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molecular absorption with the power function of temperature and pressure
(Kondratyev and Timofeyev 1970). Coefficients
C
0
(
λ
j
)arese-
lectedwithLST.Theinfluenceoftheuncertaintyof(5.8)parameterizationon
the calculations of solar irradiances does not exceed their randomSDexcluding
several points of spectrum.
The necessity of the parameterization of the dependence of the aerosol
phase function upon scattering angle, while solving the inverse problems of
atmospheric optics has been described in Sect. 4.4. To select the appropri-
ate parameterization, the uncertainties of the calculation of irradiances, while
using the approximations of the tabulated phase functions in the etalon algo-
rithm have been analyzed by Krekov and Rakhimov (1986). In other words,
while using the SNR, the signal is assumed as a difference between the irra-
diance calculations for the table and analytical approximation of the phase
function. To estimate the maximal influence of the aerosols on radiative trans-
fer, the ground values of the volume coefficients of the aerosols scattering and
absorption (Krekov and Rakhimov 1986) have been increased by five times.
Unexpectedly the good susceptibility of the solar semispherical irradiances
(especially of the upwelling irradiance) to the shape of the aerosol phase func-
tion has been revealed. This susceptibility is likely to be caused by essentially
different yields of the radiation scattered to different directions of the phase
function to the upwelling irradiance. The yield of the single scattered light
caused by the radiation scattering under the small angles exceeds the yield of
thehighestordersofthescatteringfortheaerosolextendedphasefunctions.
The SNR has turned out to exceed unity for the Henyey-Greenstein func-
tion (1.31) and even for its two-parametric modification (Minin 1988), which
is expressed by two Henyey-Greenstein functions: one is extended forward
and the other one is extended backward. The situation has improved for the
results of using the two-parametric tabulated model described in the study
by Vasilyev O and Vasilyev A (1994) based on classifying the experimentally
observed phase functions, but the uncertainty influence is also too strong in
this case. The attempts to construct the analogous two-parametric model have
provided no success on the basis of the initially tabulated phase functions
(Krekov and Rakhimov 1986). However, higher accuracy has been reached in
the calculation with the analytical presentation of the phase function not at
all angles but at several fixed ones. Based on the strong correlation between
the cross-sections of scattering and directional scattering revealed by some
authors (Gorchakov and Isakov 1974; Gorchakov et al. 1976) and testing the set
of parameterizations, it is possible to obtain the best results with the following
expressions:
λ
j
),
C
1
(
λ
j
),
C
2
(
χ
λ
=
χ
λ
χ
λ
σ
a
(
λ
χ
λ
) ln
2
σ
a
(
λ
|
x
a
(
,
)
exp(
a
i
(
,
)+
b
i
(
,
) ln
)+
c
i
(
,
))
C
1
(5.9)
1
2
=
χ
λ
χ
λ
σ
a
(
λ
χ
λ
) ln
2
σ
a
(
λ
χ
C
exp(
a
i
(
,
)+
b
i
(
,
) ln
)+
c
i
(
,
))
d
,
−1
σ
a
(
λ
χ
λ
χ
λ
where
) is the volume coefficient of the aerosol scattering,
a
i
(
,
),
b
i
(
,
),
χ
λ
c
i
(
,
) are the tables of the coefficients obtained for a certain set of wave-
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