## Scattering

As one would guess, this denotes a change in the direction in which radiation propagates. Radiation is shifted out of one direction and into another. In general, there can be a shift in frequency upon scattering as well. The wavelength dependence of molecular scattering (i.e., Rayleigh scattering) is proportional to A~4, so this scattering will be more significant in the UV range than in the visible. The change in direction of radiation associated with scattering is described by the phase function P (9, <j>; 9', ) which is dependent upon the size of the particle relative to the wavelength of interest. The phase function describes the probability that an incident photon with incident coordinates (d\ ) is scattered into the direction (9, For molecular scattering the phase function is:

where <9 is (9- 9'). Scattering by larger particles is more complex (Mie scattering), but is generally peaked in the forward direction. This would mean that the left lobe in Fig. 11.6 would be smaller than the right lobe.

Figure 11.6 Aerosol scattering pattern: Symmetric forward and backward components

Within this category, there are three sub-categories:

1. Rayleigh scattering This type of scattering occurs when the molecules/ particles in the atmosphere are smaller than the incident light's wavelength. An example is the blue sky.

Individual air molecules are much smaller than cloud droplets; their diameters are small even when compared with the wavelength of visible light. Each air molecule of O2 and N2 selectively scatters the shorter waves of visible light much more effectively than longer wavelengths. As sunlight enters the atmosphere, the shorter visible wavelengths of violet, blue, and green are scattered more effectively by atmospheric gases than are the longer wavelengths of yellow, orange, and especially red. (Violet light is scattered about 16 times more than red light (~ 1/A4)). As we view the sky, the scattered waves of violet, blue, and green strike the eye from all directions. Since our eyes are more sensitive to blue light, viewing these wavelengths together produces the sensation of blue throughout the sky.

2. Mie Scattering This occurs when the particles are equal to, or larger than, the incident wavelength. In the ambient air pollution realm, there is a peak in the aerosol size distribution near the 2 ^m - 3 ^m range. Thus, particles in this range would have corresponding Mie scattering wavelengths in the near infrared portion of the spectrum.

Associated with Mie scattering is Mie theory, a system by which electromagnetic wave theory equations are solved using the boundary conditions at the surface of the particle as it interacts with the incoming radiation. It is typically used in a limited realm of spherical particles. By solving the wave equations it is possible to determine the scattered and absorbed electric field around a particle and ascribe an index of refraction to it. This index, being a solution to the wave equation, will have real and imaginary components and characterize the physical properties of the particle. The total solution will also exhibit some phase functions for the scattered field around the particle. These solutions include Bessel and Hankel functions and are beyond the scope of this chapter. Details of these solutions can be found in 'Atmospheric Radiative Transfer' by J. Lenoble (1993).

3. Geometrical scattering This happens when the particulate mater in the air is much larger than the incident wavelength. Rain drops and dust particles fall into this classification.

As a particle increases in size, it scatters light more efficiently. When it reaches Figure 11.6 Aerosol scattering pattern: Symmetric forward and backward components

270*

270*

a size that is close to the wavelength of the incident light, it scatters more light than a particle five times its size. These particles remove twice the amount of light intercepted by its geometric cross-sectional area. The laws of geometrical optics may be used to compute the angular distribution of light, which is scattered when a plane electromagnetic wave is incident on a particle much larger than the wavelength of the incident light. Processes involving geometrical optics include rays externally reflected by the particle and rays refracted into the particle; the latter rays may be absorbed in the particle, or they may emerge from it after possibly suffering several internal reflections.

Particles much larger than the incident wavelength also scatter light by means of diffraction, which removes energy from the light wave passing by the particle. The diffraction is concentrated in a narrow lobe around the forward direction, and like geometrical reflection and refraction, it contains an amount of energy equal to that incident on the cross section of the particle. In the far field, the diffracted component of the scattered light may be approximated by the Fraunhofer diffraction theory. The diffraction pattern depends only upon the shape of the cross section of the particle.

We use the term 'ray optics' to describe geometrical reflection and refraction, plus Fraunhofer diffraction. Figure 11.7 illustrates the geometrical configuration for different contributions to light scattered by a large sphere. When hit by radiation, particles can absorb it completely, absorb and reradiate it at a lower, longer wavelength, or completely reflect it. It will generally be a combination of both. The absorption and scattering particle, or molecular cross sections <Ta and <Ts respectively, determine the ability to either absorb or scatter the incoming radiation. Absorption removes photons from the radiation field, whereas scattering changes the photon's direction of propagation. Both functions are particle size/wavelength dependent.

Figure 11.7 Representations of light rays scattered by a sphere according to ray optics, from "An Introduction to Atmospheric Radiation" by K. Liou (1980)

### 11.2.2 Absorption

Absorption occurs when gas or particulate matter in the air interacts with the UV radiation in such a way as to remove the electromagnetic energy of the UV photon,

Ligh

Ligh 0 Diffraction

1 External reflection

2 Two refractions

3 One internal reflection

### 4 Two internal reflections

Figure 11.7 Representations of light rays scattered by a sphere according to ray optics, from "An Introduction to Atmospheric Radiation" by K. Liou (1980)

0 Diffraction

1 External reflection

2 Two refractions

### 3 One internal reflection

4 Two internal reflections and as a result, increases the kinetic energy of the gas or particle. Diesel fuel burning produces a great deal of small black carbon particulate matter. These particles act as very efficient absorbers in the UV region of the spectrum, three times better than in the IR region. This is due to the particle's size (Liousse et al., 1996).