Tt X

In this region, then, the equivalent linewidth becomes

Since the absorbed radiance L^j; = L\VW, the net absorption in the strong-absorber regime varies as the square root of (Nl). This is the case for 03, CH4, and NzO in the atmosphere.

c. Strong Absorptions by C02 and H20

The results of a number of laboratory studies [see Liou (1980); and Goody and Yung (1989) for descriptions of these] have shown that for strong absorptions of C02 and HzO under conditions similar to those in the atmosphere, the total absorption band absorption area, A, can be described as the sum of three terms:

The three parameters C, D, and K can be obtained by empirical tits to the data and p is the partial pressure of nonabsorbing gases present. Since this total absorption band area is directly related to the equivalent width and hence to the absorbed irradi-ance, there is a logarithmic dependence of the net absorption on (Nl), which is the case for the strong absorption bands of both water vapor and carbon dioxide in the atmosphere. As discussed by Goody and Yung (1989), the empirically observed logarithmic dependence of absorption on concentration can be shown to be consistent with theoretical expectations based on reasonable assumptions of bandshape and line intensities.

It should be noted that the foregoing considerations apply to the major absorption bands. In some cases, weaker absorption bands of the major greenhouse gases can be sufficiently weak to fall in the linear region. This is the case, for example, for light absorption by 03 in the Chappius band, even if the strong Hartley-Huggins band (see Chapter 4.B) is saturated (e.g., see Lacis et al., 1990).

These weaker bands can have significant effects on the calculated outgoing infrared radiation. For example, Ho et al. (1998) show that much of the reported discrepancy between modeled outgoing long-wavelength radiation and satellite measurements can be attributed to not including weaker absorption bands due to C02 at 4.3 /¿m and 03 at 14 ¡xm and the weaker 03 lines located far from the center of the strong 9.6-/j,m band.

For gases that satisfy these conditions, the effects can be proportionately quite large. For example, addition of one molecule of the chlorofluorocarbons (CFCs) CFC-11 and CFC-12 is equivalent to the addition of ~ f04 additional molecules of C02 due to the stronger absorption cross sections of the CFCs that occur in the atmospheric window and to the dependence of absorption on concentration for the CFCs but on the logarithm of concentration for C02 (Ramanathan et al., 1987).

Figure 14.10 shows the absorption bands and approximate absorption band strengths for a number of molecules found in the troposphere (Ramanathan et al., 1987; Ramanathan, 1988a, 1988b). There are many gases that, on the basis of intrinsic absorption strengths in the atmospheric window, can, in principle, contribute to tropospheric heating. However, the third requirement is that they be present in sufficient concentration to lead to significant infrared absorption. Of the molecules shown in Fig. 14.10, the ones that meet all of these requirements are CH4, NzO, the chlorofluorocarbons (CFCs) and other halocarbons such as methylchloroform, and some perfluorinated compounds such as SFh (see Chapters 12 and 13).

As we shall see in the next section, the concentra tions of all of these "trace" greenhouse gases, as well as C02 and 03, have been increasing over the past century or more.

2. Trends in Trace Gas Concentrations a. C02

Carbon is, of course, extensively recycled through the earth system, including both the terrestrial biosphere and the oceans. Figure 14.11 summarizes this cycling and where the reservoirs of carbon are found. Anthropogenic activities contribute to atmospheric carbon mainly in the form of C02 emissions from fossil fuel combustion and, to a lesser extent, cement production, which total 5.5 Gt of C per year (where 1 Gt of C = 109 metric tons = 1015 g of carbon). The amount of carbon in hydrocarbons, including CH4, and CO is less than 1% of the total atmospheric carbon (IPCC, 1996). Changes in land use, including biomass burning, also contribute to changing the balance, although the net quantitative contribution is less certain. Land use changes in the tropics during the decade from f980 to f990 are estimated to have contributed approximately 1.6 Gt of C per year (IPCC, 1996), but this does not

■ Higher mean radiating height with increased greenhouse gases

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