Geoscience Reference
In-Depth Information
volume that is detected. The average returned power,
P
, received at the radar
receiver from a hydrometeor-filled atmosphere at range,
r
, between the radar and
the measured sample is given by:
CAZ
P
=
rr
(12.1)
r
where
C
r
is a constant determined by the design of the system and dependent on
the beam width, antenna gain, wavelength, and pulse duration, etc;
A
r
is a factor
representing the signal attenuation during its transit through the atmosphere; and
Z
is the
radar reflectivity factor
for the volume of atmosphere sampled by the radar
beam which is usually expressed in units of mm
6
m
−3
.
The estimated rainfall rate in mm hr
−1
,
R
, is related to the radar reflectivity fac-
tor,
Z
, by a semi-empirical power law often called the
Z-R relationship
with the
form:
b
RaZ
=
(12.2)
At microwave wavelengths, the return signal is generated by Rayleigh scattering,
which means the strength of the return signal expressed in the form of the radar
reflectivity factor is proportional to the sixth power of the diameter of the hydro-
meteors. Consequently, the sensitivity of the system is strongly influenced by the
unknown range of hydrometeor diameters present in the sample. The values of the
empirical parameters
a
and
b
in Equation (12.2) are determined by the very vari-
able size spectrum of the hydrometeors and are poorly defined. For the WSR-88D
network that covers the USA (see, for example, http://www.erh.noaa.gov/ohrfc/
ZRlisting.shtml) typical values for
a
are in the range 130-300 and for
b
in the
range 1.4-2.0, which implies the system calibration might vary by substantial fac-
tors between rainstorms. A further source of error in the system is that the hydro-
meteors are detected well above the surface so there is potential for them to
evaporate to a variable extent as they fall to the ground. Because the calibration of
the system is inherently poor, when used to estimate rainfall for hydrological
applications radar observations must be continuously recalibrated by merging the
radar estimates with observations from an underlying network of gauges. The
resulting data fields so created are called
merged products
.
The primary application of radar data is to support weather forecasting and
NEXRAD systems of the type shown in Fig. 12.9b have been deployed for this
purpose across the USA in the network shown in Fig. 12.9c. Notwithstanding the
serious calibration issues associated with radar-based precipitation observations,
they have important properties that are potentially of great value for hydrological
science. The data provided as merged radar-gauge products are area-average esti-
mates of precipitation typically for 4 km by 4 km pixels that are available with high
temporal resolution for intervals of the order of minutes. Such data could greatly
enhance skill in flood forecasting and once they have been available for long
enough, also water resource estimation. However, the very different nature of
