The Problem of Retrieving Atmospheric Parameters from Radiative Observations - Short-Wave Solar Radiation in the Earth's Atmosphere - page 162

is no problem with this grid selection: the wavelength, which the processed
characteristics are presented for, is to be used. The etalon algorithms should be
elaborated in this way only. Nevertheless, the above-mentioned problem of the
grid optimization over wavelengths arises again in the applied algorithm. The
derivativeswithrespectofthevolumecoefficientsoftheaerosolextinctionand
scattering at the excluded wavelengths are replaced with the interpolated val-
ues (at all altitudes) for this grid selection. The point of the spectral grid will be
excluded if the maximal variation of the measured characteristics during this
replacement does not exceed the fixed uncertainty. At first, the spectral grid
should be defined and then the altitudinal one is defined for every remained
wavelength points. The spectral grid for the surface albedo retrieval is selected
almost the same way.
Parameterization of the phase function of the atmospheric aerosols is the
especially complicated problem of selecting the concrete set of parameters
in the short wavelength range. The necessity of the solution of this problem
is connected with minimization of the quantity of parameters in the applied
algorithm. Indeed, the phase function is technically impossible to retrieve as
a table over scattering angle in addition to the tables of dependences upon the
altitude and wavelength. Thus, it should be described with a small quantity
of parameters. The Henyey-Greenstein function (1.31) could be an example of
such a parameterization. However, as it has been mentioned in Sect. 1.2 this
function describes the real phase functions with a low accuracy. Regretfully,
the attempts of finding a similar function with a small quantity of parameters
and describing any aerosol phase function with sufficient accuracy have not
been successful yet. Hence, the uncertainty of the aerosol phase function pa-
rameterization has still been one of the strongest and irremovable sources of
the systematic errors while elaborating the applied algorithms of the inverse
problems solving. The concrete choice of parameterization for the sounding
data processing we will discuss in Sect. 5.1. Note, that radiative characteris-
tics measured by different ways respond differently to the parameterization
accuracy. For example, the irradiance being the integral over the hemisphere
is essentially more weak connected with the shape of the phase function than
the radiance is; the latter is almost directly proportional to the phase function
(for example the single scattering approximation). Thus, the inadequacy of the
phase function statement is the most serious obstacle in the interpretation of
the satellite observations of the diffused solar radiance.
In addition to the listed problems, there is a general difficulty for the inverse
problems solving - the probable ambiguity of the obtained results. Actually,
thedesiredminimumofthediscrepancymightnotbesingleinthenonlinear
case. The numerical experiments allow conclusion of the uniqueness of the
solution after keeping the definite statistics.
The relationship between the inverse problem solution and observational
variations within the range of the random SD is studied in the numerical
experiments of the first kind . For this purpose, the direct problem is solved with
the definite magnitudes of the parameters, and then the obtained solution is
distorted by the random uncertainty using the method of statistical modeling
onthebasisoftheknownSDoftheobservations.Afterthat,theinverseproblem