13.5 Additional Possibilities of the Monte-Carlo Method
The algorithm has been considered for irradiance calculation. However other
important radiative characteristics are possible to obtain without significant transformation. It is possible to count the photon parts taken up in the atmosphere and
to write the value wð1 À oðtÞÞ to the absorption counter. It is the way for the
calculating the energy absorbed in the atmosphere that is very important for many
problems in particular in climatic models. As it was mentioned in the Chap. 1
this energy named the radiative divergence in the atmosphere. The Monte-Carlo
method is the only method providing the direct calculation of the radiative
divergence.
It is possible to obtain certain fine characteristics of the process of radiative
transfer that impossible with other approaches. In particular the ratio of the photon
interacting with the atmosphere (or with the surface) is calculated and the distribution of desired values over this ratio. The arrays with index corresponding to the
interaction ratio is to be used in spite of scalar counters. (Write the modification of
the algorithm as an exercise). This distribution is important for a set of research
problems e.g. it allows to estimate the exactness of single scattering approximation.
13.6 Practice 12
13.6.1 Objectives
The purpose of the practice is studying the dependence of irradiances transmitted by
the atmosphere (illuminating the surface) and reflected from the atmosphere top and
radiative divergence on atmosphere parameters and solar zenith angle. These values
determine solar energy reaching the surface, escaping to the space and absorbing in
the atmosphere.
For simplicity the homogeneous atmosphere model is used (i.e. optical
parameters do not depend on the optical deepnesst). Then only four parameters
describe the atmosphere: the optical thickness t 0 , the single scattering albedo o, the
mean cosine of the scattering angle (phase function asymmetry parameter) g and
the surface albedo A.
Take three the most interesting for study dependences:
1. The distribution desired values over interact ratio.
2. The dependence on solar zenith angle that point the variation of solar energy
during the day time.
3. The dependence on the atmosphere optical thickness that demonstrates variation
of desired values depending on atmospheric aerosols content.
Typical optical parameters of the atmosphere and surface are presented in the
Chap. 10 (Eddington approximation).
136
13 Monte-Carlo Method for the Solar Irradiance Calculation
The algorithm has been considered for irradiance calculation. However other
important radiative characteristics are possible to obtain without significant transformation. It is possible to count the photon parts taken up in the atmosphere and
to write the value wð1 À oðtÞÞ to the absorption counter. It is the way for the
calculating the energy absorbed in the atmosphere that is very important for many
problems in particular in climatic models. As it was mentioned in the Chap. 1
this energy named the radiative divergence in the atmosphere. The Monte-Carlo
method is the only method providing the direct calculation of the radiative
divergence.
It is possible to obtain certain fine characteristics of the process of radiative
transfer that impossible with other approaches. In particular the ratio of the photon
interacting with the atmosphere (or with the surface) is calculated and the distribution of desired values over this ratio. The arrays with index corresponding to the
interaction ratio is to be used in spite of scalar counters. (Write the modification of
the algorithm as an exercise). This distribution is important for a set of research
problems e.g. it allows to estimate the exactness of single scattering approximation.
13.6 Practice 12
13.6.1 Objectives
The purpose of the practice is studying the dependence of irradiances transmitted by
the atmosphere (illuminating the surface) and reflected from the atmosphere top and
radiative divergence on atmosphere parameters and solar zenith angle. These values
determine solar energy reaching the surface, escaping to the space and absorbing in
the atmosphere.
For simplicity the homogeneous atmosphere model is used (i.e. optical
parameters do not depend on the optical deepnesst). Then only four parameters
describe the atmosphere: the optical thickness t 0 , the single scattering albedo o, the
mean cosine of the scattering angle (phase function asymmetry parameter) g and
the surface albedo A.
Take three the most interesting for study dependences:
1. The distribution desired values over interact ratio.
2. The dependence on solar zenith angle that point the variation of solar energy
during the day time.
3. The dependence on the atmosphere optical thickness that demonstrates variation
of desired values depending on atmospheric aerosols content.
Typical optical parameters of the atmosphere and surface are presented in the
Chap. 10 (Eddington approximation).
136
13 Monte-Carlo Method for the Solar Irradiance Calculation