Geoscience Reference
In-Depth Information
6.1.1
Problem Solution in the Case of the Observations of the Characteristics
of Solar Radiation at the Top and Bottom of the Cloud Optically Thick Layer
Now appeal to (2.25) describing the upwelling and downwelling irradiance
scattered by the cloud layer at its top and bottom, which could be measured
from an aircraft board. Let the cloud layer adjoin the surface with albedo
A
=
τ 0 )/ F (
τ 0 ). Function K (
µ
F (
)andconstants m , l , n and k in (2.25) depend
on true radiation absorption and phase function extension, which in their
turn are defined by microphysical properties of cloud medium and described
by expansions over parameter s (2.29). Substituting (2.29) to (2.25), after the
algebraic transformations we obtain two equations with two unknowns -
parameter s and scaled optical thickness
τ (Melnikova 1991, 1992; Melnikova
and Mikhailov 1993, 1994). The corresponding manipulations are presented
in Appendix 2. Thus, for determining values s and
τ using the data of the
irradiances measurements, the following expressions are deduced:
F (0) 2 F (
τ 0 ) 2
=
s 2
,
µ 0 ) 2 F (
τ 0 ) 2 ]−2 a 2 (
µ 0 ) F (0) − 24 q F (
τ 0 ) F (
τ 0 )
16[ K 0 (
ln l l +
.
(6.1)
µ 0 )
1
2 s
mnK (
τ 0 =
τ 0 (1 − g )
=
3
µ 0 )− F 0
a (
In the case of using the observational dataof the solar radiances, the expressions
keep the similar structure, but they become more awkward:
K 0 (
µ
ρ 0
ρ
µ
σ
) 2 (
) 2 K 0 (
) 2
2
s 2
=
) 2 K 0 (
1− A ) 2 J
,
µ 0 ) 2 −( A σ
µ
µ
) 2 K 0 (
16 K 0 (
(6.2)
ln l l + mK (
.
µ
µ 0 )
1
2 s
) K (
τ 0 =
ρ 0
ρ
(
)
where the following is specified for brevity:
K 0 (
24 q AK 0 (
µ
µ
σ
2
)
) 2 AK 0 (
)
=
µ
ρ 0
ρ
J
)(
1− A
1− A
a 2 (
(
+ 2 A K 0 (
µ
µ
µ
µ 0 )
)
)+ n 2 K 2 (
)
) 2 + a 2 (
) a 2 (
µ
ρ 0
ρ
K 0 (
µ
ρ 0
ρ
)(
)
µ
6 q
1− A
K 0 (
)
=
F (0) − F (0) and F (
τ 0 )
=
F (
τ 0 )− F (
τ 0 )arethenetsolarfluxes
F (0)
µ 0 )is
the second coefficient in the expansion for the plane albedo of the semi-
infinite atmosphere, a
τ =
τ = τ 0 )ofthecloudlayer; a 2 (
at the top (
0) and at the bottom (
is the spherical albedo of the infinite atmosphere;
ρ = ρ
µ
µ 0 )and
σ = σ
τ 0 ,
µ
µ 0 )aretheradiances(inrelativeunitsofthe
(0,
,
(
,
π
µ
µ 0 )
=
incident solar flux
S )measured during the radiative experiments: I (0,
,
µ 0 ρ
µ
µ 0 )and I (
τ 0 ,
µ
µ 0 )
=
µ 0 σ
τ 0 ,
µ
µ 0 ). Functions K 0 (
µ 0 ), K 2 (
µ 0 )and
S
(0,
,
,
S
(
,
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