Scattering in the Earth’s Atmosphere

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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)
WhereI(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 section of one particle can be calculated using the formula below: σs=α2128π53λ4(5)

Whereα is the polarisability of the scatterer and
λ is the wavelength of the incident radiation.

From this, we can find the atmospheric optical depth due to Rayleigh scattering to be:
(6)
Where n(z) is the air number density at height z.

Mie Scattering
Mie Scattering theory applies to the interaction of radiation with aerosol and cloud droplets. Under Mie scattering conditions, we can approximate the optical depth of cloud in terms of the column abundance of liquid water (i.e. the liquid water path). The optical depth can be obtained from the equation: u= 3Σl2ρwae (7)

where ρw is the liquid water density and ae is the scattering-equivalent mean drop radius.

Cloud Radiative Forcing
Clouds increase the global reflection of solar radiation from 15 to 30%, reducing the amount of solar radiation absorbed by the Earth by about 44 W/m². [1] A quantitative description of how cloud can affect the solar radiation can be calculated by comparing the radiative fluxes at the top of the atmosphere and the at the surface in both clear day and cloudy day, over a given region the following relationship must apply:

(8)
where A is the albedo of the region
FS and FLW denote the downward shortwave (SW) and upward longwave (LW) fluxes at the TOA, respectively.

From that, the Cloud Radiative Forcing C, which is the difference between heating rates under cloudy and clear sky conditions, can be found by applying:

(9)

where the CS denotes clear sky conditions.

Method
We tried to do 10 different tasks in order to find out different aspect of the solar radiation.

Task1
For task1, Under clear sky conditions and for a range of solar zenith angles, the direct flux of the solar radiation was measured using the lightmeter and the thermopile. The direct flux was obtained by finding the difference between the diffusive flux and the total flux. The diffusive flux...
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