Geoscience Reference
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Let us consider the numerical and analytical results concerning the cloud
heterogeneity. There have been many studies in this field lately (Tarabukhina
1987; Loeb and Davis 1997; Galinsky and Ramanathan 1998; Marshak et al.
1998). It was shown that the influence of geometrical variations of the cloud
parameters is by an order of magnitude greater than the internal variations
(Titov 1998). The analytical solutions (Tarabukhina 1987; Galinsky and Ra-
manathan 1998) emphasize that the cloud heterogeneity greatly impacts the
radiance and irradiance, and this obstacle is actually described withmodifying
theescapefunction(ortheanalogousfunctions)aspertheexpressionsimilar
to (6.26).
There are different estimations of the role, which this impact plays, while
simulating the radiative transfer within clouds. In our case it is expressed
with the value of parameter
r
and the analysis of above-mentioned studies
(Tarabukhina 1987; Galinsky and Ramanathan 1998) allows us to let
r
∼
0.01−0.1. Most results also show that the minimal disturbance in the radiation
field caused by the cloud heterogeneity is at the solar angle equal to 48−49
◦
.
As has been mentioned above, all functions depending on incident angle are
approximately equal to the integrals over this angle. That is why parameter
r
doesnotinfluencetheresultifthemeasurementisaccomplishedatthisincident
angle.
Parameter
r
can be estimated from radiance or irradiance measurements in
the stable overcast conditions with the following approach. The ground-based
and satellite observations indicate that the measured radiance or irradiance
dependence upon solar incident angle is weaker than the dependences of the
calculated radiance and irradiance upon viewing and incident angles (Loeb and
Davis 1997), and it is called
the violation of the directional reciprocity
for the
reflected radiation. Both the incident and viewing angle cosine dependences
of the radiation escaped from the optically thick layer is described with the
escape function
K
(
µ
0
). Thus, the data set measured during several hours could
give us the solar incident angle dependence of the escape function. If it differs
from the radiance dependence upon viewing angle, it is possible to obtain the
value of
r
as follows:
µ
1
,
µ
2
)−
I
(
µ
2
,
µ
1
)
µ
1
)
I
(
K
0
(
=
r
.
(6.38)
µ
µ
µ
1−
I
(
1
,0.67)
K
0
(
1
)−
K
0
(
2
)
µ
0
,
µ
In this expression
I
(
) is the observed (reflected or transmitted) radiance.
In addition, the assumption of
ρ
0
(
µ
=
=
1isusedhere.The
radiationabsorption influencing the escape functionas per expression (1−3
q
s
)
is divided out in the ratio. Certainly, this way needs high stability of clouds
that is possible sometimes (but not often) especially in the North Regions. This
method seems preferable for ground-based observations.
There is another method for parameter
r
estimation from the multi-di-
rectional radiance measurements (e. g. from the measurements by POLDER
instrument). The approximate values of the optical thickness of the cloud layer
are obtained for every available viewing direction and for every pixel assuming
the conservative scattering at the first stage of data processing and (2.24). Then
,0.67)
K
0
(0.67)
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