Polarization I: Radar 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 by the CHILL radar in Oklahoma, 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 pulse Backscattered 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 part I

Scattering matrix multiplication result E b v = S vv E inc v + S vh E inc h E b h = S hv E inc v + S hh E inc h S vh 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 (Z dr ) 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=√ε r Bringi and Chandra (2001), eq 7.5b,c and appendix 1 Depends on composition and shape!

Basic S hh /S vv ratios (white text) for specified oblate scatterers  r from BC2001; water = 81; ice = 3.5) S hh and S vv calculated from previous equations. Z dr calculated accordingly. Main point: Zdr sensitivity to aspect ratio decreases as particle bulk density (as expressed by  r relative permittivity) decreases Axis ratiowaterZDRSolid IceZDR.5*ice  r ZDR.6 (oblate) dB dB dB.9 (oblate) dB dB dB

Single particle Z dr expressed as dB, curves labeled by  r Z dr (dB)=10 log 10 ((S hh / S vv ) 2 ) Plot from Herzegh and Jameson (1992)

Raindrop Characteristics and Z dr Equilibrium drop shape due to balance of surface tension and aerodynamic pressure distribution around the drop

Beard and Chuang drop shapes From 2 mm to 6 mm in 0.5 mm steps

1 < D < 9 mm; Pruppacher and Beard (1970); wind tunnel measurementsmm b/a = x10 -4 (D) – 2.628x10 -2 (D) x10 -3 (D) x10 -4 (D) 4 0 < D < 7 mm Beard and Chuang (1987); polynomial fit to numerical simulations Equations agree for D> 4 mm PB relation gives slightly more oblate drops compared to poly fit for D < 4 mm Size-shape relationships

Rayleigh-Gans Z dr 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 = – D – (D) 2 1 < D < 4 mm Fit 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: D 0 = median drop diameter; divides total water content in half D m = mass weighted mean drop diameter Mean fit equations for the above two quantities as f(Z dr ) based on thunderstorm-type DSD’s (Bringi and Chandra 2001, 7.14):

Verification of Z dr -estimated and observed D m (Bringi and Chandra (2001)

Courtesy: Kristen George

8 Sept 2002 (tropical)19 Sept 2002 (trailing squall line) Rainfall Measurement with Polarimetric -88D (JPOL 2003)

Z dr typically used to adjust basic reflectivity-based rain rate estimator for variations in D 0, etc. Low Z dr in rain -> small D 0 -> reflectivity estimator low; Use of Z dr in the denominator will adjust Z rain rate up Ryzhkov et al. (2005)

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

Ft. Collins flood: 29 July UTC CSU-CHILL 2 km MSL CAPPI Using the NEXRAD relationship R = 0.017Z This relationship is normally truncated at 55 dBZ to avoid hail contamination Using the relationship R = cZ a bZdr Where a = 0.93 b= c= 6.7 x 10 -3

R(Z) rain rates low relative to R(Z, Zdr) in tropical (small D 0 ) rain A sample from the Ft. Collins flood……….

hail rain H V Z dr = 10 log 10 (Z hh /Z vv ) 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 no polarization 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 measured Z h will exceed Z h for rain. Whereas Z dp will be approximately the same since it is insensitive to ice. So the data point formed by Z h and Z dp will lie to the right of the rain line. The distance between the vertical red lines denotes ΔZ, that is, Z h measured minus Z h,rain. Here f is the so called ice fraction, the ratio of the ice reflectivity factor to the total reflectivity factor. For delta Z = 3 dB, f is 50%. For delta Z = 10 db, f is 90%. That is, 90% of Z total is due to ice. So the difference reflectivity is very useful for determining mixed phase microphysics. -

Not all frozen hydrometeors have quasi-spherical shapes and ~0 dB Zdr. Two cold season examples: Positive Zdr layers also noted near -15 o C level in active crystal growth regimes Positive Zdr’s often occur in pristine, un-aggregated crystals near echo top