Radio Science

Observations of trapped humidity layer and Kelvin-Helmholtz instability using UHF radar and GPS sonde



[1] UHF radar observations at Gadanki (13.47°N, 79.18°E) and Vaisala type GPS sonde measurements of atmospheric thermodynamic parameters (temperature, pressure, relative humidity, wind speed, and wind direction) from Tirupati (13.63°N, 79.40°E) have shown two distinct features of the lower troposphere over this region. One of the features is the observation of trapped humidity layer just above the boundary layer. These trapped humidity layers and associated gradients are observed to contribute significantly to the UHF radar backscattering, especially at the edges of the humidity layer. The second phenomenon is the observation of a long-lasting Kelvin-Helmholtz instability (KHI), at the height of ∼3 km, which lasted for about ∼210 min. The UHF radar vertical beam echo power has shown the characteristic power bursts pattern associated with KHI. The characteristic wavelength and time period of KHI waves are found to be 3.78 km and 18.4 min, respectively. Thus these results illustrate two important processes in the lower tropical troposphere, which are very important in UHF radar backscattering.

1. Introduction

[2] Development of clear air radar at Very-High Frequency (VHF) and Ultra-High Frequency (UHF) has revolutionized the studies of lower and middle atmosphere. Particularly, the potential of clear air radars to measure the winds continuously with excellent height and temporal resolutions caught the attention of many atmospheric scientists. Since the advent of these radars, there has been an increasing interest to understand backscatter mechanism of the received echoes. Several studies have investigated the various possible mechanisms for clear-air radar backscattering [Röttger and Liu, 1978; Gage and Balsley, 1980; Jain et al., 2001]. It has often been pointed out that the prime mechanism for the received backscatter echoes from such radar are small-scale fluctuations in the radio refractive index gradient produced by the turbulent mixing in the clear atmosphere. Both the temperature and humidity gradients contribute to the radio refractive index gradients. However, at lower atmospheric heights, these inhomogeneities in the radio refractive index are mainly contributed by humidity fluctuations. Now, it has been proved that humidity structures analogous to those of temperature are responsible for the clear-air radar echoes in the lower troposphere [Muschinski and Wode, 1998; Vaughan and Worthington, 2000; Furumoto and Tsuda, 2001; Luce et al., 2001]. Luce et al. [2001] and Furumoto and Tsuda [2001] studied the effects of such humidity layers on the radar backscattering echoes. Vaughan and Worthington [2000] have examined the effects of humidity and precipitation on observed VHF radar vertical beam echoes and have shown that the intensity of these echoes are higher in the humidity range 30–70% and lower in the very dry or near saturation regions. All these studies confirmed that the humidity layers play a major role in the radar backscattering mechanisms at lower tropospheric heights and hence the studies of radar backscattering associated with these humidity layers are important for interpreting the radar echo power profiles unambiguously.

[3] As mentioned above, the turbulent mixing in the clear atmosphere produces the small-scale fluctuations in the radio refractive index gradient. The Kelvin-Helmholtz instability (KHI), which plays the vital role in the generation of clear air turbulence (CAT) [Roach, 1972], is also one of the important dynamical processes contributing to the radar backscattering. KHI is a dynamical instability produced with the hydrostatically stable layer in presence of a strong stratified shear flow [e.g., Browning and Watkins, 1970]. The waves formed due to this dynamic instability at the interface of wind shear and stable layer is known as Kelvin Helmholtz waves or billows. Amplitudes of these billows gradually grow and reach to an extreme point where it start rolling or breaking. This plays an important role in the formation and dissipation of gravity waves [Fritts and Rastogi, 1985]. These gravity waves may affect the vertical transport of mass, momentum and atmospheric constituents [Singh et al., 1999]. Also, these waves are associated with the generation of small-scale turbulence, which in turn contributes to the radar backscattering.

[4] Most of our understanding of KHI is from laboratory experiments and numerical models [Browning et al., 1973]. Laboratory experiments have shown that necessary condition for the occurrence of KHI is that Richardson number (Ri) must be less than 0.25 (its critical value) [Thorpe, 1968]. However, it is not a sufficient condition for the occurrence of KHI [Miles and Howard, 1964]. This type of dynamic instability generally occurs either above or below the stratified wind shear [Muschinski, 1996].

[5] Till now, KHI in the atmosphere has been observed by various techniques, such as visualizing the clouds [e.g., Ludlam, 1967], high power pulsed radar [e.g., Browning and Watkins, 1970], FM-CW radar [e.g., Atlas et al., 1970], aircraft instruments [Browning et al., 1973] and also by using VHF radar [e.g., VanZandt et al., 1979; Klostermeyer and Ruster, 1980, 1981; Chilson et al., 1997; Singh et al., 1999]. Browning [1971] has observed 17 different cases of KHI at different height levels of the upper troposphere (5.6 km–10.7 km), by using high power radar and radiosonde measurements. In that paper, the author reported the crest-to-trough distance is in between 0.3 km to 4.0 km with a wavelength of 0.8 km to 4.0 km. VanZandt et al. [1979] and Klostermeyer and Ruster [1980, 1981] explained the VHF radar observations of KHI by means of model computations, whereas Chilson et al. [1997] observed KHI by VHF radar using frequency domain interferometery (FDI) technique. Most of these observations have been carried out at midlatitude, and there are a few observations so far reported over low latitude [Singh et al., 1999].

[6] This paper reports two interesting features of lower troposphere in tropics, using simultaneous measurements of UHF radar located at Gadanki (13.47°N, 79.18°E) and Vaisala type of GPS sonde launched from Tirupati (13.63°N, 79.40°E). These two features refer to the observations of trapped humidity layers above the boundary layer and a long lasting KHI at a height of ∼3 km. The basic purpose of this paper is to emphasize the existence of humidity layers and their contribution to the UHF radar backscattering. So far, VHF radar backscattering is treated extensively by many researchers, but clear-air aspects of UHF radar backscattering are not explored to that extent. In the present study we show that the trapping of humidity, which takes place in the lower troposphere, plays a vital role in UHF radar backscattering. Apart from this, we show a long lasting KHI and its signature in the UHF radar observations. An attempt has also been made to study the characteristics of observed KHI and the prevailing conditions of the background atmosphere. Both of these features contribute to the structure and dynamics of the lower troposphere in this region and also make significant contributions to the observed radar backscattering.

2. Experimental Method and Observations

2.1. Instrumentation

[7] A field experiment has been carried by Sri Venkateshwara University, Tirupati, India in the month of September 2000 in collaboration with Nagoya University, Nagoya, Japan. One of the objectives of the campaign was to study the radar backscattering mechanisms. During the field experiment, the GPS sonde flights were launched from Tirupati, which is about ∼30 km from the radar site. These observations provided measurements of temperature, pressure, humidity, wind speed and wind direction with a height resolution of 3–10 m.

[8] Simultaneous UHF radar observations were performed at the National MST Radar Facility, Gadanki. This UHF radar commonly known as Lower Atmospheric Wind Profiler (LAWP) is a coherent pulsed radar, installed at Gadanki. The operating frequency of LAWP is 1357 MHz and has an effective power aperture product of 1.2 × 104 Wm2. A four-quadrant phased array is used for the transmission and reception. The beam width is 4° with a gain of 39 dB. The system is programmed to steer the beam electronically in three different look angles: zenith, 15° off-zenith in east and 15° off-zenith in north directions. This radar gives a height resolution of 150 m with a maximum duty ratio of 5%. The signal wavelength is 22 cm and hence this instrument detects backscatter echo from irregularities of ∼11 cm. UHF radar Experimental specification file (ESF) used for this experiment is given in Table 1. This system operates continuously unattended. A detailed system description is given by Krishna Reddy et al. [2001].

Table 1. Experimental Specification File (ESF) for Gadanki UHF Radar
  • a

    Zenith, east 15° off-zenith and north 15° off-zenith.

locationGadanki (13.47°N, 79.18°E)
frequency1357.5 MHz
peak power1 kW
maximum duty ratio5%
antenna3.8 m × 3.8 m (phased array)
beam width
number of beams for automatic scanelectrical steering 3 directiona
pulse width1 μs
interpulse period, μs60 and 80 (successively)
number of range gates54
number of coherent integrations50 and 70 (successively)
number of incoherent integration50 and 74 (successively)
number of FFT points128
code flaguncoded
computer systemPCAT-Pentium with TMS320C30 based signal processor

2.2. Data Set

[9] During the campaign period, three GPS sondes per day have been launched at ∼0600 hr, 1200 hr and 1700 hr LT (LT = GMT + 0530). Temperature (T), relative humidity (RH), pressure (p), wind speed (Uh), and wind directions profiles with a resolution of 3–10 m are retrieved from these observations. The height intervals of these parameters (T, RH, p, Uh) are irregular. So we have down sampled these parameters to 50 m height resolutions to estimates Stability parameter (N2), square of vertical shear of horizontal wind (S2) and Richardson number (Ri).

2.3. Data Analysis

[10] The following derived parameters are computed using GPS sonde and radar measurements:

[11] 1. The static stability parameter of the atmosphere (N2) is given by

equation image

where N, g, θ, and z are the Brunt-Vaisala frequency, acceleration due to gravity, potential temperature, and height, respectively.

[12] 2. Total vertical potential refractive index gradient M [VanZandt et al., 1978] is given by

equation image

where Md and Mw represent the contributions for the dry and wet parts, respectively, and defined as

equation image
equation image

Here q, P, and T are the specific humidity, pressure, and temperature, respectively.

[13] 3. The Richardson number (Ri) represents dynamic stability, which is defined as the ratio of the static stability (N2) to the square of the vertical shear of horizontal wind (S2), is given by

equation image

[14] 4. UHF radar data have been analyzed to get three lower order moments: the zeroth, the first and the second order moments. These three order moments give the peak spectral density, mean Doppler shift, and spectral width, respectively. For the present study, offline data analysis has been carried out for better estimation of three low order moments. An adaptive method of analysis has been used [Anandan et al., 1997]. Radar volume reflectivity (η) can be expressed in terms of signal-to-noise ratio (S/N), by assuming that the observed volume is uniformly filled with scatterers [Ghosh et al., 2001]

equation image

where r is the range of backscatter and Δr is the range resolution. The description of various parameters and their magnitudes are given in Table 2. Substituting these values and taking logarithm on both sides, equation (5) reduces to.

equation image
Table 2. Gadanki UHF Radar Parameters
λradar wavelength0.22 m
Ptpeak transmitter power1.6 × 103 W
Aeeffective antenna area10 m2
αrreceiver path loss0 dB
αttransmitter path loss−0.5 dB
NBnumber of bauds for coded pulse1 μs
NCnumber of coherent integration100
Tccosmic noise temperature10 K
Trreceiver noise temperature170 K
KBBoltzman's constant1.38 × 10−23 JK−1
Δrrange of resolution150 m

3. Results and Discussion

[15] As mentioned earlier, a campaign was carried out in the month of September, which is a post summer monsoon season for Gadanki. Southwesterly winds of ∼10 ms−1 were observed in the lower troposphere during the whole campaign. The sky was partially cloudy and no precipitations were observed during the campaign. GPS sonde did not pass through the cloud on any of the day during the campaign period, which is confirmed from the humidity profiles. The wind speed and direction derived from GPS sonde and UHF radar observations are compared. The UHF radar derived winds are averaged over 30-min periods following the launch of GPS sonde. A typical comparison between radar and radiosonde winds is shown in Figure 1. From this plot, it is evident that the winds measured by the UHF radar are quite consistent with the winds measured by GPS sonde. However, the wind speed and direction at some heights are not matching exactly due to the following reasons: (1) radar range resolution is 150 m, whereas the GPS sonde height resolution is 3–10 m; (2) the spatial separation between the two observational sites is ∼30 km.

Figure 1.

Height profiles of (a) horizontal wind speed and (b) wind direction derived from UHF radar and GPS sonde on September 4, 2000.

3.1. Trapped Humidity Layer

[16] Figures 2a–2d show the height profiles of (i) absolute temperature (T) (solid line) and virtual temperature (θv) (dotted line), (ii) relative humidity (RH), (iii) square of vertical potential refractive index gradient for wet (log Mw2) (dotted line with solid square box) and total (log M2) (dotted line with hollow square box) and volume radar reflectivity (log η), respectively, for September 4, 5, 6, and 7, 2000. All these figures show clearly layers of the enhanced humidity just above the boundary layer top and temperature inversion layer. The thicknesses of these layers of enhanced humidity are ∼1 km, and maximum observed humidity is 80–85%. The height variation of humidity is relatively less, and therefore these appear as a thin layer structure.

Figure 2.

(a)–(d) Height profiles of (i) absolute temperature (T) (solid line) and virtual temperature (θv) (dotted line), (ii) relative humidity (RH), and (iii) square of vertical potential refractive index gradient for wet (log Mw2) (dotted line with solid square box) and total (log M2) (dotted line with hollow square box) and volume radar reflectivity (log η), respectively, for September 4, 5, 6, and 7, 2000.

[17] It is apparent from Figures 2a–2d that these layers of enhanced humidity appears due to the trapping of humidity between the two temperature inversion layers which are represented by the two horizontal dotted lines in these figures. The lower line represents the top of the boundary layer, which is determined from the height profile of virtual potential temperature (θv) determined from GPS sonde measurements [Stull, 1988]. The upper line represents the temperature inversion associated with trade wind inversion, which are observed on all the days between 3.0–4.0 km. It is well established that the convective boundary layer is always capped by an inversion layer, which forms an interface between the planetary boundary layer and the free atmosphere. This interface will not allow the air from free atmosphere to mix in the boundary layer and at the same time the temperature inversion observed in the free atmosphere will act as a barrier for vertical movement of the air. Thus the air is trapped in between these two layers, and the humidity will also be trapped because of lack of vertical mixing and hence appears as humidity layers. This is one of the feasible mechanisms for the formation of the trapped humidity layer.

[18] In the present study, an attempt has been made to study the contribution of these trapped humidity layers to the observed UHF radar vertical beam reflectivity. The height profile of Mw2 and M2 derived from the GPS sonde measurements are compared with radar reflectivity averaged over a 30-min period following the launching of GPS sonde. An interesting feature to be noted from these figures is the enhancement in the UHF radar reflectivity profiles at the proximity of the edges of the humidity layer structure (Figures 2a–2d). It may also be noted that the observed reflectivity is minimum near the center of the trapped humidity layer. The height profiles of radar reflectivity on September 5, 2000 will be discussed in more detail later. Muschinski and Wode [1998] observed humidity sheets in the lower troposphere and studied the radar backscattering. Browning et al. [1998] reported the enhanced echo power layer structure, which resulted from sharp humidity gradients during the passage of a tropical cyclone. Recently, Vaughan and Worthington [2000] have reported that the VHF radar echo power is more in the moderate humidity region (30–70%) than in saturate and dry regions. Furumoto and Tsuda [2001] showed that the humidity gradient is responsible for the radar received echo power at lower atmosphere.

[19] The capping inversion over the convective boundary layer is an everyday phenomenon, and the temperature inversion associated with trade winds varies with seasons. Thus the present observations show that one has to take into account the contribution of trapped humidity layer, such as those observed in the present study, while interpreting the observed radar reflectivity.

3.2. Kelvin-Helmholtz Instability

[20] Figures 3a–3d show the height profiles of (i) wind speed, (ii) wind direction, (iii) vertical velocity, (iv) stability parameter (N2), (v) square of vertical shear of horizontal wind (S2), and (vi) Richardson number (Ri) on September 4, 5, 6, and 7, 2000, respectively. On almost all these observational days, enhancement in the N2 was observed at ∼3 km, which indicates the presence of stable layers. However, the enhancement of S2 can be noticed in the proximity of the observed stable layers only on September 4 and 5, 2000. Further, estimations of Richardson number (Ri) shows the favorable condition for the occurrences of KHI on September 4 and 5, as Ri was found to be below or nearly equal to its critical value (0.25). Even though the Ri was nearly equal to critical value on September 4, the signature of KHI was not noticed in the UHF radar observations. Now, we will focus more on these two days, which is favorable for the occurrence of KHI.

Figure 3.

(a)–(d) Height profiles of (i) wind speed, (ii) wind direction, (iii) vertical velocity, (iv) stability parameter (N2), (v) square of vertical shear of horizontal wind (S2), and (vi) Richardson number (Ri) on September 4, 5, 6, and 7, 2000, respectively.

[21] Panels iv and v of Figures 3a and 3b show the height profiles of N2 and S2 for September 4 and 5, 2000. These figures illustrate the enhancement of N2 and S2 at the same height region and the Ri were found to be 0.26 and 0.18 for September 4 and 5, respectively. On both the days, there is a possibility for the occurrences of KHI, as Richardson number is near to the critical value. However, KHI was observed only on September 5 even though prevailing background atmospheric conditions on September 4 are favorable for the occurrences of KHI. The reasons for this can be inferred by looking at panels iv and v of Figures 3a and 3b. The thickness of the shear layers on September 4 and 5 is 300 and 500 m, respectively, where as the temperature inversion layer thickness is 500 m on both the days. It is well known that the thickness of shear layer plays a vital role in generating the KHI [Chilson et al., 1997]. This may be a possible reason for not observing the KHI on September 4, 2000.

[22] Figures 4a–4c show the contour maps of observed UHF radar echo power on three consecutive days, i.e., on September 4, 5, and 6, 2000, respectively. These power contours are in arbitrary units, maximum at center (4 × 10−4 units) and gradually decreases in 10−4 units increments. The successive power bursts pattern is observed only on September 5, 2000, which is associated with the occurrence of KHI. One of the important properties of KHI is the generation of the enhanced turbulence, which is observed by radar as successive power bursts pattern [Roach, 1972; Klostermeyer and Ruster, 1981]. Strong power bursts in the radar observations of KHI occurs mainly due to one of the two mechanisms, i.e., either due to static instabilities produced by KHI induced super adiabatic lapse rate or due to the secondary dynamic or convective instabilities generated by the primary KHI [James and Browning, 1981; Ruster and Klostermeyer, 1983]. However, a strong power bursts pattern is observed for a duration of ∼210 min in the present case (see Figure 4b). The Richardson number (Ri) is 0.18, and the vertical velocity at the critical height is almost zero. This indicates the absence of convective instabilities on this day, namely, September 5, 2000. Such power burst patterns are not observed on September 4 and 6, 2000.

Figure 4.

(a)–(c) Contour of received echo power for September 4, 5, and 6, 2000, respectively. These power contours are in arbitrary units, maximum at center (4 × 10−4 units), and gradually decrease outward with interval 1 × 10−4 units.

[23] Another important debate is whether the observed power bursts are produced by scattering from small-scale irregularities associated to turbulence or by partial reflection from large-scale stratification of the refractive index. It is well known that UHF radars are not sensitive to partial reflections [Muschinski and Wode, 1998]. Therefore one of the possibilities is that the observed power burst patterns must be arising due to the back scattering from the turbulence generated by KHI. Moreover, the spectral width observations confirm that the observed power burst pattern is related with the KHI associated turbulence. Figures 5a and 5b show the time variation of vertical velocity and spectral width on September 5, at various height levels. The wave oscillations can be observed in the height regions of ∼2.25 km to 4 km in the vertical wind velocities during 1600 to 1900 hours. Figure 5a illustrates the enhancement in the vertical velocity with the reverse patterns before and after the occurrences of KHI, that is updrafts and downdrafts. Enhancement in the spectral width can be observed at the time of occurrence of KHI, which indicates the KHI associated turbulent activities (Figure 5b). Thus these observations reveal the power bursts in the vertical received power, reversal of vertical winds, and enhancement of spectral width associated with dynamic instabilities produced by KHI.

Figure 5.

(a) Time series of vertical velocity and (b) spectral width for vertical beam at 14 different heights on September 5, 2000.

[24] In order to investigate the prominent periods in the vertical wind fluctuations, spectral analysis have been performed on the vertical wind time series during 1450 to 1950 hours using Fast Fourier Transform (FFT). Figure 6 shows the power spectra at four different height levels (2.55, 2.70, 2.85, and 3.00 km) of vertical wind velocity fluctuations from which the dominate period is found to be ∼18.4 min. The power burst pattern (Figure 4b) is also has the same periodicity of ∼18.4 min, consistent with the spectral analysis of vertical wind fluctuations.

Figure 6.

Power spectra at four different height levels (2.55, 2.70, 2.85, and 3.00 km) observed on September 5, 2000. Vertical arrow indicates the dominant wave period.

[25] The horizontal wavelength of the KHI is also computed by the method given by Miles and Howard [1964] as

equation image

where Δz is the depth of the shear layer. Δz is 500 m, which gives a horizontal wavelength (λx) of 3.78 km. This is in agreement with the results obtained by Browning [1971]. The phase speed of the observed wave is estimated as ∼3.4 ms−1. The phase speed is much smaller than the background wind (∼10 ms−1) on this day. The relationship between the phase speed of the observed waves and the background wind is yet to be understood thoroughly for the KHI generated waves.

4. Summary and Conclusions

[26] Using simultaneous UHF radar and GPS sonde observations, two important atmospheric phenomena in the lower tropical troposphere are studied. These two phenomena are the trapped humidity layers and the KHI. An effort has been made to study their signature on the UHF radar backscattering. The trapped humidity layers are formed between the boundary layer and an additional temperature inversion associated with trade wind inversion, which occurs at the altitude of 3–4 km. The UHF radar reflectivity profile has shown an enhancement at the proximity of the edges of the humidity layers, which is a well-known phenomena. The reflectivity is found to be moderate inside the trapped humidity layer even though the humidity reaches 80–85%. These humidity layers and their associated gradient are observed to make a significant contribution to the radar backscattering and further confirm the importance of humidity layers in interpreting the radar returns.

[27] UHF radar observations of KHI for the duration of ∼210 min are discussed. The KHI observations for such a long duration are very rare. However, Browning [1971] observed such a long duration KHI by using high power radar for ∼240 min. The following atmospheric conditions have been observed during the occurrence of KHI: (a) existence of hydrostatically stable layer in proximity to the layer of strong stratified wind shear, (b) Ri < 0.25 at the height of occurrence of KHI, (c) enhanced fluctuation in the vertical velocity with the reversal before and after the occurrence of KHI, (d) enhancement of spectral width, and (e) successive power bursts pattern in the radar received vertical beam echoes.

[28] The above conditions have been observed on September 5, 2000, which are most favorable for the formation of KHI. On this day, UHF radar observations have shown the successive power bursts pattern with a period of ∼18.4 min. The spectral analysis of vertical wind has also shown the periodicity of 18.4 min and a horizontal wavelength of ∼3.74 km corresponding to a phase speed of 3.4 ms−1. The present study also emphasized the importance of thickness of shear layer in the formation of KHI billows.


[29] The National MST Radar Facility (NMRF) is operated by Department of Space (DOS), partially supported by Council of Scientific and Industrial Research (CSIR), Defense Research and Development Organization (DRDO), Department of Electronics (DOEs), Department of Environment (DOEn), and Department of Science and Technology (DST), Government of India. The UHF radar has been set up at NMRF in collaboration with Communication Research Laboratory (CRL), Ministry of Post and Telecommunication (MOPT), Japan. We would like to express thanks to Hydrospheric-Atmospheric Research Center, Nagoya University, Nagoya, Japan, and S. V. University, Tirupati, India, for their cooperation in launching GPS sondes from Tirupati, India, during September 2000. We would like to sincerely thank the anonymous referees for their critical examinations of the manuscript and their valuable comments and suggestions for revising the manuscript. One of the authors, S.S.D., is thankful to Indian Space Research Organisation (ISRO) for providing the fellowship and facility during the study.