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Turbulence characteristics over tropical station Gadanki (13.5°N,79.2°E) estimated using high‐resolution GPS radiosonde data

Debashis Nath,1 M. Venkat Ratnam,1 A. K. Patra,1 B. V. Krishna Murthy,2

and S. Vijaya Bhaskar Rao3

Received 28 April 2009; revised 9 November 2009; accepted 18 November 2009; published 6 April 2010.

[1] Seasonal variation of the turbulence parameters, refractivity structure constant Cn2, eddy

dissipation rate ", and eddy diffusivity K, is presented using 3 years (April 2006 toMarch 2009) of high vertical resolution GPS radiosonde measurements over the tropicalstation Gadanki (13.5°N, 79.2°E). First, a correlation analysis was done in order to studythe relative contributions of temperature (T) and relative humidity (RH) to the refractiveindex 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 betweenM andT gradients is seen, except at altitudes near the tropopause. In the present study we flagthe turbulent layers using the Thorpe sorting method and estimate the structure constantCn2 for the turbulent layers. The probability of occurrence of Cn

2 is derived from thecumulative 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 90thpercentile profile reach an altitude of ∼27 km. The demarcation between the boundary layerand the free atmosphere as well as between the troposphere and the stratosphere are quiteclear from the turbulence profile, which allows us to identify the boundary layer andtropopause heights from turbulence profiles. Thus, the present analysis introduces analternative approach to identify the height of the boundary layer as well as the tropopause andalso to characterize the probability of turbulence and thickness of turbulent eddies in theatmosphere with a finer scale size (down to 5 m) for the first time from a tropical latitude.

Citation: Nath, D., M. Venkat Ratnam, A. K. Patra, B. V. Krishna Murthy, and S. V. Bhaskar Rao (2010), Turbulencecharacteristics over tropical station Gadanki (13.5°N, 79.2°E) estimated using high‐resolution GPS radiosonde data, J. Geophys.Res., 115, D07102, doi:10.1029/2009JD012347.

1. Introduction

[2] Turbulence in the atmosphere can be described as thedissipation of mechanical energy to internal energy occurringby an energy cascade process through a series of Fouriermodes of the velocity field, in which large‐scale eddies breakup, subdividing into smaller eddies until they disappear bymeans of heat dissipation through molecular viscosity [Justus,1969]. Turbulence can be generated by nonlinear breakingand critical level interactions of upward propagating gravitywaves. Small‐scale turbulence plays a crucial role in middleatmospheric dynamics, as it is the end product of manydynamical motions in the atmosphere. It not only heats theatmosphere but also causes diffusion of momentum, heat, andmatter. It transports energy and momentum extracted fromthe wave, contributing to the eddy diffusion process. Energy

loss is significant in the dissipation region, which is separatedfrom the energy input region by the inertial subrange. Thus,all the energy is transmitted to the viscous subrange throughthe inertial subrange without any significant loss. Hence,turbulence plays a significant role in the energy budget andthermal structure of the atmosphere.[3] Atmospheric turbulence depends largely on back-

ground atmospheric parameters such as wind, temperature,and humidity [VanZandt et al., 1981]. To quantify the tur-bulence from VHF radar measurements three methods aremainly used: the Doppler spectral width method, backscattersignal power method, and velocity variance method. Withthese methods characteristics of turbulence are estimated usingmainly the turbulence refractivity structure constant Cn

2, tur-bulent eddy dissipation rate ", and turbulence or eddy diffu-sivityK. A few studies were carried out over this observationalsite using 53 MHz mesosphere‐stratosphere‐troposphere(MST) radar to quantify the turbulence parameters in the tro-posphere and lower stratosphere [Rao et al., 1997], and laterthese studies were extended to bring out the height structureof Cn

2 for different seasons using 4 years of MST radarobservations [Rao et al., 2001a] and the height structure of

1National Atmospheric Research Laboratory, Gadanki, India.2B1, CEEBROS, Chennai, India.3Department of Physics, Sri Venkateswara University, Tirupati, India.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2009JD012347

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D07102, doi:10.1029/2009JD012347, 2010

D07102 1 of 13

http://dx.doi.org/10.1029/2009JD012347

K in the troposphere, lower stratosphere, and mesosphere[Rao et al., 2001b]. Sasi and Vijayan [2001] estimated theturbulent kinetic energy dissipation rate and eddy diffusioncoefficient using MST radar data. Satheesan and KrishnaMurthy [2002] adopted the variance method and estimatedthe turbulence parameter " and the eddy diffusivity formomentum Km in the upper troposphere and lower strato-sphere. They also made a comparative study using all threetechniques. Nastrom et al. [2004] measured atmospheric tur-bulence using a dual‐beam‐width method.[4] All these studies were made under the assumption of

local homogeneity and stationarity of the refractive indexfluctuations on the basis of Kolmogorov’s [1941] theory.However, a major difficulty in radar experiments is theassumption of homogeneity and stationarity of turbulencewithin the illuminated volume, which is hardly satisfied [e.g.,see Dole et al., 2001; Wilson et al., 2005]. Atmospheric tur-bulence is known to occur in thin layers (say, 100 m depthor less) and is highly intermittent in time and space. Radarexperiments also have limitation for the height region of 13–15 km owing to the poor signal‐to‐noise ratio and, further, arelimited to an altitude of 20 km. Note that in the tropics, tur-bulence parameters show large seasonal variations because ofextreme weather phenomena such as monsoons and associatedtropical easterly jets.[5] In situ measurements from radiosonde are also used to

study the turbulence parameters. Using a small data set fromthese measurements, an attempt has been made to study Cn

2

[Ghosh et al., 2001] over this site. Recent efforts by Claysonand Kantha [2008] provided a new approach for retrievingturbulence properties in the free atmosphere from high‐resolution soundings which was originally designed foroceanic mixing. In the present paper an attempt is made tocharacterize the seasonal variation of Cn

2, ", and K using3 years of high‐resolution GPS radiosonde measurementsfollowing Clayson and Kantha [2008]. Although the tem-poral resolution is poor, GPS radiosonde provides meteoro-logical parameters with very high vertical resolution (5 m)and a height coverage of 30 km. In addition, temperaturemeasurements using radiosonde allow us to derive the pro-files of Brunt Väisälä (BV) frequency (N) and hence theRichardson number (Ri). Further, a totally different approachhas been followed to estimate the profile of Cn

2 for the tropicalstation. The purpose of this paper is threefold: first, to estimatethe probability of turbulence, a method to derive Cn

2 profilesfrom the high‐resolution radiosonde data; second, to studythe role of temperature and humidity gradients in the refrac-tive index gradient; and, finally, to calculate the thickness ofthe turbulent layer and hence Cn

2, ", and K.

2. Database

[6] High‐resolution, ground‐basedGPS radiosonde (VäisäläRS‐80, RS‐92, and Meisei) balloons were launched almostregularly over Gadanki from April 2006 to March 2009 atabout 1730 local time (LT; LT = UT + 0530). About 926profiles of temperature (T), pressure (p), relative humidity(RH), and horizontal wind, reaching an average height of30 km, were obtained in different seasons. All atmosphericparameters were collected with a height resolution of 25–30 m (sampled at 5 s intervals) from RS‐80, 10 m (sampled at2 s intervals) from RS‐92, and 5 m (sampled at 1 s intervals)

from Meisei. The resolutions provided by Meisei allow theidentification of turbulent layers as small as 10 m. In thepresent paper the analysis is carried out with the 30 m dataset for the whole length of the observations as well as withthe 5 m data set for Meisei sondes (May 2007 onward) sep-arately. Continuity and consensus average techniques [Raoet al., 1998] have been applied to remove spurious values.Note that there is no difference in the atmospheric parametersretrieved from RS‐80, RS‐92, and Meisei except for a betteraccuracy of humidity in the latter two cases. Horizontal winds,T, and RHweremeasuredwith an accuracy of 0.5m s−1, 0.5 K,and 5% (2% in RS‐92), respectively, for all types. Qualitychecks were then applied to remove outliers arising for variousreasons following Tsuda et al. [2006] to ensure high‐qualitydata that would not contaminate the results. About 96.6% ofthe balloons reached the height of the tropical tropopause(∼16 km), and 86.4% and 65.5% reached heights of >20and >25 km, respectively.

3. Methodology

[7] In this section, we briefly introduce various turbulenceparameters andmethodology adopted to identify the turbulencelayers. In order to quantify turbulence, Cn

2, ", and K can becalculated for individual radiosonde launches. The turbulentlayers in the atmosphere can be identified from estimatesof Ri. Generally, Ri < 0.25 is taken to be a condition forturbulence associated with the dynamical instability of theatmosphere. It is the ratio of the work done against gravityand the kinetic energy, i.e., the square of the BV frequencyto the kinetic energy available in the shear flow. Thesmaller the value of Ri, the less the stability of the flowand the greater the likelihood of turbulence. Ri < 0.25 isgenerally considered as the critical condition (necessarybut not sufficient) for the atmosphere to be unstable. If Riis negative, then the region becomes convectively unstable.However, note that unstable does not necessarily mean tur-bulent, as turbulent regions are, strictly speaking, regions ofoverturning, meaning regions with Ri ≤ 0. Nevertheless, onceturbulence is established within a shear layer, it can besustained as long as Ri < 1.0 [Wallace and Hobbs, 1977].In the present study we flagged the turbulent layers usingthe Thorpe sorting method and calculated Cn

2, ", and K forthe turbulent layers.[8] The potential refractive index gradient in the vertical,

M, is related to the strength of turbulence. Generally, thevertical gradient contributes significantly to the mean gra-dient for the production of small‐scale atmospheric inho-mogeneities by turbulent mixing. According toWarnock andVanZandt [1985] the potential refractive index gradient Mcan be expressed as

M ¼� 77:6�10�6 � p

T

@ ln �

@z1þ 15; 500q

T� 15; 500

2T

dq=dz

@ ln �=@z

� �;

ð1Þ

where � is the potential temperature, T is the ambient tem-perature (K), p is the pressure, and q is the specific humidity:

q ¼ �e

p; ð2Þ

NATH ET AL.: TURBULENCE CHARACTERISTICS OVER GADANKI D07102D07102

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where e is the partial water vapor pressure and d = 0.622 isthe ratio of the gas constant for dry air to that for water vapor.[9] Cn

2 is the parameter generally used to describe thestrength of atmospheric turbulence. Cn

2 and CT2 can be cal-

culated following Tatarskii [1971] as

C2n ¼ a2AL4=30 M 2

C2T ¼ C2

n

�79� 10�6 P

T2

� �2

; ð3Þ

where a2 is a dimensionless constant that lies within 1.5–3.5but is most commonly used at a value of 2.8 [Monin and

Yaglom, 1971]. A = K/[Km(1 − Ri)] is a numerical constantgenerally considered to be equal to unity. L0 is the outer scaleof turbulence, which was derived from the vertical profile ofpotential temperature using the following equations:

Lo ¼ "

N3

� �1=2; ð4Þ

" ¼ CkL2TN

3; ð5Þ

where " is the eddy dissipation rate,N is the BV frequency,Ck

is the empirical constant taken as 0.3 [Clayson and Kantha,

Figure 1. Typical profiles of (a) wind speed (WS), (b) potential temperature (PT), (c) specific humidity(SH), (d) potential refractive index gradient (M), (e) Richardson number (Ri), (f) vertical shear of horizontalwind (dU/dz), (g) Brunt Väisälä frequency (N), (h) refractive index structure constant (Cn

2), (i) Thorpe dis-placement (LT), (j) eddy diffusivity (K), (k) eddy dissipation rate ("), and (l) temperature structure constant(CT

2) observed using GPS radiosonde data on 1 June 2008 at 1730 LT at Gadanki. Vertical lines are drawnat Ri = 0 (solid line) and Ri = 0.25 (dashed line) in Figure 1e, and a vertical bar is shown at Cn

2 values lessthan 10−21 m−2/3 in Figure 1h.


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2008], and LT is the Thorpe scale or displacement. Detailsof the Thorpe sorting method are given by Clayson andKantha [2008]. In brief, it is assumed that the density orthe potential temperature profiles are generally staticallystable but contain regions of overturns or inversions resultingfrom turbulence. Thorpe sorting will rearrange the observedpotential temperature profile into a monotonic profile withno overturns. Suppose that in a potential temperature profilethe sample at a certain height Zi needs to be moved to Zj tocreate a monotonous stable profile containing no inversions;the resulting displacement ∣Zj − Zi∣ is called the Thorpedisplacement.[10] When " and N are known, the eddy diffusivity K can

be obtained from the TKE equation; that is,

K ¼ �"N�2; ð6Þ

where g is the mixing efficiency, which is taken as 0.25[Clayson and Kantha, 2008].[11] The Cn

2 profiles are calculated for individual radio-sonde launches with an average height resolution of 30 mfrom April 2006 to March 2009, including both Väisälä andMeisei types of sondes, and also with an average heightresolution of 5 m using Meisei to resolve the finer‐scale

turbulent structures in the atmosphere. Cn2, ", and K are cal-

culated only for the turbulent layers.

4. Results and Discussion

[12] Typical profiles of wind speed, potential temperature(PT), specific humidity (SH), potential refractive indexgradient, Ri, vertical shear of horizontal wind (dU/dz), BVfrequency (N), Cn2, LT, log(K), log("), and CT

2 observed on1 June 2008 at 1730 LT are plotted in Figures 1a–1l, with30 m vertical resolution. Note that wind speed (Figure 1a)exceeds 25 m s−1 around 15 km owing to a tropical easterlyjet steam prevailing during monsoon season, where largeshears (Figure 1f) are expected. The profile of PT shown inFigure 1b reveals a gradual increase up to 15 km and a sharpincrease thereafter. The profile of SH (Figure 1c) revealslarge magnitudes up to 3 km (boundary layer height) and asharp reduction thereafter. Large gradients inM 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, graduallyincreases through 15–19 km, and becomes fairly constantat ∼5.0 × 10−4 (rad s−2) in the stratosphere. Large values oflog " (Figure 1j) and log K (Figure 1k) can be seen within theboundary layer and between 8 and 15 km, corresponding to

Figure 2. Profiles of temperature (T) and refractive index (M) gradients observed on 1 June 2008 between(a) 2.5 and 5 km, (c) 5 and 7.5 km, (e) 7.5 and 10 km, and (g) 16 and 18.5 km. Figures 2b, 2d, 2f, and 2h arethe same as Figures 2a, 2c, 2e, and 2g but show the profiles of relative humidity (RH) gradients and M.


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high LT values (Figure 1i) and Ri < 0.25 (Figure 1e). It can beseen that the mean value of log " is around −6 m2 s−3 in theupper troposphere, falling to roughly −8 m2 s−3 in the lowerstratosphere. Note that there is a high variability in log ",ranging from −9 to −2 m2 s−3 in the troposphere. The valuesin the stratosphere are somewhat lower, reaching about−4 m2 s−3. The mean logK in the troposphere ranges between1 and 6 m2 s−1, with values decreasing to below −1 m2 s−1 inthe stratosphere, which is more or less consistent with in situmeasurements by Clayson and Kantha [2008]. Seasonalvariation of these parameters is discussed in section 4.8.[13] 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. Forconvenience Cn

2 is plotted on the logarithmic scale. Theexistence of thin turbulent layers separated by stable layersin the free atmosphere (i.e., discrimination between internalwave motions and turbulence) is explained by Bufton [1973]and Barat [1982]; this is clear in Figure 1e. As expected, thetroposphere is observed to be more turbulent, with a gradualdecrease of Cn

2 value with height. For altitudes above thetropopause (∼16 km) the atmosphere is relatively stable.These features are quite consistent in the vertical profile ofCT2 as shown in Figure 1l. A similar analysis was done with

the data collected at 5 m resolution, and details are presentedin section 4.7.

4.1. Relation Between T, RH, and M Gradients

[14] Before proceeding to further details on turbulence, therelation between T, RH, and M is studied. A typical exampleof the T, RH, and M gradients observed on 1 June 2008 indifferent height regions is shown in Figure 2. It is evidentfrom Figure 2 that the gradient of T and that of M show a

negative correlation. However, the relation between RH andM gradients shows a positive correlation up to the height ofabout 10 km. This relation becomes reversed above the heightof 10 km. The variation between 10 and 16 km is not shown inFigure 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 eachprofile during April 2006 toMarch 2009, and the correlationsbetween them, were sorted according to season, are shown inFigure 3.[15] During premonsoon season a positive correlation of

about 50% between T and M exists initially, increases up toan altitude of 2 km, then drastically decreases and becomesnegative at an altitude of 3 km, continuing up to an altitudeof 10 km. Above 10 km, the correlation gradually starts toincrease and then becomes negative around the tropopauseheight. It becomes positive around 19 km and continues upto 35 km. In the case of RH and M, a positive correlation ofabout 25% exists initially and increases up to 100% at analtitude of 3 km, continuing up to 8 km. Above this altitude,it gradually decreases up to the tropopause, then starts toincrease. Although RHmeasurements from radiosonde abovealtitudes of temperature −40°C are difficult to detect, notethat systematic correlations exist between the two. A mirror‐image pattern can be noted between the correlation of Tand M and that of RH and M.[16] Similar features are seen during monsoon season,

although there are differences in the correlations and thealtitudes up to which they are correlated. Note that the heightat which a negative correlation between T and M starts issignificantly 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 tropopauseheight is not visible during monsoon season, although a

Figure 3. Correlation between temperature (T), relative humidity (RH), and refractive index gradients (M)observed during the (a) premonsoon (MAM), (b) monsoon (JJA), (c) postmonsoon (SON), and (d) winter(DJF) seasons over the period April 2006 to March 2009. Dotted lines are drawn at the mean atmosphericboundary layer height and tropopause height, along with standard deviations (vertical bars).


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similar correlation between RH and M exists. Also, theextent of the negative correlation between T and M is smallin monsoon season.[17] In postmonsoon season, although a mirror image

between the correlation of T and M and that of RH and Mexists, large differences can be noticed compared to otherseasons. Although a negative correlation between T and Mexists around the tropopause, similarly to premonsoon season,it is not seen in the middle troposphere. Interestingly, thealtitude at which the correlation between RH andM becomesalmost 100% is still higher than in monsoon season but isvalid only for a small height region.[18] During winter season a positive correlation between T

andM exists only for the first 1 km; this changes to a negativecorrelation, with a sharp increase up to 2 km, then graduallydecreases up to an altitude of 10 km, and above 10 km apositive correlation exists. This, however, becomes negativearound the tropopause, similarly to premonsoon and post-monsoon seasons, with a slight height difference. The extentof the 100% positive correlation between RH and M ishighest in winter. This suggests that the contribution of Tand RH to M varies drastically for different seasons. More

changes occur in the first few kilometers (atmosphericboundary layer (ABL)height) and also in the upper tropo-sphere. Thus, one can distinguish the ABL and tropopause.From this analysis, which is discussed in more detail insections 4.2–4.5. In summary, humidity and temperatureplay a major role in determining the index of refraction atlow and high altitudes, respectively.

4.2. Cumulative Distribution of Cn2

[19] Figure 4 shows a histogram of Cn2 at different heights

from 1.5 to 24 km constructed from the total data set (April2006 to March 2009, with 30 m resolution). The histogramexcludes the stable layers (Cn

2 ≤ 10−21 m−2/3). The medianvalue in the histogram decreases with height from 10−7 to10−17 m−2/3. The histogram is normalized to the total num-ber of samples with turbulence, representing the probabilitydensity function in the presence of turbulence. The per-centage of occurrence of samples used for normalization isalso shown in Figures 5b, 6b, 7b, 8b, and 9b. Consideringthe lognormal turbulent part, the mean and standard deviationare derived using the stochastic variable logCn

2. A broadrange exists up to an altitude of 10 km, then becomes sharp,

Figure 4. Normalized distribution of Cn2 at different heights from 1.5 to 24 km. Data from 926 radio-

sonde launches during April 2006 to March 2009 are considered.


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with a minimum range around tropopause height. Since thedistribution does not represent a true symmetric shape, theprobability of occurrence is considered as percentiles insection 4.3.

4.3. Probability of Occurrence of Cn2

[20] The probability of occurrence ofCn2 is derived from the

cumulative distribution at each height. The 90th, 50th, 25th,and 10th percentiles were calculated considering the areaunder the nonsymmetric distribution at each height and areshown 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 structureconstant in the 90th percentile is about 10−16 m−2/3 around17 km, indicating that only 10% of the measurements exceedthis value. Sharp changes in the Cn

2 value, with a steepergradient 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 thebreaking of planetary waves and/or inertia‐gravity waves.

4.4. Probability of Turbulence

[21] The probability of occurrence of turbulence as afunction of height is shown in Figures 5b, 6b, 7b, and 8b forthe periods mentioned in section 4.3. The probability ofturbulence was derived using the Thorpe sorting method asdiscussed in section 3. In the present study we estimated theturbulent regions in the profile and calculated the percentageoccurrence at each height, i.e., considering only the samplesthat are turbulent. Thus, the abscissa indicates the probabilityin the percentage. From Figures 5b, 6b, 7b, and 8b it is clearthat the probability of turbulence is higher in the boundarylayer, with a gradual decreasing trend up to the isothermallevel (∼5 km), then an increase to the maximum around 15 kmand a drastic decrease up to tropopause height. It remainsmore or less constant between 20 and 25 km and then increases

Figure 5. (a) Probability of occurrence of Cn2 derived from the cumulative distribution at each height for

10%, 50%, 60%, 75%, and 90%. (b) Probability of turbulence as a function of height. (c) Percentiles(mean, 90%, 75%, 60%, and 50%) derived from the probability distribution of Cn

2 conditioned to havingturbulence. (d) Percentiles (90%, 80%, 75%, and 60%) for thickness of turbulent layers obtained fromThorpe sorting. The mean and standard deviation of cold point (blue) and boundary layer (black) heightare shown; lines are the averages during premonsoon (March–May) season over 3 years (156 launches)with a resolution of 30 m.


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again above this altitude. The patterns shown in Figures 6band 8b for the monsoon and winter seasons have quite dif-ferent features. During monsoon season, tropical convectionand wind shear at the upper tropospheric height due to jetstreams are the major sources of turbulence, whereas duringwinter meridional wind shear and topography are the proba-ble sources [Venkat Ratnam et al., 2008]. In Figure 6b theprobability decreases to 18%–20% around 5 km, then sharplyincreases to ∼65% at ∼15 km and decreases to the minimumof 5% near the tropopause. In Figure 8b the probabilitydecreases to 25% around 3 km, increases to 45–50%, thendecreases to the minimum of 5% at tropopause height, whichcontinues up to 25 km, with a gradual increase afterward,similarly to monsoon season. A further enhancement inprobability is observed above 25 km due to zonal wind shear(not shown here). Moreover, the density of the turbulentsamples is higher in winter compared to monsoon season inthe height region of 3 to 13 km, which indicates the role ofmeridional wind shear [Nath et al., 2009] in generatingturbulence. In Figures 5b and 7b, i.e., during premonsoonand postmonsoon seasons, in the troposphere the featuresare almost the same as those in monsoon season, with aprobability of ∼50%–60% at upper tropospheric height,whereas in the stratosphere (above 25 km) a sharp increase inprobability can be noted.

4.5. Percentiles of Cumulative DistributionConditioned to Turbulence

[22] The probability of the occurrence of Cn2 conditioned

to the occurrence of turbulence as a function of height canbe derived from Figures 5–8 using the empirical relation

PCn2<x zð Þ ¼ PTurb zð Þ � PCn2<x=Turb zð Þ; ð7Þ

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 shownin Figures 5b, 6b, 7b, and 8b, and PCn2 > x∣ Turb(z) is given inFigures 5c, 6c, 7c, and 8c for the periods mentioned insection 4.3. The weighted mean, 90%, 75%, 60%, and 50%probabilities as a function of height are shown by differentsymbols. During the premonsoon, monsoon, and winterseasons the mean and 90th percentile profiles reach altitudesof ∼27 and ∼18 km, respectively, whereas during post-monsoon season they reach altitudes of ∼20 and ∼18 km. Inall four seasons the probability is significantly high within theboundary layer and decreases sharply afterward.

4.6. Thickness of the Turbulent Layer

[23] The thickness of the turbulent layers was estimatedusing the Thorpe sorting method as discussed in section 3.

Figure 6. Same as Figure 5 but for monsoon season (June–August) only, over 3 years (283 launches). Themean (dashed line) and standard deviation (gray vertical bar) of the height of strong shear are also shown.


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Figures 5d, 6d, 7d, and 8d show the percentiles as a functionof height derived from the cumulative distribution of thethickness of turbulent layers at each height. Thickness wasderived first from the Thorpe sorting method and then fromthe probability of occurrence of thickness (90%, 80%, 75%,and 60%) conditioned to the occurrence of turbulence as afunction of height and is shown in Figures 5d, 6d, 7d, and8d for the periods mentioned in section 4.3. Figures 5d, 6d,7d, and 8d show that the turbulent layers are thicker in theboundary layer, with values of ∼900, ∼850, ∼700, and ∼750mduring the premonsoon, monsoon, postmonsoon, and winterseasons, respectively, whereas the thickness varies between500 and 600 m at upper tropospheric heights. A suddenenhancement is also observed above 25 km during the pre-monsoon and winter seasons. The role of zonal and meridi-onal wind shear in increasing the thickness of the turbulentlayer is also prominent during the monsoon and winter sea-sons, respectively. Although the trend is different, the valuesare quite consistent with the outer scale turbulence derivedfor different seasons by Eaton and Nastrom [1998].

4.7. Turbulence With 5 m Resolution

[24] In order to investigate the turbulence characteristicswith the very fine resolution of 5 m, we used Meisei radio-sonde data available from May 2007 to March 2009. Asimilar analysis was made, and the probability of occurrenceof Cn

2, probability of turbulence, percentiles of cumulativedistribution conditioned to the turbulence, and thickness ofthe 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 valuesof Cn

2 can be noted, and the probability of occurrence of tur-bulence is also high in the upper troposphere and lowerstratosphere. This leads to a change in the features of Cn

2

conditioned to the turbulence. The mean and 90% profilesreach up to 25 km, whereas the 75%, 60%, and 50% profilesreach only up to the tropopause. In this case more often thethickness of the turbulence is found to be <30 m in the theupper troposphere and lower stratosphere region, and otherfeatures are similar to those in the previous case. In summary,the inferred characteristics of turbulence very much dependon the resolution of the measurements. Therefore, radiosondeprobing of the atmosphere should be at as high a resolutionas feasible.

4.8. Seasonal Variation of Eddy Dissipation Rate (e)and Eddy Diffusivity (K)

[25] As mentioned in section 3, we have also estimated "and K. The seasonal mean of log " and log K are shown inFigure 10. In general the values of log " and log K lie within−8 to −3 and −2 to 3 m2 s−1, respectively. A decreasingtrend from the surface to about 10 km in both log " and log Kis noticed and starts increasing above up to an altitude of20 km; it then remains more or less constant above. Thevalues are significantly higher in the lower stratosphere com-pared to the troposphere, and large values can be noted in theboundary layer. The mean value of log " in the upper tropo-sphere is around −6 m2 s−3, increasing to roughly −4 m2 s−3

Figure 7. Same as Figure 5 but for postmonsoon season (September–November) only, over 3 years(257 launches).


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in the lower stratosphere in all seasons except monsoonseason. 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 sea-sons. Another enhancement is observed around 20 km duringthe premonsoon, postmonsoon, and winter seasons. Thevalue 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 " and log K presentedhere are comparable with that observed byMST radar [Rao etal., 2001a] at this location, although the times and detailedfeatures are different. In future studies we intend to comparethe MST radar‐observed turbulence parameters with thoseobserved by radiosonde using simultaneous data.

5. Identification of Tropopause and AtmosphericBoundary Layer Heights

[26] The demarcation between the boundary layer and thefree atmosphere as well as between the troposphere and thestratosphere is quite clear from Figures 3–10. There is agradual increase in the probability of turbulence as well asthe thickness of turbulent layers from the top of the boundarylayer to the bottom of the tropopause, with a rapid decreaseafterward. Note that the boundary layer height was estimatedusing a gradient method applied to all the parameters (PT,virtual PT, mixing ratio, and refractivity), which is presentedin detail by Basha and Ratnam [2009]. Figure 11 shows a

comparison of the cold point tropopause and boundary layerheights estimated from temperature and refractivity, respec-tively, and the height of the inflection point in the probabilityof occurrence of Cn

2 conditioned to having turbulence. It canbe seen that the two are in good accordance, particularly in thecase of boundary layer height. During winter the heights ofcapping inversion matches the height of minimum thicknesswith a better correlation. Tropical convection and tropicaleasterly jets during monsoon season trigger turbulent eddiesto overshoot the entrainment zone and the tropopause,respectively, whereas during winter, topography and merid-ional wind shear (upper troposphere) are the probable trig-gering sources but with less intensity [Venkat Ratnam et al.,2008]. Therefore, the height of the inflection point as shownin Figure 11 slightly overestimates the height of the tropo-pause and boundary layer derived from the meteorologicalparameters during monsoon and postmonsoon months, whileit underestimates it during winter months. Notwithstandingthese differences, the present analysis introduces a newapproach to identify the height of the boundary layer aswell as the tropopause and also characterizes the probabilityof turbulence and the thickness of turbulent eddies in theatmosphere at a finer scale size.

6. Summary and Conclusions

[27] Three years of high vertical resolution GPS radio-sonde data have been used for the first time to study the

Figure 8. Same as Figure 5 but for winter (December–February) only, over 3 years (230 launches).


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characteristics of turbulence over tropical station Gadanki(13.5°N, 79.2°E) with an approach that has not been used inearlier investigations from this station. The main findings canbe summarized as follows.[28] 1. The strong positive correlation between M and RH

gradients suggests that the contribution of water vapor isgreater up to 10 km, slowly decreases, then increases again inand around the tropopause. A negative correlation between TandM gradients up to 10 km and a positive correlation above10 km are noted except near the tropopause, where a strongnegative correlation is seen, particularly during premonsoonand postmonsoon seasons.[29] 2. The cumulative distribution of Cn

2 shows that themedian value of the histogram decreases with height from10−17 to 10−7 m−2/3. A broad range (nonsymmetric shape)exists up to an altitude of 10 km, then becomes sharp, withthe minimum range around the tropopause.[30] 3. The probability of occurrence of Cn

2 derived fromthe cumulative distribution in the 90th percentile is about10−16 m−2/3 around 17 km, indicating that only 10% of themeasurements can exceed this value. Sharp changes in the Cn

2

value with a steeper gradient above the tropopause are sig-nificant in all seasons.[31] 4. The probability of turbulence is high in the bound-

ary layer, with a gradual decrease up to the isothermal levelFigure 10. Seasonal variation of (left) log (K) and (right)log (") with a vertical resolution of 30 m.

Figure 9. Same as Figure 5 but observed during May 2007 to March 2009 (569 launches, Meiseiradiosonde) with a resolution of 5 m.


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(∼5 km), then increases to the maximum around 15 km anddecreases again in the stratosphere.[32] 5. Percentiles of cumulative distribution conditioned

to the turbulence during the monsoon and winter seasonsshow that the mean and 90th percentile profiles reach analtitude of ∼27 and ∼18 km, respectively. In all four seasons,the probability is significantly high within the boundarylayer and decreases sharply afterward.[33] 6. For the 90th percentile profiles the turbulent layers

are thicker (700–900 m) in the boundary layer and in theupper tropospheric heights (400–500 m). The role of zonaland meridional wind shear in thickening the turbulent layeris also prominent during the monsoon and winter seasons,respectively.[34] 7. The mean value of log " in the upper troposphere is

around −7 m2 s−3, increasing to roughly −3 m2 s−3 in thelower stratosphere, in all seasons except monsoon season,with more values in the stratosphere. The mean log K in thetroposphere ranges between −1 and 1 m2 s−1, with valuesdecreasing to below −1 m2 s−1 in the stratosphere duringmonsoon and postmonsoon seasons.[35] 8. Tropopause height and boundary layer height iden-

tified using turbulence profiles are found to match well withthose obtained using traditional methods.[36] A comparison between the collocated simultaneous

MST radar‐measured refractive index gradients and high‐resolution radiosonde observations must be undertaken tounderstand the role of temperature and humidity gradients,with a special focus on and around the tropopause region.

[37] Acknowledgments. The authors are grateful to the technicalstaff at National Atmospheric Research Laboratory (NARL), Gadanki,

for their efforts in making the observations used in the present study. Wewish to thank all three reviewers for providing constructive comments thathelped to improve the manuscript significantly.

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Figure 11. (top) Monthly mean and standard deviation ofthe cold point height (CPH) derived from temperature dataand the height of the inflection point in the vertical profileof the probability of occurrence of Cn

2 conditioned to havingturbulence. (bottom) Monthly mean and standard deviationof boundary layer height (BLH) derived from refractivityand the height of the inflection point in the vertical profileof the probability of occurrence of Cn

2 conditioned to havingturbulence.


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S. V. Bhaskar Rao, Department of Physics, Sri Venkateswara University,Tirupati 517502, Andhra Pradesh, India.B. V. Krishna Murthy, D. Nath, A. K. Patra, and M. Venkat Ratnam,

National Atmospheric Research Laboratory, Gadanki, 517112, AndhraPradesh, India. ([email protected])


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