WMOD00399

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

- 36 -

2.10 Most targets scatter non-isotropically but for convenienge the concept
of the target's effective back-scattering cross section u is introduce~, determined
in such a way that

P r = Pt

G2.X2
(411")3 r4

u

~

This is, in fact, the radar equation of a single target with an effective back-
scattering cross section u

2.11 Rain drops, snow crystals and cloud particles are examples of an
important class of radar targets known as"multiple targets". In this case, a radar
detects simultaneously a large quantity of particles included in a volu'me determined
by the antenna's beam pattern, but with pulsed signals and a spatial e~tension of the
sounding pulse. If the scatterers in the pulse volume move in relatio~ to each other,
the radio echo signal from this volume fluctuates. Such fluctuations are character-
istic of radar echo signals from meteorological phenomena in which the :relative
particle movement is caused by the presence of various fall speeds and non-homogeneous
distribution of wind speed in the pulse volume. The instantaneous power of a
fluctuating signal depends both on the particles' back-scattering cross~ section and
on their mutual arrangement at the given moment. However, the signal's' mean power
(or an estimate of it over a fairly long averaging period) is described: by the
relationship:

-.-
Pr = Pt

G 2 X 2
(41T)3r

-L u
4 v

where ~ (J' is the 'sum of the back-scattering cross sections of all the particles
in the pulse volume. This volume is approximately described by the relbtionship

V = 11" (r20)~;

where h = cr is the spatial pulse-length, and e is the beam width.

Combining these two preceeding equations, we obtain

Pr =

Pt

(411")3

11". (~\ ~). 11
r 4 2 / \2

G 2 ^ 2

where 7j = L u designates the total back-scattering cross section of one unit.
i i
2.12 In all the expressions, the antenna gain is assumed to be; uniform
throughout the width of the beam and equal to zero outside it, which is!not strictly
correct. Likewise, the effective scattering volume should really be determined
through the integral according to the emission pattern rather than simp+y taking
the area about the axis of the diagram where Pu does not change by more: than 3 dB.
It has been shown that most of the meteorological radars with a sufficient accuracy
for practical purposes have a beam pattern ~pproximated by the Gaussian'curve as
I
follows: G 2 X 2 e 2 h
Pr = Pt . 7j
4 5 71" 2 1 n (2 r 2)

'"