Geoscience Reference
In-Depth Information
N
(
D
)
D
6
d
D
.
Z
=
(3.7)
Marshall and Palmer (
1948
) for the first time formulated the distribution
N
(
D
)as
function of drop size
D
in mm and precipitation intensity
R
in mm h
−
1
:
N
0
e
−
D
,
N
(
D
)
=
(3.8)
10
3
m
−
3
mm
−
1
4.1 R
−
0.21
mm
−
1
with
N
0
=
8
·
and
Λ
=
the well-known Z-R
relation is found:
N
0
4.1
−
7
R
1.47
aR
b
.
Z
=
6
!
=
(3.9)
1.47. Today, different
a
and
b
are used for different types of precipitation. Inserting this Z-R relation into the
RADAR equation allows calculating the rain rate from the backscattered power
P
R
.
Thus, principally, a quantitative rain measurement is possible. Because the reflectiv-
ity Z can take a huge range of values a logarithmic measure with
Z
0
=
Marshall and Palmer (
1948
) found
a
=
296 and
b
=
1mm
6
m
−
3
is formed,
dBZ
=
10
·
log
10
(
Z
/
Z
0
).
(3.10)
The difficulty is to find the right Z-R relation. From the combination of drop size
measurements and RADAR observations, the following typical values have been
found:
a
=
200 and
b
=
1.6 for stratiform clouds and
a
=
350 and
b
=
1.4 for
convective clouds. For snow
a
2 is a possible choice. Table
3.3
gives typical values for the relation between the reflectivity and the rain rate using
a
=
2000 and
b
=
=
=
1.47.
RADARs can be operated as pulsed RADARs or as frequency-modulated
continuous-wave RADARs (FMCW-RADAR). The operational principle of S-band
FMCW-RADARs, which are especially suited for boundary layer research, has
recently been reviewed by Ince et al. (
2003
). While pulsed RADARs determine
the range via the delay between the emission and the receiving of the pulse,
continuous-wave RADARs principally cannot do so. Therefore, range-resolving
continuous-wave RADARs must be operated with a constantly changing emission
269 and
b
Table 3.3
Typical RADAR reflectivities as function of the rain rate
Z[mm
6
m
−
3
]
Rain rate [mm h
−
1
]
DBZ
Notes
1mmm
−
3
1
0
0.04
One drop with
D
=
200
23
1.00
Light rain
5mmm
−
3
15 625
42
15
One drop with
D
=
257 800
54
100
Heavy rain
10
6
60
205
Very heavy rain (probably with hail)
10
7
70
Very large hail stones
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