Novel Approach in Cross-Spectral signal Analysis using Interferometry Technique.

Transcription

1 Novel Approach in Cross-Spectral signal Analysis using Interferometry Technique.. Professor, Dept of ECE, Gayatri Vidyaparishad College of Engineering (Autonomous), Visakhapatnam. Abstract 1. Radar Interferometer technique in spatial domain basically provides information on the angular position of the discrete scatters and their aspect sensitivity to the radar backscatter in the vertical plane containing the interferometer baseline. It is also possible to derive the drift of the scatterers along the direction of the baseline by tracking their positions as function of time. The technique has been used extensively for studies on plasma irregularities in the ionosphere (1), (2), (3), (4), (5), (6), (7), (8), (9) and also used this technique for lower atmospheric observation. The radar interferometer technique was first introduced for ionospheric application (1) and later developed in more detail (2), offers a powerful means to determine the small aspect angles associated with the backscatter from the FAI. The technique is so remarkable that it could be effectively used to measure aspect angles of the order of 10-2 degrees, as demonstrated by (7) for the equatorial spread F irregularities. The method involves measuring the complex cross-spectrum of the signals received at two-phase centers of the interferometer baseline. The cross-spectral phase and magnitude (coherence) provide the mean angle of arrival and rms deviation of the angular distribution of the returned signal respectively. Using the phase measurements as function of time, it is possible to derive the drift velocities along the baseline as shown (2). In the presence of moderate to heavy precipitation, Doppler spectra at VHF often contain two peaks: one due to hydrometeors and the other due to clearair back scattered echoes. The peak at larger Doppler velocity (taking sign into consideration) is coming from the refractive index fluctuation where as the second one is due to precipitation. Various 833 techniques for separating these echoes are reported. They generally follow two approaches: 1. Fitting Gaussian function to the turbulence (clear air) echo by (10), (11), (12) 2. Separation of these two echoes by considering the minimum power point between these two peaks represents the boundary (13). Recently, attempts have also been made to separate these echoes objectively (14), (16) from VHF radar spectra. With VHF radars, it is, thus, possible to measure mean vertical air motion (up- and down-drafts) and also fall speed spectrum of precipitation particles. Studies on precipitating systems with VHF wind profilers have been made by many researchers in the past by (17), (18), (19), (20), (10],(21), (13), (22), (23), (11)and (12). Some of these studies focused on characterizing different types of precipitating systems, the radar bright band and turbulence and precipitation echo structures, while other studies focused on retrieving the rain drop size distributions using a single frequency technique. These studies tried to reveal the structure of mesoscale wind circulations during the passage of typhoons and to study the disturbances (or waves) they generate during their passage over the radar site. All these observations made when radar is operating under Doppler Beam Swinging technique and there is no severe changes in atmosphere during the observation time. This chapter presents the results of a study on atmospheric radar signals during a severe convective event using spatial domain interferometry technique. During convective event atmosphere is highly turbulent and wind field will be changing very fast in time and space. There is strong updraft and down draft of mass is observed along with heavy precipitation during the event. This will lead in to multiple echoes with in the radar observational volume. Due to its complexity, the

2 extraction of information is very difficult using conventional technique such as Doppler beam swinging and power spectral analysis could not reveal desired information from the observation. In this paper, we are reporting an approach using Space Domain Interferometry (SDI) technique to extract the information. Using SDI, coherence and phase of the bi-modal signal has shown unique characteristics which helps in identifying the velocity of clear air and precipitation echoes. 2. Experiment Description and Method of Analysis The Gadanki MST radar is a coherent pulse Doppler radar operating at 53 MHz with a peak poweraperture product of 3x1010 Wm2. A detailed description of various subsystems and operation of the radar was given [24]. Hence the description given here is relevant to the radar interferometer experiments as applied to the lower atmosphere. The antenna system occupying an area of 130 m x 130 m is a phased array of 32 x 32 three-element Yagi antennas consisting of two orthogonal sets, one for each polarization (magnetic E-W and N-S). The array can be illuminated in either of the polarizations using 32 transmitters, each feeding a linear sub-array of 32 Yagi antennas. The outputs of the 32 transmitters are connected to 32 linear subarrays through equal number of transmit-receive (T/R) and polarization selection switches. The receiver part consists of 32 channels corresponding to the 32 linear sub-arrays. The signals received through the 32 channels, after passing through the front-end amplifier and mixer units, are combined and fed to a phase coherent receiver at the IF level. This feature of the antenna and receiver network has been made use of for the radar interferometer application. For interferometeric mode of operation, signal reception, the whole array was divided into two equal parts along the geomagnetic north-south baseline with each part consisting of 16 linear subarrays with their phase centers separated by a distance of 65 m. Since there is only one receiver for reception, it was switched between the two halves of the antenna array every sampling interval, which corresponds to the coherent integration period of 2 ms. This was accomplished by introducing an SPDT switch, operating in 834 synchronism with the coherent integration pulses, between the two halves of the antenna array and the receiver. For the transmission purpose, the whole antenna array was used, thereby restricting the region probed to the main lobe of the interferometer pattern. The antenna array was phased in such a way that both transmit and receive beams are formed at a zenith angle. The complex voltage amplitudes of the backscattered signals were recorded in the form of in-phase and quadrature-phase components for the two antennas. Following expression given by (24), the mean angle of arrival and its variance can be obtained from the complex normalized cross spectrum of the signals received cross spectrum of the signals received at the two antennas. The expressions are derived as follows: The signal received at antenna 1 can be expressed as v1 (t) = Aj exp i( t + j) Where j is a j random phase angle that corresponds to a particular scatterer, and Aj is the corresponding amplitude, Fourier transforming a relatively small segment of the data, we get V1 ( ) = Aj exp (i j) j Similarly for the signal from the second antenna of the same gain, V2 ( ) = Aj exp i ( j - kd j) j Where k is the radar wave number, d is the length of the baseline and j, is the angular position of the jth scatterer. (sin j is replaced by j, since the angles of interest are small and j are uniformly distributed over 0 to 2 ). Taking ensemble averages (equivalent to temporal or spatial averages) leads to: exp i j = 0 V1( )V2*( ) = Aj2 exp ikd j j Defining the normalized complex cross spectrum as S12 we obtain V1 V2* V V

3 S12 ( ) = exp (ikd j) If we assume that the radar backscatter arrival angle j have a Gaussian distribution with a mean and a variance 2, S12( ) can be expressed as k 2 d 2 2 S12 exp ikd 2 The cross-spectrum magnitude (coherence) and phase are given as : S12 exp ( k 2 d 2 2 ) 12 ( ) kd 3. Results and Discussion Figure 5.1(a) and (b) show a sample power spectrum of the echoes received from radar during the convective event. Figure 3.1 (a) is the Doppler power spectrum plotted in a range normalized mode Subsequent to that heavy precipitation follows. where as 3.1(b) plotted in colour coded form. It can be noticed that, there are multiple echoes spread over entire band width of observation. During convection it is difficult to measure the wind vectors due to changes in instantaneous velocity field within the radar observation volume. Moreover the medium also will be highly turbulent which result in spreading the Doppler spectrum. This brings in difficulty in measuring the mean Doppler velocity and other parameters. It is evident from the power spectrum plotting that the direct computation of mean Doppler shift is tedious due to large fluctuations. VHF radars generally detect clear air echoes but it can also detect heavy precipitation with in the radar observation volume. During convection strong winds were observed along large up-drafts and down drafts. (a) (b) Figure 3.1 Doppler Power spectrum from the radar back scattered echoes during a convective event ( a) 2- dimensional plot normalized to individual range bin (b) same as a but in colour code. 835

4 So it is possible to generate two type of echoes one due to up draft and other due to downward motion of the Precipitation as shown in figure 3.1 Using conventional approach it is difficult to distinguish the echoes and identify the mean Doppler due to clear air and that of due to precipitation. It is also difficult to average number of frames, since characteristics of the spectrum vary from frame to frame due to instantaneous change in wind fields. Important aspect of cross spectral analysis is the identification of the mean Doppler shift when the spectra become very complex and influenced by large disturbances due to turbulence. Using cross spectral analysis of signal received from two receivers separated a distance (phase centers of the antenna systems are 64 m) for the height range of 3.6 to 20.7 km is shown in figure 3.2 (a) to (p). One plot shows the coherence and subsequent to that is phase derived using complex cross spectral analysis. By looking at the cross spectrum output in terms of coherence and phase one can find that there are two distinct echoes (strong peaks) present in each range gate and when the coherence is high there is linear phase change. By identifying the maximum coherence and mean value of the phase in the linear range one can find corresponding mean Doppler. The slope of the phase is measure of apparent velocity (14) in the horizontal direction. So it is easy to estimate mean Doppler velocity at particular height by this method. In the cross spectral analysis there are two peaks observed in the coherence and there is corresponding linear phase. This observed up to 5.85 km distinctly and at higher altitudes echoes due to turbulence only visible as shown in the figure 3.2(a) to (c). In normal precipitation the two peaks are observed once ice melts down at the melting layer. It is reported that these are at the height of around 4 kms. In convection the melting layer disappears due to strong updraft and there are chances of the water droplets/ice particle lifting above 10 km. (a) Once convection is over there is a transition and stratic form rain starts along with the presence of melting layer. 836

5 (b) (c) 837

6 (d) (e) 838

7 (f) (g) 839

8 (h) (i) 840

9 (j) (k) 841

10 (l) (m) 842

11 (n) (o) 843

12 (p) Figure 3.2 (a) to (p) Cross spectral analysis of radar back scattered signals. Upper panel shows Coherence and lower panel shows Phase Once the cross spectral analysis is over, identify the peak corresponds to highest coherence and its frequency values. Figure 5.3 shows the frequency profile plotted over the Doppler power spectrum for clear air echoes. Since multiple peaks are generated in power spectrum and the strongest Figure 3.3 Mean Doppler (frequency) profile plotted over Doppler power spectrum. Mean Doppler is identified using cross spectral analysis 844

13 peak corresponds to precipitation echoes (as visible in the Doppler power spectrum positive side of the frequency) from 3.6 to 6 km, it is almost impossible to identify the clear echoes in lower range gates. Cross spectral analysis helps in detecting the echoes correctly as shown in the figure Conclusion An algorithm is developed for the analysis of atmospheric radar back scattered echoes. A detailed analysis is carried out on observation during a convective event. The spectra show multiple peaks and distinctly showing bimodal characteristics. Identification of two distinct Doppler and its mean velocity is become more difficult when the medium is highly unstable and turbulent. Space Domain Interferometry technique is applied to extract these two echoes. The high coherence and linear phase shown in cross spectral analysis helps to identify the clear air and precipitation echoes in a highly complex signal pattern. Large number data sets were tested with this technique and found to be successful in identifying the multiple peaks echoes in a highly disturbed environment. Spatial Domain Interferometry of atmospheric observation and cross spectral analysis has considerable advantage in analyzing the signal during the disturbed condition of the atmosphere and multiple targets (echoes) were present. Example given clearly demonstrate the capability of the technique and the signal analysis for atmospheric radar applications. 5.References: [1]Woodman, R.F., Inclination of the geomagnetic field measured by an incoherent scatter technique, J. Geophys. Res., 76, 178, [2] Farley, D.T., H.M. Ierkic, and B.G. Fejer: Radar interferometry: A new technique for studying plasma turbulence in the ionosphere, J. Geophys. Res., 86, 1467, [3] Kudeki, E., B.G.Fejer, D.T.Farley, and H.M. Ierikic, Interferometer studies of equatorial F region irregularities and drifts, Geophys. Res. Lett., 8, 377, [4] Providakes, J.P., W.E Swartz, D.T.Farley, and B.G.Fejer, First VHF auroral VHF interferometer observations, Geophy. Res. Lett., 10, 401, [5] Riggin, D., W.E.Swartz, J.Providakes, and D.T.Farley, Radar studies of long wavelength associated with mid latitude sporadic E layers, J. Geophy. Res. 91, 8011, [6] Kudeki, E., and D.T. Farley, Aspect sensitivity of equatorial electrojet irregularities and theoretical implications, J. Geophys. Res., 94, 426, [7] Farley, D.T., and D.L. Hysell: Radar measurements of very small aspect angles in the equatorial ionosphere, J. Geophys. Res., 101, 5177, [8] Hysell, D.L., D.T.Farley, Implications of the small aspect angles of equatorial spread F, J. Geophys. Res. 101, 5165, [9] Chilson, P.B., R.D Palmer, MF Larsen, CW Ulbrich, S. Fukao, M. Yamomoto, T.Tusda, S.Kato: First observation of precipitation with a spatial interferometer, Geophy. Res. Let. Vol. 19, PP , [10] Rajopadhyaya, D. K., P. T. May, and R. A. Vincent: A general approach to the retrieval of raindrop size distributions from VHF wind profiler Doppler spectra: Modeling results. J. Atmos. Oceanic Technol., 10, , [11]Lucas, C., A. D. MacKinnon, R. A. Vincent, and P. T. May: Raindrop Size Distribution Retrievals from a VHF Boundary Layer Profiler. J. Atmos. Oceanic Technol., 21, 45-60, [12]McDonald, A. J., T. K. Carey-Smith, D. A. Hooper, G. J. Fraser, and B. P. Lublow, The effect of precipitation on the wind-profiler clear air returns. Ann. Geophys., 22, , [13]Rao, T. N., D. N. Rao, S. Raghavan: Tropical precipitating system observed with Indian MST Radar Radio Sci., 34, , [14]Campos, E. F., F. Fabry, and W. Hocking: Precipitation measurements using VHF wind profiler radars: Measuring rainfall and vertical air velocities using only observations with a VHF radar. Radio Sci., 42, RS3003, doi: /2006RS003540, [16]Radhakrishna, B., T. N. Rao, D. N. Rao, and N. V. P. K. Kumar: Separation of turbulence echo from the multi-peaked VHF radar spectra observed during precipitation. Submitted to J. Atmos. Oceanic Technol, [17]Fukao, S., K. Wakasugi, T. Sato, S. Morimoto, T. Tsuda, I. Hirota, I. Kimura, and S. Kato: Direct measurement of air and precipitation particle motion by very high frequency Doppler radar. Nature, 316, , 1985.

14 [18]Wakasugi, K., A. Mizutani, M. Matsuo, S.Fukao, S.Kato: A direct method for deriving drop size distribution and vertical air velocities from VHF Doppler radar spectra, J. Atmos. Oceanic Technol., 3, , [19]Sato, T., Radar Principles, ISAR, Lecture notes edited by Fukao, 1988 Sato, T., H. Doji, H. Iwai, I. Kimura, S. Fukao, M.Yamamoto, T.Tsuda, S.Kato: Computer processing for deriving drop-size distribution and vertical air velocities from VHF Doppler radar spectra. Radio Sci., 25, , [20]Chu, Y.H., and Lee-Po.C: The investigation of the atmospheric precipitations by using Chung-Li VHF radar., 26, , [21]Ralph, F.M: Using radar measured radial vertical velocities to distinguish precipitation scattering from clear air scattering, J. Atmos. Oceanic Technol., 12, , [22]Rao, T. N., D. N. Rao, K. Mohan, and S. Raghavan: Classification of tropical precipitating systems and associated Z-R relationships, J. Geophys. Res., 106, 17, , [23]Reddy, K.K., K. Nakamura, T. Kozu, A.R.Jain, D.N.Rao: Tropical precipitation studies using 846 VHF/L band wind profilers and disdrometer over Gadanki, India, Proc. SPIE, 4152, 62-72, [24]Rao, P. B., A. R. Jain, P. Kishore, P. Balamuralidhar, S. H. Damle, and G. Viswanathan, Indian MST radar: 1. System description and sample wind measurements in ST mode, Radio Sci., Vol. 30, pp , Author Profile Dr D.B.V.Jagannatham received the B.Tech. degree in Electronics and communication engineering from Andhra University, Waltair, India, M.Tech-DSCE degree from Jawaharlal Nehru Technological University, Hyderabad, and Ph.D (Doctoral Degree) from JNTU Hyderabad, Experimentation work done at NARL-Gadanki, Near Tirupati (ISRO Laboratories) Andhra PradeshINDIA. He is currently as a Professor in the Department of Electronics and Communication Engineering, Gayatri Vidyaparishad College Engineering (Autonomous),Madhurawada,Visakhapatnam. His area of interest is Algorithm development for NonLinear and Non-Stationary signal Processing Applications.