Geoscience Reference
In-Depth Information
2.2.5
The Case of the Conservative Scattering
In the absence of the true absorption, according to the definition, we have
ω
0
=
1 and the expressions for the radiative characteristics are particularly
simple (Sobolev 1972; Minin 1988).
For the reflection and diffusion functions:
µ
0
)
K
0
(
µ
4
K
0
(
)
ρ
µ
µ
0
,
ϕ
=
ρ
0
(
µ
µ
0
,
ϕ
3
(1 −
g
)
3(1−
A
)
(0,
,
)
,
)−
,
τ
0
+
δ
4
A
+
(2.45)
µ
0
)
K
0
(
µ
4
K
0
(
)
σ
τ
µ
µ
=
3
(1 −
g
)
3(1−
A
)
;
(
0
,
,
0
)
τ
0
+
δ
4
A
+
π
for the semispherical fluxes in relative units of
S
µ
0
)
4
K
0
(
F
↑
(0,
µ
0
)
=
3
(1 −
g
)
3(1−
A
)
1−
,
τ
0
+
δ
4
A
+
(2.46)
µ
0
)
4
K
0
(
F
↓
(
τ
0
,
µ
0
)
=
3(1 −
A
)
(1 −
g
)
3(1−
A
)
,
τ
0
+
δ
4
A
+
and, finally, the simple expression for the net flux that summarizes both equa-
tions (2.46) is feasible at any level in the conservative medium because the net
flux is constant without absorption (Minin 1988)
µ
0
)(1 −
A
)
3(1 −
A
)[(1 −
g
)
4
K
0
(
τ
µ
0
)
=
F
(
,
.
(2.47)
τ
0
+
δ
]+4
A
It should be emphasized that equality
F
↑
(
µ
0
)iscorrect
in the semi-infinite conservatively scattered atmosphere with a thick optical
depth, where the sense of escape function
K
0
(
τ
µ
0
)
=
F
↓
(
τ
µ
0
)
=
,
,
K
0
(
µ
) frequently met in our consid-
eration is clear from. The case of the conservative scattering becomes true in
a certain cloud layer at the single wavelengths within the visual spectral range.
Equations (2.45)-(2.47) are correct in the wider interval of the optical depth
(
τ
0
≥
3) than (2.24), (2.26), (2.28) derived with taking into account the absorp-
tion. Corresponding relations of the characteristics of the inner radiation field
are written as:
For the radiance:
µ
0
K
0
(
µ
0
)
{
(1 −
A
)[3(1 −
g
)(
τ
0
−
τ
δ
µ
S
)+1.5
+3
]+4
A
}
τ
µ
=
I
(
,
)
,
(2.48)
τ
0
+3
δ
(1 −
A
)[3(1 −
g
)
]+4
A
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