CO₂ as a greenhouse gas

There has been a growing awareness of the problem of CO₂ emissions by human activity. CO₂ is an important greenhouse gas because of the infrared absorption by its bending mode. The bending mode at 667 cm^-1 is sufficiently intense that nearly all of the earth’s emission in the region of 15 micron wavelength is absorbed. This may seem like a fairly small part of the total spectrum of the earth’s thermal emission, which is peaked near 11 microns. Yet, infrared absorption byCO₂ in this portion of the spectrum has important consequences because of feedback loops that lead to greater vaporization of water. Water is also an important natural greenhouse gas due to its rotational transitions. As glaciers melt and temperatures rise there is a greater average vapor pressure. We can understand this from the Clausius-Clapyeron equation, which gives the dependence of the water vapor pressure on temperature. From these considerations we see that spectroscopy and thermodynamics are both important for an understanding of the role played by CO₂ as a greenhouse gas.

We have seen in Chapter 4 that CO₂ has four normal modes of vibration. The asymmetric stretch and bending modes are infrared active. Although CO₂ lacks a permanent dipole moment these modes distort CO₂ away from its symmetric structure. The oscillation creates a time-dependent (and position-dependent) dipole moment. Since the difference dipole moment, , is not zero, the vibrations have infrared intensity according to the transition moment (Eqn. 4.4.3),

The absorption of radiation occurs at 667 cm^-1 and 2349 cm^-1 for the bending and asymmetric stretching vibrational modes, respectively (see Figure 4.5). This corresponds to wavelengths of 14.9 m and 4.3 m, respectively. The relative importance of these modes depends on their position relative to the Earth’s blackbody emission. The peak of the Earth’s blackbody emission is given by the Wien displacement law (Eqn. 1.3.1), which can be written as,

Thus, the peak of the Eath’s emission is approximately intermediate between the wavelengths of the two vibrational modes. The relative importance of the modes is determined by their intensity (i.e. the magnitude of . It turns out that the bending mode is the most important for absorption of the Earth’s radiant heat. The detailed calculation of the effect must take into account the change in density of the atmosphere, and the fact that infrared radiation can lead to both absorption and stimulated emission of the infrared light. This calculation is beyond the scope of this Chapter. However, the detailed analysis of the absorption by the CO₂ bending mode proves that this mode alone will contribute to heat capture by the atmosphere proportional to the CO₂ partial pressure.

The consequences of the heating of the atmosphere produced by increased partial pressure of CO₂ include melting of snow packs and glaciers, and increased temperature that leads to high water vapor pressure. A small increase in water vapor pressure can have a large impact on absorption of microwave radiation by the water pure rotational spectra. Since water has a large dipole moment along two of its moment of inertia axes, the rotational absorption gives rise to intense absorption of microwave radiation. These are investigated further in the Exercises.