Effect of scattering

Since the air molecules are much smaller than the wavelengths of solar radiation, the efficiency with which they scatter light is proportional to 1/14, in accordance with Rayleigh's Law. Scattering of solar radiation is therefore much more intense at the short-wavelength end of the spectrum, and most of the radiation scattered by the atmosphere is in the visible and ultraviolet ranges.

Some of the radiation scattered from the solar beam is lost to space, and some finds its way to the Earth's surface. In the case of 'pure' Rayleigh scattering (scattering entirely due to air molecules, with a negligible contribution from dust), there is as much scattering in a forward, as in a backward, direction (Fig. 2.2; Chapter 4). Thus, ignoring for simplicity the effects of multiple scattering, half the light scattered from a

Fig. 2.2 Polar plot of intensity as a function of scattering angle for small particles (r « 0.025 mm) for green (1 « 500 nm) and red (1 « 700 nm) light. (By permission, from Solar Radiation, N. Robinson, Elsevier, Amsterdam, 1966.)

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Fig. 2.2 Polar plot of intensity as a function of scattering angle for small particles (r « 0.025 mm) for green (1 « 500 nm) and red (1 « 700 nm) light. (By permission, from Solar Radiation, N. Robinson, Elsevier, Amsterdam, 1966.)

sunbeam in a dust-free atmosphere will be returned to space and half will continue (at various angles) towards the Earth's surface. The total solar energy reflected (by scattering) back to space by a cloudless dust-free atmosphere alone after allowing for absorption by ozone, is about 7%.1141

The atmosphere over any part of the Earth's surface always contains a certain amount of dust, the quantity varying from place to place and with time at any given place. Dust particles scatter light, but are generally not sufficiently small relative to the wavelength of most of the solar radiation for scattering to obey the Rayleigh Law. They exhibit instead a type of scattering known as Mie scattering (see Chapter 4), which is characterized by an angular distribution predominantly in the forward direction, and a much weaker dependence on wavelength, although scattering is still more intense at shorter wavelengths. Although dust particles scatter light mainly in a forward direction, they do also scatter significantly in a backward direction; furthermore, a proportion of the light scattered forward, but at large values of scattering angle, will be directed upwards if the solar beam is not vertical. Since the particle scattering is additive to the air molecule scattering, a hazy (dusty) atmosphere reflects more solar energy to space than does a clean atmosphere.

That fraction of the solar flux which is scattered by the atmosphere in the direction of the Earth's surface constitutes skylight. Skylight appears blue because it contains a high proportion of the more intensely scattered, blue light from the short-wavelength end of the visible spectrum. In a hazy atmosphere the increased scattering increases skylight at the expense of the direct solar flux. The proportion of the total radiation received at the Earth's surface which is skylight varies also with the solar elevation. As the atmospheric pathlength of the solar beam increases with decreasing solar elevation, so more of the radiation is scattered: as a consequence the direct solar flux diminishes more rapidly than does skylight.

At very low solar elevations (0 °-20 °) in the absence of cloud, the direct solar beam and the diffuse flux (skylight) contribute approximately equally to irradiance at the Earth's surface. As solar elevation increases, the irradiance due to the direct beam rises steeply but the irradiance due to skylight levels off above about 30 At high solar elevations under cloudless conditions, skylight commonly accounts for 15 to 25% of the irradiance and the direct solar beam for 75 to 85%:928 in very clear dry air the contribution of skylight can be as low as 10%.

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