Geoscience Reference
In-Depth Information
According to Yanovitskij (1991, 1997) and Dlugach and Yanovitskij (1983)
functions
p
(
τ
0
)and
q
(
τ
0
)havebeenspecifiedforaccountingthesurfacereflec-
tion
1
1
τ
0
)
=
µ
τ
0
)
µ
µ
τ
0
)
=
µ
τ
0
)
µ
µ
p
(
2
u
(
,
d
,
q
(
2
v
(
,
d
,
(2.51)
0
0
τ
0
)+
q
(
τ
0
)
=
moreover, relation
p
(
1 is correct for these functions. The irradi-
ances outgoing from the layer at the boundaries with the reflecting surface at
the bottom are described as
F
↑
(
1−
f
[
u
(
τ
0
+1)−1]
,
τ
0
)] +
AF
↓
[
p
(ch
k
µ
0
,
τ
0
)
=
µ
0
,
τ
0
)ch
k
τ
0
−
v
(
µ
0
,
|
(1 −
A
)+
Af
[
p
(ch
k
τ
0
+1)−1]
.
(2.52)
F
↓
(
µ
0
,
τ
0
)
=
µ
0
,
τ
0
)−
v
(
µ
0
,
τ
0
)ch
k
τ
0
]
f
[
u
(
The above-presented expressions may be useful for computing the solar ir-
radiances in the case of lower optical thickness (cirrus clouds or cloudless
atmosphere with a heavy gaze).
2.3
Calculation of Solar Irradiance and Radiance in the Case
of the Multilayer Cloudiness
The radiation field in themultilayer cloudiness was considered inmany studies
(e. g. Sobolev 1974; Germogenova and Konovalov 1974; Ivanov 1976). Applying
the approaches developed in these studies, numerical difficulties arise connect-
ing with the necessity of accounting the total interrelation of all layers. While
solving the inverse problems, these difficulties are intensifying. However, it is
possible to neglect the whole totality of the interrelations and consider every
layer independently with taking into account the approximate influence of the
neighbor layers in real problems concerning cloud layers of rather large opti-
cal thickness. Just such an approach was elaborated in a study (Melnikova and
Minin 1977) for computing the downwelling and upwelling solar irradiances
in the vertically heterogeneous medium consisting of two optically thick lay-
ers with different optical properties. It has been assumed that the irradiance
transmitted by the upper layer accepted as an incident flux for the lower layer.
Theinfluenceofthelowerlayerontheupperradiationfieldisdetermined
by its spherical albedo, i. e. the lower layer is accepted as a reflecting surface
for the upper layer. That is to say, the angle distribution of diffused radiation
incoming from the bottom to the upper layer and from the top to the lower
layer is accounted for approximately. The test of the approach has indicated
the relative error of such approximation to be less than 1%.
Let the total optical thickness of the systemof
N
cloud layers be
τ
0
=
Στ
i
>>
1,
τ
i
is the optical thickness of
i
-thsublayer.Thesinglescatteringalbedo
of the
i
-th sublayer is
where
ω
0
i
, moreover the true absorption is weak compared
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