Corresponding author: M. Venkat Ratnam, National Atmospheric Research Laboratory (NARL), Gadanki, Tirupati, India. (email@example.com)
 A comprehensive study on the ducting conditions prevailing over the Indian tropical station of Gadanki (13.5°N, 79.2°E) is made using more than 5 years (April 2006 to September 2011) of high-resolution GPS radiosonde observations. In the present study, the characteristics of ducts occurring over Gadanki were examined statistically using the modified refractivity. Strong diurnal and seasonal variation in the percentage occurrence of the ducts was found with the highest and lowest occurrences during winter and monsoon seasons, respectively. Duct strength is very strong during midnight to the morning hours than in the evening hours particularly during winter. The mean thickness of the duct and the duct strength were found to be the highest and the strongest in postmonsoon and winter seasons, whereas they are the lowest and the weakest in the monsoon season. Elevated ducts were found to be stronger than the surface and the surface-based ducts. The characteristics of ducts during stable and unstable conditions were also investigated, and it was found that the duct altitude is higher during the stable conditions and is higher during premonsoon followed by postmonsoon, winter and minimum in the monsoon. The maximum wavelength being trapped was investigated, and it was found that wave trapping occurs for the radars with frequencies of 60 GHz and above.
 The present study is concerned with the class of anomalous propagation (AP) known as ducting in which radio waves become trapped within a shallow and near-horizontal layer. Under such conditions, the propagation is greatly enhanced. In radio wave and radar applications, knowing where the signal is traveling is quite important. Ducting occurs when a radio ray originating at the earth's surface is sufficiently refracted so that it is either bent back toward the earth's surface or travels in a path parallel to the earth's surface. The concentration of energy within the duct, however, results in a corresponding reduction of the signal just above or below the ducting layer and the formation of a “radar hole,” where detection ranges are much reduced [Battan, 1973; Turton et al., 1988].
 The existence of AP conditions substantially affects the weather radar performance, i.e., communication devices such as ground-to-ground or ground-to-satellite links. Atmospheric refraction is one of the causes for AP, which is associated with the variation in the refractivity of the atmosphere that is closely associated with strong vertical gradients of temperature and/or water vapor pressure leading to existence of duct. The refractivity of the atmosphere at microwave frequencies is given by [Glickman, 2000]
where p is atmospheric pressure (mb), T is absolute temperature (K), and e is water vapor pressure (mb). Note that the contribution of electron density gradients term in the above equation is not included as we are dealing with the troposphere. The various classes of AP and corresponding effects on electromagnetic signals are summarized by Battan  and Turton et al. , such as subrefraction, standard refraction, superrefraction, and ducting (trapping). Since the vertical variations of temperature, water vapor pressure, and pressure dominate over horizontal scales, the propagation of electrometric signal depends on the vertical gradient of refractivity. The effect of the earth's curvature (radius R, 6378 km) at an altitude z can be accounted for by considering a modified refractivity M [Bean and Dutton, 1968; Turton et al., 1988].
where N is the refractivity, z is the altitude above mean sea level (m), and M is the dimensionless modified refractivity. The trapping or ducting occurs when the modified refractivity gradient becomes negative (dM / dz < 0).
 The electromagnetic signal in this case is forced to move within the ducting boundaries. However, the ducting layers do not have rigid boundaries, and they let some electromagnetic energy leak [Patterson et al., 1994]. This effect is related to the strength of the duct. The larger the amount of electromagnetic energy that is trapped, the stronger the duct. Ducting is often associated with the existence of boundary layer inversions in temperature and moisture. To propagate energy within a duct, the angle made by the electromagnetic energy with the duct must be small, usually less than 1°.
 A duct occurs when the index of refraction rapidly decreases with altitude, but as the refractivity is a product of temperature and water vapor, temperature must increase and/or humidity (water vapor content) must decrease with altitude. Temperature inversions will produce superrefractions, whereas water vapor gradients are alone effective than temperature gradients [Fabry et al., 1997]. When warm air moves from land to cooler bodies of water, it causes temperature inversion, which results in the formation of ducts. At the same time, moisture is added by evaporation from the water surface producing a moisture gradient. Evaporation or surface ducts are common just above the earth surface, where air may become saturated by evaporation from sea surface. Over land, ducting is often caused by radiative cooling during clear nights, particularly when the ground is moist. Thus, over land, ducting is most noticeable at night and tends to disappear during the warmest part of the day [Moszkowicz et al., 1994]. Superrefraction or surface-based ducts occur when cool air spreads out from the base of a thunderstorm, resulting to temperature inversion within several hundred meters. The moisture gradient along the outflow of the boundary is also appropriate for the formation of ducts. Although several studies [Brooks et al., 1999; Haack and Burk, 2001; von Engeln and Teixeira, 2004; Atkinson and Zhu, 2005; Mentes and Kaymaz, 2007; Ao, 2007] on ducting exist across the globe using several techniques, over the Indian region, no study still exists due to the lack of high-resolution upper air observations. Thus, the present study is a first of its kind using high-resolution measurements over the Indian region.
 In this present study, the ducting characteristics over a tropical station, Gadanki (13.5°N, 79.2°E), were studied extensively using long-term high-resolution radiosonde data. First, diurnal variations observed in duct characteristics during different seasons were studied. Second, the duct characteristics, i.e., duct altitude, duct strength, and duct thickness, were analyzed statistically. Third, ducting characteristics during stable and unstable conditions were investigated. Finally, the frequencies trapping over this region are presented. Since several radars exist and a few more are going to be added to this site (www.narl.gov.in), this study will be useful in knowing what frequencies will be trapped over this region.
2.1 GPS Radiosonde Data
 High-resolution ground-based radiosonde (Väisälä RS-80, RS-92, and Meisei RS-01GII) balloons have been launched regularly over Gadanki since 19 April 2006, the location of which is depicted in Figure 1a. In the present study, we made use of data from 19 April 2006 to September 2011. Majority of these radiosondes were launched around 1730 local time, LT (LT = UT + 0530 h). In total, 1126 profiles of temperature (T), pressure (P), relative humidity (RH), and horizontal wind are obtained in different seasons. A large data gap exists during the months of December 2006 (only six balloons were launched) and April 2007 (nil). All these atmospheric parameters were collected with an altitude resolution of 25–30 m (sampled at 5 s intervals) using the RS-80 type (April 2006 to March 2007) and 10 m (sampled at 2 s intervals) using RS-92 (from 17 July 2006 to 31 August 2006) and Meisei (May 2007 to September 2011). The entire data set has been gridded to 100 m vertical interval to remove outliers arising from random motions of the balloon. Quality checks were also applied to eliminate further outliers arising due to various reasons for better results. On average, 25 radiosondes have been launched every month, which is shown in the Figure 1b. Besides these, radiosondes were also launched every 3 h for 72 h in each month since October 2010, which were used to study the diurnal variation of various ducts.
3 Background Conditions
3.1 Topographical Conditions
 The Gadanki location is a rural area with a small population and with an irregular mix of agriculture, which is situated 120 km northwest of Chennai. Figure 1a shows a topography map of the Indian subcontinent showing Gadanki's location. This station is located around 375 m above mean sea level and is surrounded by small hills of about 500–550 m and within 30 km radial distance from hills that are about 1000 m high, situated on both the northern and southern sides of the observation site.
3.2 Weather Conditions
 On the basis of the meteorological conditions over Gadanki, seasons are divided into winter (December, January, and February), summer/premonsoon (March, April, and May), monsoon/ progressing southwest monsoon (June, July, August, and September), and postmonsoon/retreating southwest (SW) monsoon (October and November). Gadanki experiences two monsoons, i.e., southwest (SW) and northeast (NE). The onset of the SW monsoon over Gadanki is around the second/third week of June, and its withdrawal is during the end of October. During October, over the southern part of India, the NE monsoon occurs, which starts around the first week of October and ends in mid-December.
3.3 Background Meteorological Conditions
 Gadanki experiences a strong diurnal variation in meteorological parameters. In the afternoon, around 1300–1500 LT, convection dominates. There will be significant variations in the relative humidity from winter to the monsoon season. Humidity will be very low (about 50%) during winter, and it occurs only in the first few kilometers and becomes almost negligible above it. However, during other seasons, particularly in the monsoon season, high humidity concentrations (60%–70%) may be observed up to the middle troposphere. The rainfall pattern is highly localized. A clear annual oscillation with some interannual variations are observed in all the meteorological parameters. See Basha and Ratnam  for more details.
4 Methodology for Identification of Ducts
 It is well known that ducts occur whenever there is a sharp decrease in humidity with altitude often associated with a corresponding temperature inversion. Therefore, the gradients in temperature (T) and mixing ratio (r) are considered for identifying the ducts. Figures 2a and 2b show the typical examples of T and r observed on 19 December 2008 along with their gradients, respectively. Similar changes can be noticed in N (Figure 2c), which is a function of T and r. While considering the earth's curvature, the parameter M, which is also used to identify the ducts, is shown in Figure 2d. From the minimum gradients, one can easily identify the precise ducting altitude (in this case, it is 1.7 km) from M.
 As mentioned earlier, there exist several types of ducts [Patterson et al., 1994; Hitney et al., 1985]. If the refractivity gradient decreases ≤157 N units or when the gradient in M becomes negative, ducting occurs, i.e., the electromagnetic signal gets trapped in the duct altitude. In general, three types of ducts occur in the atmosphere, which are illustrated in Figure 3 using observational data. Surface duct and surface-based duct occur just a few meters above the Earth's surface. The surface duct (Figures 3a and 3b) observed on 2 February 2011 at 0200 h LT occurs around 0.5 km, which is just 125 m above Gadanki's location. The surface-based duct observed on 19 January 2011 at 2300 h LT occurs around 0.9 km. The thickness of ducts in surface and surface-based ducts refers to the difference between the surface altitude and the duct altitude. In general, the surface and surface-based duct occur only in the morning over Gadanki. In this present study, since we have used radiosonde data extensively, which is launched at 1730 h LT (except for a few days in each month when radiosondes were launched every 3 h), there is a maximum possibility of noticing the elevated ducts, which was typically exemplified by the observations made on 12 December 2009 at 1730 h LT from N and M profiles, as shown in Figures 3e and 3f, respectively. In this example, the duct altitude is around 1.6 km, and the duct thickness is obtained by taking the difference between the base and the top of the trapping layer.
4.1 Diurnal Variation of Ducting
 Before showing the monthly and seasonal variation of the duct characteristics, the diurnal variation is first studied. Figure 4 depicts the diurnal variation observed in the duct characteristics during different seasons. As mentioned earlier, from October 2010 to October 2011, we launched radiosondes every 3 h for 3 days every month except in November 2010. Figures 4a–4d show the diurnal variation of ducting altitude observed during different seasons; vertical bars show the standard deviations obtained while averaging over a season. Large diurnal variation can be observed in all the seasons. During early morning hours, surface-based ducts followed by elevated ducts during afternoon/evening hours can be noticed. The duct altitude increases from early morning hour to forenoon, i.e., up to 1600 h LT, and then starts to decrease thereafter in all the seasons. Higher duct altitude is observed during premonsoon, followed by monsoon and postmonsoon, and becomes lower in winter. No significant diurnal variation is observed in duct strength (Figures 4e–4h) except in winter. Duct strength is very strong during midnight to the morning hours than during the evening hours particularly during winter. In the case of ducting thickness (Figures 4i–4l), no significant diurnal variation is observed in all the seasons.
4.2 Characteristics of Elevated Ducts
 For each radiosonde ascent, we calculated the duct altitude, corresponding strength, and its thickness from profiles of M. Table 1 shows the monthwise distribution of radiosonde accents and corresponding occurrence of ducts at 1730 h LT from April 2006 to September 2011. Out of 1304 radiosonde ascents, ducting was observed in 778 cases. Figure 5a shows the percentage occurrence of ducting during each month, integrated between April 2006 and September 2011. The percentage occurrence was high in January, gradually decreased and reached its minimum in August, and then started increasing again thereafter. The occurrence of ducts was at its maximum during the winter months (80%), followed by premonsoon (55%) and postmonsoon (44%), and then reached its minimum in monsoon (20%). Note the higher standard deviations in duct occurrence during the premonsoon and postmonsoon seasons. The annual average of percentage occurrence of ducts is about 50%. Figure 5b shows the occurrence of duct altitude during different months. The duct altitude was found to be at its maximum during monsoon (2.8 km), closely followed by premonsoon (2.5 km) and postmonsoon (2.5 km), and at its minimum in winter (2 km). The duct strength shown in Figure 5c follows the duct altitude, and it is strong during winter. The duct thickness shown in Figure 5d is an important parameter in estimating the maximum wavelength being trapped. Maximum thickness was noticed during the winter months, and minimum thickness was observed in the monsoon months. It peaked in December and reached its minimum around June. The reason why the occurrence of ducts was higher during winter might be the formation of fog/dew in the early morning periods since four sides of Gadanki are covered with hilly rocks. Strong inversion occurs when crops become senescent and surface moisture sources reduce significantly. These conditions are favorable for the formation of subsidence inversion during the winter months, usually in the range of 1.5–2.5 km deep. These subsidence inversions may persist during winter months under the dome of high pressure. Strong inversion days are influenced by high-pressure systems as well as a consistent difference in wind direction; on all inversion days, wind comes from the north or northeast.
Table 1. Distribution of Elevated Ducts Observed During Each Month from Year 2006 to 2011 Along with Number of Radiosonde Accents
 More detailed characteristics of ducts are shown in Figure 6. Figure 6 shows the distribution of the duct altitude, strength, and thickness observed during different seasons. The histogram shows the percentage occurrence at different altitude ranges. The occurrence of ducts at higher altitudes is higher during the premonsoon (Figure 6a) and postmonsoon (Figure 6c) seasons, followed by the monsoon (Figure 6b) season, and is at minimum altitudes in winter (Figure 6d). The occurrence of duct altitude is maximum within 2–3 km, except during winter, when it is within 1–2 km. The occurrence of ducts during winter is about 25 times more than during other seasons. Similarly, duct strength is presented in Figures 6e–6h starting from 0 to –500, with an increment of –25. In all the seasons, the duct strength rapidly decreases exponentially from 0 to 100 M units, and the occurrence of strength is high between 0–100 M units only. The occurrence of duct strength is high during winter, followed by the premonsoon and postmonsoon seasons and minimum during the monsoon season. The duct thickness presented in Figures 6i–6l for different seasons is about 100–200 m on average in all the seasons expect in the monsoon season. Especially during winter, the duct thickness can reach as high as 400 m, and minimum duct thickness can be noticed during the monsoon season.
4.3 Ducting Characteristics during Stable and Unstable Conditions
 Over Gadanki, in the afternoon, i.e., between 1400 h LT and 1500 h LT, convection dominates. During the monsoon season, convection dominates throughout the season. In addition, over Gadanki, NE monsoon dominates during the postmonsoon seasons, as mentioned in section 3.3. Thus, convection will be there for about 70% of the year over Gadanki. Therefore, in this section, we discuss the ducting characteristics observed during stable and unstable conditions. The stability of the atmosphere is defined by the variations in the virtual potential temperature gradients vertically [Arya, 1988; Stull, 1989]. We have calculated the stability conditions as defined by Mentes and Kaymaz . The static stability parameter “s” is defined as a function of virtual potential temperature gradient and is given as [Arya, 1988]
 Here, g is gravitational acceleration (ms–2), TV is the mean virtual temperature within the ducting layer (K), is the virtual potential temperature gradient within the ducting layer (K m–1), and d is the altitude difference. In qualitative terms, atmospheric stability can be divided into three types: s>0 if the atmosphere is stable, s<0 if the atmosphere is unstable, and s=0 if the atmosphere is neutral.
 Figure 7 shows the ducting altitude, strength, and thickness observed during stable and unstable conditions over Gadanki. Out of 1304 radiosonde observations, we found 635 (56) falling under stable (unstable) conditions. The number of stable (unstable) cases observed during premonsoon, monsoon, postmonsoon, and winter are 154 (33), 75 (6), 145 (5), and 263 (12), respectively. It can be noticed that a higher number of cases fall under stable conditions than unstable conditions. This is mainly due to the data availability during late afternoon hours (1730 h LT). The percentage occurrence of duct altitude is higher during stable conditions and during premonsoon, followed by post-monsoon and winter, and at its minimum during monsoon. A similar behavior in the seasonal variations can be seen in unstable conditions. The duct strength decreases rapidly from 0 to –500 M units. The duct strength is high in winter, followed by premonsoon and postmonsoon, and at its minimum during monsoon under stable conditions. During winter, the duct thickness is high compared to all the seasons, followed by premonsoon and post-monsoon, and low in monsoon in the case of stable conditions. In unstable conditions, the duct thickness is greater in premonsoon. These statistics are more or less similar to those presented in Figure 6, suggesting that most of the time during 1730 h LT, stable conditions prevail over Gadanki.
4.4 Maximum Wavelength Trapped
 The altitude and strength of the duct are controlling factors for radar propagation and must be determined accurately to assess propagation ranges [Brooks et al., 1999]. The strength of a radar duct is expressed in terms of the maximum wavelength (or minimum frequency) trapped by the duct. For a simple surface-based or elevated duct, this is given by the following expression:
where λmax is the maximum trapped wavelength (m), D is the duct depth (m), ΔM is the difference between the minimum in M at the top of the duct and the maximum value within the duct, and C = 3.77 × 10–3 for a surface-based duct and C = 5.66 × 10–3for an elevated duct [Turton et al., 1988]. By using the above equation, we have estimated the maximum wavelength being trapped in the duct, and the monthly variation of trapping wavelengths is shown in Figure 8. Over Gadanki, the frequencies that are trapped range from 60 to 120 GHz. The wavelength trapped is at its maximum during the monsoon season and minimum during winter.
 For the first time, the ducting characteristics are reported using high-resolution radiosonde observations over Gadanki region. The main findings of the present study are as follows:
Strong diurnal variation in ducting characteristics is noticed in all the seasons. The duct altitude is higher during premonsoon, followed by monsoon and postmonsoon, and minimum in winter. The duct strength is higher during early hours but very strong during winter seasons.
The percentage occurrence of ducts is higher during winter, followed by premonsoon and postmonsoon, and minimum in monsoon seasons, whereas the duct altitude and strength (thickness) are higher during monsoon (winter) followed by premonsoon and postmonsoon, and minimum in winter (monsoon) seasons. During the winter season, the percentage occurrence of duct altitude is double that during other seasons, but the duct strength is the same during winter and premonsoon. The occurrence of duct thickness is higher and also at higher levels during winter and summer.
The percentage occurrence of elevated ducts in stable and unstable conditions is about 48% and 4%, respectively. Duct altitude is greater during stable conditions and is higher during premonsoon, followed by postmonsoon and winter, and minimum in monsoon.
The frequencies being trapped over Gadanki range from 60 to 120 GHz.
 This study will also serve as a comparative study of atmospheric refractivity for the Indian region. In future studies, these characteristics are expected to be incorporated in the models of the refractivity fields and microwave propagation over this region.
 We thank the National Atmospheric Research Laboratory (NARL) for providing the necessary facilities to carry out this work. We wish to thank two anonymous reviewers for providing fruitful comments/suggestions, which helped us improve the manuscript content.