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racy is needed for the direct problemsolving. The applied algorithmcontaining
the definite simplifications and approximations proceeding from the technical
demands to the calculations is used in the process of the iteration solving of
theinverseproblem.Theaccuracyoftheseapproximationsisdefinedbythe
comparison of the results of the etalon and applied algorithms. To simplify the
presentation we will estimate the accuracy of the corresponding approxima-
tions while describing certain elements of the etalon algorithm, i. e. present the
etalon and applied algorithms simultaneously. For all the calculations consid-
ered here, the authors have used the aerosol model of the atmosphere described
in the study by Krekov and Rakhimov (1986), and the model of the profiles
of the temperature, pressure, and absorbing gases (Anderson et al. 1996) with
adding the profiles from the program code Gometran (Rozanov et al. 1995). To
select the data from the models the computer tools presented in the study by
Vasilyev A (1996) have been applied.
For the direct problem solving, i. e. for the model calculations of the mea-
sured solar irradiances, the Monte-Carlo method has been chosen; the expe-
diency of this choice has been described in Sect. 2.5. Here we just emphasize
the simplicity and flexibility of this method, which allows “turning on” and
“turning off” different concrete variants of the description of the processes
of radiative transfer, i. e. to transform the etalon algorithm to the applied one
without difficulty. The followingmodel is considered as an atmospheric model
both for the etalon and applied algorithms: the reflecting characteristics of
the surface and the optical characteristics of the aerosols are specified directly
and the volume coefficients of the molecular scattering and absorption are
calculated with the formulas of Sect. 1.2. Thus, in a general problem statement
the vertical profiles of the temperature and absorbing gases are used as pa-
rameters, which the measured values depend on, and hence, are the subjects
for retrieval together with the above-described parameters during the inverse
problem solving.
The atmospheric pressure is accepted as a vertical coordinate in the observa-
tions of solar radiation (Chap. 3). Hence, it is necessary to pass fromthe altitude
scale to the pressure one during the mathematical modeling of the observa-
tional process. For this transformation it is enough to take into consideration
that the optical thickness has no dimensions, then,
τ
=
α
z
(
z
)
dz
=
α
P
(
P
)
dP
,
α
z
(
z
) is the volume extinction coefficient connected with altitude
z
(for example, in km
−1
),
where
α
P
(
P
) is the volume extinction coefficient connected
with pressure
p
(for example, in mbar
−1
). The following is obtained using
hydrostatic equation
d
P
µ
−
g
(
z
)
(
z
)
RT
(
z
)
=
dz
,where
g
(
z
)isthefreefallacceleration,
µ
(
z
) is the air molecular mass,
T
(
z
) is the air temperature and
R
is the gas
constant:
RT
(
z
)
g
(
z
)
α
P
(
P
(
z
))
=
α
z
(
z
)
.
(5.1)
µ
(
z
)
P
(
z
)
Recalculation of the volume coefficients is carried out with (5.1) where the
subscript at extinction coefficient
α
P
is omitted and the pressure is used as
a vertical axis and considered as an independent variable. Incidentally, all
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