High-Resolution X-band Dual-Polarization
Weather Radar: Theory and Applications
Sense and Nonsense on precipitation
and drop size distribution estimation
Background on Radar Physics
Hydrometeor
Ice
Rain
Pr 

R4
 4 
 
Zh   5
  K 2  hh
w 

 – wavelength of the
radar
hh – Radar cross
section at horizontal
polarization
Kw – dielectric factor of
water
Background on Radar Physics
the reflected power returned to the radar is related to the size, shape, and
ice density of 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
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
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
further from the cloud, the width of the radar beam broadens, the power
becomes more diffuse, and the number of cloud and precipitation
particles "illuminated" by the radar becomes larger.
Background on Radar Physics
Return 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

a
2
(~ 1/6 of the wavelength)
Background on Radar Physics
A "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).
cPRF
u  
4f
Dual-Polarization Technology
1. Differential reflectivity ZDR
2. Total differential phase
ΦDP
3. Specific differential
phase KDP
4. Cross-correlation
coefficient ρhv
Differential reflectivity ZDR
Zv
Zh
ZDR (dB)  Zh (dB)  Z v (dB)
ZDR depends on the particle size, shape,
orientation, and density
Dual-Polarization Technology
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
H
• ρhv is an important parameter for data quality
assessment and classification of radar echoes
V
time
H
ΦDP
V
ΦDP
• 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
time 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=sZht
• R=aKdpb
• R=aZhbKdpbZdrd
(classic estimator)
(Matrosov et al. 2002)
• R=aZhbZdrc
• R/Nw=c(Ah/Nw)d
(Testud et al. 2000)
R/Nw=s(Zh/Nw)t with s, t, c, d depending on droplets shape factor b
or equivalently γ(b), (Anagnostou et al. 2004)
• R=
aZhb, Zh<=35 dBZ (Park et al. 2005)
cKdpd
, Zh> 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.
DSDs estimated from Radar products
D0  f Z DR 
N w  f Z H , Z DR 
 1 

  f  
 m m
D0  3.76  
Mass-weighted mean diameter (Dm = f(D0,μ)
Large Operational Radar Networks
Lower 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 Rb (e.g. Z= 300
R1.4, 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
• X-band frequency offers an increased sensitivity on differential phaseoperational radar networks; short range hydrological applications.
based estimation of weak targets (such as stratiform rain rates)
compared to S-band and C-band systems (a factor of 3).
• Polarimetric capability would introduce additional variables (ZDR & ΦDP);
needed to create more stable estimation algorithms;
• 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.
…but there are open issues…
x3
• 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 FDP);
• 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), 6080 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 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
XPOL high-resolution data from Athens (2006)
140
60
120
50
40
80
Zh (dBZ)
Fdp (deg)
100
measured
corrected
30
ZPHI
(Testud
et
al.
2000)
with
combined
Φdp-Zdr constraint self
60
20
40
consistent
method (Bringi et al. 2001) in rain cells defined by ρhv>0.8.
10
measured
The20method is independent
of
calibration.
filtered 3 km
0
-20
0
estimated
5
10
15
range (km)
20
25
30
0
-10
0
5
10
15
range (km)
20
25
30
XPOL high-resolution measurements in
highly complex terrain: Crete
Partial beam blockage of the radar beam
(α)
(β)
Brightband Effect
clear melting layer
smoothing effe
problems due to discontinuity
of bright band
ΔZ(dBZ) = f(r) (r in km)
mean profile Zh (VPR)
β
ideal situation Zh
htop
(Matrosov et al. 2007)
hbase
ΔZ1 ~ 1.5 dBZ
  7.3 (dB / Km)
ΔΖ1
ΔΖ
bright band
enhancement
of Zh
overestimates
rain with e.g.
Z-R method
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