0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Wavelength (nm)

FIGURE 3.13 Approximate regions of maximum light absorption of solar radiation in the atmosphere by various atomic and molecular species as a function of altitude and wavelength with the sun overhead (from Friedman, 1960).

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Wavelength (nm)

FIGURE 3.13 Approximate regions of maximum light absorption of solar radiation in the atmosphere by various atomic and molecular species as a function of altitude and wavelength with the sun overhead (from Friedman, 1960).

which the light passes, as expected from the BeerLambert law. The path length, that is, the distance from the outer reaches of the atmosphere to an observer on the earth's surface, is a function of the angle of the sun and hence time of day, latitude, and season. In addition, reflection of light from the earth's surface alters the light intensity at any given point in the atmosphere, as does the presence of clouds.

The angle of the sun relative to a fixed point on the surface of the earth is characterized by the solar zenith angle 6, defined, as shown in Fig. 3.14, as the angle between the direction of the sun and the vertical. Thus a zenith angle of zero corresponds to an overhead, noonday sun, and a zenith angle of ~ 90° approximates sunrise and sunset. The greater the zenith angle, the longer is the path length through the atmosphere and hence the greater the reduction in solar intensity by absorption and scattering processes.

The path length L for direct solar radiation traveling through the earth's atmosphere to a fixed point on the earth's surface can be estimated geometrically using Fig. 3.14. This "flat earth" approximation is accurate for zenith angles < 60°. One can approximate L using cos 9 = h/L (T)

A common term used to express the path length traversed by solar radiation to reach the earth's surface is the air mass, m, defined as

Length of path of direct solar radiation through the atmosphere m = -----. (V)

Length of vertical path through the atmosphere

With reference to Fig. 3.14, for zenith angles less than 60°, m = L/h = sec 9. (W)

At larger angles, corrections for curvature of the atmosphere and refraction must be made to L and m.

Table 3.5 shows values of the air mass at various zenith angles 9, either estimated using m = sec 9 or corrected for curvature of the atmosphere and for refraction; it is seen that only for 9 > 60° does this correction become significant.

b. Solar Spectral Distribution and Intensity in the Troposphere

When the radiation from the sun passes through the earth's atmosphere, it is modified both in intensity and

in spectral distribution by absorption and scattering by gases as well as by particulate matter. As a result, the actual actinic flux to which a given volume of air is exposed is affected by the zenith angle (i.e., time of day, latitude, and season), by the extent of surface reflections, and by the presence of clouds. Madronich (1993) discusses these variables, with particular emphasis on the effects on the UV reaching the earth's surface.

To estimate the solar flux available for photochemistry in the troposphere then, one needs to know not only the flux outside the atmosphere but also the extent of light absorption and scattering within the atmosphere. We discuss here the actinic flux F(A) at the earth's surface; the effects of elevation and of height above the surface are discussed in Sections C.2.d and C.2.e.

The reduction in solar intensity due to scattering and absorption can be estimated using a form of the Beer-Lambert law:

In Eq. (X), /„ is the light intensity at a given wavelength incident at the top of the atmosphere and I is the intensity of the light transmitted to the earth's surface; t is the total attenuation coefficient described below and m is the air mass as defined earlier. For the sun directly overhead (i.e., zenith angle 0 = 0) the air mass is unity (m = 1.0); the attenuation coefficient then reflects the minimum possible attenuation by the atmosphere. As 9 increases until the sun is on the horizon (i.e., sunset or sunrise), m also increases (Table 3.5); thus the attenuation of the sunlight increases due to the increased path length in the atmosphere through which the light must travel to reach the earth's surface.

The attenuation coefficient, t, represents a combination of light scattering and absorption by gases and

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