Polarization I:Polarization I:Radar concepts and ZDR part IRadar concepts and ZDR part I

Dual polarization radars can estimate several return signal properties beyond those available from conventional, single polarization Doppler systems.

Consider a dual linear polarization coherent radar in which both transmission and reception are possible in the horizontal (H) and vertical (V) polarization states. (Polarization defined by plane in which electric field lies).

Some useful quantities that such a radar can measure are:

Ratio of the H and V signal powers (ZDR)

Phase difference between the H and V returns (dp)

Degree of correlation between the H and V returns (hv)

Ratio of orthogonal to “on channel” signal power (LDR)

Seliga and Bringi, 1976 J. Appl. Meteor.

First measurements of Zdr made bythe CHILL radar in Oklahoma, 1977.

Alternating HHH, VVV, HHH, VVV……….

Polarization of the electric field transmitted by the radar(and incident on the scatterers) is imposed by internal microwave signal paths in the antenna feed horn.

Backscattered electric field from an individual scatterer is described by the scattering matrix. “S” values are complex numbers that depend on the scatterer shape, orientation and dielectric constant

Incident field due to transmitted radar pulseBackscattered electric

field; contains both H and V components

Here, subscripts are transmit, receive from the particle viewpoint

Largest terms are “co-polar” (repeated subscript) matrix elements

Matrix scanned from Bringi et al. 1986 part I

Scattering matrix multiplication Scattering matrix multiplication resultresult

Ebv = SvvEinc

v + SvhEinch

Ebh = ShvEinc

v + ShhEinch

Svh means particle scatters in v due to

illumination in h

Computation of scattering matrix elements is simplified by considering particle shapes to be spheroids

From appendix 1 of Bringi and Chandra (2001) text

Polarimetric variable #1: Ratio of the co-polar H and V return signal powers: Differential reflectivity (Zdr)

Differential reflectivity ratio: linear scale power ratio as defined in Bringi and Chandra (2001); dependence on

axis ratio (r) and diameter (D) explicitly shown

Co-polar scattering matrix terms under Rayleigh-Gans conditions. V = particle volume; r = relative permittivity;

spheroid axis lengths = a,b; z = depolarizing factor

Recall that n=√εr

Bringi and Chandra (2001), eq 7.5b,c and appendix 1

Depends oncompositionand shape!

Basic Shh/Svv ratios (white text) for specified oblate scatterers

r from BC2001; water = 81; ice = 3.5)

Shh and Svv calculated from previous equations. Zdr calculated accordingly.

Main point: Zdr sensitivity to aspect ratio decreases as particle bulk density (as expressed by r relative permittivity) decreases

Axis ratio water ZDR Solid Ice ZDR .5*ice r ZDR

.6 (oblate) 1.79 5.0 dB 1.32 2.43 dB 1.13 1.09 dB

.9 (oblate) 1.13 1.05 dB 1.06 0.5 dB 1.03 0.22 dB

Single particle Zdr expressed as dB, curves labeled by r

Zdr (dB)=10 log10 ((Shh / Svv)2)

Plot from Herzegh and Jameson (1992)

Raindrop Characteristics and Zdr

Equilibrium drop shape due to balance of surface tension and aerodynamic pressure distribution around the drop

Beard and Chuang drop shapesFrom 2 mm to 6 mm in 0.5 mmsteps

/ 1.03 0.062( )b a D 1 < D < 9 mm; Pruppacher andBeard (1970); wind tunnel measurementsmm

b/a = 1.0048 + 5.7x10-4(D) – 2.628x10-2(D)2 + 3.682x10-3(D)3

- 1.677x10-4 (D)4 0 < D < 7 mm

Beard and Chuang (1987); polynomial fit to numerical simulations

Equations agree for D> 4 mmPB relation gives slightly more oblate drops compared to polyfit for D < 4 mm

Size-shape relationships

Rayleigh-Gans Zdr from equilibrium (single) drop shape

Plot from Herzegh and Jameson (1992)

Drop oscillations occur as diameter exceeds ~1 mm

Image of modeled drop oscillations from K. Beard UIUC

Vortices shed in drop wake flow can help induce / sustain drop oscillations

Saylor and Jones, Physics of Fluids (2005)

On average, observed raindrop shapes are somewhat less oblate than equilibrium force balance would dictate. Turbulent air motions and drop collisions also

broaden the observed axis ratio range at a given diameter

Andsager et al., (1999; laboratory study using 25m fall column)

Range of size/shape relationships

b/a = 1.012 – 0.01445D – 0.01028 (D)2 1 < D < 4 mmFit to lab data

Lab study

Basic exponential DSD: N(D)=N0*e-D (D=diameter; is the slope parameter).Here, N0’s have been adjusted to give the same reflectivity.Zdr is the reflectivity factor-weighted mean axis ratio of the drop size distribution.Drop population shift towards smaller diameters on the right is revealed by lower Zdr.(Note: rain rate estimation based on Z alone would be the same for these two DSD’s.)

(See Andsager et al, JAS, 1999 equations 3 and 4)

Integral quantities from the rain DSD:

D0 = median drop diameter; divides total water content in half

Dm = mass weighted mean drop diameter

Mean fit equations for the above two quantities as f(Zdr) based on thunderstorm-type DSD’s (Bringi and Chandra 2001, 7.14):

Verification of Zdr-estimated and observed Dm (Bringi and Chandra (2001)

Courtesy: Kristen George

8 Sept 2002 (tropical) 19 Sept 2002 (trailing squall line)

Rainfall Measurement with Polarimetric -88D (JPOL 2003)

Zdr typically used to adjust basic reflectivity-based rain rate estimator for variations in D0, etc.

Low Zdr in rain -> small D0 -> reflectivity estimator low;

Use of Zdr in the denominator will adjust Z rain rate up

Ryzhkov et al. (2005)

B. Amer. Met. Soc., February, 1999

Ft. Collins flood: 29 July 1997 0208 UTC CSU-CHILL 2 km MSL CAPPI

Using the NEXRAD relationshipR = 0.017Z 0.714

This relationship is normally truncated at 55 dBZ to avoid hail contamination

Using the relationshipR = cZa 10 0.1bZdr

Where a = 0.93b= -3.43c= 6.7 x 10-3

R(Z) rain rates low relative to R(Z, Zdr) in tropical (small D0) rain

A sample from the Ft. Collins flood……….

hail

rainH

V

Zdr = 10 log10 (Zhh/Zvv)

Hail signal, Z and Zdr.

Insects are typically more oblate than raindrops, giving highly positive Zdr values.Zdr magnitudes and spatial textures are useful in identifying non-meteorological targets.

Difference Reflectivity, Z dp

For a rain-ice mixture, we can write:

Ice is isotropic so there is nopolarization dependence.

Therefore we can form the difference reflectivity as:

Difference reflectivity only sensitive to oblate drops in the mixture.

Bringi and Chandrasekar (2001)

When ice is present, the measuredZh will exceed Zh for rain. WhereasZdp will be approximately thesame since it is insensitive toice. So the data point formedby Zh and Zdp will lie to the right of the rain line. The distance between thevertical red lines denotesΔZ, that is, Zh measuredminus Zh,rain.

Here f is the so called ice fraction, the ratio of the ice reflectivity factor to thetotal reflectivity factor. For delta Z = 3 dB, f is 50%. For delta Z = 10 db, f is90%. That is, 90% of Ztotal is due to ice. So the difference reflectivity is very useful for determining mixed phase microphysics.

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Not all frozen hydrometeors have quasi-spherical shapes and ~0 dB Zdr.Two cold season examples:

Positive Zdr layers also noted near -15oC level in active crystal growth regimes

Positive Zdr’s often occur in pristine, un-aggregated crystals near echo top