Absolutely Small - Michael D. Fayer [119]
THE EARTH’S BLACK BODY SPECTRUM
In Chapters 4 and 9, we discussed black body radiation. Figure 9.1 shows the black body spectrum of the sun, whose surface temperature is almost 6000° C. The black body emission has a good deal of its intensity in the visible portion of the spectrum, with a substantial amount of light being emitted in the ultraviolet and the near infrared portions. The colors emitted by a hot object depend on the object’s temperature. Hotter objects emit shorter wavelengths. The Earth is, of course, much colder than the sun. Nonetheless, it is a black body emitter. Still, the wavelengths it emits are very long (very low energy photons). Sunlight with the spectrum given in Figure 9.1 falls on the Earth. Some of this light is reflected back into space by ice and other highly reflecting surface features. However, much of the light energy is converted into heat, which warms the Earth. Black body emission by the Earth radiates some of the energy that comes from the sun back into space.
The top portion of Figure 17.1 shows three calculated black body spectra of the Earth for three temperatures. The three curves are normalized, that is, their amplitudes adjusted to all have a maximum value of 1. 15° C (59° F) is the average surface temperature of the Earth; 27° C (81° F) is the surface temperature in the tropics; and -16° C (3° F) is the surface temperature in subarctic regions. While the curves vary somewhat, they are, by and large, very similar. The differences do not matter for discussing the influence of carbon dioxide.
Absorption of the Earth’s Black Body Radiation
The bottom two spectra in Figure 17.1 (note the frequency scale is different from the top spectrum) show the atmospheric transmission of infrared radiation through carbon dioxide and water in the long wavelength regions. A transmission of 1 means all of the light passes through the atmosphere. Zero transmission means that none of the light passes through the atmosphere. These spectra differ depending on which region of the Earth they are measured. The spectra shown are representative. In addition, a good deal of fine structure (peaks and troughs), particularly in the water spectrum, is not shown. The purpose of these curves is to display the essential features of the infrared absorption by carbon dioxide and water that are in the intense part of the Earth’s black body spectrum. These absorptions are indicated by the shaded regions. Water also has a strong absorption centered around 1750 cm-1, which is also shaded. The infrared absorption prevents a portion of the Earth’s black body emission from being radiated into space. Without the atmospheric absorption, the Earth would be much colder.
FIGURE 17.1. Top: Calculated Earth black body spectra for three temperatures (solid curves). The shaded regions show the portions of the spectrum that are strongly absorbed by water and carbon dioxide in the atmosphere. Middle and bottom: spectra of the strong absorption by carbon dioxide and water in the range of 0 to 1000 cm-1. Note the scale difference with the top part of the figure.
The Reason Carbon Dioxide Is So Important
The reason carbon dioxide is so important can be seen by looking at the shaded regions of the black body spectrum and the absorption spectra. Water absorbs essentially everything at wavelengths longer than 500 cm-1. However, the bottom two spectra in Figure 17.1 show that carbon dioxide absorbs strongly in the region where water absorption is not very strong. The carbon dioxide absorption is very close to the peak of the Earth’s black body emission spectrum, as shown in the top part of Figure 17.1, regardless of which Earth surface temperature is used. Therefore, carbon dioxide strongly absorbs the Earth’s black body radiation in an important spectral range where other components of the atmosphere, particularly water, do not. The carbon dioxide spectrum (middle