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of the transfer equation at a fixed wavelength to its solving for the atmosphere
with the specified parameters monotonically dependent on wavelength (on
integration variable). This problemhas not been solved completely yet and the
existing algorithms are based on certain approximations. Thus, expanding the
transmission function into a sum of exponents (as has been proposed in the
study by Minin (1988)) or taking into account the photon free path (Lenoble
1985) is provided by assumption about the atmosphere homogeneity. While
using the Monte-Carlo method, the most adequate approach is the passing to
probability density of appearing the definite magnitude of volume molecular
absorption coefficient
κ
m
.However, themodernalgorithms of this passage (e. g.
in the study byTvorogov 1994) demand very awkwardpreliminary calculations,
which are ill adapted to the computing of the derivatives with respect to
κ
m
,
which is necessary for the inverse problems solving.
Nevertheless, taking into account the demands to the etalon algorithm we
are assuming (5.4) as an initial one while noting the following. Based on
the general formal scheme of the Monte-Carlo method wavelength
λ
could
λ
). Then
the method of double randomization is applied as per the topic by Marchuk
et al. (1980), whose kernel consists of the inessentiality of integration order
for the Monte-Carlo method. Hence, it is enough to simulate only one photon
trajectory for every randomwavelength. As a result, wewill estimate the values
ofthedesiredintegral(5.4)fromthecountersmagnitudes.Afterthemodeling
of randomwavelength while accounting for the triangle instrumental function
of the K-3 spectrometer and (2.6) the following is obtained:
be simulated for computing integral (5.4) by probability density
f
(
λ
(1 −
2
λ
=
λ
i
−
∆λ
β
β
≤
1
|
),
2,
(5.5)
(1 −
2−2
λ
=
λ
i
−
∆λ
β
β
≥
1
|
),
2.
TheinstrumentalfunctionoftheK-3spectrometerisknownwithinanerrorof
1% (Sect. 3.1) that is comparable with the observational uncertainty. However,
this uncertainty is significant only in the spectral intervals with the molecular
absorption bands. Thus, its account as an additional yield to the uncertainty of
the direct problem solution should be accomplished only within the following
spectral intervals selected from the analysis of the radiative flux divergence
(Sect. 3.3): 330-360 nm(O
3
), 676-730 nm(H
2
O), 756-780 nm(O
2
), 804-850 nm
(H
2
O), 910-978 nm (H
2
O). In addition, the solar constant should be assumed
invariant within a narrow spectral interval [
λ
i
−
∆λ
λ
i
+
∆λ
]toavoidthe
difference between the observational data and the calculation results, because
the solar irradiances have been corrected with the incident solar spectrum
taking into account the instrumental function, while processing the sounding
data.
Thus, computingwith (5.4) is reduced, in fact, to constructing themaximally
fastandaccuratealgorithmoftheprofile
,
κ
m
calculation with (2.18) for the
wavelength randomly selected within the interval [
λ
i
−
∆λ
λ
i
+
∆λ
]. From that
point of view, we are using
thealgorithmofthesimplifyingaccountoftheyieldof
the spectral lines wings to the absorption
elaborated by Virolainen and Polyakov
,
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