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authors of another study (Zuev and Naats 1990) have inferred the existence of
a certain limit to the observational accuracy, conditioned by possibilities of the
contemporary methods of the direct problem solutions of atmospheric optics.
Beyond this limit, the further increasing of the accuracy becomes useless (but
accentuate, that it is valid only in ranges of the considered approach of the
inverse problem solving).
The algorithmof the direct problemhas to account for all factors influencing
the radiation transfer maximally accurate and full for decreasing uncertainty
Y . However, the similar algorithmcould turn out rather complicated and awk-
ward for the practical application. Besides, the operational speed and memory
limits of computers demands the appropriate algorithms and computer codes
for the inverse problem solving. Therefore, different simplifications and ap-
proximations are inevitable in the radiative transfer description. It leads to the
necessity of elaboration and realization of two algorithms while solving the
inverse problems of atmospheric optics. The first algorithm is an etalon one
that solves the direct problem in detail with sufficient accuracy; and the second
algorithm is an applied one proceeding from the concrete technical demands
and possibilities (in the limit the applied algorithm might coincide with the
etalon one, but in reality it is almost impossible). The accuracy estimation
of the simplifications and approximations of the applied algorithm obtained
bythecomparisonofthecorrespondedresultsoftwo(appliedandetalon)
algorithms is to be used as an uncertainty of direct problem solution
Y .
In the aspect of the accuracy of the direct problem solution, a quite impor-
tant question is the selection of the set of parameters X subject to retrieval.
In practice, the total selection of the retrieved parameters is always evident
and is defined by the problems, which the experiment has been planned for.
Particularly the inverse problem of atmospheric optics formulated concerning
the atmospheric parameters (Timofeyev 1998) is to obtain the vertical profiles
of the temperature, contents of the gases absorbing radiation, aerosol charac-
teristics, and ground surface parameters. However, as has been mentioned in
Sect. 4.1 the direct problem algorithm depends on a wider set of parameters
in reality. For example, the parameters of the separate lines of the atmospheric
gases absorption (see Sect. 1.2) are needed for the volume coefficient of the
molecular absorption. However, all parameters of the direct problem solution
(all components of vector U ) without excluding are known without absolute
exactness, but with a certain error. Thus, the problem of general selection of
retrieved parameters X could be formulated as follows: it is not only to select
vector X but to take into account the influence of the uncertainty of the initial
parameters, whose magnitudes are assumed to be known, i. e. U
X .
The above-formulated problem of taking into account the uncertainty of
components U
\
=
U ,i.e.will
assume all parameters of the direct problem to be unknown. Then using the
method of statistical regularization and setting the a priori mean values and
covariance matrix for X
\
X is solved elementarily. Indeed, let us set X
=
U we obtain the analogous posterior parameters
after the inverse problem solving, with the solution depending on the a priori
covariance matrix, in particular, the posterior SD depends on the a priori one.
Thus,wewilltakeintoaccounttheinfluenceoftheaprioriindetermination
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