Theoretical Base of Solar Irradiance and Radiance Calculation in the Earth Atmosphere - Short-Wave Solar Radiation in the Earth's Atmosphere - page 45

Theoretical Base of Solar Irradiance
and Radiance Calculation
in the Earth Atmosphere

In this chapter, we are considering two concrete calculation methods for the
solar radiances and irradiances needed for observational data interpretations.
They are the Monte-Carlo method for clear atmosphere and the asymptotic
method for overcast sky. The authors are not presenting or even reviewing all
numerical and analytical methods of the radiative transfer theory, referring
readers to the topic by Lenoble (1985). The reasons of our choice among the
diversity of methods will be explained during the consideration below.

2.1
Monte-Carlo Method for Solar Irradiance and Radiance Calculation

The Monte-Carlo method (the more strict name is the method of statistical
modeling) is a most powerful method of radiative transfer theory. It allows
us to solve the problems concerned with the radiance calculation while taking
into account spherical geometry, polarization, heterogeneity of the atmosphere
and surface, etc. (Marchuk et al. 1980). Here we are applying this method for
solving the rather simple (compared with the above-mentioned) problem of
the solar radiance and irradiance calculation in the horizontally homogeneous
and plane parallel atmosphere.
There are twoapproaches todescribe theMonte-Carlomethodapplication in
atmospheric optics (Kargin 1984; Marchuk et al. 1980). The first one describes
it as a method of formal mathematical solving the problems (equations) of
radiative transfer and the second one considers it as a method of simulation of
the physical processes of radiative transfer in the atmosphere, when it is not
needed to attract a body of the transfer theory. Concerning our problem the
second way is easier for understanding so we are following it concurring with
the author of topic (Kargin 1984) and then we will show that the elaborated
algorithm corresponds to the mathematical state of the problem considered in
Sect. 1.3.
Unlike other approaches in the Monte-Carlo method, it is appropriate not
to divide radiation to the direct, diffused and reflected from the surface. In
addition, we are not considering the optical thickness

τ ,butthealtitude z as

a vertical coordinate. The reasons for this can be seen in Chap. 5.
Thus, we are solving the problem for the atmospheric model shown in
Fig. 2.1. Let the parallel solar flux F 0 = π µ 0 ,0) to S income from direction (