The Earths Atmosphere as a Filter

Above, we described the solar resource at the top of the atmosphere. The atmosphere acts as a continuously variable filter for the ETR radiation. The atmosphere has stable components of 78% nitrogen, 21% oxygen, and 1% argon and other "noble" gases. There are also variable components in the atmosphere, such as water vapor (0% to 2% of the total composition), and gases dumped into the atmosphere by man-made and natural process, such as carbon dioxide, (0.035%), methane, and nitrous oxides.6

At a concentration of only 0.3 parts per million, Ozone absorbs and attenuates the dangerous UV radiation below 280 nm. Water vapor absorbs mainly in the infrared, contributing to the heating of the atmosphere. Similarly, small concentrations of "greenhouse" gases such as carbon dioxide and methane absorb in the infrared, but with such strength that their increasing concentration may pose a threat to the stability of the Earth's climate. Suspended particulates such as aerosols, dust and smoke, as well as condensed water vapor (clouds) also strongly modify the solar resource as the atmosphere is traversed by photons from the top of the atmosphere to the surface. As the photons propagate through the atmosphere, radiation in the narrow cone of light from the solar disk (the direct beam) interacts with the atmosphere by being absorbed or scattered out of the beam. Molecules of atmospheric gases, aerosols, dust particles, and so on, do the absorption and scattering. Scattered radiation contributes to the bright blue of the clear sky dome, or the dull gray of overcast skies. The scattered radiation also illuminates clouds, which reflect most of the wavelengths of light in the visible region, making them appear white. Figure 3 schematically shows this process of atmospheric sorting of the radiation into three components: the direct beam, the scattered radiation (called diffuse radiation) and the combination of the direct and diffuse radiation, called the total hemispherical, or global radiation from the entire sky dome.

As a result of the absorption and scattering processes in the atmosphere, the ETR spectral distribution is significantly modified. Figure 4 shows the effect of the atmosphere on the ETR spectral distribution for a very specific solar geometry, referred to as Air Mass 1.5. As indicated in Fig. 3, Air Mass 1.0 occurs when the sun is directly overhead. The angle between the horizon and the observer (solar elevation) is then 90°, and the angle between the zenith (overhead point) and the observer is 0°. The relative position of the sun with respect to the horizon or zenith is specified as the elevation angle, e, or zenith angle, z, respectively. The term Air Mass refers to the relative path length through the atmosphere, with respect the minimum path length of 1 for zenith angle 0°. Geometrically, Air Mass M is:

Figures 5 and 6 show how the direct beam and global horizontal spectral distributions are modified on a clear day as a function of increasing Air Mass. Note how, as the Air Mass increases, the direct beam spectra change more than the global sky

Sun Angle Absorption Atmosphere Position

Fig. 3. Scattering of the direct beam photons from the sun by the atmosphere produces diffuse and global sky irradiance.

Fig. 3. Scattering of the direct beam photons from the sun by the atmosphere produces diffuse and global sky irradiance.

Graph Etr Irradiance

200 500 800 1100 1400 1700 2000 2300 2600 2900 3200 3500 3800 4100 Wavelength (nanometers)

Fig. 4. The attenuation and absorption of the ETR spectral distribution by the atmosphere. Top curve is the ETR spectral distribution. In decreasing order, the global, direct, and diffuse spectral distributions at the bottom of the atmosphere (at sea level) for the sun at zenith angle

200 500 800 1100 1400 1700 2000 2300 2600 2900 3200 3500 3800 4100 Wavelength (nanometers)

Fig. 4. The attenuation and absorption of the ETR spectral distribution by the atmosphere. Top curve is the ETR spectral distribution. In decreasing order, the global, direct, and diffuse spectral distributions at the bottom of the atmosphere (at sea level) for the sun at zenith angle

Zenith Sun

Fig. 5. Progressive reduction in direct beam spectral distributions as air mass in increased. The plots representing uniformly increasing 10° steps in zenith angle from 0° (top curve) to 80°

(bottom curve).

Fig. 5. Progressive reduction in direct beam spectral distributions as air mass in increased. The plots representing uniformly increasing 10° steps in zenith angle from 0° (top curve) to 80°

(bottom curve).

Solar Spectra Angle

Fig. 6. Progressive reduction in global total hemispherical spectral distributions as Air Mass is increased, as in Fig. 5.

Fig. 6. Progressive reduction in global total hemispherical spectral distributions as Air Mass is increased, as in Fig. 5.

spectra. This is because the energy scattered out of the direct beam is "transferred" into the global spectra, as increasing contributions to the diffuse sky radiation.

Figure 5 in particular illustrates the shift of the spectral peak to longer (red) wavelengths associated with red skies at sunset and sunrise. Figure 7 schematically shows the relationship of absolute temperatures, and color as perceived by the human eye for various outdoor natural conditions, and artificial indoor sources. Our eyes adapted to take advantage of the energy peak in solar spectral distribution between 400 nm and 700 nm, and evolved under the spectral distribution of our sun. Therefore, the match (or mismatch) of artificial source spectral distributions with the solar spectral distribution is important for both natural and artificial lighting applications.

As mentioned above, other elements besides the gases in the atmosphere interact with the ETR spectral distribution. One of the most important of these other atmospheric constituents are small particles called aerosols. Particles scatter radiation most efficiently when the wavelength of the radiation is smaller than the particle size. Many of the particles that work their way into our atmosphere (dust, decaying organic material, smoke from fires, etc.) have diameters that scatter shortwave (UV) and visible light very efficiently. This removes a great deal of energy from the direct beam, and redistributes the energy over the sky dome.7

A measure of the scattering power of aerosols is the amount of energy removed from (or the attenuation of) the beam radiation. The Beer-Bouger-Lambert law for the attenuation of a beam of intensity Io to intensity I, resulting from the amount, x, of a material is given by: I/Io = e-T x or I = Io e-T x where t is the attenuation coefficient, called the aerosol optical depth , or AOD. The attenuation by aerosols is both exponential, and a strong function of wavelength, implying a large impact on the direct beam solar spectral distribution. Anders Angstrom first proposed a relation between the wavelength and t, dependent on two parameters and a reference point at a wavelength of 1000 nm as t= p A-a. p is related to the size of the particles, and ranges from about 1 to 2. a is related to the scattering properties of the particles, and ranges from about 0.001 to 0.5.

Most often, AOD is referred to a specific wavelength, usually 500 nm, or occasionally 550 nm. An AOD of 0.01 at 500 nm represents very clean, pristine, clean atmosphere. Values of AOD at 500 nm of 0.1 to 0.2 are quite typical of average conditions. Values of 0.4 or greater represent a heavy aerosol load and very hazy skies. Figure 8 shows the clear sky direct beam spectral distribution at Air Mass 1.5 for a range of AOD from 0.05 to 0.40

From the discussion above and Figs. 5 to 7, the fluctuations in the solar spectrum at the Earth's surface are dependent on many factors. These variations can be characterized with measurements and models to account for their impact on solar renewable energy technologies.

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