Diurnal variability of the tropical tropopause: Significance of VHF radar measurements

Authors


Abstract

[1] VHF radars have been used for the detection of atmospheric stable layers such as the tropopause for quite sometime. This opened up a possibility of using VHF radars to study the short period variability of the tropopause with a better time and height resolution as compared to conventional radiosonde measurements. In the present study, a method to determine the tropopause height using VHF radar located at Gadanki (13.5°N, 79.2°E) is discussed and the results are compared with the simultaneous balloon observations. Comparison of radar measurements of cold-point tropopause height (CPT) with simultaneous balloon ascents on 58 occasions has shown a very good agreement with a correlation coefficient of 0.85. The data collected during four different campaigns, which were carried out by employing radar and radiosonde/GPS sonde observations to study the different aspects of lower atmospheric dynamics, are used for this purpose. The radar measurements are then extensively used to study the diurnal variation of tropopause height for the first time over this latitude. The results showed that the tropopause does respond to the diurnal oscillations, which are consistent with the earlier radar studies reported from other geographical locations. During one of the campaigns, the tropopause height has also exhibited the semidiurnal oscillation, which is first of its kind. The diurnal observations clearly demonstrated the usefulness of the radar-detected tropopause. Further, the oscillations in the tropopause height showed a phase delay of ∼1 h and 4–6 h with zonal and meridional wind tidal oscillations, respectively. The observed diurnal/semidiurnal oscillations in the tropopause height are interpreted as tidal manifestations. However, the diurnal variation of convective activity, which also contributes to the diurnal variation of tropopause height, is also accounted. The significance of the present study lies in showing the response of tropopause height to the propagating tides, which can provide some new insights in stratosphere-troposphere exchange processes.

1. Introduction

[2] The tropopause is a stable layer, formed due to natural atmospheric temperature inversion, which separates the troposphere (consider to be in radiative-convective equilibrium) from stratosphere (consider to be in radiative equilibrium). This natural stable layer plays a significant role in the stratosphere-troposphere exchange (STE) as various minor constituents enter stratosphere from troposphere through this region and vice versa [Reid, 1994]. The tropics play a vital role in these exchange processes as maximum solar radiation is received in this region, which gives rise to convection, thunderstorms and cyclones. Thus, tropical tropopause is considered to be an important source region from where the air enters to the stratosphere [Holton et al., 1995]. The tropical tropopause plays a key role in determining the amount of water vapor in lower stratosphere [Brewer, 1949; Newell and Gould-Stewart, 1981; Dessler, 1998; Zhou et al., 2001; Jain et al., 2006]. Therefore, monitoring of tropical tropopause structure, height and its variability can yield a better insight on STE processes and associated dynamics.

[3] Owing to the importance of tropopause variability, many experiments were carried out to study its variability on different scales. Annual, seasonal and monthly variability of tropopause height have been reported in the literature [Reid and Gage, 1981, 1985, 1996; Krishnamurthy et al., 1986; Highwood and Hoskins, 1998; Shimizu and Tsuda, 2000; Randel et al., 2000; Nishida et al., 2000; Seidel et al., 2001]. Tsuda et al. [1994] and Satheesan and Krishna Murthy [2005] examined change in tropical tropopause structure during the passage of equatorial atmospheric waves. Both the studies emphatically showed that the tropopause height respond to the passage of equatorial waves. Shimizu and Tsuda [2000] reported tropopause height oscillations of 10–25 and 25–50 days period, which the authors associated with Kelvin waves and Madden-Julian oscillations, respectively. Jain et al. [2006] discussed the possible role of atmospheric convection and Kelvin-wave of 7–9 days period in producing extreme cold tropopause temperature (<191 K). Scott and Cammas [2002] reported the breaking of Rossby waves on the isentropic surface that modulates the tropopause structures. Sherwood and Dessler [2003] showed the impact of convection on the structure of tropical tropopause.

[4] Conventionally, the height and structure of the tropopause is examined using the temperature height profile obtained from radiosonde/GPS sonde observations. However, the radiosonde/GPS sonde observations are generally taken twice a day at 00:00 and 12:00 GMT, except during some special field campaigns/experiments. Therefore, balloon measurements have limited time resolutions. Almost all the above mentioned studies, which discussed the tropopause variability on longer timescales, were using the balloon measurements. However, balloon measurements are not useful to study the short period variability of the tropopause such as diurnal variation, which demands the better temporal resolution. Moreover, the balloon measurements are not possible in severe weather conditions such as mesoscale convective systems and cyclones.

[5] The space born GPS radio occultation (GPSRO) technique is also making significant contributions for the tropopause related studies [Randel et al., 2003; Ratnam et al., 2005; Narayana Rao et al., 2007]. The atmospheric refractivity profiles measured using the GPSRO technique is converted into temperature profiles, which is further used to study the characteristics of the tropopause on global scale. However, the GPSRO technique will not be much useful to study the short-period variation of tropopause at diurnal (24 h) and semidiurnal (12 h) tide scales. On the other hand, ground based VHF radars have distinct advantage of making tropopause measurements with a good time and height resolution. Many investigators across the globe utilized the VHF radar to detect and monitor the stable layers [e.g., Gage and Green, 1979; Larsen and Rottger, 1985; Jaya Rao et al., 1994; Jain et al., 1994]. Detection of the tropopause height from the VHF radar observations was first reported by Gage and Green [1979]. At the tropopause level, which acts as an interface to the stable and unstable atmosphere, sharp gradient in the temperature lapse rate gives the enhanced radar echo power. The air around the tropopause will have sharp change in refractive index, which gives rise to a persistent radar reflectivity layer at the tropopause level. Thus, VHF radars are extensively used to determine the height of the tropopause [Gage and Green, 1982; Riddle et al., 1984; Gage et al., 1986; Nastrom et al., 1989; Atlas et al., 1996; Worthington and Thomas, 1997; Hermawan et al., 1998; Jaya Rao and Jain, 2000; Jain et al., 2000; Yamamoto et al., 2003; Satheesan and Krishna Murthy, 2005]. Apart from vertical beam echo power, radar aspect sensitivity is also used to detect the tropopause height [Gage and Green, 1979, 1982; Jain et al., 1994]. Nastrom et al. [1989] studied day-to-day variability of tropopause height associated with tropopause folding using VHF radar. Kumar [2006] reported the disturbed tropopause structure during the passage of mesoscale convective systems and their implication in STE studies using VHF radar observations. The author emphasized the smaller scale processes, associated with deep convection must be considered in order to understand the finer details of STE. In a seminal work, Yamamoto et al. [2003] have shown that the altitude of the tropopause can be determined with a high time resolution of 3 h by the VHF radar and also demonstrated that the short-term variations of the tropopause altitude can be studied using such observations. Further, the spectral analysis carried out by the authors showed a clear peak at 1-day with amplitude as small as 0.1 km. Nevertheless, this valuable study demonstrated the capability of radar observations to study the tidal oscillations in the tropopause height. The authors have proposed diurnal convective activities and diurnal tides as a cause of the diurnal variation of the tropopause altitude. However, the high temporal resolution studies of tropopause height are very sparse and call for more such observations to draw any general conclusion. In this regard, data collected during the four campaigns at Gadanki, which were carried out to explore the various aspects of atmospheric dynamics using VHF radar and radiosonde/GPSsonde observations, are used to divulge the short period variation of tropical tropopause height at diurnal scales. The central objective of the preset study is to demonstrate the VHF radar technique to detect the tropopause height and comparing the results with simultaneous radiosonde/GPS sonde measurements over Gadanki. An effort is also made for the first time over this latitude to discuss the diurnal variability of tropopause height using VHF radar observations. Experimental details are given in section 2, section 3 discuss the VHF radar technique for detecting the tropopause height, section 4 presents the results and discussion and concluding remarks are given in section 5.

2. Experimental Details

[6] VHF radar located at Gadanki (13.5°N, 79.2°E), commonly known as Indian mesosphere-stratosphere-troposphere radar, is a high power pulse coherent radar, operating at 53 MHz, corresponding to wavelength of 5.66 m with an average power apertures product of 7 × 108 Wm2. A detailed description of this radar located at Gadanki, a tropical location in the southern part of India, can be found in Jain et al. [1994] and Rao et al. [1995], and data processing in Anandan et al. [2001].

[7] Four intensive campaigns were carried out to study the various aspects of atmospheric dynamical processes associated with atmospheric convection, turbulence, waves and tides. The first campaign (campaign-I) was carried out from 19 July to 14 August 1999 and second campaign (campaign-II) was from 20 September to 26 October 2002. During the campaign-I, everyday the radar was operated in two modes. In the first mode (see Table 1, experimental specification file 1 (hereafter ESF 1)) the radar was operated to obtain the three-dimensional wind fields (zonal, meridional and vertical) for ∼15 min and in second mode the radar was operated continuously for about ∼2 h in vertical beam mode (Table 1, ESF 2). The second mode radar observations were used to collect the vertical beam echo power and vertical wind velocity. During campaign-I, two diurnal mode observations were also carried out on 28–29 July and 4–5 August 1999. Along with radar observations, simultaneous in situ measurements were also carried out by launching radiosonde everyday at ∼16:00 IST (IST = GMT+05:30 h). These radiosondes are of standard design developed by Indian Meteorological Department (IMD) [Jain et al., 2006]. The height resolution of the radiosonde measurements is 300–400 m. Simultaneous GPS sonde observations were carried out at Gadanki for campaign-II along with radar observations using ESF-3 (see Table 1). GPS sonde provides fine height resolution of the order of 3–10 m [Das et al., 2004]. The ascent rate of the balloon (radiosonde/GPS sonde) was 300–350 m/min and it took 40–50 min to reach the tropopause.

Table 1. VHF Radar Experimental Specification Files Used for the Present Studya
ParameterESF-1ESF-2ESF-3
  • a

    ESFs, Experimental Specification Files.

  • b

    East, west, north, and south respectively and number indicate the oblique angle in degree. Zx and Zy indicate zenith beam position with x and y polarizations, respectively.

Frequency53 MHz53 MHz53 MHz
Transmitter Peak Power2.5 MW2.5 MW2.5 MW
Maximum Duty Ratio2.5%2.5%2.5%
Antenna1024 (130 × 130 m2)1024 (130 × 130 m2)1024 (130 × 130 m2)
Beam Width
Number of Beams6 (E-10, W-10, Zx, Zy, N-10, S-10)b1 (Zx)b36 (E-6,9,10,12,15) (W-6,9,10,12,15) (N-6,9,10,12,15) (S-6,9,10,12,15) (Zx,Zy)b
Number of Coherent Integrations6412864
Number of Incoherent Integration111
Number of FFT Points512256256
Pulse Width16 μs (coded with 1 μs baud length)16 μs (coded with 1 μs baud length)16 μs (coded with 1 μs baud length)
Inter Pulse Period (IPP)1000 μs1000 μs1000 μs
Range Resolution150 m150 m150 m

[8] Campaign-III was carried out to study atmospheric waves associated with Tropical Easterly Jet (TEJ) [Sasi et al., 2000]. The radar was operated for 10 min with an interval of 4 h from 10:00 h (IST) on 23 September to ∼06:00 h (IST) on 26 September 1997 using ESF-1. Similarly, to study diurnal and semidiurnal tides in zonal and meridional winds, campaign-IV was carried out with high time resolution. In this campaign radar was operated for ∼15 min with an interval of ∼1 h from 9:30 h (IST) on 13 September to ∼13:30 h (IST) on 15 September 2004 using ESF-I. Details of all the ESFs are given in Table 1, whereas instruments used for the detection of the tropopause height and purpose of the campaigns are given in Table 2.

Table 2. List of Campaigns, Their Purpose, and the Instruments Used for the Present Study
CampaignCampaign PeriodRadar ESF UsedInstruments UsedPurpose of the Campaign
Campaign-I19 Jul to 14 Aug 1999 28–29 Jul 1999 (Diurnal) 4–5 Aug 1999 (Diurnal)ESF1 and ESF 2Radar and RadiosondesConvection, turbulence, gravity wave and diurnal oscillation
Campaign-II20 Sep to 26 Oct 2002ESF 3Radar and GPS SondeConvection and gravity wave
Campaign-III23–26 Sep 1997ESF 1RadarAtmospheric waves associated with TEJ
Campaign-IV13–15 Sep 2004ESF 1RadarDiurnal variability and tides

3. Tropopause Height Detection Using VHF Radar

[9] There are various definitions of tropopause based on the thermal properties of the atmosphere and each of them has their own advantage. Most frequently used definitions of tropopause are lapse rate tropopause (LRT) and cold point tropopause (CPT). The LRT, also known as WMO (World Meteorological Organisation) tropopause is defined by WMO as the lowest level at which the average lapse rate is less than 2°K km−1 and lapse rate between this level and at all higher levels within next 2 km does not exceed 2°K km−1. The CPT is the coldest point of the sounding, i.e., the level where the minimum temperature occurs. This height represents the convective and radiative equilibrium between the troposphere and stratosphere. Therefore, CPT has its own physical significance for STE [Highwood and Hoskins, 1998]. Keeping its physical significance in view, only CPT is considered for the present study.

[10] The radar vertical beam echo power has been used widely for detection of the atmospheric stable layers [Gage and Green, 1979; Larsen and Rottger, 1985; Jaya Rao et al., 1994; Jain et al., 1994]. This technique has also been used to develop an objective method for determining the height of the tropopause [Gage and Green, 1982; Riddle et al., 1984; Gage et al., 1986]. This method was first applied to the observations at midlatitudes. Later, Jaya Rao and Jain [2000] modified this algorithm for tropical latitudes where the temperature in the lower stratosphere shows an increase at the rate of ∼3.5 K km−1. The detailed method is given in Appendix A. Although in principle it is possible to determine the tropopause height using each vertical beam received power, it is desired to integrate the vertical beam profiles at least for 4 scan cycles (∼15 min) and 3-range gate running averaging to obtain better signal delectability. Figure 1 demonstrates the radar method for obtaining the CPT and LRT heights from the VHF radar vertical beam intensity measurements. The simultaneous radiosonde observations of CPT and LRT height are also shown in the Figure 1.

Figure 1.

(left) The height profile of temperature (solid line) and lapse rate (dotted line) from radiosonde observations. (right) Illustration of method used to determine the height of the tropopause. The arrow in the first panel indicates the CPT height, and the two different arrows in the second panel indicate the CPT and LRT.

4. Results and Discussion

4.1. Comparison of Radar and Radiosonde/GPS Sonde Derived CPT Heights

[11] Using all the data collected during above mentioned four campaigns, extensive comparison is carried out between radar and radiosonde/GPS sonde measurements. The self-consistency of height of CPT determined using radar (hereafter RM) and the radiosonde measurements (hereafter RS) is demonstrated in Figures 2–4. Figure 2a shows the height time section of radar vertical beam echo power with radar and radiosonde derived tropopause marked. This figure clearly demonstrates the potential of VHF radar observations for identifying the tropopause. For better understanding of comparison between radar and radiosonde observations, day-to-day variation of CPT height as determined using RM and RS from 19 July to 14 August 1999 is shown in Figure 2b. From this figure it can be inferred that both the methods agree well within ∼400 m on average. Figures 3a and 3b show the diurnal variability of CPT using RM and RS on 28–29 July 1999 and 4–5 August 1999, respectively. One more comparison is shown in Figure 4 from 20 September to 26 October 2002. The self-consistency of the CPT height determined using RM with RS method is evident from these figures. It is to be noted that RM gives a height resolution of ∼150m, which corresponds to the radar range resolution, whereas RS gives a height resolution of 300–400 m. However, GPS sonde gives a very high height resolution of 3–10m. The mean tropopause height determined from 58 balloon ascents and radar measurements are 16.73 ± 0.44 km and 16.69 ± 0.43 km, respectively. The root mean square difference between RS and RM is estimated to be 286 m, which is within the radar range resolution and radiosonde/GPS sonde height resolution. A correlation analysis of CPT height determined by radar and radiosonde has been carried out and the same is shown in Figure 5. The correlation coefficient between RM and RS is 0.85, which is significant at 1% level and standard deviation error (SDE) is 0.004. All these comparisons beyond any doubt confirm that the radar method can be used for the detection of the tropical tropopause height.

Figure 2.

(a) Height time section of vertical beam echo power from 19 July to 14 August 1999 with the radar and radiosonde tropopause height marked. (b) Day-to-day variability of CPT height from 19 July to 14 August 1999, derived from radar method and compared with conventionally detected tropopause height using radiosonde ascents.

Figure 3.

Diurnal variability of tropopause height derived from radar method and compared with radiosonde detected tropopause height on (a) 28–29 July 1999 and (b) 4–5 August 1999.

Figure 4.

Day-to-day variability of CPT height from 20 September to 26 October 2002 derived from radar method and compared with conventionally detected tropopause height using GPS sonde ascents.

Figure 5.

Scatterplot with best fit line for the tropopause height detected from balloon measurements (radiosonde and GPS sonde) versus tropopause height detected from radar method. Here, n and r indicates the number of points and correlation coefficient, respectively.

4.2. Diurnal Variation of Tropical Tropopause

[12] By now, it is well established that atmospheric tides global oscillations with a period of a solar day and subharmonics. It is also known that they are excited by solar heating of water vapor in the troposphere and ozone in the stratosphere. Diurnal and semidiurnal tidal oscillations in the troposphere and lower stratosphere over Gadanki have been reported in the past [e.g., Sasi et al., 1998, 2001]. Diurnal observations of zonal and meridional winds have been extensively used for that study.

[13] As the present radar method gives high-resolution observations of CPT height, it will be very interesting to examine whether tropopause height respond the propagating tides or not. Figures 6 and 7show the diurnal variation of tropopause height on 23–26 September 1997 and 13–15 September 2004, respectively. As mentioned earlier, the data collected during campaign-III was for ∼68 h with an interval of 4 h, whereas during campaign-IV, it was for ∼53 h with an interval of 1 h. It is to be noted that both the campaigns (i.e., campaign-III and campaign-IV) were carried out during the post-monsoon period. Diurnal and semidiurnal oscillations are clearly seen from Figure 7, whereas only diurnal oscillation is seen from Figure 6. However, it is very interesting to note the diurnal/semi diurnal oscillation manifestation in the tropopause height. Further, to check the consistency, the wind analysis has been carried out. Figures 8 and 9show the time series plots of zonal (top panel) and meridional (bottom panel) winds for 23–26 September 1997 and 13–15 September 2004, respectively. These figures also show similar characteristics of diurnal and semidiurnal variations as seen in the tropopause height. As it is already well established that the diurnal/semi diurnal oscillations in the winds are due to propagating tides, it is reasonable to state that the oscillations observed in the tropopause height is also due to tides. However, further analysis is carried out to confirm this point.

Figure 6.

Diurnal variation of cold-point tropopause detected using radar from ∼10:00 IST on 23 September to 06:00 IST 26 September 1997.

Figure 7.

Same as Figure 6 but from 09:30 IST on 13 September to 13:30 IST on 15 September 2004.

Figure 8.

Diurnal variation of (top) zonal and (bottom) meridional wind derived from radar observation from ∼10:00 IST on 23 September to 06:00 IST on 26 September 1997.

Figure 9.

Same as Figure 8 but from 09:30 IST on 13 September to 13:30 IST on 15 September 2004.

[14] To estimate the dominant periodicity in the tropopause height and winds (zonal and meridional), the time series data are subjected to harmonic analysis. Figures 10 and 11 show the periodograms corresponding to zonal wind (red line), meridional wind (blue line) and tropopause height (black line) for 23–26 September 1997 and 13–15 September 2004, respectively. The dominant periodicity in the tropopause height, zonal and meridional winds is noted to be ∼23 h on 23–26 September 1997. However, on 13–15 September 2004, there are two peaks in all the three parameters (namely, tropopause height, zonal and meridional wind) corresponding to the periodicity of ∼12 h and ∼19 h. This observation clearly reveals the dominance of semidiurnal tide on this particular day. These observations, thus, show the similar dominating periodicity close to diurnal/semidiurnal tides in tropopause height as well as in horizontal winds.

Figure 10.

Periodogram of tropopause height, zonal, and meridional wind oscillations on 23–26 September 1997.

Figure 11.

Same as Figure 10 but for 13–15 September 2004.

[15] Further, to establish the phase relation between tropopause height and wind oscillations, the diurnal component of these parameters are extracted and are compared. As per the authors knowledge, this is the first such an attempt to establish the diurnal phase relation between tropopause height and winds. Figures 12 and 13 show the cross-correlation between tropopause height, zonal (solid line) and meridional (dotted line) winds for the two campaign periods. This is computed by applying band-pass filter of 19–28 h on 23–26 September 1997 and 14–23 h on 13–15 September 2004. A phase delay of ∼1 h is observed between tropopause height and zonal wind, whereas 3–6 h phase delay is observed between tropopause height and meridional wind. Observations from both the campaigns show the similar feature in contest of phase relation between tropopause height and winds. There is a consistent phase relation between the tropopause height and horizontal winds. Yamamoto et al. [2003] suggested both diurnal convective activities and diurnal tides as a cause of the diurnal variation of the tropopause altitude. The present study shows the diurnal as well as semidiurnal oscillations in the tropopause height and a consistent phase relation of diurnal oscillation of CPT height and winds. These observations, thus provides the ample evidence for tidal activity as causative mechanism for the observed diurnal variation in tropopause height.

Figure 12.

Cross-correlation between tropopause height, zonal, and meridional wind on 23–26 September 1997.

Figure 13.

Same as Figure 12 but for 13–15 September 2004.

[16] By now, it is well established that atmospheric tides are global oscillations with a period of a solar day and its subharmonics. It is also known that they are excited by solar heating of water vapor in the troposphere and ozone in the stratosphere. The atmospheric tides are predominantly observed in the pressure, temperature and winds. As the tropopause altitude also depends on the background temperature, which is modulated by the propagating tides. Thus, it is obvious to believe that the tropopause altitude will also be modulated by the atmospheric tides. As we do not have continuous temperature measurements at tropopause altitude, we used radar wind measurements to show the tidal signature at tropopause altitude as both temperature and winds are modulated by the propagating atmospheric tides. However, the diurnal variation of convective activity may also contribute to the observed diurnal oscillation of CPT height. Further studies at this latitude will be aimed to quantify the contribution of tidal activity and convective activity to the diurnal oscillation of tropopause height.

5. Conclusions

[17] A VHF radar method for detecting the CPT height is discussed. The comparison between the radar method and in situ balloon measurements on 58 occasions has shown a very good agreement with a correlation coefficient of 0.85. After validating the radar method, high resolution CPT height measurements carried out in four different campaigns are extensively used to study the diurnal variation of tropopause. On two occasions, the radar observations of diurnal variability of tropopause height are compared with balloon measurements, which also have shown a very good agreement. The spectral analysis revealed the diurnal oscillations of CPT with amplitude of ∼400 m. It was quite exciting to see the semidiurnal oscillation also in one of the occasion in CPT height. These observations thus provided an evidence for tidal modulation of CPT height. To further confirm this point, spectral analysis of zonal and meridional winds is carried out. Similar periodicities are observed in zonal and meridional winds as observed in CPT heights. Phase relation between CPT height and zonal wind is estimated to be ∼1 h whereas 3–6 h delay is observed between CPT height and meridional wind. Thus, the present observations confirm the tidal modulation of CPT height. However, the diurnal variation of convective activity should also be accounted for the observed diurnal variation. Nevertheless, the VHF radar observations presented here can be used to study the short period variations in the CPT. A thorough understanding of the tropopause oscillations in response to atmospheric wave activity could help in better understanding the STE processes in finer details.

Appendix A:: VHF Radar Methods for the Determination of Tropopause Height

[18] The range corrected echo power Sv( = Prr2) at the heights above 10 km, where humidity can be neglected is given by [Gage et al., 1986; Jaya Rao and Jain, 2000]

equation image

where B is a constant, p is the atmospheric pressure, T is the atmospheric temperature, Γd is the dry adiabatic lapse rate, z is height, zo is the reference height, and H is the scale height.

[19] Equation (A1) gives the expected radar echoes power in terms of the various atmospheric parameters. The algorithm used for the determination of the height of the tropopause involves estimation of model power profiles, corresponding to minimum tropopause temperature (i.e., CPT). It may appear from equation (A1) that measurement of atmospheric parameters is necessary for determination of tropopause. However, the algorithm is developed in such a way that these atmospheric measurements are not required. The lapse rate of the temperature in the lower stratosphere is obtained from model given by Sasi and Sengupta [1986], which is applicable for the Indian low latitude zone and the same is determined to be –3.5 K km−1. Considering the variation of p, T and H from model temperature profiles, the range corrected echo power Sv (given in equation (A1)), expressed as

equation image

where To and Ho are the temperature and scale height corresponding to the reference level zo respectively. The reference level zo in equation (A2) should lies on the stratospheric height and for present analysis we have considered zo = 18.6 km and its corresponding temperature To is taken from the model given by Sasi and Sengupta [1986]. However, it should be noted that zo can be chosen any value in the lower stratosphere up to 20 km (as dT/dz = −3.5 K/km in lower stratosphere upto 20 km), provided the corresponding temperature To should be taken from the model given by Sasi and Sengupta [1986]. Here, Q is a constant for the height range under consideration and the same is given by

equation image

For the heights corresponding to the lower stratosphere

equation image

where Qs = Qo at z = zo and equation image = 0 K

equation image

[20] The value of Qs can be obtained by fitting a straight line between z and log(Sv) (see equation (A4)) and obtaining the value of log(Sv) at z = zo. Value of Qo can then be obtained from equation (A5).

[21] For (equation image) = 0 K km−1 and Qs = Qoequation (A2) can be rewritten as

equation image

For (equation image) = −2 K km−1 the equation (A2) can be rewritten as

equation image

where Q−2 = Qo + 0.2. The value of Ho is again obtained from model atmosphere. The interception of the straight line represented by equations (A6) and (A7) with observed log (Sv) curves, represents the height of CPT and LRT, respectively.

Acknowledgments

[22] The authors would like to thank many of their colleagues at the National Atmospheric Research Laboratory (NARL), Gadanki, who have contributed to the collection of data reported in this paper. Thanks are also due to the Indian Meteorological Department (IMD) for successfully conducting the radiosonde campaign from NARL during the July–August 1999 period. Thanks are also due to G. S. Bhatt for his support in conducting the GPS sonde campaign from NARL and B. V. Krishnamurthy for his valuable suggestions. One of the authors S.S.D. would like to thank NARL and the Indian Space Research Organisation (ISRO) for the award of Senior Research fellowship during this study. S.S.D. would also like to thank Centre for Wind Energy Technology (C-WET) for it logistic support in revising the paper. A.R.J. would like to thank ISRO/Department of Space (DOS) for their support as a visiting scientist at NARL and the National Physical Laboratory (NPL).

Ancillary