Geoscience Reference
In-Depth Information
While approximating the profile by the altitude grid, it is evident that the
lower the altitude step the more accurate the approximation. There is no
problem of selecting the grid in the range of the etalon algorithms. The grid
provided by the algorithm should be as detailed as possible. However, during
the construction of the applied algorithm, the less number of points that are in
the grid the less the number of the retrieved parameters that is available, hence,
the shorter computing time is used. Therefore, the problem of the optimal
altitude grid selectionproviding themaximal accuracywith theminimal points
quantity arises. Regretfully, this problem has not often been studied in the
theoretical aspect. Thus, different empirical approaches have to be used for the
optimal grid selection. In particular, we have used the path described below.
Write the variations of the calculated values through the variations of the
retrieved components using the linear item of the Taylor series:
∂
N
y
i
∆
=
∆
y
i
x
k
,
∂
x
k
=
j
1
∆
where
x
k
is the profile of the retrieved parameter, variation
x
k
corresponds
∂
|∂
∆
to the a priori SD. The corresponding term (
x
k
is calculated for every
altitude level
k
of the initial maximally detailed grid. The excluding of the level
corresponds to the replacement of its derivative with the arithmeticmean value
over two neighbor levels and it is replaced with zero at the last level (the top
oftheatmosphere).Theincreasingofderivatives(
y
i
x
k
)
∂
|∂
∆
y
i
x
k
)
x
k
regulates and
∆
consequently excludes the levels until variation
y
i
maximal over all numbers
i
remains less than the fixed magnitude is. The parameter for the break of the
excluding is obviously linkedwith observation uncertainty
y
i
.Wehaveusedthe
value equal to one third of the SD. We should mention that the obtained grids
(and the altitudes of the top of the atmosphere) essentially differ for the vertical
profilesofdifferentparameters,butthegridoverthemallwillbethesuitable
one. Quite often, the vertical grid is selected similar to the standard models,
radiosounding data, etc. without the above-described details, i. e. without the
accuracy estimation that is not methodically correct on our opinion.
Thesecondapproximationoftheprofilewithacertainfunctionisusedin
the algorithms of the operative data processing because it allows for a decrease
of the quantity of the retrieved parameters by many times. Usually the func-
tion is constructed using the mean standard profiles cited in the references.
However, it is necessary to accomplish the analysis of its accuracy with the
etalon algorithm and a maximally detailed grid (Mironenkov et al. 1996).
Theessentialfeatureofinverseproblemsintheshortwavespectralrangeis
the necessity of aerosol optical parameters retrieval. The volume coefficients
of the aerosol scattering and absorption depend not only on altitude but on
wavelength as well. Thus, parameterization of both the altitudinal and spectral
dependence is necessary. In some particular problems, we succeed in describ-
ing the spectral dependence with a function of small quantity of the parameters
(Polyakov et al. 2001). However, the specification of the spectral dependence
as a grid over wavelengths is to be considered as a general case. In fact, there
Search WWH ::
Custom Search