High-Resolution X-band Dual-Polarization Weather Radar: Theory and Applications Sense and Nonsense on precipitation and drop size distribution estimation.

High-Resolution X-band Dual-Polarization High-Resolution X-band Dual-Polarization Weather Radar: Theory and ApplicationsWeather Radar: Theory and Applications

Sense and Nonsense on precipitation and drop size distribution estimation

Background on Radar Physics

Ice

Rain

Hydrometeor

hh

w

hK

Z

25

4

– wavelength of the radarhh – Radar cross section at horizontal polarizationKw – dielectric factor of water

4RPr

Background on Radar Physics

the reflected power returned to the radar is related to the size, shape, and the reflected power returned to the radar is related to the size, shape, and ice density oice density of f each cloud and precipitation particle that it illuminates. each cloud and precipitation particle that it illuminates.

Well, think of the radar as a big flash light. If you are standing in a dark Well, think of the radar as a big flash light. If you are standing in a dark room with a flashlight, the closer you are to a wall, the brighter the room with a flashlight, the closer you are to a wall, the brighter the beam is and the smaller the area that it illuminates. However, as you beam is and the smaller the area that it illuminates. However, as you back away from the wall, the weaker the returned power and the larger back away from the wall, the weaker the returned power and the larger the area that is illuminated. Such is the case with radars. As you get the area that is illuminated. Such is the case with radars. As you get further from the cloud, the width of the radar beam broadens, the power further from the cloud, the width of the radar beam broadens, the power becomes more diffuse, and the number of cloud and precipitation becomes more diffuse, and the number of cloud and precipitation particles "illuminated" by the radar becomes larger. particles "illuminated" by the radar becomes larger.

Background on Radar PhysicsReturn echoes from targets, reflectivity, are analyzed for their intensities in order to establish the precipitation rate in the scanned volume. The wavelengths used (1 to 10 cm) ensure that this return is proportional to the rate because they are within the validity of Rayleigh scattering which states that the targets must be much smaller than the wavelength of the scanning wave (by a factor of 10).

How small is small? From the figure above, the radius of the particle, a, must be

2a (~ 1/6 of the wavelength)

Background on Radar PhysicsA "Doppler" radar has the capability of measuring some information about winds (on top of the usual echo strength all radars measure) by using the Doppler effect.

The most common wind information measured by a Doppler radar is the radial velocity, which is the component of the wind going in the direction of the radar (either towards or away).

f

cPRFu

4

Dual-Polarization Technology1. Differential reflectivity ZDR

2. Total differential phase ΦDP

3. Specific differential phase KDP

4. Cross-correlation coefficient ρhv

Zv

Zh

)dB(Z)dB(Z)dB(Z vhDR ZDR depends on the particle size, shape, orientation, and density

Differential reflectivity ZDR

Dual-Polarization Technology

time

H

H

V

V

time

ΦDP

ΦDP

ΦDP is not affected by radar miscalibration, attenuation, and partial beam blockage

Cross-correlation coefficient ρhv

H and V are complex voltages and Ph and Pv are powers of radar signals at orthogonal polarizations

• ρhv is an important parameter for data quality assessment and classification of radar echoes

• ρhv is high (close to 1) for rain (have most uniform shape) and dry snow, moderately low for hail and wet snow in the melting layer (mixture of different shapes and particles sizes generally exceed those that satisfy the conditions of Rayleigh scattering), snow and very low for non meteorological scatterers (ground clutter /AP, biological scatterers, chaff, and tornado debris)

Polarimetric Rainfall Retrieval Algorithms

•R=sZR=sZhhtt (classic estimator)(classic estimator)

•R=aKR=aKdpdpbb

•R=aZR=aZhhbbKKdpdp

bbZZdrdrdd (Matrosov et al. 2002) (Matrosov et al. 2002)

•R=aZR=aZhhbbZZdrdr

cc

•R/NR/Nww=c(A=c(Ahh/N/Nww))dd (Testud et al. 2000)(Testud et al. 2000)

R/NR/Nww=s(Z=s(Zhh/N/Nww))t t with s, t, c, d depending on droplets shape factor b with s, t, c, d depending on droplets shape factor b

or equivalently or equivalently γγ(b), (Anagnostou et al. 2004)(b), (Anagnostou et al. 2004)

•R= aZR= aZhhbb, Z, Zhh<=35 dBZ (Park et al. 2005)<=35 dBZ (Park et al. 2005)

cKcKdpdpdd , Z , Zhh> 35 dBZ> 35 dBZ

Drop Size Distribution Retrievals• Let assume that the DSDs are typically represented by a

“normalized” gamma: N(D) = F(D0,Nw,μ);

μ: is the distribution-shape parameter;D0: is the raindrop median volume diameter;

Nw: is the normalized intercepted parameter.

76.3

1

,

0

0

D

fmm

ZZfN

ZfD

DRHw

DR

DSDs estimated from Radar productsDSDs estimated from Radar products

Mass-weighted mean diameter (Dm = f(D0,μ)

Large Operational Radar NetworksLower frequencies (S-/C-band or longer wavelengths) are used for operational radar networks in US (WSR-88D) and other countries such as in Europe and Canada:• Low attenuation;• Long range rainfall detection (> 150 km);

Empirical: Z = a REmpirical: Z = a Rbb (e.g. Z= 300 (e.g. Z= 300 RR1.41.4, Nexrad), Nexrad)

Open Issues with Large Operational Radars•Z-R relations changes for different raindrop size spectra.

•Low spatial resolution (2x2 to 4x4 km2); issues on detecting localized intense convective systems; Therefore issues on monitoring small flood prone watersheds;

• Complex terrain environments introduces marginal gaps to the operational radar network coverage; Furthermore, it requires the use of higher elevations that lead to problems in the retrieval due to VRP effects.

• Current operational radar systems use single polarization that introduces uncertainties due to the significant variability in reflectivity-rainfall relationship;

• Issues with radar calibration, which introduces biases on the rain measurements. Use of rain gauge data are one approach on removing mean radar biases, but has limitations, especially in cases of sparse gauge networks and high precipitation variability.

Proposed solutions….• Small inexpensive systems could possibly used as ‘gap filler’ of the large Small inexpensive systems could possibly used as ‘gap filler’ of the large operational radar networks; short range hydrological applications.operational radar networks; short range hydrological applications.

• Polarimetric capability would introduce additional variables (ZPolarimetric capability would introduce additional variables (ZDRDR & & ΦΦDPDP); );

needed to create more stable estimation algorithms;needed to create more stable estimation algorithms;

• X-band frequency offers an increased sensitivity on differential phase-based estimation of weak targets (such as stratiform rain rates) compared to S-band and C-band systems (a factor of 3).

• a radar beam at X-band is associated with greater resolution than the lower frequencies (S-band/C-band) for the same antenna size, and is less susceptible to side lobe effects.

x3x3…but there are open issues…

• Limits on attenuation correction place limits on DSD retrieval ;• Deal with resonance effects in cases of high concentrations of large drop diameters (e.g. δ effect in DP);• Deal with mixed phase precipitation where polarimetric signal is low;• Algorithms are sensitive to choices we make concerning raindrops: oblateness-size relation, measurement noise, hydrometeor phase, and DSD model.

High-Resolution X-band Dual-Polarization Mobile Weather Radar

• 9.37 GHz simultaneously (copolar) transmission at horizontal and vertical transmission, 60 kW peak power

• PIRAQ (NCAR)• GPS position and alignment, wireless operation• 0.9o 3dB-beamwidth, selectable pulse length (40-150m resolution volumes), 60-

80 km normal operation• 0.2-0.3 dB noise of the Zh and Zdr=Zh-Zv, 3ο noise of ΦDP, ρhv, Vr

• 2 dB Zh and1.5 dB Zdr normal calibration with the help of a 2D video disdrometer

2D-Video Disdrometer2D-Video Disdrometer

•Two orthogonal light beams and fast line-scan cameras

•Records the shape, velocity and orientation of particles

(0.2-10 mm diameter) falling through the light beams

•Used in radar calibration (T-matrix theoretical scatter calculations)

•Combined with clusters of tipping rain gauges

0 5 10 15 20 25 30-20

0

20

40

60

80

100

120

140

d

p (

de

g)

range (km)

measuredfilteredestimated

3 km

0 5 10 15 20 25 30-10

0

10

20

30

40

50

60Z

h (

dB

Z)

range (km)

measuredcorrected

XPOL high-resolution data from Athens (2006)

ZPHI (Testud et al. 2000) with combined Φdp-Zdr constraint self consistent method (Bringi et al. 2001) in rain cells defined by ρhv>0.8. The method is independent of calibration.

XPOL high-resolution measurements in highly complex terrain: Crete

Partial beam blockage of the radar beam(α) (β)

Brightband Effect

mean profile Zh (VPR)

ideal situation Zh

(Matrosov et al. 2007)

ΔΖΔΖ1

hbase

htop

β

clear melting layer

bright band enhancement of Zh overestimates rain with e.g. Z-R method

problems due to discontinuity of bright band

ΔZ(dBZ) = f(r) (r in km)

ΔZ1 ~ 1.5 dBZ

)/(3.7 KmdB

smoothing effect

Correcting PPIs due to bright band effect

melting layer (bright band) boundaries detection based on ρhv

XPOL high-resolution measurements in Mountainous Terrain: HO Italian Alps.

3-deg 2-deg