Geoscience Reference
In-Depth Information
by the collisions with the air molecules and the coefficient of the temperature
dependence correspondingly
6
The calculations of the aerosol scattering and absorption cross-sections
so as an aerosol phase function are based on the simulations. The aerosol
particles are approximated with the certain geometrical solids of the known
chemical composition. Usually there are considered the homogeneous spher-
ical particles. The calculation of the optical characteristics for such particles
is accomplished according to the formulas of Mie theory, which we are not
adducing here referring the reader to corresponding topics. The basis of the
theory and the formula derivations are presented in the topics by Hulst (1957)
and Bohren and Huffman (1983), the transformation to the characteristics of
the elementary volume is presented in the topic by Deirmendjian (1969), the
applied algorithms of the calculations are presented in Bohren and Huffman
(1983) and Vasilyev (1996, 1997). An important process influencing the optical
characteristics of the aerosol particles especially in the troposphere is their
rehydration - the absorption of the water molecules on the particle surface. It
leads to the essential variations of the aerosol optical properties depending on
the air humidity. The two-layer particle - “sphere in shell” - is the model for
the rehydrate particle. The methods of its calculation are presented in Bohren
and Huffman (1983) and Vasilyev and Ivlev (1996, 1997). The calculations are
usually accomplished in advance due to their large volume and the resulting
aerosol volume coefficients of the scattering and absorption together with the
phase function are used in problems of radiation transfer theory as look-up
tables. These data together with the incident data for the above-mentioned cal-
culations form the base of
the aerosol models
. Nowadays there aremany studies
concerning the aerosol models. Here we are only mentioning that the choice
or the creation of the aerosol model is definite with the features of a concrete
problem. We will do this in Chapter 5 referring to the corresponding models.
The phase function of the aerosol scattering is presented in the above-
mentioned calculations as a look-up table with the grid over the scattering
angle. It is not convenient for some problemswhere the phase functionneeds an
analytical approximation. One of the widely used approximations is a Henyey-
Greenstein function (Henyey and Greenstein 1941):
1−
g
2
(1 +
g
2
−2
g
cos
γ
=
x
(
)
,
(1.31)
|
γ
)
3
2
where
g
is the approximation parameter (0
g<
1). Parameter
g
is often
called
the asymmetry factor
becauseitgovernsthedegreeofthephasefunction
forward extension. The function describes the main property of the aerosol
phase functions - the forward peak - (the prevalence of the scattering to the
forward hemisphere 0
≤
≤
γ
≤
π|
2 over the scattering to the back hemisphere
6
It should be marked that the spectroscopic data of both the first and the second kind have been
obtained from the observations, so they contain errors. Moreover, the formulas for the spectral line
contour either of empirical (1.30) or the theoretical (1.29) are approximations. Therefore, the calculation
using (1.29) and (1.30) gives an uncertainty. Nevertheless, the molecular absorption within the short-
wave range is weak enough, and we are not taking into account these uncertainties.
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