Annales Geophysicae (2001) 19: 965–973 c ○ European Geophysical Society 2001

Abstract. The turbulence refractivity structure constant (C 2 n ) is an important parameter of the atmosphere. VHF radars have been used extensively for the measurements of C 2 n . Presently, most of such observations are from mid and high latitudes and only very limited observations are available for equatorial and tropical latitudes. Indian MST radar is an excellent tool for making high-resolution measurements of atmospheric winds, associated shears and turbulence refractivity structure constant (C 2 n ). This radar is located at Gadanki (13.45° N, 79.18° E), a tropical station in India. The objective of this paper is to bring out the height structure of C 2 n for different seasons using the long series of data (September 1995 – August 1999) from Indian MST radar. An attempt is also made to understand such changes in the height structure of C 2 n in relation to background atmospheric parameters such as horizontal winds and associated shears. The height structure of C 2 n , during the summer monsoon and post-monsoon season, shows specific height features that are found to be related to Tropical Easterly Jet (TEJ) winds. It is important to examine the nature of the radar back-scatterers and also to understand the causative mechanism of such scatterers. Aspect sensitivity of the received radar echo is examined for this purpose. It is observed that radar back-scatterers at the upper tropospheric and lower stratospheric heights are more anisotropic, with horizontal correlation length of 10–20 m, as compared to those observed at lower and middle tropospheric heights. Key words. Meteorology and atmospheric dynamics (climatology; tropical meteorology; turbulence)

Abstract.The turbulence refractivity structure constant (C 2 n ) is an important parameter of the atmosphere.VHF radars have been used extensively for the measurements of C 2 n .Presently, most of such observations are from mid and high latitudes and only very limited observations are available for equatorial and tropical latitudes.Indian MST radar is an excellent tool for making high-resolution measurements of atmospheric winds, associated shears and turbulence refractivity structure constant (C 2 n ).This radar is located at Gadanki (13.45 • N, 79.18 • E), a tropical station in India.The objective of this paper is to bring out the height structure of C 2 n for different seasons using the long series of data (September 1995-August 1999) from Indian MST radar.An attempt is also made to understand such changes in the height structure of C 2 n in relation to background atmospheric parameters such as horizontal winds and associated shears.The height structure of C 2 n , during the summer monsoon and post-monsoon season, shows specific height features that are found to be related to Tropical Easterly Jet (TEJ) winds.
It is important to examine the nature of the radar back scatterers and also to understand the causative mechanism of such scatterers.Aspect sensitivity of the received radar echo is examined for this purpose.It is observed that radar back-scatterers at the upper tropospheric and lower stratospheric heights are more anisotropic, with horizontal correlation length of 10-20 m, as compared to those observed at lower and middle tropospheric heights.

Introduction
Study of the nature and characteristics of the atmospheric turbulence is of basic importance for understanding the atmospheric dynamics and coupling processes.It is well known that the intensity and nature of the atmospheric turbulence Correspondence to: A. R. Jain (nmrf@isro.ernet.in)depend on background atmospheric parameters such as atmospheric wind, temperature and humidity (VanZandt et al., 1981).These atmospheric parameters depend on the latitude of the station and the season.The atmospheric turbulence parameters are therefore expected to show large seasonal dependence (Nastrom et al., 1986).At tropical latitudes the turbulence parameters are expected to show distinct seasonal variations due to the presence of weather phenomena such as the South-West monsoon and the associated Tropical Easterly Jet (TEJ) winds.
MST radar is an excellent tool for making high-resolution measurements of atmospheric winds, associated vertical shears of horizontal winds and various atmospheric turbulence parameters.However, most of such studies are confined to mid and high latitudes (VanZandt et al., 1978;Smith et al., 1983;Nastrom et al., 1986) and only a few measurements are available at low latitudes (Sato and Woodman, 1982;Tsuda et al., 1985;Jain et al., 1995;Narayana Rao et al., 1997).The received radar echo intensity is generally used for determination of the parameter refractivity structure constant (C 2 n ).The received radar echo intensity for the zenith beam is due to back-scatter from refractivity structure associated with atmospheric turbulence and also Fresnel reflection/scatter from gradients in the potential radio refractive index (M) (Röttger and Liu, 1978;Gage et al., 1978).At oblique angles, with beam zenith angle (χ) greater than or equal to 10 • (i.e.χ ≥ 10 • ), it is generally presumed that echos arise mainly due to radio refractivity structures associated with turbulence (Hooper and Thomas, 1998).The received radar echo intensity is therefore aspect sensitive and this particular feature is utilised to determine the horizontal correlation length and the characteristics of the radar backscatterers giving rise to observed echo (Hooper and Thomas, 1995;Jain et al., 1997).In the present paper, Indian MST radar observations for four years, September 1995 -August 1999, are utilized to bring out the height structure of C 2 n for different seasons.An effort is also made to understand the seasonal changes in C 2 n in terms of background atmospheric parameters such as horizontal winds and associated vertical shears.These observations have also brought out specific features of height structure of C 2 n during the tropical monsoon season and the same are seen to be related to the easterly jet winds, near the tropopause, prevalent in the summer monsoon season.
2 Observations and method of computing C 2 n Indian MST radar is a very sensitive, coherent, pulse Doppler radar with peak power aperture product of 3x 10 10 Wm 2 .The technical features of this radar are discussed by Jain et al. (1994) and Rao et al. (1995).The major parameters of the radar are given in Table 1.In the present study, daily evening common mode observations made using Indian MST radar during the period from September 1995 -August 1999 are utilised.Figure 1 shows the histogram of number of days of observations for each month during the period of observation.The measurements have been carried out every day for about 45 min during evening time between 16:30 to 17:15 (IST) (i.e.11:00-11:45 UT).The experimental specification file (ESF) used for these experiments is given in Table 2.These measurements have height, time and velocity resolution of 150 m, 2 min and 0.2 m/s respectively and covered the height range of 3.6 to 32 km.For these measurements six beams, were used (see Table 2).The techniques used for signal and data processing are discussed by Anandan (1996).The zeroth moment of the spectrum received from the radar echo is used to compute the signal to noise ratio (SN R).The mean SNR (i.e.SNR) for all the oblique beams, for each day, is used for the computation of the radar volume reflectivity (η) and C 2 n .The expression used for computations of parameters η and C 2 n are given as (Jaya Rao, 1998;Ghosh et al., 2000) where (S/N) • is SNR for oblique beams and P t is the peak transmitted power; other symbols used in Eq. ( 1) are defined : 8 * E 10y = Beam direction 10 • east from the zenith in the East-West plane W10y = Beam direction 10 • west from the zenith in the East-West plane Zy = Vertical beam direction formed using the East-West plane array Zx = Vertical beam direction formed using the North-South plane array N10x = Beam direction 10 • north from the zenith in the North-South plane S10x = Beam direction 10 • south from the zenith in the North-South plane in Table 1.
The turbulence refractivity structure constant C 2 n is related to the radar volume refractivity After substituting the values of the various parameters given in Tables 1 and 2, Eqs. ( 1) and ( 2) can be rewritten as where (S/N) dB is the SNR for oblique beams in dB.In the present study, Eq. ( 4) is used for the determination of C 2 n .It should, however, be mentioned here that the actual value of P t for each day of observation is used for the computation of C 2 n .The mean oblique and vertical beam SNR is used to determine the echo aspect sensitivity and the horizontal correlation length of the radar backscatterers adapting the standard method (Hocking et al., 1989(Hocking et al., , 1990;;Hooper andThomas, 1995 andJain et al., 1997).The horizontal correlation length gives an idea of the horizontal length and anisotropy associated with the back-scatterers and is given by where λ is the radar wavelength and θ s is e −1 of the half width the polar diagram of the radar backscatter expressed in degrees.Small values of θ s means large anisotropic scattering.Received signal intensity (SNR) at the vertical and oblique beam is used for determination of θ s (Hocking, 1986;Hocking et al., 1990;Hooper and Thomas, 1995).

Results
3.1 Monthly mean height profiles of horizontal winds (U H ), vertical shear of horizontal winds (s) and refractivity turbulence structure constant (C 2 n ) Figures 2, 3 and 4 represents, for each year, the monthly mean height profiles of U H , S and C 2 n .These figures show the height structure of the parameters for each month and so it is possible to examine month-to-month and also seasonal change of the parameters.South-West monsoon is a prominent weather phenomenon in the Tropical region of India.Therefore, the atmospheric changes can be understood with reference to monsoon conditions and the year is accordingly divided into four seasons viz., Winter (December, January and February), Pre-monsoon (March, April and May), Monsoon (June, July and August) and Post-monsoon season (September, October and November).shows a secondary peak between 16-19 km suggesting that enhanced radar reflectivity (η) and C 2 n may be caused by enhanced wind shears present in these height ranges, which are upper edge of the TEJ (see Figs. 3 and 4).

Post monsoon season
As seen from Fig. 2, the easterly winds continue to prevail in September and October.However, during these months winds are weaker as compared to jet winds prevalent in monsoon months.In the month of November, however, these peak winds are absent.Accordingly, as seen from the Fig. 3, shears of magnitude 0.01-0.02s −1 are observable in the height range 16-19 km but in the month of November shears are relatively weak (< 0.01 s −1 ).The secondary peak in C 2 n is observable in month of September and October also in the same height range but clearly much weaker for in November (see in Fig. 4).These results thus clearly indicate that     shears are contributing to enhanced radar reflectivity and C 2 n .A distinct minimum is observable in C 2 n in the height range of 12-16 km in monsoon and post monsoon months.This minimum could be due to lack of wind shears (see Fig. 3) or it may be due to weak potential refractive index gradient (M), in this height range.

Winter season
In these months, winds are relatively weak and peak winds (10-20 m/s) are in the height range of 10-14 km.Accordingly, shears are also very weak (see Fig. 3) and therefore there is no clear secondary peak is observable in η and C 2 n in the height range of 14-19 km.The value of C 2 n above 12 km is almost constant (see Fig. 4).

Pre-monsoon season
The winds continue to be very weak in the months of March and April as in the case of winter months and, accordingly, associated shears are also weak (see Figs. 2 and 3); there is no clear secondary peak in η and C 2 n in the height range 14-19 km.In month of May, however, the wind patterns are different and easterly winds in some years are observable with a peak between 16-19 km (see Fig. 2) and corresponding shears and secondary peak in η and C 2 n is also seen (Figs. 3 and 4).Therefore, for these years the height structure of C 2 n in May is similar to that observable in monsoon and post-monsoon months.

Monthly mean height profiles of horizontal correlation length (ζ )
The monthly mean height profiles of ζ are presented in Fig. 5. From these figure it is clear that values of ζ above 16 km are ∼10-15 m which are much larger than the value of 5-10 m observed in lower and mid troposphere.This suggests that more anisotropic scatterers are present at the heights above 16 km.This is expected due to the temperature inversion associated with the tropopause and other stable layers present in lower stratosphere.This suggests that, above 16 km, enhanced static stability represented by N 2 could also contribute to the enhanced radar reflectivity.A recent paper by Jain et al., 2001, discussed these aspects in more details.

Contour maps of C 2 n
To get an over all idea of the month-to-month and year-toyear variability of height structure of C 2 n , heightmonth contour maps of C 2 n intensity are drawn for different years and these are presented in Fig. 6.The following points can be noted: (a) The large year-to-year variability is noticeable in the height structure of C 2 n for all the months.(b) The band of minimum C 2 n between 10-16 km is broader in height range during winter and pre-monsoon months as compared to remaining months.(c) The secondary peak in C 2 n is distinctly visible in monsoon and post-monsoon months between 16-19 km.However, in some years, for example in 1996, it is comparatively stronger than for other years.This again brings out year-to-year variability in C 2 n .
3.4 Seasonal and month-to-month variation of C 2 n height structure n .This is consistent with large variability of the observed winds and shears at this latitude during these months i.e.March, April and May (see Fig. 2).
In addition to the seasonal variation, month-to-month variation of C 2 n is also examined, as shown in Fig. 8.In this figure panel [A] and [B] shows the plots of monthly mean C 2 n obtained using all the available data for each month at nine heights.The following points emerged clearly from this figure: i) The parameter C 2 n is minimum in the month of February and March at all heights but this minimum is more distinct at heights above 15 km.ii) The parameter C 2 n shows an almost a flat peak for the months of May to October at lower heights and June to October at higher heights.These results are consistent with those presented in Figs. 4,  6 and 7.

Discussion and conclusion
The turbulence refractivity structure constant (C 2 n ) is one of the basic parameters of atmospheric turbulence which can be determined using the radar measurements of the received radar echo intensity (for example see VanZandt et al., 1978;Hocking et al., 1989).The radar echo arises due to refractive index irregularities, associated with turbulence on a scale equal to half of the radar wavelength λ/2).For Indian MST radar, which operates at 53 MHz, half of the radar wavelength is about 3 m and thus, the radar samples the refractive index irregularities of this scale.
Most of the observation of C 2 n using VHF radars have been carried out at mid and high latitudes (VanZandt et al., 1978;Gage et al., 1978Gage et al., , 1980;;Hocking et al., 1989;Smith et al., 1983;Nastrom et al., 1986); only a few measurements are available at tropical and low latitude regions (Sato and Woodman, 1982;Tsuda et al., 1985;Narayana Rao et al., 1997).Therefore, more measurements are necessary to have a better idea of C 2 n in this region.Jain et al. (1995) presented first measurements of C 2 n in the height range of 4-11 km using Indian MST radar in ST mode with a peak power aperture product of 4.8 × 10 6 Wm 2 .Narayana Rao et al. (1997) have presented measurements of C 2 n made using Indian MST radar in MST mode with an average power aperture product of 3 × 10 10 Wm 2 .These authors made use of one year of observations taken during the period January 1993 to December 1993.In the present paper, four years of evening common mode observations for the period September 1995 to August 1999 are utilized for the determination of C 2 n .These measurements are analyzed to examine the height structure of C 2 n at this tropical station in India.An effort is also made to bring out the seasonal features of the C 2 n height structure and relate the same to the background atmospheric winds and vertical shears associated with these winds.Some interesting results are brought out from this study.In monsoon and post-monsoon seasons, a secondary peak is observed in C 2 n in the height range of 16-20 km and a minimum in the height range of 12-16 km.This secondary peak in C 2 n is found to be closely associated with the vertical shear of horizontal winds that are observed to occur at the upper edge of the TEJ.In winter and the pre-monsoon season, the secondary peak in C 2 n is absent and almost constant values of C 2 n are observed for heights above 12 km.This height structure of C 2 n is noted to be consistent with weak horizontal winds and associated shears observed in these seasons.The height structures of C 2 n in winter and the pre-monsoon season are significantly different than those observed in monsoon and post-monsoon season.From these results it is evident that the presence of strong wind shears does contribute to the height structure of C 2 n significantly.Tsuda et al. (1985), using high-resolution measurements with the Aericibo radar, show that there is a good correlation between echo power and wind shear.Several measurements of atmospheric turbulence associated with jet stream due to strong shears show enhancement in C 2 n (Gage et al., 1980;VanZandt et al., 1981;Smith et al., 1983).However, most of these results are confined to mid latitudes.
The month-to-month variation of C 2 n is also examined in details.The parameter C 2 n is found to show a clear mini-mum at all heights in the months of February and March and may be due to the lack of wind shear and humidity.The value of C 2 n is almost constant during May-October months at lower heights i.e. 4-10 km, and for the months of June-October at greater heights.High humidity during the months of May-October at a lower height is the most likely cause of enhanced C 2 n during these months.At greater heights, enhanced wind shears, observed during June-October, appear to contribute significantly to enhanced C 2 n during this period.Narayana Rao et al. (1997) have also reported a similar monthly variation of C 2 n for Gadanki.However, in the present study an attempt is also made to relate the same to the background atmospheric parameters for a better understanding of the causative mechanism of turbulence.In addition to the significant month-to-month and season-to-season variability in height structure of C 2 n , considerable year-to-year variability is also observed.These variabilities need to be taken into account in designing new atmospheric radar for studies at tropical latitudes.
thank the staff of the National MST Radar Facility for their support in collection of data used in this paper.We thank the anonymous reviewers, whose suggestions have resulted in substantial improvement of the paper.Topical Editor J.-P.Duvel thanks R. Schumann and another referee for their help in evaluating this paper.

Fig. 1 .
Fig. 1.Histogram showing the number of days of MST radar observations for each month during the period September 1995 to August 1999.
3.1.1Monsoon season As seen from Fig. 2, Tropical Easterly Jet (TEJ) associated winds are observed in this season at the altitude range of 14-16 km.Here, range refers to the height intervals under discussion.Strong jet winds are observed during July and August.Strong vertical shears associated with strong jet winds are observed at the upper edge of TEJ in the height range of 16-18 km.An examination of the height profiles of C 2 n

Fig. 2 .
Fig. 2. Monthly mean height profiles of Wind speed for each month during the period September 1995 -August 1999.

Fig. 3 .
Fig. 3. Same as Fig. 2 but for vertical shear of horizontal wind.

Fig. 4 .
Fig. 4. Same as Fig. 2 but for turbulence refractivity structure constant logC 2 n .The scale of radar reflectivity (η) is also marked in the figure.

Fig. 6 .
Fig. 6.HeightMonth and logC 2 n contour maps for the period September 1995 -August 1999.Vertical white bands represent the data gaps.

Figure 7
Figure 7 shows the mean height profiles for each season for different years to bring out the variability of the height structure of C 2 n .The following points can be seen in this figure: (a) The secondary peak in C 2 n , as discussed earlier, is clearly seen for monsoon and post-monsoon months.The values of C 2 n at the height of about 17 km are close to the value of C 2 n at the altitude of about 10 km.(b) In winter months, the values of C 2 n are minimal compared to other months and above 12 km values of C 2 n are more or less constant.(c) In pre-monsoon months, considerable year-to-year variability is observed in the height structure of C 2n .This is consistent with large variability of the observed winds and shears

Fig. 7 .
Fig. 7. Mean height profiles of log C 2 n for each season i.e.Winter, Pre-monsoon, Monsoon and Post-monsoon for each year of observation.

Fig. 8 .
Fig. 8. Plots of monthly mean C 2 n , taken over the four years of observations, at nine different heights in the troposphere and the lower stratosphere, [A] 4-10 km and [B] 15-19 km.

Table 1 .
Values of radar parameters used in the computation of η and C 2

Table 2 .
Experimental specification file (ESF) for the measurements using Indian MST radar