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

2. Background on Radar Physics
Hydrometeor
Ice
Rain
l – wavelength of the radar
shh – Radar cross section at horizontal polarization
Kw – dielectric factor of water

3. 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.

4. 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
(~ 1/6 of the wavelength)

5. 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).

6. Dual-Polarization Technology
Differential reflectivity ZDR
Total differential phase ΦDP
Specific differential phase KDP
Cross-correlation coefficient ρhv
Differential reflectivity ZDR Zv Zh
ZDR depends on the particle size, shape, orientation, and density

7. 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
time H V
ΦDP
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)

8. Polarimetric Rainfall Retrieval Algorithms
R=sZht (classic estimator)
R=aKdpb
R=aZhbKdpbZdrd (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

9. 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
Mass-weighted mean diameter (Dm = f(D0,μ)

10. 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)

11. 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.

12. Proposed solutions…. …but there are open issues…
Small inexpensive systems could possibly used as ‘gap filler’ of the large operational radar networks; short range hydrological applications.
Polarimetric capability would introduce additional variables (ZDR & ΦDP); 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. x3
…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 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.

13. 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), km normal operation
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

14. 2D-Video Disdrometer
Two orthogonal light beams and fast line-scan cameras
Records the shape, velocity and orientation of particles
( mm diameter) falling through the light beams
Used in radar calibration (T-matrix theoretical scatter calculations)
Combined with clusters of tipping rain gauges

15. XPOL high-resolution data from Athens (2006)
3 km
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.

16. XPOL high-resolution measurements in highly complex terrain: Crete

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

18. Brightband Effect clear melting layer smoothing effect
mean profile Zh (VPR)
ideal situation Zh
(Matrosov et al. 2007) ΔΖ
ΔΖ1
hbase
htop β
problems due to discontinuity
of bright band
bright band enhancement of Zh overestimates rain with e.g. Z-R method
ΔZ(dBZ) = f(r) (r in km)
ΔZ1 ~ 1.5 dBZ

19. Correcting PPIs due to bright band effect
melting layer (bright band) boundaries detection based on ρhv

20. XPOL high-resolution measurements in Mountainous Terrain: HO Italian Alps.
3-deg
2-deg