Geoscience Reference
In-Depth Information
ω
0
i
<<
1.Thevolumeextinctioncoefficientisspecified
to the scattering, 1 −
ε
i
, the absorption coefficient of the
i
-th layer is
κ
i
=
ε
i
(1 −
ω
0
i
), and the
as
α
i
=
ε
i
ω
0
i
. We are neglecting the radiation scattering
in the optically thin clear atmosphere between the cloud layers and in the
underlying clear layer and assuming that the lower layer adjoins the ground
surface with albedo
A
.
Remember that
thediffusedirradiances
outgoing from the optically thick
layer are described in relative units
scattering coefficient is
π
S
by (2.27). The albedo for the upper layer
is accepted as the value of the spherical albedo of the second layer (counting
from above):
a
2
−
n
2
m
2
l
2
exp(−2
k
2
τ
2
)
=
A
1
.
1−
l
2
l
2
exp(−2
k
2
τ
2
)
Va l u e
a
2
specifies the spherical albedo of the infinite atmosphere with proper-
ties of the second layer:
a
2
s
2
. The subscripts indicate for which
layer the values are calculated. In the system of
N
layers the escape function
K
(
=
δ
1−4
s
2
+6
µ
0
)ofthelayerwithnumber
i>
1isreplacedwiththeintegralofthefunction
with respect to the value
µ
0
(with value
n
i
)andmultipliedbytheirradiance
transmitted by the upper layer
n
i
F
↓
(
τ
i
−1
). The following specifications have
been accepted in the study by Melnikova and Zhanabaeva (1996):
τ
i
)
1−
l
i
l
i
exp(−
k
i
m
i
exp(−
k
i
f
τ
i
)
=
(
,
σ
τ
i
)
m
i
l
i
exp(−2
k
i
τ
i
)
1−
l
i
l
i
exp(−2
k
i
l
i
e
−
k
i
τ
i
f
f
τ
i
)
=
τ
i
)
=
(2.53)
(
(
,
ρ
σ
τ
i
)
n
i
1−
A
i
a
i
=
n
i
.
Finally the expressions of the diffused irradiances at its boundaries are derived
for the layer with number
k>
1:
k
µ
0
)
n
1
K
(
F
k
=
n
i
n
i
f
F
k
−1
n
k
n
k
f
τ
i
)
=
τ
k
),
(
(
σ
σ
(2.54)
=
i
1
F
k
=
τ
k
)]
F
k
−1
.
[
a
k
−
n
k
f
(
ρ
and
=
a
i
+1
−
Q
i
+1
f
τ
i
+1
).
A
i
(
ρ
The formulas for computing the solar diffused radiance are derived as above by
substituting the product that described diffused radiation incoming to layer:
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