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5.3
Results of the Retrieval of Parameters of the Atmosphere and the Surface
Theinverseproblemoftheretrievalofatmosphericandsurfaceparameterswas
solvedwith themethod described in Sect. 4.3, i. e. with themethod of statistical
regularization as per (4.53) (Vasilyev A and Ivlev 1999). Before discussing the
retrieval results, we are pointing at the selection of the a priori and covariance
matrices of the desired parameters necessary for the inverse problem solving.
The corresponding a priori models of temperature, water vapor, and ozone
were taken from the topic by Zuev and Komarov (1986). Two cases: “mid-
latitudinal winter” for the observations above the ice and snow and “mid-
latitudinal summer” for the observations above the water and sand surfaces.
ThesemodelswerecompletedwiththedatafromthestudybyAndersonetal.
(1996) to expand them to the top of the atmosphere (0.5mbar). While com-
pleting, the traditional exponential approximation was used for the covariance
matrices (Biryulina 1981).
=
z
i
−
z
j
|
|
corr(
X
(
z
i
),
X
(
z
j
))
exp(−
|
r
)
(5.49)
where
X
is the temperature or content of the atmospheric gas;
z
i
,
z
j
are the
altitudes, where the correlation is calculated,
r
is the correlation radius and
the only scalar parameter, which the standard altitude of 5 km was used for
(Biryulina 1981).
The mean profiles of NO
2
and NO
3
were adopted from the text of GOME-
TRAN computer code (Rozanov et al. 1995; Vasilyev A et al 1998). The co-
variance matrices were modeled according to (5.49), and the a priori SD was
assumed equal to 100%.
The mean values and the covariance matrices of the albedo of sand, snow,
and pure lake water were calculated directly from the observations of the spec-
tral brightness coefficient, presented in Sect. 3.4. In the approximation of the
orthotropic surface, the albedo is equal to the spectral brightness coefficient.
Construction of the a priori aerosol models is the most difficult problem,
because there is no data about the variations and correlation links of the aerosol
parameters in the cited literature in spite of the significant amount of optical
aerosol models. In addition, the known models are not intended for applying
to the inverse problems solving and consists of not detailed enough grids over
altitudes and wavelengths. Thus, the special aerosol models for the regions and
seasons of the observations should be elaborated while taking into account the
features of the problem.
While elaborating such models, in addition to the cited literature data, the
results of the direct airborne observations of the number concentration and
chemical composition of the aerosol particles were used as well. These observa-
tions were accomplished by the team of the Laboratory for Aerosols Physics of
the Atmospheric Physics Department of the Physical Institute of the Leningrad
University above the Kara-Kum Desert and Ladoga Lake (Dmokhovsky et al.
1972; Kondratyev and Ter-Markaryants 1976). The following approach, tradi-
tional for the modern modeling of the optical properties of the aerosols was
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