Environmental Engineering Reference
In-Depth Information
Reflectivity factor
Multi-Parameter Radar andDual-Polarization
Measurements
The reflectivity factors at horizontal and vertical
polarizations are given by:
Radar generates a pulse of high-power microwave
(electromagnetic) energy in some specific direc-
tion. This pulse travels at the speed of light and if a
reflective target (e.g. precipitation particles) lies
along the path of the beam, then a small percent-
age of the energy is reflected back (also at the speed
of light) to the radar and collected by the antenna.
This backscattered energy can then be related to
the rainfall rate using empirical equations. Its
location can be determined from the direction of
the radiated pulse and the time it took to travel
fromthe radar to the target and back again. In order
to fully exploit and interpret the backscattered
electromagnetic radiation from hydrometeors, it
is necessary to take into account four fundamental
properties of electromagnetic waves: the ampli-
tude, phase, frequency and polarization (Jameson
and Johnson 1990) of the signal. The use of the
reflectivity factor Z
h
exploits the amplitude prop-
erty and has been themost important parameter in
the estimation of precipitation from the earliest
days of weather radar development. However,
there are several sources of uncertainty using the
reflectivity factor that can be minimized by the
use of dual-polarization techniques. The dual-
polarization measurements are sensitive to size,
shape, orientation and phase of the hydrometeors
(Herzegh and Jameson 1992) and can in principle
improve the estimation of precipitation from
weather radars (Zrnic and Ryzhkov 1999). How-
ever, the practical realization of the potential from
these additional measurements can be limited by
the electromechanical problems inherent in cur-
rent dual-polarization radar technology.
Dual-polarization weather radars alternately
transmit vertically and horizontally polarized
electromagneticwaves and receive polarized back-
scattered signals. The backscattering characteris-
tics of a single precipitation particle are described
in terms of the backscattering matrix S (Bringi and
Chandrasekar 2001). The dual-polarization radar
measurements (Bringi and Hendry 1990) are
related to the scattering elements of the backscat-
tering matrix and they are defined below.
ð
4
l
Z
h
;
v
¼
s
h
;
v
ð
D
Þ
N
ð
D
Þ
dD
ð
7
:
1
Þ
2
p
5
K
jj
where D is the drop diameter, l is the radar wave-
length, K
2
is the refractive index of the hydro-
meteors (approximately 0.93 for water and 0.20 for
ice),
sð
jj
Þ
is the backscattering cross-sections of
the scatterers and N(D) is the drop size distribu-
tion. If the scatterers are considered to be water
spheres with small radii when compared to the
radar wavelength, then the approximation due to
Rayleigh applies andEquation 7.1 can be expressed
as:
D
ð
D
6
N
Z
¼
ð
D
Þ
dD
ð
7
:
2
Þ
Differential reflectivity
Pruppacher and Beard (1970) found that large
raindrops falling to the ground are generally dis-
torted into oblate spheroids due to aerodynamic
forces. Their maximal dimensions are horizon-
tally oriented even when turbulence, drop colli-
sions and aerodynamic instability may disturb
their orientation. Taking advantage of this, Seliga
and Bringi (1976) proposed the use of differential
reflectivities at orthogonal polarizations to im-
prove the estimation of precipitation. The back-
scattering cross-section for raindrops is larger for
a horizontal polarized wave than for a vertical
polarized wave and the differential reflectivity is
given by:
Z
h
Z
v
Z
dr
¼
10 log
ð
7
:
3
Þ
Seliga and Bringi (1976) showed that the mean
volumetric diameter of raindrops is related to the
value of Z
dr
. Therefore Z
dr
is a measure of the
