25 Sept. 2006ERAD2006 Crossbeam Wind Measurements with Phased-Array Doppler Weather Radar Richard J. Doviak National Severe Storms Laboratory Guifu Zhang School of Meteorology, University of Oklahoma Norman, Oklahoma

25 Sept. 2006ERAD2006 Spaced Antenna Interferometry (Overview) Interferometry: –Complementary to the Doppler method –Used by the MST community for a half century Weather applications: –NCAR’s Multiple Antenna Profiling Radar (MAPR) –UMass’s Dual-polarization Spaced Antenna (DPSA) system National Weather Radar Testbed (NWRT); (phased-array weather radar) –Good opportunity to revisit spaced antenna interferometry

25 Sept. 2006ERAD2006 Phase Array Radar (scanning diversity;multi-mission*; etc.) *ARSR;ASR;TDWR;WR

25 Sept. 2006ERAD2006 National Weather Radar Testbed Monopulse Antenna on the University of Oklahoma’s Campus (1) (2)

25 Sept. 2006ERAD2006 Monopulse Antenna Patterns (Sum and Azimuth Difference) SUM Azimuth Difference

25 Sept. 2006ERAD2006 Monopulse Antenna Outputs: 1) Sum 2) Elevation difference 3) Azimuth difference C SS ( τ) C DD (τ) C SD (τ) C 11 (τ) C 12 (τ) Correlations of Sum and Difference Signals Weather Signals V s (t);V D (t) Correlations of Signals from the Left and right halves of array Within V 6

25 Sept. 2006ERAD2006 Possible configurations of SAI Dual-beams to separate shear and turbulence three channels: Sum Azimuth difference Elevation difference Azimuth SAElevation SA v oy ’ V 1 (t) V 2 (t)   T   R   T   R R 1 R 2 R 1 R 2 Azimuth cross correlation:

25 Sept. 2006ERAD2006 Auto and cross correlation coefficients Cross-correlation peak shifts due to the delay of diffraction pattern passing over antennas from R 1 to R 2 c 11 c 12

25 Sept. 2006ERAD2006 Tilted Cartesian Coordinate System ; Mean wind ; First order perturbations

25 Sept. 2006ERAD2006 Azimuth cross correlation coefficient (to obtain horizontal component of crossbeam wind) Where, are apparent crossbeam winds

25 Sept. 2006ERAD2006 Apparent wind versus angular shear Apparent wind in the azimuth direction: Angular shear in the azimuth direction: Wind estimation using cross correlation ratio:

25 Sept. 2006ERAD2006 Showing why SAI cannot distinguish crossbeam wind from crossbeam shear of along-beam axis wind v y (0) Crossbeam wind Crossbeam shear of along-beam axis wind Beam axis

25 Sept. 2006ERAD2006 Auto & cross-correlation coefficients Auto- and cross-correlation coefficients for the NWRT PAR. Meteorological parameters are:v y ′ (0) = 20, v z ′ (0) = 5,σ tx ′ = 0.5 m s -1, s x ′ = 0. (a) Dependence on r 0, s y′ = 0, s z ′ = s -1 ; (b) Dependence on shear s y ′ at r 0 = 30 km; (a)(b) c 11 c 12

25 Sept. 2006ERAD2006 Separating shear and turbulence (dual beamwidth method)   T   R   T   R Transmit beam Azimuth receive beam Elevation receive beam

25 Sept. 2006ERAD2006 Auto-correlation for narrow (Sum) beam Auto-correlation for broad beam (left or right side of array Shear Turbulence Separating shear & turbulence

25 Sept. 2006ERAD2006 Theoretical performance About 10 s needed for 2 m s -1 crossbeam wind accuracy at near ranges for 0.5 m s -1 turbulence CCR FCA

25 Sept. 2006ERAD2006 Comparison of SAI and DBS SAI better than DBS if angular separation < Beam Width

25 Sept. 2006ERAD2006 Summary and Conclusions It has been shown that SAI (NWRT): (1) measures angular shear of radial velocities within V 6 (2) IFF transverse shear of the Cartesian wind component parallel to the beam axis is negligible, can crossbeam wind within V 6 be measured (3) separates shear and homogeneous turbulence so that turbulence within V 6 can be measured Limitations of crossbeam wind measurements with SAI: (1) Uniform wind and reflectivity required (2) Long dwell times (i.e., seconds) for accurate crossbeam measurements

25 Sept. 2006ERAD2006 End of Slide Show

25 Sept. 2006ERAD2006 Differences between current weather surveillance and PAR Technology A wide transmit beam and Multiple receive beams

25 Sept. 2006ERAD2006 Advantages of a phased array weather radar 1) significant reduction in the time to make measurements over storm volumes 2) obtaining more frequent measurements of meteorological hazards, (e.g., tornado cyclones, etc.) 3) monitoring, at a lower revisit rate, areas void of weather 4) faster update rates of selected storms (i.e., better retrieval of storm properties to predict developing hazards) 5) better ground clutter canceling and compensation for reflectivity biases 6) the angular resolution of a stationary beam (i.e., no smearing due to rotation) 7) Multiple mission (tracking aircraft; weather; etc.) 8) direct measurement of crossbeam wind using interferometric techniques

25 Sept. 2006ERAD2006 Testbed Basic Radar Parameters Radar Antenna System 3.66 m diameter with 10° tilt-back; 4,000 elements Az/El Broadside Beamwidth: 1.6°(Tx); 1.8°(Rx) Nominal Gain = 41 dB Linear Vertical Polarization Scan volume (electronic):  45  Az, 0° - 55° El Transmitter: WSR-88D (NEXRAD) Output Power = 700 KW; λ = 10.cm Pulsewidths = 1.57  s, 4.71  s Maximum Duty Factor = 0.002

25 Sept. 2006ERAD2006 General formulation Configuration sketch Received signals

25 Sept. 2006ERAD2006 Definition Velocity approximation Derived cross-correlation function Derivation of cross correlation function

25 Sept. 2006ERAD2006 Physics explanation Time delay in both cases Configuration shifted or rotated Transverse windTransverse shear of radial wind