The Problem of Retrieving Atmospheric Parameters from Radiative Observations - Short-Wave Solar Radiation in the Earth's Atmosphere - page 163

is solved for these data and its result is compared with the initial parameters.
If the inverse problem solution coincides with the initially stated parameters
after a sufficient quantity of this statistical testing, it should be concluded that
the random observational error does not cause the solution ambiguity (and
theconfidentprobabilitycouldbeaccessed).Itisespeciallyappropriateto
solve the direct problem with the Monte-Carlo method as it allows for easy
simulation of the results just as random values.
As the random observational error is not usually large, the indeterminacy
of the choice of zeroth approximation could significantly affect the solution
ambiguity while solving the nonlinear inverse problems. Thus, the numeri-
cal experiments of the second kind arenecessary,wherethedependenceof
the solution upon zeroth approximation choice is studied, while allowing the
variations of this approximation to be as large as possible (Zuev and Naats
1990). To reduce the computing time it is appropriate to combine the numer-
ical experiments of the first and second kinds and to model both the random
error and indeterminacy of the zeroth approximation. Just this approach has
been applied in the study by Vasilyev O and Vasilyev A (1994) to this class of
problems and to the concrete problem of the sounding data processing during
the procedure of testing the computer codes. The solution uniqueness has re-
mained with the variation of the zeroth approximation within three a priori
SD of parameters. Note that this complex approach to the implementation of
the numerical experiment opens wide perspectives when taking into account
the possibilities provided by modern computers (Mironenkov et al. 1996). In
particular, it is possible to vary statistically the totality of the direct problem
parameters together with the zeroth approximation, a priori covariancematrix
etc. It should be emphasized that with the accumulation of sufficient statistics
of such complex numerical experiments, it is possible to estimate the accuracy
of the inverse problems solution without simplification formulas similar to
(4.49).
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