25 Sept. 2006 ERAD2006

Crossbeam Wind Measurements with Phased-Array Doppler

Weather RadarRichard J. Doviak

National Severe Storms Laboratory

Guifu Zhang School of Meteorology, University of Oklahoma

Norman, Oklahoma

25 Sept. 2006 ERAD2006

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

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Phase Array Radar(scanning diversity;multi-mission*; etc.)

*ARSR;ASR;TDWR;WR

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National Weather Radar Testbed Monopulse Antenna on the

University of Oklahoma’s Campus

(1) (2)

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Monopulse Antenna Patterns(Sum and Azimuth Difference)

SUMAzimuthDifference

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Monopulse Antenna Outputs:1) Sum 2) Elevation difference3) Azimuth difference

Monopulse sum & difference

SA Left & Right

Auto/Cross correlation estimates

Wind, Shear, & Turbulence

CSS(τ)CDD(τ)CSD(τ)

C11(τ)

C12(τ)

Correlations ofSum and DifferenceSignals

WeatherSignalsVs(t);VD(t)

Correlations of Signals from theLeft and righthalves of array

Within V6

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Possible configurations of SAI

Dual-beams to separate shear and turbulence

three channels:• Sum• Azimuth difference• Elevation difference

Azimuth SA Elevation SA

voy’

V1(t) V2(t)

)()()( 21)(

12 tVtVC

T

R

T

R

R1 R2

R1

R2 )()( 21 tVtV

Azimuth cross correlation:

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Auto and cross correlation coefficients

Cross-correlation peak shifts due to the delay of diffraction pattern passing over antennas from R1 to R2

c11

c12

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Tilted Cartesian Coordinate System z

z y

R2( y 2, z 2)

z

r n (t)

v

r 0

O

x T

r n (t )

r 01

r 02

y ,

ˆ a y'

x,

ˆ a x'

R1( y 1, z 1)

0

)()0()()( rsvvrvrv xtxx

)0(),0(),0()0(

)()0(

zyx vvvv

rvvv

; Mean wind

; First order perturbations

y

x

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Azimuth cross correlation coefficient(to obtain horizontal component of

crossbeam wind)

22222)(12 2)0(2exp)(

xtxRx skjkvc

2

12222222 2/)0()0( yvkvk yaezae

)0()0( 0 yyya vsrv )0()0( 0 zzza vsrv

Where,

are apparent crossbeam winds

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Apparent wind versus angular shear

• Apparent wind in the azimuth direction:

• Angular shear in the azimuth direction:

• Wind estimation using cross correlation ratio:

va y (0)1

2k2e2 y 12

lnC12( )

C12( )

va y (0) r0s y v y (0)

s va y / r0

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Showing why SAI cannot distinguish crossbeam wind from crossbeam shear

of along-beam axis windvy(0)

vy(0)

Crossbeam wind Crossbeam shear ofalong-beam axis wind

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Auto & cross-correlation coefficients

Auto- and cross-correlation coefficients for the NWRT PAR. Meteorological parameters are:vy ′(0) = 20, vz ′(0) = 5,σtx ′ = 0.5 m s-1, sx ′ = 0. (a) Dependence on r0, sy′ = 0, sz ′ = 0.002 s-1; (b) Dependence on shear sy ′ at r0 = 30 km;

(a) (b)c11

c12

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Separating shear and turbulence(dual beamwidth method)

T

R

T

R

Transmit beam

Azimuth receive beamElevation receive beam

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• Auto-correlation for narrow (Sum) beam

• Auto-correlation for broad beam (left or right side of array

• Shear

• Turbulence

Separating shear & turbulence

t x 2

1

2k2 2

T2

e2 T

2ln

| cB( ) ||cN ( ) |

e2

e2 T

2ln

| cB( ) ||cN ( ) |

ln | cB( ) |

cN ( ) | css( ) |exp 2k2 tx '2 2 k2r0

2T2 (s

2 s2 ) 2

cB( ) | c11( )exp 2k2 tx '2 2 k2r0

2T2 (s )2 k2r0

2e2 (s )2

s2

1

k2r02 2(e

2 T2 )

ln| cN ( ) |

| cB( ) |

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Theoretical performance

About 10 s needed for 2 m s-1 crossbeam wind accuracyat near ranges for 0.5 m s-1 turbulence

CCR

FCA

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Comparison of SAI and DBS

• SAI better than DBS if angular separation < Beam Width

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Summary and Conclusions• It has been shown that SAI (NWRT):

(1) measures angular shear of radial velocities within V6

(2) IFF transverse shear of the Cartesian wind component parallel to the beam axis is negligible, can crossbeam wind within V6 be measured

(3) separates shear and homogeneous turbulence so that turbulence within V6 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

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End of Slide Show

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Differences between current weather surveillance and PAR Technology

A wide transmit beam and

Multiple receive beams

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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

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Testbed Basic Radar ParametersRadar Antenna System3.66 m diameter with 10° tilt-back; 4,000 elementsAz/El Broadside Beamwidth: 1.6°(Tx); 1.8°(Rx)Nominal Gain = 41 dBLinear Vertical PolarizationScan volume (electronic): 45 Az, 0° - 55° El

Transmitter: WSR-88D (NEXRAD)Output Power = 700 KW; λ = 10.cmPulsewidths = 1.57 s, 4.71 sMaximum Duty Factor = 0.002S K I P

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General formulation• Configuration sketch

• Received signals

V(r 01,t1) A1n

n1

N

W1n exp jk |r 0

r n(t1) | |

r 01

r n( t1) |

V(r 02 ,t2 ) A2n

n1

N

W2n exp jk |r 0

r n(t2 ) | |

r 02

r n( t2 ) |

R2

R1

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• Definition

• Velocity approximation

• Derived cross-correlation function

Derivation of cross correlation function

C12( )S exp 2 jkv x (0) 2k2 R2s x

2 t x 2 2

k2e2 r0s z v z (0) z 12 / 2 2 k2e

2 r0s y v y (0) y 12 / 2 2

v x (r ) v x (0) v t x (

s r )

v x (0) v tx' s x x s y y s z z

C12(t2 t1)V*(r 01,t1)V(

r 02 ,t2 )C12( )

C12( )n1

N

A2nW2nA1 n * W1 n

* exp jk |r 0

r n '(2 ) | |

r 02

r n '( t2 ) | |

r 0

r n(t1) | |

r 01

r n( t1) |

n '1

N

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Physics explanation

• Time delay in both cases

• Configuration shifted or rotated

Transverse wind Transverse shear of radial wind