Scattering in the Earth’s Atmosphere
Scattering in the Earth’s Atmosphere Tony Yuk Hei Chan Abstract
Introduction
When the sun radiates light to the earth, incoming solar radiation often is scattered from its original direction of propagation as it enter earth’s atmosphere. This is due to the scattering effect from different particles in the earth’s atmosphere. When the scattering occur, the phase and the polarization of solar radiation are often changed. In this experiment, we aimed to investigate the effect of two of the most comment types of scattering upon the incident solar radiation – Mie scattering and Rayleigh Scattering. We also looked into the effect to the solar radiation from cloud.
Theory Beer–Lambert–Bouguer law:
In optics, Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is traveling. Consider a case when there is a clear sky, a parallel beam of incident radiation pass through a medium which absorb the light. By assuming that the medium is a non-scattering, absorbing medium, the intensity of the light after passing though the medium is given by: (1)
Where I(0) is the intensity at s=0, a is the absorption cross section of a single particle for radiation of wavelength , n is the number density of the medium, and s is the length of the medium.
We can apply the relationship to solar radiation passing though the atmosphere. From equation 1, we find that , the transmissivity of the slant path of the atmosphere at a given wavelength is given by: (2) where u is the optical depth of the vertical column and is given by (3) and Z is the zenith angle of the sun we also know that the transmissivity and the albedo, A, are related by (4)
Rayleigh scattering
Rayleigh scattering theory describes the interaction of sunlight with molecules in a simple way. It applies to particles much smaller than the wavelength of the incoming radiation.
For Rayleigh scattering, the scattering cross
Introduction
When the sun radiates light to the earth, incoming solar radiation often is scattered from its original direction of propagation as it enter earth’s atmosphere. This is due to the scattering effect from different particles in the earth’s atmosphere. When the scattering occur, the phase and the polarization of solar radiation are often changed. In this experiment, we aimed to investigate the effect of two of the most comment types of scattering upon the incident solar radiation – Mie scattering and Rayleigh Scattering. We also looked into the effect to the solar radiation from cloud.
Theory Beer–Lambert–Bouguer law:
In optics, Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is traveling. Consider a case when there is a clear sky, a parallel beam of incident radiation pass through a medium which absorb the light. By assuming that the medium is a non-scattering, absorbing medium, the intensity of the light after passing though the medium is given by: (1)
Where I(0) is the intensity at s=0, a is the absorption cross section of a single particle for radiation of wavelength , n is the number density of the medium, and s is the length of the medium.
We can apply the relationship to solar radiation passing though the atmosphere. From equation 1, we find that , the transmissivity of the slant path of the atmosphere at a given wavelength is given by: (2) where u is the optical depth of the vertical column and is given by (3) and Z is the zenith angle of the sun we also know that the transmissivity and the albedo, A, are related by (4)
Rayleigh scattering
Rayleigh scattering theory describes the interaction of sunlight with molecules in a simple way. It applies to particles much smaller than the wavelength of the incoming radiation.
For Rayleigh scattering, the scattering cross
Bibliography: The fundamentals of Acoustics: Waves on a String and Fourier Theory lab script – Department of Physics, Imperial College London