# The Atmospheric Absorption Spectrum

A property of the blackbody radiation curve is that the wavelength of maximum energy emission, Xm, satisfies

This is known as Wien's displacement law. Since the solar emission temperature is about 6000 K, the maximum of the solar spectrum is (see Fig. 2.2) at about 0.6 ^m (in the visible spectrum), and we have determined Te = 255 K for the Earth, it follows that the peak of the terrestrial spectrum is at

XEmarth = 0.6 ^m x 6000 - 14 Mm. 255

Thus the Earth's radiation to space is primarily in the infrared spectrum. Normalized (see Appendix A.1.1) blackbody spectra for the Sun and Earth are shown in Fig. 2.6. The two spectra hardly overlap, which greatly simplifies thinking about radiative transfer.

Also shown in Fig. 2.6 is the atmospheric absorption spectrum; this is the fraction of radiation at each wavelength that is FIGURE 2.6. (a) The normalized blackbody emission spectra, T-4XBX, for the Sun (T = 6000 K) and Earth (T = 255 K) as a function of ln X (top), where Bx is the blackbody function (see Eq. A-2) and X is the wavelength (see Appendix A.1.1 for further discussion). (b) The fraction of radiation absorbed while passing from the ground to the top of the atmosphere as a function of wavelength. (c) The fraction of radiation absorbed from the tropopause (typically at a height of 11km) to the top of the atmosphere as a function of wavelength. The atmospheric molecules contributing the important absorption features at each frequency are also indicated. After Goody and Yung (1989).

FIGURE 2.6. (a) The normalized blackbody emission spectra, T-4XBX, for the Sun (T = 6000 K) and Earth (T = 255 K) as a function of ln X (top), where Bx is the blackbody function (see Eq. A-2) and X is the wavelength (see Appendix A.1.1 for further discussion). (b) The fraction of radiation absorbed while passing from the ground to the top of the atmosphere as a function of wavelength. (c) The fraction of radiation absorbed from the tropopause (typically at a height of 11km) to the top of the atmosphere as a function of wavelength. The atmospheric molecules contributing the important absorption features at each frequency are also indicated. After Goody and Yung (1989).

absorbed on a single vertical path through the atmosphere. From it we see that:

• The atmosphere is almost completely transparent in the visible spectrum, at the peak of the solar spectrum.

• The atmosphere is very opaque in the UV spectrum.

• The atmosphere has variable opacity across the IR spectrum. It is almost completely opaque at some wavelengths, and transparent at others.

• N2 does not figure at all in absorption, and O2 absorbs only in the far UV (where there is little solar energy flux) and, a little, in the near IR. The dominant constituents of the atmosphere are incredibly transparent across almost the whole spectral range of importance.

• The absorption of terrestrial radiation is dominated by triatomic molecules—O3 in the UV; H2O, CO2, and others in the IR—because triatomic molecules have rotational and vibrational modes that can easily be excited by IR radiation. These molecules are present in tiny concentrations (see Table 1.2) but play a key role in the absorption of terrestrial radiation (see Fig. 2.6). They are known as greenhouse gases. This is the fundamental reason why atmospheric radiation may be so vulnerable to the human-induced changes in composition shown in Fig. 1.3.