The atmosphere contains greenhouse gases that absorb and re-emit longwave (infrared) radiation, thus warming the surface. If the greenhouse gas concentration increases, we can therefore expect temperatures to rise. Thus, a reasonable hypothesis is that the increase in anthropogenic greenhouse gases, and in particular CO2, over the past several decades is responsible for the increase in temperature. In chapter 1 we constructed a very simple mathematical model of this process; we now present a somewhat more refined argument that, although having a similar basis, shows how the vertical profile of temperature plays a role.
Referring to figure 7.5, suppose the temperature profile is initially that labelled "Before." Then let us suppose that we add some greenhouse gases to the atmosphere, increasing its emissivity and absorptivity. Now, the total outgoing longwave radiation to space must remain the same because this radiation balances the incoming solar radiation (which of course stays virtually the same). However, because the absorptivity of the atmosphere has increased, the outgoing longwave radiation, on average, originates from a higher level in the atmosphere (radiation emitted from lower levels is reabsorbed by the atmosphere). But the temperature at which the outgoing radiation originates must stay virtually the same so that total outgoing longwave radiation stays the same. Thus, the temperature of the atmosphere at the new level where it is emitting radiation to space must increase and, unless the vertical profile of temperature changes significantly (which is unlikely), the surface temperature must increase, as in figure 7.5.
The argument above illustrates an important aspect of the greenhouse effect, which is that an increase in CO2
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