λ | Wavelength | µm | Wavelength of the incident solar radiation |
γ | Angular distance | arc min | Angular distance from the center of the Earth’s shadow |
RS | Angular radius | arc min | Angular radius of the Sun |
R | Angular distance | arc min | Angular distance from the center of the solar disk |
ɛ0 | Angle | arc min | Maximum angle under which the elementary ring at the solar disk is visible from point E′ (Fig. 1) |
ɛ | Angle | arc min | Angle that defines the position of a certain point at the elementary ring (Fig. 1) |
ρ | Angular distance | arc min | Angular distance of the elementary ring from point E′ (Fig. 1) |
πS | Parallax of the Sun | arc min | Angle subtended by the Earth’s equatorial radius at the center of the Sun at the mean distance between Earth and the Sun |
πM | Parallax of the Moon | arc min | Angle subtended by the Earth’s equatorial radius at the center of the Moon at the mean distance between the Earth and the Moon |
dS | Area | km2 | Surface at the lunar plane illuminated by flux of light when no refraction takes place in the Earth’s atmosphere |
dS′ | Area | km2 | Surface at the lunar plane illuminated by flux of light when refraction takes place in the Earth’s atmosphere |
κλ | Coefficient dependent on the wavelength | Dimensionless | Coefficient that characterizes the luminosity distribution at the solar disk |
cλ | Light dispersion | Dimensionless | Coefficient that refers to the light dispersion in the Earth’s atmosphere |
h0 | Altitude | km | Minimum altitude of the ray in the Earth’s atmosphere |
h | Altitude | km | Altitude of the general point on the sunbeam trajectory |
ℜ | Radius of the Earth | km | Radius of the Earth |
H | Scale height | km | Altitude up to which a homogeneous molecular atmosphere would extend |
ρG | Air density | kg m−3 | Air density at the ground |
r | Particle radius | µm | Radius of the particle |
rm | Particle modal radius | µm | Modal radius of the particle size distribution function f(r) |
a | Parameter of the particle size distribution function | Dimensionless | Refers to modified gamma size distribution function f(r) ∼ rae−br |
b | Parameter of the particle size distribution function | µm−1 | Refers to modified gamma size distribution function f(r) rae−br |
B | Euler angle | rad | Specify the particle’s orientation with respect to the laboratory reference frame |
Θ | Euler angle | rad | Specify the particle’s orientation with respect to the laboratory reference frame |
Φ | Euler angle | rad | Specify the particle’s orientation with respect to the laboratory reference frame |
m | Refractive index | Dimensionless | Complex refractive index of the particle |
x | Size parameter | Dimensionless | Size parameter defined as 2πr/λ |
eλ(γ) | Relative irradiance | Dimensionless | Irradiance of a certain point at distance γ from the center of the Earth’s shadow (including atmospheric effects) |
Eλ(γ) | Relative irradiance | Dimensionless | Irradiance of a certain point at distance γ from the center of the Earth’s shadow (excluding atmospheric effects) |
Dλ(γ) | Optical density | Dimensionless | Negative common logarithm of the ratio of irradiances Eλ(γ) and eλ(γ) (Fig. 1) |
bλ(ρ, ɛ) | Relative luminosity | Dimensionless | Relative amount of energy the element at the solar surface radiates in unit time |
ω(h0) | Angle of refraction | arc min | Refraction of the rays of light passing through the atmosphere horizontally |
iλ(h) | Apparent zenith angle | rad | Angle subtended at a general point on the trajectory by its radius vector with the ray (Fig. 1) |
Tref(h0) | Transmission coefficient | Dimensionless | Factor by which the radiation flux is reduced (due to atmospheric refraction) when reaching altitude h0 |
Text(h0) | Transmission coefficient | Dimensionless | Factor by which the radiation flux is reduced (due to atmospheric extinction) when reaching altitude h0 |
Tair | Transmission coefficient | Dimensionless | Factor by which the radiation flux is reduced (due to molecular scattering) when reaching altitude h0 |
Tozone | Transmission coefficient | Dimensionless | Factor by which the radiation flux is reduced (due to ozone absorption) when reaching altitude h0 |
Taerosol | Transmission coefficient | Dimensionless | Factor by which the radiation flux is reduced (due to aerosol extinction) when reaching altitude h0 |
δλ(h) | Aerosol coefficient | Extinction km−1 | Fraction of radiant flux lost from a collimated beam per unit thickness of aerosol |
αλ(h) | Ozone coefficient | Extinction km−1 | Fraction of radiant flux lost from a collimated beam per unit thickness of ozone due to absorption |
βλ(h) | Rayleigh coefficient | Extinction km−1 | Fraction of radiant flux lost from a collimated beam per unit thickness of air molecules due to scattering |
τλ(h0) | Aerosol optical thickness | Dimensionless | Negative natural logarithm of ratio of incident radiant flux and the flux transmitted through aerosol environment |
Cext(λ, r) | Extinction cross section | µm2 | This quantity equals the total monochromatic power removed by the particle from the incident beam divided by the incident monochromatic energy flux |
Qext(λ, r) | Efficiency coefficient for extinction | Dimensionless | Dimensionless quantity defined as a ratio of Cext/πr2 (for spherical particles of radii r) |
fh0(r) | Particle size distribution | µm−3 | Columnar aerosol size distribution function at base altitude h0 |
Sh0(r) | Particle size distribution | µm−1 | Columnar surface aerosol size distribution function at base altitude h0 |
s(r, h) | Particle size distribution | m−2 | Altitude-dependent particle size distribution function |