Geoscience Reference
In-Depth Information
4. Some quantitative examples in Sicily and Piedmont
4.1 Quantitative precipitation estimation (QPE)
While Section 3 dealt with qualitative examples, in the present Section 4 we will present
hourly radar-derived precipitation amounts as obtained from weather echoes aloft to be
compared with point rainfall measurements acquired at the ground by rain gauges.
4.1.1 From instantaneous radar reflectivity to hourly rain rate amounts
We have seen in Sec. 2.3 that the mini-radar finally provides an instantaneous radar
reflectivity value once per minute for each radar bin of 3° by 120 m. This value is in turn the
average of 288 samples (among them, at least 32 samples are independent, see Sec. 2.3).
It is well known that the backscattered power caused by rain drops is, unfortunately, only
indirectly linked to the rain rate, R ([R] = mm/h). The backscattered power caused by the
hydrometeors and detected by the radar is, in fact, directly proportional to the radar
reflectivity factor, Z. A fundamental quantity for precise assessment of both Z and R is the
drop size distribution (DSD), N(D), which is defined as the number of rain drops per unit
volume in the diameter interval D, i.e. between the diameter D and D+D. The radar
reflectivity factor, Z, is defined as the 6
th
moment of the DSD, namely:
6
.
(1)
ZNDDdD
()
0
In radar meteorology, it is common to use the dimensions of mm for drop diameter, D, and
to consider the summation (integral) to take place over a unit volume of 1 m
3
. Therefore, the
conventional unit of Z is in mm
6
/m
3
. For the assessment of rain rate, another fundamental
quantity is needed: the terminal drops fall velocity as a function of the diameter, (D). Since
it is common to use [] = m/s, then the relationship is
4
3
.
(2)
R
610
( )
D D v D dD
( )
0
If precipitating hydrometeors in the radar backscattering volume were all spherical raindrops
(which is almost never the case!) and the DSD could be described to a good approximation by
an exponential DSD, then a simple power-law would relate Z to R. The first ever exponential
DSD presented in a peer-reviewed paper and probably the most quoted is the Marshall-
Palmer (M-P) distribution. The power law derived using the exponential fit proposed in Eq. (1)
and (3) of the famous paper by
Marshall and Palmer
[1948] is Z=296R
1.47
.
Here we have used the following Z-R relationship Z = 316R
1.5
to derive the variable of
interest, R, from the geophysical observable, Z, which is detected by the meteorological
radar. Such values have been retrieved by
Doelling et al.
[1998] using seven years of
measurements in central Europe. It is also worth noting that for the 2 radars in Sicily prior to
any processing, the radar reflectivity values were increased by 4 dB to compensate system
losses not properly compensated in the ''traditional'' radar equation.
For each radar bin, a maximum of 60 clutter-free radar reflectivity values are then
transformed into R using
2/3
RZ
(
/ 316)
and then averaged to derive the corresponding
hourly rain rate used in this study.
