# Velocity Aliasing Example Velocity Aliasing Example

Velocity Aliasing Example Velocity Aliasing Example

Velocity Aliasing Example

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Large Raindrop

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Reflectivity Factor Factor at at Horizontal

Polarization, Z h (dBZ)

h (dBZ)

int

= Z − α

■ Z h is measured

■ Z int h is the intrinsic Z h due to the hydrometeors

■ α h (r) is the two-way way attenuation

■ OES stands for Other Error Sources

Z

– system noise

– calibration errors

Zh

– sidelobe contamination

– statistical uncertainty of estimate

h h h

+

int

() r OES

⎡ 4 Deh

= Deh,

λ

= 10log⎢

5 2 ∫σ

⎢⎣

π K

Deh

= Deh,

max

( D ) N( D )

min

eh

Measures amount

eh

dD

eh

⎥⎦

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Differential Reflectivity, Z DR (dB)

DR (dB)

int

Z

DR

= Z

DR

− α

dp() r + OES

■ Z DR is measured

■ Z

int DR is the intrinsic Z DR due to the hydrometeors

■ α dp (r) is the two way differential attenuation

■ OES stands for Other Error Sources

– system noise

– mismatched main-lobe power patterns

– mismatched sidelobe power patterns

– statistical uncertainty of estimate

Z

DR

=

Z

h

Z

Measures shape

v

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Z DR

Z DR Example

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Correlation Coefficient, |ρ |ρ hv (0)|

hv (0)|

int

() 0 = ρ () 0 ES

hv hv

+

■ |ρ hv (0)| is the measured magnitude of the correlation

coefficient at zero time lag between horizontally and vertically

polarized signals

■ |ρ hv (0)| int is the intrinsic |ρ hv (0)| due to the hydrometeors

■ ES stands for Error Sources

– Sidelobe contamination

– Low SNRs (system noise)

– Spectral shape (non-Gaussian spectra)

– Phase noise (of transmitter)

– Spatial phase pattern of transmitted signal

ρ

Measures hydrometeor diversity

Resonant (δ) scattering

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

|ρ hv

|ρ hv (0)| hv Example

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Phase Phase Variables

φ DP (°), DP (°), K DP (° DP (° km km -1 -1 ), ), and and δ (°)

(°)

φ DP

φ

sys m

DP

= φDP

+ φDP

+ δ +

ES

■ φ DP is the measured two-way way differential propagational

phase shift

■ φ

sys DP is the system, or initial (r(

= 0), φ DP

■ φ DPm is the φ DP owing to the propagation medium

■ δ is the backscatter differential phase

■ ES stands for Error Sources

int 1 ∂φ

K

DP

=

– System noise

2 ∂r

– Nonuniform beamfilling

– Sidelobe contamination

– Statistical uncertainty of estimate

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

m

DP

Measures amount and shape

Good for R

φ DP

φ DP Example

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Dual. Pol. . Hydrometeor Classification

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Dual. Pol. . Precipitation Estimation

Courtesy of Dr. Alexander Ryzhkov

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Dual. Pol. . of Tornadic Supercell

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

different viewing

angles give the

quasihorizontal

wind field

Dual Doppler

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

Dual Doppler (Cont.)

■ The anelastic continuity equation

∇ ⋅( ρ0

v) = 0

can then be used to diagnose the vertical wind field

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METR 3223: Weather Radar (aliasing, dual-pol., and dual-Doppler)

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