Kumar, Anil C P

Thangaraj, N

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Indian J. Phys. 80(1). 37-41 (2006)4 V - ^ ^A  study of refractive index structure constant from radar dataC P Anil Kumar** and N Thangaraj^'Elquatorial Geophysical Research Lahcnalory. Indian Instiiute of Gcomagneiism, Knshnapuram (BO),Maharajanagar (PO). Tirunclvch^27 011, Tamil Nadu, India ^Department of Physics, V H N S N Coll<3|ge. Virudhunagar, Tamil Nadu, IndiaE-mail : cpaniIC«^i^s.iigm.res.in Received 25 April 2005, accepted 24 October 2005Abstract : The work focuses on the measurement of refractive index stnictuie constant from the backscatlcred signal strength. For this purpose, I have made use of the equatorial data mcasuicd by medium Ircqucncy (1.98 MHz.) Partial Reflection Radar, located at Tirunelveli (8.7®N. 77.8®E. 0.3'^N magnetic dip.). This radar has been operated continuously by the Indian Institute of Geomagnetism; the data obtained with this radar have been providing valuable information on middle atmosphere dynamics. This is a preliminary study conducted in the equatorial region and the Partial Reflection Radar is not an efUoenl tool for turbulent studies, hence the estimation of refractive index structure constant of turbulence i.e, C^  ^ is very difficult. ITie refractive index structure constants for turbulence is calculated numerically and plotted with the vertical wind velocity. values show an enhancement during post sunset htmrs. It may be due to the fact that the plasma within the geomagnetic flux tube becomes unstable because of pre-reversal enhancement (E’ x B clectrodynamic drift) and takes part in the up-welling process thus making turbulence within the volume.Keywords Retractive index .structure constant, turbulence, radar data.PACSNo-s. : 94.10.Lf. 84.40.Xb1. IntroductionRadar is a means o f collecting information about distant object.s by sending electromagnetic waves on them. When transmitted energy falls on a distant object like clouds, winds, eti\, it reflects back some portion o f this energy (echo). The reflected energy is scattered in all directions with intensities, a function o f object's geometry and object’s materials.At the Equatorial Geophysical Research Laboratory (EGRL), Krishnapuram, a high-power medium frequency (MF) partial reflection radar was installed in 1992 under an Indo-Australian collaborative project, the main purpose being to obtain continuous measurements o f neutral winds in the altitude region 60-lCX) km.2. Mathematical analysisan antenna with radiating power P, and with the gain Of illuminates a target o f cross-sectional area at aThe paf>er was presented at the 11th International Symposium on Equatorial Acronomy (ISEA) Taiwan, May 9-14, 2005.Corresponding Authordistance ‘ r' away from the antenna, we can write the incident power P, on the target asP, = P,Cf,s/4/rr. (1)For a monostatic radar system, the back scattered power received by the antenna isPfGf a A ,L (2 )A J l r  4 P r-where is the effective area o f the antenna, L  is the efficiency o f the antenna and X is the wavelength, andG, =  (3 )Then eq. (2) reduces to_  PfA^aL(4 )this is the standard radar equation for a single scattering target situated in the antenna beam. For a randomly distributed scatterer,©  2006 lACS38 C P  Anil Kumar and N  ThangarajPAnX -r^'cp 47TA (5)p , a ; lThe radio refractive index o f the atmosphere v r  is defined asn = (6)where is the relative pemieability o f air for the atmosphere, and 4r is the dielectric constant o f the mediumm .Again, a general formula for refractive index o f radio waves propagating through middle atmosphere can be expressed as [2]in - 1 ) :3.73xJ0"'<> 7.76xl0*/» - N ,2N„(7)where e is the partial water vapour pressure in mbars, P  is the total atmospheric pressure in mbars, T  is the absolute temperature in Kelvin, N^ . is the number o f density o f electrons and N^ . is the critical plasma density.The first term in eq. (7) is the contribution due to water vapour, and is only relevant within the troposphere. The second term is due to dry air and is dominant above the tropopause. The third term is due to free electrons, and is dominant at ionospheric heights. From eq. (5), we have the backscatter cross section 13~5] :o - = (4 X ?,.l4 )r*P^yP,A f.L . (8)The relationship between the strength o f atmospheric radar backscatter and the intensity o f refractive index structure constant for turbulence has been reformulated asC “ = of0,00655 X (9)where is the potential refractive index structure constant and A is the radar wavelength.More precisely, these are the clear air echoes produced by fluctuations o f the atmospheric index o f refraction. Partial Reflection Radar means transmitting signal from the earth is partially reflected in the E-region o f  ionosphere and remaining signal transverses into the higher region o f the ionosphere. 7'hen the receiver collects the reflected signal from the ionosphere. The received power is very small as compared to transmitted power. The radar receiver is o f super-heterodyne type. Input o f  the receiver is a low-noise device which has the capability o f receiving weak signals. Details are given in Section(3). The radar operating at VHF-UHF bands is mainly sensitive to inhomogeneities in the radio refractive indexassociated with small-scale atmospheric turbulence, the backscattered signal can be effectively used for the quantification o f turbulence f5,6J.3. System detailsThe transmitting array is arranged in a square, and consists o f four center-fed half wave dipoles, 75 m in length. The antennas are constructed from 3 mm pre­stretched copper wire. One set o f dipole is arranged parallel to the Earth’s magnetic field and the other is arranged orthogonal to it. This is because Tirunelveli is close to the magnetic equator and the ordinary and the extra ordinary rays arc linearly polarized parallel to, and at right angles to the magnetic field, respectively. One set o f dipoles is used for O-mode during the day lime and the other is used for transmitting E-mode during the night time. The O-modc dipoles are oriented in the north-south direction. The <^-mode dipoles are oriented in the east-west direction. The ideal height o f the transmitting antenna is one quarter o f the transmitting wavelength (30 m) above the ground plane.The receiving antennas are o f the inverted V-iype, and are situated at the vertices o f an equatorial triangle in which the basic spacing is 180 m. The centers o f both the transmitting and receiving arrays coincide, making this truly monostatic system, 'fhe impedance o f each receiving antenna was 50 ohm to match the co-axial cable taking the signal back to the receiving system.The transmitter operates at a frequency o f 1.98 MHz, although this is adjustable by -0.2 MHz, and is fully phase coherent. The transmitter power is 25 kW peak to peak, with a variable pul.se length o f 10-50 micro seconds, usually operated at 30 micro seconds which corresponds to a 4 km height resolution. The pulse repetition frequency is 50 Hz with 32 point integration. Super-heterodyne receivers are used in the system. In each receiver, signal o f 1.98 M Hz is mixed with a 2.475 M Hz local o.scillator signal to produce a 477 KHz Intermediate Frequency which is then fed to the signal proce.ssing unit. This signal is fed to phase detectors and then digitized to 16- bit revsolution 12]. Receiver details are provided in Table 1.The Partial Reflection Radar is mainly used for studying wave processes; it can be inferred from the wind motion which is directly recorded. Wave effects on the atmosphere are the changes in density, temperature and air flow. Here, the density and temperature changes result in the variation o f pressure which subsequently results in the flow  o f  air.A study o f refractive index structure constant from radar data 39Table 1. Receiver details of Partial Reflection Radar.No. .Specification Details1 Number <^ f receivers2 Center frequency3. Band width (3 dB)4 .Sensitivity5 Maximum gainb. CJaiii coniiol7 Gain control range8 Input impedanceq Signal proccs.sors10 .Sampling starlingheight1.98 Mil/-30 KH/-10 )Av60 dBl*iogrammable in steps ol 1 dB 60 dB 50 12The digiti/eis have 16-bit rest»Iinuui 60-08 km (day): 70-08 km (night)4. Middle atmosphere and turbulenceWind ari.ses due to temperature, density and pressure gradients. Depending upon the nature and lime scales o f external restoring forces, different types o f wave motions aie produced in atmosphere. When thc.se atmospheric waves travel Irom one region to another region ot the globe both vertically and horizontally, a dynamical coupling is created among the different regions o f atmosphere 17). A .study o f perturbation in any o f the aforesaid parameters would be helpful in understanding the dynamics o f Earth's atnu^sphere loo.d’he tropical atmosphere is inllucnced by solar radiation which drives both large scale circulation and cumulus convection. The conolis lorce is smaller, hence this allows certain wave modes which get trapped in equatorial legion. Since the gas density exponentially decreases with height, the atmospheric waves grow m amplitude upwards, and become significant contributors to the momentum and energy budgets o f the middle upper atmosphere (80-100 km).The measured wind field over Tirunelveli (8.7 'N, 77.8“E) exhibits variability on .several time .scales. Several wave events lasting for a few days to few lens o f days have been ob.servcd, revealing the innuence o f lower atmospheric wave excitation processes on the region up to 100 km [8-lOJ.Tides are known for many years to play an important role in the dynamics o f  the middle atmosphere. Atmospheric tides are global scale oscillations in temperature, density, pressure and wind at periods which iirc sub-harmonics o f a solar/lunar day. Solar tides are primarily generated by thermal force due to absorption o f solar radiation by water vapour or ozone [11,12]. They are further classified into two : (i) migrating tides and (ii) non-migrating tides.Tides have in general, amplitudes larger than other wave motions and they dominate in the atmospheric dynamics. They iiansport momentum and wave energy Upward Irom iheii source regions to the regions in which they are displaced by various instabilities such as (i) Inertial instability (ii) Shear instability (iii) Bart)lropic and Baro clinic instability and hence, affect the mean circulation and structure o f the atmosphere |1.3 —15|.Many have concentrated on large scale motions w'hich are prevalent in the atmosphere. In fact, the most ctnnmon Stale ol any lluid is turbulent flow' and only some o f the flow can be termed laminar. It is only becau.se the atmosphere is turbulent that we can use partial reHection radar to study it in a limited manner.rurbulence can exist only if energy available for its generation is greater than the buoyancy effects. The dclcrminatitm the structure o f the turbulence is often one o f tile primary objectives o f atmosphere dynamics studies. In that case, the velocity and density fluctuations can often be thought o f as being composed o f a number ol sinusoidal lluctuations o f varying scales, and varying spatial orientations. We can therefore, by analyzing the wind or density fluctuations, discover something about the spectrum o f turbulence. The energy spectrum is divided into three distinct regions based on the distinct characteristics o f turbulence within each region, known as the buoyancy range, inertial range and viscous range.Middle atmosphere turbulence (80-120 km) is thought to be due to gravity waves and tides, which generate turbulence through many different processes including non-linear breaking, shear instabilities, convective over­turning, and critical level interactions. Turbulence is important becau.se it is a large contributor to the diffusion of momentum, heat and matter. Meso.sphcric turbulence can be both spatially and temporally intermittent and may occur in patches or in horizontal layers. I'hc layers may be upto several kilometers thick and may be in a ‘sandwich'-type arrangement such that the turbulent layers arc bound by non-turbulent regions. Around an altitude o f 110 km, the molecular vi.scosity becomes large enough to damp out any turbulence, and this region is referred to as the turbopausc. While turbulence in the neutral atmt^sphere has been observed to heights o f -130 km, above the turbopausc it only plays a minor physical role.4'urbulcnce is one o f the primary generators o f both spatial and temporal variations in the refractive index o f the atmosphere; it creates a medium which scatters electromagnetic radiation thereby enabling one to probe40 C P Anil Kumar and N  Thangarajthe almospherc and study both the long-term and sliort- lerm dynamics as well as turbulence itself.5. Rei'ractivc index structure constantIn the thet)ry o f electromagnetic wave propagation in turbulence, the refractive index structure constant is taken as a measure o f the strength o f the turbulence. A  lot o f efforts have been made to measure this parameter at different regions and seasons. However, this parameter docs not indicate the fluctuation strength directly. It is found that the strength o f turbulence is the variance o f the refractive index. In the inertial sub-range, the structure function o f refractive index generally depends on both the variance and the turbulence outer scale 13).6. Methodt)logyThis is a preliminary study conducted in the equatorial region and since the Partial ReHection Radar is not an efficient tool for turbulent studies, the estimation o f C,p is very difficult. However, this paper tried to develop a method to derive profiles from available high resolution partial reficction radar data. To simplify the analysis, wc make the assumption that there are no errors in the radial velocities and the radial velocity terms have been perfectly converted into horizontal components. Starting with the horizontal components, there is an in-built post-processing software to compute the horizontal divergence at each level which is then integrated to get the vertical velocity. Software program has been developed based on the eqs. (8) and (9) to compute C,f values from the received signal power {P^), Radar can measure the refractive index structure function, because C„“ is proportional to the radar reflectivity fl2 ].C ; =where // is the radar reflectivity and A is the radar wavelength.7. Results and discussionData from first January 2005 to thirty first January 2(X)5 had been taken for the present analysis. 24 hours data is used for the evaluation o f Partial Reflection Radar normally provides information from 80—110 km, for the sake o f computation windowing is done between 80-88 km ranges. The receiver-1 value is given asC^^ and rcceiver-2 values are given as C^2* ^  comparative study o f different C l (average) has been made for this equatorial station.The values were studied to see what activity proceeded in the thermosphere during the sun set and sunrise hours in this zone. 7b show the effect, we selected three type viz. severe, moderate and weak having different C,7 values. It was found that most o f the days showed the post-sun.scl peak at 20.(X)-2l.(X) 1ST as depicted in Figure 1. The figure depicts the refractive index structure constant C “,, C„2 and vertical velocity (data o f 1st January 2005); both and C„ 2  shc)wed an enhancement.Moderate C~ values were al.so observed on 15th, 17th and 20lh January as shown in Figure 2. The minimum values were noted in rare cases and depicted as such in Figure 3.Hetractive tniiex structure constant10'"^  10- 10- 10- 10”Figure 1. The refractive mdex .structure constant f ( a  ). and verticalvclocuy (— ) [data from partial reflected echoesl.Refractive index structure cor^stantVfcRTICAL V t lO C IT Y  (m/s)Figure 2. The retractive index structure constant •) and verticalvelocity (— ) (data from partial rcllccted echoes].Refractive index structuro constantlo ‘* 10*'VERTICAL VELOCITY (m/a)Figure 3. The refractive index structure constant and verticalvelocity (— ) (data from partial reflected echoes].A study o f refractive index structure constant from radar data 41The study reveals that the association between the refractive index structure function C,^  is proportional to the radar reflectivity. The quantification of lurbulence in this regime may provide the Physics of E-Iayer dynamics after the post-sunset hours. However, the detail examination and classification of the cause will requiie further investigations.8. ConclusionsA study of radar based measurements of is carried out in this paper. The determination of the refractive index structure constant of the turbulence is often one of the primary objectives in any study of turbuicnce. In the ihci^ry of electromagnetic wave propagation in turbulence, the refractive index structure constant is taken as a measure of the strength of the turbulence. 1 he lefraeiive index structure constants for turbulence is calculated numerically and plotted with the vertical wind velocity. c l  values show an enhancement during post-sunset hours. It may be due to the fact that plasma within the geomagnetic flux tube becomes unstable because of pre- reversal enhancement (E x B electrodynamic drift) and take part in the up-wcIling process thus creating turbulence within the volume.AcknowledgmentsThe authors would like to acknowledge the criticalcomments from the referee wliich enabled a better presentation o\' the paper. Tins research work is supported by the Department of Science and lechnology. Govt, of India.KfiViTiices111 UK lican anil I'. J Duilon Riulin Mctenmldi^v (New '^ 'ork . U»>vci) (196X)\2D|4|7|9HOHiI12H-^H4H5Dra/cii Losicar PhD JhcM\ (Univcrsily of AdclaickO I W K I locking AJr Sfuac Rrs 7 17I (19S7)W K Hoiking/\^A .S>/cc Rc  ^ 1 2 2 0 7 ( l W )W K Hoiking J Atmos Ictn /Vma. 45 SO (1983)D Naiayana Rao, T  N Rao. M Vcnkalarainam, S I Imlasuaman, S V U Rao, P Snmvasalu anil 1* B Rao Radio. Su 36 1439 (2001 )S Kato Developments in hiuth iind Planetatv Si'icm es (Tokyo . D R oidcl)(l9S0)S Guinharan and R Kajaiam ./ Geophxs Res 106 31817 (2(K)l)R Rajarum and S Gurubaran Ann Geophw 'n ae 16 197 ( 1998)S Gurubaran and R Rajaiam Geophy. Res. U'tt. 2 6  1113 (1999)B 11 Biiggs, G J Phillips and H H Shmn I*ror, Phvs. S o< . (London) 63B 1 0 6 (1 9 5 0 )11 OUcistcn Radio Sl /. 4 1179 (1969)R S Licbcrman and I* B H.iys ./ Atmos. Si i 51 3094 {1994)J M forbes and F Vital J Atoms terr Phy 51 649 (1 98 9)J M Forbes /  Gcophs's. Res. 87 5222 (1982)

A Study of Refractive Index Structure Constant from Radar Data

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A Study of Refractive Index Structure Constant from Radar Data

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