WMOD00399

• Title: WMO Training Workshop on Weather Modification for Meteorologists - Lecture Notes
• Date: 12/1/1979
• Weather Modification - Doc Type: Report

- 38 -

2.15

1

is used, the radar equation takes the fbrm

If the value Z

rr 3 C r Pt G :t r 8 2 ] I -I:z.
1024 i n 2 . "2 K r 2
L A I
This is a more suitable form of notation for the radar e~uation in
which the radar's parameters are separated from those of the target. According to
this equation the assumed power can be expressed through the radar ref+ectivity
using the logarithmic relationship:
10 i g Pr = 101,9 Z - 201g r + c

Pr = Pt

;
where c is a constant determined by the radar's parameters. The log~rithmic
notation for the equation is useful because the variation range of IPr: and Z is
very wide. Usually Pr is measured in milliwatts, whilst the value 10 igPr is
the power in dBM (decibels in relation to one milliwatt); Z is measured in mm6/m3;
whilst the value 10 I, gZ is called the reflectivity in dBZ (decibels' in relation
to one mm6 / m3).

2.16 From the determination of Z it follows that this value;depends on
the drop-size distribution and, because of the sixth power relationshi~, is very
sensitive to the large-drop part of th~ distribution." Direct measurements of the
raindrop size ranges show that they have.a roughly exponential form of:distribution.
Marshall and Palmer were the firt to note that raindrop distributions, :except for
drops of the smallest dimensions, can be roughly described by the functions:

N ( D.) = No e - l). D 1

in which the coefficient A depends only on the rain's intensity and is expressed
in the form 41 R 0.21 I
"A ( R) =

h .. -1 dR'
were A 1S 1n em ,an 1n
according to the Marshall-Palmer
the reflectivity is equal to

mm/hour. If the raindrops are distributed
law throughout the size range, it can Ibe shown that

Z = N 6! . R 1.47
o (41)7
This relationship is in good agreement with empirical data on the
in rain which can be approximated well by the relation:

Z = 200 R 1.6

Z-R irelationship
!

2.17
intensities

i
The following table shows the Z values for various precipitation
R calculated according this empirical relationship: i

~
R (mm/hour) 0.1 1 10 100
Z 6 3) 5 200 7950 316000
(mm /mm
10 19 Z (dBZ) 7 23 39 ! 55