10.2 Interaction Between Radiation and Aerosol Particle
Separate aerosol particle is to be modeled as an object of definite shape for
mathematical description. The simplest shape is a sphere.
The problem of calculating electromagnetic waves interaction with homogeneous sphere was solved in 1908 by German physicist Gustav Mie, and derived a
theory called the Mie theory. According to the Mie theory all necessary optical
characteristics of the spherical particle are obtained by assuming that the relation
y ¼ 2pr/l, where r is the radius of the sphere and l is the wavelength of incident
radiation, as well as the complex refractive index (CRI) of the sphere matter
y ¼ 2pr/l. The meaning of m is considered in details in the book. Here we’ll
only clarify that the real part of CRI is the refractive index (the ratio of light
velocity in a vacuum and in the matter), and imaginary part characterizes the
radiation absorption by the particle matter.
Resulting formulas of the Mie theory are cumbersome and are not presented
here, details are in books. For 100 years a significant additional work has been done
for transforming Mie formulas to convenient forms for calculations. Finally we use
the algorithm for computer codes.
Hence, input data are: the parameter y ¼ 2pr/l, and CRI of the particle matter m
(l) depends also on wavelength l. Output data are assumed the cross-section of
interaction particle and radiation: the extinction cross-section C e (y,m); the scattering
cross-section C s (y,m); absorption cross-section C a (y,m) and the scattering phase
function x(g,y,m), where g is the scattering angle. It is to be mention that the aerosol
absorption is not selective as distinct from gas absorption. The rigorous definition of
interaction cross-sections is in references (Joseph et al. 1976). Here we’ll only
clarify the physical meaning of the notion.
10.3 Ensemble of Aerosol Particles
While applying the Mie theory to problems of atmospheric optics it is to be
accounted for that real aerosol particles range in size from about 10
À4
mm to tens
of micrometers. This property is called the particle dispersivity. The collection of
particles of all possible dimensions is called the ensemble of particles.
The characteristic of aerosol particles number in the air is the concentration: the
number of particles in the volume unites. Depending on the particle size and the
geographical location particle concentration ranges from about 10
7 to 10
À6 cm
À3
.
The aerosol dispersivity leads to particle concentration being inadequate for the
ensemble describing. It is evident that particles of different sizes have different
concentrations. Hence it is yet one characteristic to be introduced for linking the
particle concentrations and radius.
Let the number of all particles (in the volume unite) with radius less or equal
r be N(r). Then particle number with radiuses in range from r to r þ Dr is
100
10 Calculating Optical Characteristics of Atmospheric Aerosol
Separate aerosol particle is to be modeled as an object of definite shape for
mathematical description. The simplest shape is a sphere.
The problem of calculating electromagnetic waves interaction with homogeneous sphere was solved in 1908 by German physicist Gustav Mie, and derived a
theory called the Mie theory. According to the Mie theory all necessary optical
characteristics of the spherical particle are obtained by assuming that the relation
y ¼ 2pr/l, where r is the radius of the sphere and l is the wavelength of incident
radiation, as well as the complex refractive index (CRI) of the sphere matter
y ¼ 2pr/l. The meaning of m is considered in details in the book. Here we’ll
only clarify that the real part of CRI is the refractive index (the ratio of light
velocity in a vacuum and in the matter), and imaginary part characterizes the
radiation absorption by the particle matter.
Resulting formulas of the Mie theory are cumbersome and are not presented
here, details are in books. For 100 years a significant additional work has been done
for transforming Mie formulas to convenient forms for calculations. Finally we use
the algorithm for computer codes.
Hence, input data are: the parameter y ¼ 2pr/l, and CRI of the particle matter m
(l) depends also on wavelength l. Output data are assumed the cross-section of
interaction particle and radiation: the extinction cross-section C e (y,m); the scattering
cross-section C s (y,m); absorption cross-section C a (y,m) and the scattering phase
function x(g,y,m), where g is the scattering angle. It is to be mention that the aerosol
absorption is not selective as distinct from gas absorption. The rigorous definition of
interaction cross-sections is in references (Joseph et al. 1976). Here we’ll only
clarify the physical meaning of the notion.
10.3 Ensemble of Aerosol Particles
While applying the Mie theory to problems of atmospheric optics it is to be
accounted for that real aerosol particles range in size from about 10
À4
mm to tens
of micrometers. This property is called the particle dispersivity. The collection of
particles of all possible dimensions is called the ensemble of particles.
The characteristic of aerosol particles number in the air is the concentration: the
number of particles in the volume unites. Depending on the particle size and the
geographical location particle concentration ranges from about 10
7 to 10
À6 cm
À3
.
The aerosol dispersivity leads to particle concentration being inadequate for the
ensemble describing. It is evident that particles of different sizes have different
concentrations. Hence it is yet one characteristic to be introduced for linking the
particle concentrations and radius.
Let the number of all particles (in the volume unite) with radius less or equal
r be N(r). Then particle number with radiuses in range from r to r þ Dr is
100
10 Calculating Optical Characteristics of Atmospheric Aerosol