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Long-standing Problems

- Distinguishing, ice and liquid phases of precipitation using
- radar
- Identifying specific hydrometeor populations, such as hail or
- supercooled water
- Quantifying, rain, snow and hailfall rates using radar.

Multi-Parameter Measurements

(Measurements of two or more parameters of the radar signal)

- Standard Doppler radar (ZHH, Vr, )
- Polarization radar (signals of two different polarizations are
- processed): Many parameters can be derived

* Note notation: ZHH

Transmitted at horizontal polarization

Received at horizontal polarization

Literature

Zrnic, D. S., and A. Ryzhkov: Polarimetry for Weather Service Radars. BAMS, 1999, 389-406

Doviak and Zrnić, 1993: Doppler Radar and Weather Observations. Academic Press.

Bringi and Chandrasekar, 2001: Polarimetric Doppler Weather Radar. Cambridge University Press.

Vivekanandan, Zrnić, Ellis, Oye, Ryzhkov, Straka, 1999: Cloud microphysical retrieval using S-band dual-polarization radar measurements. Bull. Amer. Meteor. Soc., 80, 381-388.

Straka, Zrnić, Ryzhkov, 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis and Relations. J. Appl. Meteor., 39, 1341-1372.

http://www.nssl.noaa.gov/~schuur/radar.html

Outline

- Polarization of electromagnetic waves

- Linear polarimetric observables (ZDR, LDR, ΦDP (KDP), ρHV,)

- Types of dual-polarization radars today

Research and Applications: - Hydrometeor classification - Rainfall estimates

Circular Polarization

Practical use of circular polarization: Tracking aircraft in precipitation.

Light to moderate rain: removal of a large portion (e.g. 99%) of the precipitation echo (transmitted right-hand circular polarized waves become, when scattered from small spherical drops, left-hand polarized).

Scattering may be Rayleigh or Mie

Scattering cross section for spherical drops assuming Rayleigh scattering

(spherical drops with D small compared to λ)

- Theoretical and experimental work has been done relating particles scattering cross section to other shapes, sizes and mixture of phases.

Copolar power: Power received at the same polarization as the transmitted power

(e.g. transmit horizontal, receive horizontal,

transmit vertical, receive vertical)

Cross-polar power: Power received at the opposite polarization as the transmitted power

(e.g. transmit horizontal, receive vertical,

transmit vertical, receive horizontal)

Two ways in which hydrometeors affect polarization measurements:

Backscatter effects by particles located within the radar resolution volume

Propagation effects by particles located between the radar resolution volume and the radar

Backscatter effects by particles located within the radar resolution volume

Six basic backscatter variables:

1. Reflectivity factor for horizontal polarization ZHH

2. The ratio of the reflected power (or reflectivity factor) at horizontal/vertical polarization (PHH/PVV or ZHH/ZVV) called the Differential Reflectivity (ZDR).

3. The ratio of cross-polar power to copolar power (PVH/PHH) called the Linear Depolarization Ratio (LDR)

Backscatter effects by particles located within the radar resolution volume

Phase difference in H and V caused by backscattering

Six basic backscatter variables:

4. The correlation coefficient between copolar horizontally and vertically polarized echo signals

5. The complex correlation coefficient between copolar horizontal and cross-polar (horizontal transmission) echo E(VHH*VHV)

6. The complex correlation coefficient between copolar vertical and cross-polar (vertical transmission) echo E(VHH*VHV)

Propagation effects by particles located between the radar resolution volume and the radar

1. Attenuation of the horizontal component

2. Attenuation of the vertical component

3. Depolarization

4. Differential phase shift (phase difference in returned signal for the two polarizations) DP

- Depends on axis ratio
- oblate: ZDR > 0
- prolate: ZDR < 0
- For drops: ZDR ~ drop size (0 - 4 dB)

2.7 mm 1.8 mm 1.4 mm

(Pruppacher and Klett, 1997)

Differential Reflectivity ZDR- ZDR [dB]= 10 log( )

zHH zVV

ZDR (cont.)

ZDR = 10 log( )

zHH zVV

- For ice crystals:
- columns (1 – 4 dB)
- plates, dendrites (2 – 6 dB)

(Pruppacher and Klett, 1997)

ZDR (cont.)

zHH zVV

- ZDR = 10 log ( )

- For hail: (-1 – 0.5 dB)
- For graupel: (-0.5 – 1 dB)
- For snow: (0 – 1 dB)

(Pruppacher and Klett, 1997)

ZDR (cont.)

- Independent of calibration
- Independent of concentration (but can depend on how the concentration is distributed among various sizes
- Is affected by propagation effects (e.g. attenuation)

Spheroidal hydrometeors with their major/minor axis aligned or orthogonal to the electric field of the wave: LDR - dB

- Detects tumbling, wobbling, canting angles, phase and irregular shaped hydrometeors:
- large rain drops (> -25 dB)
- Hail, hail and rain mixtures (-20 - -10 dB)
- wet snow (-13 - -18 dB)

8

Linear Depolarization Ratio LDRLDR [dB]= 10 log( )

zHVzHH

4 mm 3.7 mm 2.9 mm

(Pruppacher and Klett 1997)

LDR (cont.)

- Susceptible to noise (cross-polar signal is 2-3 orders of magnitude smaller than copolar signal)
- Independent of radar calibration
- Independent of number concentration
- Lowest observable values : -30 dB (S-Pol), -34 dB (Chill)

Differential Propagation Phase ΦDP

ΦDP [deg.]= ΦHH – ΦVV

ΦHH, ΦVV: cumulative differential phase shift for the total round trip between radar and resolution volume).

ΦHH, ΦVV = differential phase shift upon backscatter

+ differential phase shift along the propagation path

ΦDP (cont.)

ΦDP = ΦHH – ΦVV

- Statistically isotropic particles produce similar phase shifts for horizontally and vertically polarized waves.
- Statistically anisotropic particles produce different phase shifts for horizontally and vertically polarized waves.
- A volume with oblate hydrometeors (large rain, ice crystals): horizontal polarized wave propagates more slowly than vertically polarized wave => larger phase shifts (ΦHH) per unit length => ΦDP increases.

ΦDP (cont.)

(Doviak and Zrnić, 1993)

ΦDP (cont.)

(Doviak and Zrnić, 1993)

2(r2 – r1)

Specific Differential Propagation Phase KDPKDP [deg/km] =

- Independent of receiver/transmitter calibration
- Independent of attenuation
- Less sensitive to variations of size distributions (compared to Z)
- Immune to particle beam blocking

Correlation Coefficient ρHV

Correlation between horizontally and vertically polarized weather signals

Physical occurrence of decorrelation: Horizontal and vertical backscatter fields, caused by each particle in the resolution volume, do not vary simultaneously.

ρHV (cont.)

(Doviak and Zrnić, 1993)

ρHV (cont.)

- Influenced by particle mixture (e.g. rain/hail mixture)
- Influenced by the differential phase shifts ΦHH, ΦVV (e.g. oscillation of large drops)
- Influenced by the distributions of eccentricities (e.g. oscillation of large drops)
- Influenced by canting angles (large drops)
- Influenced by irregular particle shapes (e.g. hail, graupel)

ρHV (cont.)

- Independent of radar calibration
- Independent of hydrometeor concentration
- Immune to propagation effects

S-Pol (NCAR)

- NSF funded
- S-band dual polarization Doppler radar
- Highly mobile (fits in 6 sea containers)
- Antenna diameter 8.5 m
- Beam width 0.91 deg
- Range resolution 150 m

(Photos: Scott Ellis)

Chill (CSU)

- NSF funded
- S-band dual polarization Doppler radar
- Antenna diameter 8.5 m
- Beam width (3 dB) 1.1 deg
- Range resolution 50, 75, 150 m

Dual-polarized Radar Systems

(Polarization-agile/dual-receiver systems)

S-Pol

Chill

(Bringi and Chandrasekar, 2001)

Koun WSR-88D Radar(NSSL Norman, OK)

- Polarimetric upgrade of NEXRAD radar, completed in March 2002
- Simultaneous/hybrid transmission scheme

Wyoming King Air Cloud Radar (UW)

- K-band
- Dual/single polarization Doppler radar
- Beam width 0.4 – 0.8 deg (depending on antenna type)
- Antenna configurations down, side, up

NOAA Developments

- Millimeter-wave cloud radar (MMCR) to study the effects of clouds on climate and climate change
- Ground-based cloud radar for remote icing detection (GRIDS) to provide automated warnings of icing conditions
- Mobile X-band dual-polarization Doppler radar (Hydro-Radar) to study storm dynamics, boundary layer turbulence and ocean-surface characteristics

DLR

- C-band
- First meteorological radar system designed to measure time-series of “instantaneous” scattering matrices

Polarization variables from Cimmaron radar, which is located north of the squall line

Attenuation

Note KDP vs Z estimate of rain

Hydrometeor classification

Vivekanandan, Zrnić, Ellis, Oye, Ryzhkov, Straka, 1999: Cloud microphysical retrieval using S-band dual-polarization radar measurements. Bull. Amer. Meteor. Soc., 80, 381-388.

- Algorithm runs in real time
- Based on a fuzzy logic method

Overall Design

Real time application

Fuzzy logic technique

5 observed and computed polarimetric variables

Temperature profile

Hydrometeor type

Result: For each volume element one particle type

Reflectivity

1

hail

0

35 45 55 65

ZDR

Membership functions

1

0

LDR

-1 0 1 2

1

0

-30 -25 -20 -15

FuzzificationRain Hail

P= 0.8 0.2

P= 1 0

P= 0.5 0.1

Sum= 2.3 0.3

Z = 47 dBZ

ZDR = 1.2 dB

LDR = -24

Other Algorithms

Precursor: Hard boundaries

Successor: neuro-fuzzy system (combination of neural network and fuzzy logic)

The performance of a fuzzy logic classifier depends critically on the membership functions. A neuro-fuzzy system learns from data and can adjust the membership functions.

Rainfall Estimation

- Attempt to solve the inverse electromagnetic problem of obtaining – resolution volume averaged – rainrates from backscatterer measurements such as Z, ZDR and KDP together with an underlying rain model.
- One Z-R relationship used by WSR-88D radars:
- R(Z) = 0.017 Z
- Requires accurate knowledge of the radar constant
- Prone to errors in absolute calibration

0.714

R(Z, ZDR) Algorithm

a1 0.1 b1 ZDR

R = c1 Zh 10 [mm/h]

- ZDR can be measured accurately without being affected by absolute calibration errors

Table from Bringi and Chandrasekar, 2001

R(KDP) Algorithm

0.85

R = 40.5 (KDP) [mm/h]

- Valid for 10 cm wavelength and the Pruppacher and Beard model for the raindrop shape
- Unaffected by absolute calibration errors and attenuation
- Unbiased if rain is mixed with spherical hail
- KDP is relative noisy at low rainrates
- Estimated over finite path (trade off between accuracy and range resolution)

Standard Deviation KDP

(Bringi and Chandrasekar, 2001)

R(KDP, ZDR) Algorithm

a3 0.1 b3 ZDR

R = c3 KDP 10 [mm/h]

- ZDR can be measured accurately without being affected by absolute calibration errors

Table from Bringi and Chandrasekar, 2001

Advantages

- Distinction of rain from other types of hydrometeors possible (important step prior to rainfall estimates)
- Estimation of rainfall rates not only on the ground (vertical structure gives insight in precipitation processes)

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