Geoscience Reference
In-Depth Information
Theobtainedexpressionswouldbesuitablefortheopticalparametersretrieval
but there is one obstacle complicating the solution. Namely, functions
u
(
µ
0
,
τ
0
)
µ
0
,
τ
0
)dependnotonlyonthecosineofthesolarzenithangle
µ
0
but
and
v
(
τ
0
, therefore (6.18) is inconvenient in this case. We
propose two ways for getting round this difficulty:
also on optical thickness
1. The problem is solved with successive approximation. To begin with,
the optical thickness is estimated from other approaches (e. g. with the
assumption of the conservative scattering) then the values of functions
u
(
τ
0
) are taken from the look-up tables. After that pa-
rameter
s
2
is calculated and
µ
0
,
τ
0
)and
v
(
µ
0
,
τ
0
is defined precisely using the observational
data of semispherical irradiances
F
↓
,
F
↑
atthecloudtopandbottom.The
process is repeated, and it is broken after the preliminary fixed difference
between the values of the desired parameters obtained at the neighbor
stepsisreached.
2. Otherwise the analytical approximationof functions
u
(
τ
0
)
together with the approximation of value
p
included in (6.22) should be
derived. Thus, it is necessary to deduce the formulas similar to (6.18).
µ
0
,
τ
0
)and
v
(
µ
0
,
6.1.5
Inverse Problem Solution for the Case of Multilayer Cloudiness
The cloudy system consisting of the separate cloud layers has been discussed
in Sect. 2.3, and the model of multilayer cloudiness together with the set of the
formulas solving the direct problem (2.54), (2.57) for irradiances and (2.55)
for radiances has also been presented there. The inversion of these formulas
for the optical parameters retrieval is analogous to the above-described pro-
cedures. The expressions for the upper cloud layer (
i
=
1) is similar to those
=
for the one-layer cloud with surface albedo
A
A
1
. In formulas for all below
µ
0
) is substituted with
F
↓
(
τ
i
−1
) and second
layers (
i>
1), escape function
K
0,
i
(
µ
0
) is substituted with value 12
q
(Melnikova
and Zhanabaeva 1996a). The derivation of the expressions using the observa-
tional data of the irradiance has been presented in Melnikova and Fedorova
(1996) andMelnikova and Zhanabaeva 1996a,b), which yields the following for
parameter
s
2
:
coefficient of the plane albedo
a
2
(
F
(0)
2
−
F
(
τ
1
)
2
s
1
=
=
, r
i
1,
µ
0
)
2
−
F
↑
(
τ
1
)
2
]−2
a
2
(
µ
0
)
F
(0) − 24
q
F
↑
(
τ
1
)
F
(
τ
1
)
16[
K
0
(
τ
i
−1
)
2
−
F
(
τ
i
)
2
F
(
s
i
=
, r
i>
1,
16[
F
↓
(
τ
i
−1
)
2
−
F
↑
(
τ
i
)
2
]+24
q
[
F
↓
(
τ
i
−1
)
2
−
F
↓
(
τ
i
)
2
]
[
F
↓
(
τ
i
−1
)
F
↑
(
τ
i
−1
)−
F
↓
(
τ
i
)
F
↑
(
τ
i
)]
×
(6.20)
τ
i
)arethenetfluxesatthe
top of the whole cloud system and at the layer boundaries correspondingly.
=
τ
i
)
=
τ
i
−1
)−
F
↑
(
1−
F
↑
(0) and
F
(
F
↓
(
where
F
(0)
Search WWH ::
Custom Search