.0 [Wallace and Hobbs, 1977]. In the present study we flagged the turbulent layers using the Thorpe sorting method and calculated Cn2, ɛ, and K for the turbulent layers.
 The potential refractive index gradient in the vertical, M, is related to the strength of turbulence. Generally, the vertical gradient contributes significantly to the mean gradient for the production of small-scale atmospheric inhomogeneities by turbulent mixing. According to Warnock and VanZandt  the potential refractive index gradient M can be expressed as
where θ is the potential temperature, T is the ambient temperature (K), p is the pressure, and q is the specific humidity:
where e is the partial water vapor pressure and δ = 0.622 is the ratio of the gas constant for dry air to that for water vapor.
Cn2 is the parameter generally used to describe the strength of atmospheric turbulence. Cn2 and CT2 can be calculated following Tatarskii  as
where a2 is a dimensionless constant that lies within 1.5–3.5 but is most commonly used at a value of 2.8 [Monin and Yaglom, 1971]. A = K/[Km(1 − Ri)] is a numerical constant generally considered to be equal to unity. L0 is the outer scale of turbulence, which was derived from the vertical profile of potential temperature using the following equations:
where ɛ is the eddy dissipation rate, N is the BV frequency, Ck is the empirical constant taken as 0.3 [Clayson and Kantha, 2008], and LT is the Thorpe scale or displacement. Details of the Thorpe sorting method are given by Clayson and Kantha . In brief, it is assumed that the density or the potential temperature profiles are generally statically stable but contain regions of overturns or inversions resulting from turbulence. Thorpe sorting will rearrange the observed potential temperature profile into a monotonic profile with no overturns. Suppose that in a potential temperature profile the sample at a certain height Zi needs to be moved to Zj to create a monotonous stable profile containing no inversions; the resulting displacement ∣Zj − Zi∣ is called the Thorpe displacement.
 When ɛ and N are known, the eddy diffusivity K can be obtained from the TKE equation; that is,
 The Cn2 profiles are calculated for individual radiosonde launches with an average height resolution of 30 m from April 2006 to March 2009, including both Väisälä and Meisei types of sondes, and also with an average height resolution of 5 m using Meisei to resolve the finer-scale turbulent structures in the atmosphere. Cn2, ɛ, and K are calculated only for the turbulent layers.
4. Results and Discussion
 Typical profiles of wind speed, potential temperature (PT), specific humidity (SH), potential refractive index gradient, Ri, vertical shear of horizontal wind (dU/dz), BV frequency (N), Cn2, LT, log(K), log(ɛ), and CT2 observed on 1 June 2008 at 1730 LT are plotted in Figures 1a–1l, with 30 m vertical resolution. Note that wind speed (Figure 1a) exceeds 25 m s−1 around 15 km owing to a tropical easterly jet steam prevailing during monsoon season, where large shears (Figure 1f) are expected. The profile of PT shown in Figure 1b reveals a gradual increase up to 15 km and a sharp increase thereafter. The profile of SH (Figure 1c) reveals large magnitudes up to 3 km (boundary layer height) and a sharp reduction thereafter. Large gradients in M can be noted (Figure 1d) up to 15 km. The BV frequency (Figure 1g) varies from ∼1.0–1.5 × 10−4 (rad s−2) below 14 km, gradually increases through 15–19 km, and becomes fairly constant at ∼5.0 × 10−4 (rad s−2) in the stratosphere. Large values of log ɛ (Figure 1j) and log K (Figure 1k) can be seen within the boundary layer and between 8 and 15 km, corresponding to high LT values (Figure 1i) and Ri < 0.25 (Figure 1e). It can be seen that the mean value of log ɛ is around −6 m2 s−3 in the upper troposphere, falling to roughly −8 m2 s−3 in the lower stratosphere. Note that there is a high variability in log ɛ, ranging from −9 to −2 m2 s−3 in the troposphere. The values in the stratosphere are somewhat lower, reaching about −4 m2 s−3. The mean log K in the troposphere ranges between 1 and 6 m2 s−1, with values decreasing to below −1 m2 s−1 in the stratosphere, which is more or less consistent with in situ measurements by Clayson and Kantha . Seasonal variation of these parameters is discussed in section 4.8.
 In Figure 1h, the vertical bar shows the data points for the stable layers (Cn2 set to 10−21) and the scattered dots at greater than 10−21 are considered the turbulent layers. For convenience Cn2 is plotted on the logarithmic scale. The existence of thin turbulent layers separated by stable layers in the free atmosphere (i.e., discrimination between internal wave motions and turbulence) is explained by Bufton  and Barat ; this is clear in Figure 1e. As expected, the troposphere is observed to be more turbulent, with a gradual decrease of Cn2 value with height. For altitudes above the tropopause (∼16 km) the atmosphere is relatively stable. These features are quite consistent in the vertical profile of CT2 as shown in Figure 1l. A similar analysis was done with the data collected at 5 m resolution, and details are presented in section 4.7.
4.1. Relation Between T, RH, and M Gradients
 Before proceeding to further details on turbulence, the relation between T, RH, and M is studied. A typical example of the T, RH, and M gradients observed on 1 June 2008 in different height regions is shown in Figure 2. It is evident from Figure 2 that the gradient of T and that of M show a negative correlation. However, the relation between RH and M gradients shows a positive correlation up to the height of about 10 km. This relation becomes reversed above the height of 10 km. The variation between 10 and 16 km is not shown in Figure 2, as it is more or less the same as that at 7.5 and 10 km. The relation between T, RH, and M was checked for each profile during April 2006 to March 2009, and the correlations between them, were sorted according to season, are shown in Figure 3.
 During premonsoon season a positive correlation of about 50% between T and M exists initially, increases up to an altitude of 2 km, then drastically decreases and becomes negative at an altitude of 3 km, continuing up to an altitude of 10 km. Above 10 km, the correlation gradually starts to increase and then becomes negative around the tropopause height. It becomes positive around 19 km and continues up to 35 km. In the case of RH and M, a positive correlation of about 25% exists initially and increases up to 100% at an altitude of 3 km, continuing up to 8 km. Above this altitude, it gradually decreases up to the tropopause, then starts to increase. Although RH measurements from radiosonde above altitudes of temperature −40°C are difficult to detect, note that systematic correlations exist between the two. A mirror-image pattern can be noted between the correlation of T and M and that of RH and M.
 Similar features are seen during monsoon season, although there are differences in the correlations and the altitudes up to which they are correlated. Note that the height at which a negative correlation between T and M starts is significantly higher in monsoon than in premonsoon season. A similar feature is seen between RH and M. Interestingly, a negative correlation between T and M around tropopause height is not visible during monsoon season, although a similar correlation between RH and M exists. Also, the extent of the negative correlation between T and M is small in monsoon season.
 In postmonsoon season, although a mirror image between the correlation of T and M and that of RH and M exists, large differences can be noticed compared to other seasons. Although a negative correlation between T and M exists around the tropopause, similarly to premonsoon season, it is not seen in the middle troposphere. Interestingly, the altitude at which the correlation between RH and M becomes almost 100% is still higher than in monsoon season but is valid only for a small height region.
 During winter season a positive correlation between T and M exists only for the first 1 km; this changes to a negative correlation, with a sharp increase up to 2 km, then gradually decreases up to an altitude of 10 km, and above 10 km a positive correlation exists. This, however, becomes negative around the tropopause, similarly to premonsoon and postmonsoon seasons, with a slight height difference. The extent of the 100% positive correlation between RH and M is highest in winter. This suggests that the contribution of T and RH to M varies drastically for different seasons. More changes occur in the first few kilometers (atmospheric boundary layer (ABL)height) and also in the upper troposphere. Thus, one can distinguish the ABL and tropopause. From this analysis, which is discussed in more detail in sections 4.2–4.5. In summary, humidity and temperature play a major role in determining the index of refraction at low and high altitudes, respectively.
4.2. Cumulative Distribution of Cn2
Figure 4 shows a histogram of Cn2 at different heights from 1.5 to 24 km constructed from the total data set (April 2006 to March 2009, with 30 m resolution). The histogram excludes the stable layers (Cn2 ≤ 10−21 m−2/3). The median value in the histogram decreases with height from 10−7 to 10−17 m−2/3. The histogram is normalized to the total number of samples with turbulence, representing the probability density function in the presence of turbulence. The percentage of occurrence of samples used for normalization is also shown in Figures 5b, 6b, 7b, 8b, and 9b. Considering the lognormal turbulent part, the mean and standard deviation are derived using the stochastic variable logCn2. A broad range exists up to an altitude of 10 km, then becomes sharp, with a minimum range around tropopause height. Since the distribution does not represent a true symmetric shape, the probability of occurrence is considered as percentiles in section 4.3.
4.3. Probability of Occurrence of Cn2
 The probability of occurrence of Cn2 is derived from the cumulative distribution at each height. The 90th, 50th, 25th, and 10th percentiles were calculated considering the area under the nonsymmetric distribution at each height and are shown in Figures 5a, 6a, 7a, and 8a for premonsoon months (March–May, 156 launches), monsoon months (June–August, 283 launches), postmonsoon months (September–November, 257 launches), and winter months (December–February, 230 launches), respectively. The magnitude of the structure constant in the 90th percentile is about 10−16 m−2/3 around 17 km, indicating that only 10% of the measurements exceed this value. Sharp changes in the Cn2 value, with a steeper gradient above the tropopause, are significant in Figures 5a, 6a, 7a, and 8a. A sudden enhancement in Cn2 value just above the tropopause is noted in all seasons, perhaps due to the breaking of planetary waves and/or inertia-gravity waves.
4.4. Probability of Turbulence
 The probability of occurrence of turbulence as a function of height is shown in Figures 5b, 6b, 7b, and 8b for the periods mentioned in section 4.3. The probability of turbulence was derived using the Thorpe sorting method as discussed in section 3. In the present study we estimated the turbulent regions in the profile and calculated the percentage occurrence at each height, i.e., considering only the samples that are turbulent. Thus, the abscissa indicates the probability in the percentage. From Figures 5b, 6b, 7b, and 8b it is clear that the probability of turbulence is higher in the boundary layer, with a gradual decreasing trend up to the isothermal level (∼5 km), then an increase to the maximum around 15 km and a drastic decrease up to tropopause height. It remains more or less constant between 20 and 25 km and then increases again above this altitude. The patterns shown in Figures 6b and 8b for the monsoon and winter seasons have quite different features. During monsoon season, tropical convection and wind shear at the upper tropospheric height due to jet streams are the major sources of turbulence, whereas during winter meridional wind shear and topography are the probable sources [Venkat Ratnam et al., 2008]. In Figure 6b the probability decreases to 18%–20% around 5 km, then sharply increases to ∼65% at ∼15 km and decreases to the minimum of 5% near the tropopause. In Figure 8b the probability decreases to 25% around 3 km, increases to 45–50%, then decreases to the minimum of 5% at tropopause height, which continues up to 25 km, with a gradual increase afterward, similarly to monsoon season. A further enhancement in probability is observed above 25 km due to zonal wind shear (not shown here). Moreover, the density of the turbulent samples is higher in winter compared to monsoon season in the height region of 3 to 13 km, which indicates the role of meridional wind shear [Nath et al., 2009] in generating turbulence. In Figures 5b and 7b, i.e., during premonsoon and postmonsoon seasons, in the troposphere the features are almost the same as those in monsoon season, with a probability of ∼50%–60% at upper tropospheric height, whereas in the stratosphere (above 25 km) a sharp increase in probability can be noted.
4.5. Percentiles of Cumulative Distribution Conditioned to Turbulence
 The probability of the occurrence of Cn2 conditioned to the occurrence of turbulence as a function of height can be derived from Figures 5–8 using the empirical relation
where z is the height, x is a given value of Cn2, PCn2 > x(z) is represented in Figures 5a, 6a, 7a, and 8a, PTurb(z) is shown in Figures 5b, 6b, 7b, and 8b, and PCn2 > x∣ Turb(z) is given in Figures 5c, 6c, 7c, and 8c for the periods mentioned in section 4.3. The weighted mean, 90%, 75%, 60%, and 50% probabilities as a function of height are shown by different symbols. During the premonsoon, monsoon, and winter seasons the mean and 90th percentile profiles reach altitudes of ∼27 and ∼18 km, respectively, whereas during postmonsoon season they reach altitudes of ∼20 and ∼18 km. In all four seasons the probability is significantly high within the boundary layer and decreases sharply afterward.
4.6. Thickness of the Turbulent Layer
 The thickness of the turbulent layers was estimated using the Thorpe sorting method as discussed in section 3. Figures 5d, 6d, 7d, and 8d show the percentiles as a function of height derived from the cumulative distribution of the thickness of turbulent layers at each height. Thickness was derived first from the Thorpe sorting method and then from the probability of occurrence of thickness (90%, 80%, 75%, and 60%) conditioned to the occurrence of turbulence as a function of height and is shown in Figures 5d, 6d, 7d, and 8d for the periods mentioned in section 4.3. Figures 5d, 6d, 7d, and 8d show that the turbulent layers are thicker in the boundary layer, with values of ∼900, ∼850, ∼700, and ∼750 m during the premonsoon, monsoon, postmonsoon, and winter seasons, respectively, whereas the thickness varies between 500 and 600 m at upper tropospheric heights. A sudden enhancement is also observed above 25 km during the premonsoon and winter seasons. The role of zonal and meridional wind shear in increasing the thickness of the turbulent layer is also prominent during the monsoon and winter seasons, respectively. Although the trend is different, the values are quite consistent with the outer scale turbulence derived for different seasons by Eaton and Nastrom .
4.7. Turbulence With 5 m Resolution
 In order to investigate the turbulence characteristics with the very fine resolution of 5 m, we used Meisei radiosonde data available from May 2007 to March 2009. A similar analysis was made, and the probability of occurrence of Cn2, probability of turbulence, percentiles of cumulative distribution conditioned to the turbulence, and thickness of the turbulent layer are shown in Figure 9. Although the overall features remain the same as with coarse-resolution (30 m) data, the detailed features are different. Higher values of Cn2 can be noted, and the probability of occurrence of turbulence is also high in the upper troposphere and lower stratosphere. This leads to a change in the features of Cn2 conditioned to the turbulence. The mean and 90% profiles reach up to 25 km, whereas the 75%, 60%, and 50% profiles reach only up to the tropopause. In this case more often the thickness of the turbulence is found to be <30 m in the the upper troposphere and lower stratosphere region, and other features are similar to those in the previous case. In summary, the inferred characteristics of turbulence very much depend on the resolution of the measurements. Therefore, radiosonde probing of the atmosphere should be at as high a resolution as feasible.
4.8. Seasonal Variation of Eddy Dissipation Rate (ɛ) and Eddy Diffusivity (K)
 As mentioned in section 3, we have also estimated ɛ and K. The seasonal mean of log ɛ and log K are shown in Figure 10. In general the values of log ɛ and log K lie within −8 to −3 and −2 to 3 m2 s−1, respectively. A decreasing trend from the surface to about 10 km in both log ɛ and log K is noticed and starts increasing above up to an altitude of 20 km; it then remains more or less constant above. The values are significantly higher in the lower stratosphere compared to the troposphere, and large values can be noted in the boundary layer. The mean value of log ɛ in the upper troposphere is around −6 m2 s−3, increasing to roughly −4 m2 s−3 in the lower stratosphere in all seasons except monsoon season. The mean log K in the troposphere ranges between −1 and 1 m2 s−1, with values decreasing to below −1 m2 s−1 in the stratosphere during monsoon and postmonsoon seasons. Another enhancement is observed around 20 km during the premonsoon, postmonsoon, and winter seasons. The value is large in the stratosphere compared to the troposphere, perhaps owing to gravity wave and planetary wave breaking. It is interesting that the values of log ɛ and log K presented here are comparable with that observed by MST radar [Rao et al., 2001a] at this location, although the times and detailed features are different. In future studies we intend to compare the MST radar-observed turbulence parameters with those observed by radiosonde using simultaneous data.
5. Identification of Tropopause and Atmospheric Boundary Layer Heights
 The demarcation between the boundary layer and the free atmosphere as well as between the troposphere and the stratosphere is quite clear from Figures 3–10. There is a gradual increase in the probability of turbulence as well as the thickness of turbulent layers from the top of the boundary layer to the bottom of the tropopause, with a rapid decrease afterward. Note that the boundary layer height was estimated using a gradient method applied to all the parameters (PT, virtual PT, mixing ratio, and refractivity), which is presented in detail by Basha and Ratnam . Figure 11 shows a comparison of the cold point tropopause and boundary layer heights estimated from temperature and refractivity, respectively, and the height of the inflection point in the probability of occurrence of Cn2 conditioned to having turbulence. It can be seen that the two are in good accordance, particularly in the case of boundary layer height. During winter the heights of capping inversion matches the height of minimum thickness with a better correlation. Tropical convection and tropical easterly jets during monsoon season trigger turbulent eddies to overshoot the entrainment zone and the tropopause, respectively, whereas during winter, topography and meridional wind shear (upper troposphere) are the probable triggering sources but with less intensity [Venkat Ratnam et al., 2008]. Therefore, the height of the inflection point as shown in Figure 11 slightly overestimates the height of the tropopause and boundary layer derived from the meteorological parameters during monsoon and postmonsoon months, while it underestimates it during winter months. Notwithstanding these differences, the present analysis introduces a new approach to identify the height of the boundary layer as well as the tropopause and also characterizes the probability of turbulence and the thickness of turbulent eddies in the atmosphere at a finer scale size.
6. Summary and Conclusions
 Three years of high vertical resolution GPS radiosonde data have been used for the first time to study the characteristics of turbulence over tropical station Gadanki (13.5°N, 79.2°E) with an approach that has not been used in earlier investigations from this station. The main findings can be summarized as follows.
 1. The strong positive correlation between M and RH gradients suggests that the contribution of water vapor is greater up to 10 km, slowly decreases, then increases again in and around the tropopause. A negative correlation between T and M gradients up to 10 km and a positive correlation above 10 km are noted except near the tropopause, where a strong negative correlation is seen, particularly during premonsoon and postmonsoon seasons.
 2. The cumulative distribution of Cn2 shows that the median value of the histogram decreases with height from 10−17 to 10−7 m−2/3. A broad range (nonsymmetric shape) exists up to an altitude of 10 km, then becomes sharp, with the minimum range around the tropopause.
 3. The probability of occurrence of Cn2 derived from the cumulative distribution in the 90th percentile is about 10−16 m−2/3 around 17 km, indicating that only 10% of the measurements can exceed this value. Sharp changes in the Cn2 value with a steeper gradient above the tropopause are significant in all seasons.
 4. The probability of turbulence is high in the boundary layer, with a gradual decrease up to the isothermal level (∼5 km), then increases to the maximum around 15 km and decreases again in the stratosphere.
 5. Percentiles of cumulative distribution conditioned to the turbulence during the monsoon and winter seasons show that the mean and 90th percentile profiles reach an altitude of ∼27 and ∼18 km, respectively. In all four seasons, the probability is significantly high within the boundary layer and decreases sharply afterward.
 6. For the 90th percentile profiles the turbulent layers are thicker (700–900 m) in the boundary layer and in the upper tropospheric heights (400–500 m). The role of zonal and meridional wind shear in thickening the turbulent layer is also prominent during the monsoon and winter seasons, respectively.
 7. The mean value of log ɛ in the upper troposphere is around −7 m2 s−3, increasing to roughly −3 m2 s−3 in the lower stratosphere, in all seasons except monsoon season, with more values in the stratosphere. The mean log K in the troposphere ranges between −1 and 1 m2 s−1, with values decreasing to below −1 m2 s−1 in the stratosphere during monsoon and postmonsoon seasons.
 8. Tropopause height and boundary layer height identified using turbulence profiles are found to match well with those obtained using traditional methods.
 A comparison between the collocated simultaneous MST radar-measured refractive index gradients and high-resolution radiosonde observations must be undertaken to understand the role of temperature and humidity gradients, with a special focus on and around the tropopause region.
 The authors are grateful to the technical staff at National Atmospheric Research Laboratory (NARL), Gadanki, for their efforts in making the observations used in the present study. We wish to thank all three reviewers for providing constructive comments that helped to improve the manuscript significantly.