Richard J. Doviak 1,2,3 , Yinguang Li 3,4 , Guifu Zhang 2,3,4

1. Application of Interferometric Techniques to the National Weather Radar Testbed Monopulse Phased Array Radar Richard J. Doviak1,2,3, Yinguang Li3,4, Guifu Zhang2,3,4 1 National Severe Storms Laboratory, USA2School of Meteorology, University of Oklahoma, USA3 School of Electrical and Computer Engineering, University of Oklahoma, USA 4 Atmospheric Radar Research Center, University of Oklahoma, USA

2. National Weather Radar Testbed (NWRT) Motivation:To support research and develop ideas for weather observations with Phased Array Radar (PAR)The NWRT is available to students and faculty of any University Motivation for this research: To determine the accuracy of measuring crossbeam wind and turbulence, within the radar’s resolution volume, using Spaced Antenna (SA) techniques

3. What does SA measure wind? • Crossbeam wind is measured if wind is uniform. • If wind has transverse shear, SA measures an apparent crossbeam wind (i.e., the angular shear of the radial wind; Zhang and Doviak, JTECH, 2007) • A pair of SA antennas measures the component of angular shear parallel to the baseline of the SA pair (i.e., the apparent baseline wind)

4. The NWRT Monopulse Antenna on the University of Oklahoma’s Campus λ = 9.38 cm Phase centers ● ● (L) (R) Conventional Spaced Antenna Interferometry (SAI) requires signals from the Left & Right (or Top and Bottom) sides of the array to measure crossbeam wind. But there are no ports on the monopulse antenna that give signals from the left & right halves (or top and bottom halves) of the array; nor do we know their phase centers and beamwidths; these parameters are needed for conventional SA analysis.

5. Columns (10) of Modules (136) contribute to the Monopulse Sum and Difference Signals 3.66 m 3.84 m Sub-array Module (32 Elemental apertures) in column 1 Column 10 Right half Total number of elemental apertures: 4,352

6. Schematic of the NWRT Monopulse Antenna -Antenna phase shifters a(1 of 32 shown for each module)steer the beam. -Power Combiners (PC) weight the aperture distribution

7. Summing, differencing, and weighting to form sum and AZ difference signals PC3 Weights for the Taylor Distribution PC4 Weights for the Bayliss distribution ΔA Σ There are no ports for conventional Spaced Antenna (SA) analysis

8. Because there are no ports for spaced receiving apertures, how can we obtain the apparent crossbeam wind? Two approaches: Approach 1: Relate the sum and difference signals to virtual left and right receiving antennas, their phase centers, and beamwidths. (This allows conventional SA analysis to be applied). Approach 2: Develop a theory that relates the monopulse sum and difference signals directly to the apparent baseline wind. We shall explore both approaches and compare, through theory and simulation, the standard error of the apparent baseline wind estimated using these two approaches.

9. Approach 1:Relating Sum and Difference Signals to Virtual Signals from the Left and Right Sides of the Array vl and vr are the “virtual” signals from the left and right sides Expressions for the correlation functions of sum and difference signals are related to the correlation functions of signals received by the virtual left and right sides of the array.

10. Relating sum and difference signals to virtual signals from the left and right sides of the array Conventional SA algorithms can now be applied. But (see next slide) • The previous four equations can be solved for the correlation functions of virtual signals from the left and right sides of the array (Assume )

11. To use conventional SA algorithms we need: • Phase center separation Δyrlof the virtual left and right side arrays, and • Beamwidths of the virtual left and right side arrays. (These parameters can be obtained from sum and difference pattern measurements)

12. Comparison of theoretical and measured sum and difference receive radiation patterns

13. Virtual left and right side patterns deduced from sum and difference patterns Sum pattern Virtual left (or right) side Array pattern Difference Pattern

14. The Virtual Left and Right Apertures Δyrl Virtual Right Side aperture Virtual Left Side Aperture • The left and right side apertures of the virtual SA are overlapped. • Phase center separation Δyrl= 1.22 m (derived from pattern measurements).

15. Comparing two SA methods to estimate apparent baseline wind • Full Correlation Analysis (FCA, Briggs, 1984): Auto-correlation, Cll, and cross-correlation Crl functions are used, or the • Cross correlation ratio (CCR) method of Zhang et al., (2003) (For the comparison we assume SNR = 0, and use a two-lag estimation technique; e.g., pulse pair processing)

16. EXAMPLE: AUTO- AND CROSS-CORRELATION COEFFICIENTSFor Gaussian-FCA, 3 parameters (η,τp, τc) uniquely specify the correlations Cll estimates Cll Least Squares Fit Crl estimates Crl Least Squares Fit N (Cll(0)-N)exp[-η] τc For the CCR Method Crl(+τ) τp Crl(-τ)

17. Theoretical standard deviation of apparent baseline wind measured using virtual spaced antennas Vx’(0) = 0, Vay’ =20m s-1, Vaz’=0, σtx’ = 0 to 3m s-1 Gaussian-Cross Correlation Ratio (G-CCR) method Gaussian-Full Correlation Analysis (G-FCA) Next two slides will compare this theory with simulated results

18. The MU Phased Array RadarShigaraki, Japan λ = 6 m; D = 100 m This PAR has also been used for crossbeam wind measurements (i.e., horizontal wind for vertically directed beams)

19. COMPARISON OF THEORY (Doviak et al., 2004) WITH MU RADAR SIMULATIONS (Kawano, et al., 2002](0.5 = 50 m, Td = 175.1 s, vox = 30 m/s) Phase center spacing Δx (m)

20. Approach 2:Directly using the sum and difference auto- and cross-correlation functions.(Several algorithms can be used) For example, apparent baseline winds from: • Difference autocorrelation (no calibration required) • The cross-correlation of the sum and difference signals (analogous to SZL) • The intersection of the difference auto-correlation and the cross-correlation functions (i.e., INT(cdd, csd); analogous to the FCA)

21. A Monopulse analog of the FCA;Comparison of theory and simulations |csd|: simulation; theory |cdd|: simulation; theory Vay’ = 20m s-1, Vaz’ = 0, Vx’ = 0, σtx’ = 0 Dwell Time: 10s The Intersection of |cdd(τ)| and csd(τ)|

22. The effect of turbulence on the INT (|csd|,|cdd|) method σtx’= 1 m s-1 σtx’= 0

23. The INT (|csd|,|cdd|) method (Continued) Apparent baseline wind: τl τr |Csd| |Cdd| τi= (τr-τl)/2

24. Comparing theory and simulations Using monopulse signals Using virtual Left/right signals

25. Conclusions • Strictly SA measures angular shear, not crossbeam wind. • SA can separate turbulence from shear within the beam. • Conventional algorithms using virtual signals outperforms the Intersection method applied to monopulse signals. • SA for weather applications appears to be limited to within the beam measurements. • Alternatives to measure wind within the beam: 1) fitting spectral data to wind field model (Zrnic/Doviak, 1975, JAM,; Yu et al., JAOT, 2007; many others) 2) Cross-spectra Phase (Zhang/Doviak, JAOT, 2008) 3) DBS techniques at closely spaced angles (for given resolution SA outperforms DBS; Doviak et al., URSI/USA Meeting, 2004) 4) Monopulse ratio method (Teshiba, et al.,AMS Annual Meeting, 2008)

26. The END • Questions?

27. Gaussian parameter SDTheory vs Simulation: (τc--correlation time) Td = 10 s No. of Exp.: 100 Vay’ = 20 m s-1 Vx’ = 0 Vaz’= 0 SD[τc]x103

28. Gaussian parameter SD-continuedTheory vs Simulation continued: (τp---time to correlation peak) Td = 10 s No. of Exp.: 100 Vay’ = 20 m s-1 Vx’ = 0 Vaz’= 0 SD[τp]x104

29. Gaussian parameter SD-continuedTheory vs Simulation continued: (η---dtime to correlation peak)

30. A Monte Carlo Simulator Based on the Configuration of the NWRT

31. A Monte Carlo Simulator Based on the Configuration of the NWRT (Continued) • The Motions of the Scatterers (vay’=50m/s, σtx’=3m/s, vx’(0)=0)

32. Showing why SAI cannot distinguish crossbeam wind from crossbeam shear of along-beam axis wind vy(0) Beam axis Beam axis vy(0) Crossbeam wind Crossbeam shear of along-beam axis wind