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FIGURE 14.7 Model-calculated atmospheric temperature changes as a function of altitude due to an increase in C02 from 315 ppm in 1960 to 370 ppm projected for 2000 (no feedbacks taken into account) (adapted from Rind and Lacis, 1993).

greenhouse gas such as C02 on the temperature of the atmosphere depends on the altitude and temperature. For example, once C02 reaches the stratosphere, its density is too small to trap radiation to a significant extent. In addition, the temperature is increasing with altitude in the stratosphere. Thus, from the Boltzmann relationship (Eq. (A)), the relative concentrations of the excited emitting states are increasing, resulting in a greater net emission of energy to space. The result is that although C02 in the troposphere leads to warming, in the stratosphere it leads to cooling (e.g., see Roble and Dickinson, 1989; Cicerone, 1990; Rind et al., 1990; and Rind and Lacis, 1993).

Figure 14.7 shows one model calculation of the atmospheric temperature change due to increasing the C02 concentration from 315 to 370 ppm, corresponding to the change over the years from 1960 to 2000 (Rind and Lacis, 1993). Heating in the troposphere and cooling in the stratosphere are clearly evident. It is interesting that this cooling of the stratosphere due to C02 may have some interesting side effects. For example, Yung et al. (1997) estimate using model calculations that a doubling of C02 would increase the erythema-weighted UV by ~1% at the earth's surface due to the temperature effect on the UV absorption cross sections for 03.

3. Dependence of Net Infrared Absorption on Atmospheric Concentrations

Net infrared absorption is determined by the intrinsic strength of the absorption for that particular

FIGURE 14.7 Model-calculated atmospheric temperature changes as a function of altitude due to an increase in C02 from 315 ppm in 1960 to 370 ppm projected for 2000 (no feedbacks taken into account) (adapted from Rind and Lacis, 1993).

molecule and transition (i.e., the absorption cross section), the effective path length, and the concentration of the absorbing gas. C02, H20, and to a lesser extent 03, all absorb infrared radiation strongly in the atmosphere. As discussed in more detail shortly, other infrared-absorbing trace gases, particularly those that have strong absorptions in the relatively clean atmospheric window from 7 to f3 /¿m where C02, HzO, and 03 do not absorb strongly, also contribute to the net absorption of this radiation. However, as discussed in detail by Shine (1991), even a gas that absorbs in the same regions as the major greenhouse gases can contribute to trapping of infrared radiation; the contribution due to an increase in a particular trace gas depends on the combination of absorption region, initial concentration of the gas, and its absorption coefficients.

The dependence of absorption on concentration is linear only for weak absorption lines in the atmospheric window; this is the case, for example, for the chlorofluorocarbons. For stronger absorptions such as those due to 03, CH4, and N20, absorption at the peak of the absorption bands approaches saturation; in these case, the net absorption varies with the square root of the absorber concentration. For very strongly absorbing peaks such as those due to C02 and HzO, absorption only occurs at the fringes of the band and the net absorption varies with the logarithm of the absorber concentration (Dickinson and Cicerone, 1986; Mitchell, 1989). The reasons for this are discussed in books devoted to the subject of atmospheric radiation, which should be consulted for details (e.g., see Liou, 1980; Goody and Yung, 1989; and Lenoble, 1993). A brief account is given in Box 14.1. The absorption cross sections of a variety of gases of atmospheric relevance that are needed for these calculations are available in the literature. See, for example, the HITRAN database (Rothman et al., 1992).

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