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FIGURE 3.15 Attenuation coefficients (i) for light scattering (Rayleigh scattering) and absorption (ozone absorption) by gases and for scattering and scattering plus absorption (aerosol extinction) by particles [from Peterson (1976) and Demerjian et al. (1980)].

In the atmosphere, light absorption in the ultraviolet region is predominantly due to 03 and this is predominantly in the stratosphere (Figs. 3.12 and 3.13). Since the absorption coefficients (a) of 03 are reasonably well established, a variant of the Beer-Lambert law can be applied to determine how much of the incident light is absorbed by 03:

A is the effective column 03 (molecules cm-2), a its absorption cross section at that wavelength, and m the air mass. One needs to know, in addition to a, the 03 concentration as a function of altitude (z), that is,

Using the published absorption coefficients (a) as a function of wavelength, one can then apply the Beer-Lambert law to calculate the intensity of light transmitted through such a vertical column to the earth's surface or to an altitude z. The resulting attenuation coefficients for 03 are shown in Fig. 3.15 for an overhead sun. Clearly, 03 is responsible for most of the attenuation of light directly from the sun of À < 310 nm reaching the earth's surface.

This region of the spectrum around 300 nm is a crucial one for tropospheric photochemistry in both clean and polluted atmospheres. As we have indicated earlier, it is here that species such as ozone and aldehydes photolyze to produce atoms and free radicals critical to the chemistry of the troposphere.

Scattering and absorption of light by particulate matter are much more complex and will not be treated in detail here. Clearly, the size distribution and chemical composition, as well as the concentration of the particles, are very important in determining the extent of light scattering and absorption. Since these parameters will vary significantly geographically, seasonally, and diurnally, accurately estimating their impact on light intensities at a particular location at the earth's surface is difficult. Simplifications for the attenuation coefficient for scattering by particles such as

are often made, where b depends on the concentration of particles and n on their size; for example, n decreases from ~ 4 to 0 as the particle size increases (Leighton, 1961).

One estimate of the attenuation coefficients for light scattering by particles, t is also given in Fig. 3.15

(Demerjian et al., 1980). Also shown are these researchers' estimates of total scattering plus absorption due to particulate matter, known as the aerosol extinction:

sp dp

In this case, the radii of the particles were assumed to fall between 0.01 and 2.0 ^m; the peak in the number versus size distribution was at 0.07 yu,m.

Given estimated values for the attenuation coefficients for scattering and absorption of light by gases and particles (i.e., i , i , t , and t \ one can calculate from Eq. (X) the fraction of the direct solar intensity incident on the top of the atmosphere that is transmitted to the earth's surface at any given wavelength. However, when one considers the actual light intensity that reaches a given volume of gas in the troposphere, one must take into account not only this direct solar radiation but also two other sources of indirect light: (1) light, either from the sun or reflected from the earth's surface, that is scattered to the volume by gases or particles, known as diffuse solar radiation or sky radiation, and (2) light that is reflected from the earth's surface. These are illustrated in Fig. 3.16.

Estimating the intensity of the scattered light at a given point in the atmosphere is difficult because of the substantial uncertainties and variability involved in the factors that contribute to light scattering; for example, the size distribution, concentration, and composition of particles, which to a large extent cause this scattering, are highly variable geographically and temporally and are not always well known for a particular point in space and time.

The amount of light reflected from the earth's surface to a volume of air clearly depends on the type of surface, as well as the wavelength of light; thus snow is highly reflecting, whereas black lava rock reflects very little of the incident radiation. The term used to describe the extent of this reflection is the surface albedo, which is the fraction of light incident on the surface that is reflected. Reflection can be specular, in which the angles of incidence and reflection are equal (e.g., a water surface at large zenith angles), or diffuse, in which light is reflected equally in all directions regardless of the angle of incidence (e.g., white rocks or buildings); the latter is known as "Lambertian" reflection. Table 3.6 gives some reported values of surface albedos for different types of surfaces. It should be noted that, as expected, albedos are wavelength dependent (e.g., see McLinden et al. (1997) for wavelength dependence of ocean albedos and Herman and Celar-ier (1997) for albedos in the UV from 340 to 380 nm).

One can thus estimate the total light intensity incident on a given volume of air in the troposphere due to direct solar radiation, scattering, and reflection. The light absorbed in that volume can then be calculated

FIGURE 3.16 Different sources of radiation striking a volume of gas in the atmosphere. These sources are direction radiation from the sun, radiation scattered by gases and particles, and radiation reflected from the earth's surface.
TABLE 3.6 Some Typical Albedos for Various Types of Surfaces

Type of surface

Albedo

Reference

Snow

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