Geoscience Reference
In-Depth Information
The latter group of formulas presupposed the same difficulties as (6.18) does,
because functions
u
(
µ
τ
i
),
v
(
µ
τ
i
),
p
(
τ
i
)and
q
(
τ
i
) depend onoptical thickness
τ
i
.
,
,
6.2
Some Possibilities of Estimating of Cloud Parameters
6.2.1
The Case of Conservative Scattering
Sometimes there is no true absorption of solar radiation by clouds at separate
wavelengths,sothecaseofconservativescatteringoccurs.Thesinglescatter-
ing albedo is equal to unity:
ω
0
=
1. Equations (2.45)-(2.49) describing the
radiative characteristics are rather simple. The expressions of scaled optical
thickness 3(1 −
g
)
τ
0
are readily derived using (2.45) for the radiance data:
−
6
q
+
,
µ
0
)
K
0
(
µ
4
K
0
(
)
4
A
1−
A
τ
0
=
3(1 −
g
)
ρ
0
(
µ
µ
0
)−
ρ
,
(6.28)
−
6
q
+
,
µ
0
)
K
0
(
µ
4
K
0
(
)
4
A
1−
A
τ
0
=
3(1 −
g
)
σ
and for the irradiance data using (2.46):
)
−
6
q
+
,
µ
0
)
1−
F
↑
(
4
K
0
(
4
A
1−
A
τ
0
=
3(1 −
g
)
τ
(6.29)
)(1 −
A
)
−
(6
q
+4
A
)
µ
0
)
4
K
0
(
τ
0
=
3(1 −
g
)
τ
F
↓
(
1−
A
and for net flux data using (2.47):
−
6
q
+
.
µ
0
)
4
K
0
(
4
A
1−
A
τ
0
=
3(1 −
g
)
(6.30)
τ
F
(
)
Thus, it is possible to retrieve the optical thickness of the conservative ho-
mogeneous layer measuring the data of net flux
F
(
τ
=
F
↓
(
τ
)−
F
↑
(
τ
)atany
level - within the cloud or at its boundaries - as the net flux is constant over
altitude. The observation at one viewing direction only is enough for the case
of conservative scattering.
It shouldbenoted that the expression for the optical thickness using airborne
radiance observations has been derived and applied in two studies (King 1987;
King et al. 1990).
Remember that conservative scattering is a priori assumed in many studies
concerning the deriving of optical thickness from radiation data (King 1987,
1993; King et al. 1990; Zege and Kokhanovsky 1994; Kokhanovsky et al. 2003).
We present the result of analyzing the possible uncertainties of this approx-
imation. The accuracy verification of applying (6.28)-(6.30) shows that they
)
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