= Solution
Much stratospheric heating is supplied by absorption of solar <ultraviolet> radiation by <oxygen> and <ozone>, whereas <carbon dioxide> is an important emitter of thermal infrared radiation. In the usual stratospheric balance, increasing <carbon dioxide> enhances net infrared cooling at the original <temperature> without supplying a matching increase in the solar heating. <Temperature> must fall until infrared emission and absorption again balance the heating.
A useful optically thin schematic is $Q_{\rm solar}=c_{\rm CO_2}K[B(T)-\overline J]$, where $B(T)$ represents the relevant thermal source function and $\overline J$ the incident infrared radiation field. With positive fixed solar heating and an approximately fixed radiation field, increasing $c_{\rm CO_2}$ lowers the required $B(T)-\overline J$, hence lowers $T$. This explains why the surface greenhouse argument cannot simply be applied locally to the <stratosphere>. Spectral blocking of upwelling radiation contributes too; the real response depends on altitude, <ozone> heating and <radiative transfer>, rather than emissivity alone.<Why CO2 cools the middle atmosphere - a consolidating model perspective by Helge F. Goessling and Sebastian Bathiany>[Earth System Dynamics 7 (2016), abstract and sections on the blocking and indirect solar effects]{ref}
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