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Helge F. Goessling coauthored work on the radiative response of the middle atmosphere to increased carbon dioxide. The paper develops a model perspective that distinguishes local emission and absorption from the whole-column energy budget.^[ref]

It illustrates why the effect of changing an absorber cannot be inferred from its absorption strength alone. Optical depth, temperature and the surrounding radiation field jointly determine whether a layer gains or loses energy.

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 $Q_{\mathrm{solar}}=c_{\mathrm{C}{\mathrm{O}}_2}K[B(T)-\overline{J}]$, 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 $c_{\mathrm{C}{\mathrm{O}}_2}$ 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.^[ref]

Sebastian Bathiany coauthored an analysis explaining why increasing carbon dioxide can cool the middle atmosphere while contributing to warming elsewhere. The work compares radiative regimes rather than treating a gas as having one temperature effect independent of its surroundings.^[ref]

The physical interpretation depends on the balance of absorbed and emitted radiation, the atmospheric structure and the level at which energy escapes. This is a concrete application of radiative transfer to climate.

An increase of atmospheric carbon dioxide can cool the stratosphere through enhanced infrared cooling relative to non-infrared heating and through changes in the spectrum of upwelling radiation. A local emissivity-only explanation is incomplete because absorption and emission both change. The response depends on ozone solar heating, spectral opacity, altitude and adjustments of the layers below.^[ref]