Ground-Based Remote Sensing of Cloud Properties ...
331
The backscatter cross section CTb is defined by (BH, 4.6)
4 (
S2,;(1800))2
CTb= 7r
kc
'
(13.11b)
so that the power density at the receiver antenna becomes
P ( B "') = _l_CTb (A(B, ¢))2
ant r, ,'fI
8
2
7rTJo r
r
(13.11c)
We are now in a position to compare this description of the transmission process with the more
widely used description based on power densities.
13.2.2 The power description of the transmitted signal
Scattering from a Single Isolated Particle
In terms of the properties of the radar, let Pt represent the average power density over a single
cycle of the electromagnetic radiation that is delivered to the transmitter antenna input port.
If the wave is stable over the duration of the pulse (Le., the amplitude and frequency of the
sinusoid in Figure 13.3 do not change over the pulse.), Pt also represents the average power over
the entire pulse. If the antenna were to radiate isotropically, the power density a distance r away
would be Pt/47rr 2 j however, the transmitter antenna provides a gain Gt along the main beam
axis with a falloff in power away from the axis given by the beam pattern P(B, the power density a distance r from the antenna in the direction (B, (13.12)
As the beam travels a distance r, it is attenuated by atmospheric constituents, such as oxygen, water vapor and hydrometeors. Letting k.(r) represent the extinction coefficient of the
atmosphere along the beam path (units of m- 1 ), the attenuation is (DZ, 3.3)
[ -1 _
-.r k,(r)dr
t
- e 0
(13.13)
where, in keeping with Doviak and Zrnic (DZ, 3.3), we have written the loss as a quantity
greater than one. Therefore, (13.12) becomes
(13.14)
Comparing (13.1Ob) and (13.14), the electric field amplitude A(B, parameters is
A(B, (13.15)
Now suppose that at r the pulse encounters an object of some sort. The amount of energy
scattered by the object in any direction is characterized by the object's scattering cross section
CT(B', is (DZ, 3.2)
(13.16)
331
The backscatter cross section CTb is defined by (BH, 4.6)
4 (
S2,;(1800))2
CTb= 7r
kc
'
(13.11b)
so that the power density at the receiver antenna becomes
P ( B "') = _l_CTb (A(B, ¢))2
ant r, ,'fI
8
2
7rTJo r
r
(13.11c)
We are now in a position to compare this description of the transmission process with the more
widely used description based on power densities.
13.2.2 The power description of the transmitted signal
Scattering from a Single Isolated Particle
In terms of the properties of the radar, let Pt represent the average power density over a single
cycle of the electromagnetic radiation that is delivered to the transmitter antenna input port.
If the wave is stable over the duration of the pulse (Le., the amplitude and frequency of the
sinusoid in Figure 13.3 do not change over the pulse.), Pt also represents the average power over
the entire pulse. If the antenna were to radiate isotropically, the power density a distance r away
would be Pt/47rr 2 j however, the transmitter antenna provides a gain Gt along the main beam
axis with a falloff in power away from the axis given by the beam pattern P(B, the power density a distance r from the antenna in the direction (B, (13.12)
As the beam travels a distance r, it is attenuated by atmospheric constituents, such as oxygen, water vapor and hydrometeors. Letting k.(r) represent the extinction coefficient of the
atmosphere along the beam path (units of m- 1 ), the attenuation is (DZ, 3.3)
[ -1 _
-.r k,(r)dr
t
- e 0
(13.13)
where, in keeping with Doviak and Zrnic (DZ, 3.3), we have written the loss as a quantity
greater than one. Therefore, (13.12) becomes
(13.14)
Comparing (13.1Ob) and (13.14), the electric field amplitude A(B, parameters is
A(B, (13.15)
Now suppose that at r the pulse encounters an object of some sort. The amount of energy
scattered by the object in any direction is characterized by the object's scattering cross section
CT(B', is (DZ, 3.2)
(13.16)