How Clear-Sky Spectral Overlap Shapes Radiation in Cloudy Atmospheres

Optically-thick clouds largely emit thermal radiation at their cloud top temperature across the longwave spectrum. However, the degree to which cloud top temperature dominates outgoing longwave radiation depends on how the clouds share spectral space with Earth's major greenhouse gases. In this work we leverage analytical models of spectral emission by CO₂ and  H₂O  to understand how spectral overlap between gases and clouds impacts the longwave cloud radiative effect (CRE) and all-sky feedbacks. We demonstrate that CRE is linear in the difference between surface and cloud top temperature because of water vapor's greenhouse effect and that low clouds exert a small CRE not exclusively because their temperature is close to surface temperature but primarily because they are masked by H₂O and CO₂. Spectral decomposition of feedbacks  reveals that the changing emission temperature of greenhouse gases stabilizes the climate even in fully cloudy columns, and clouds that warm with the surface provide additional stabilization in the water vapor window. We find good agreement between our analytical expressions and both full-physics line-by-line calculations as well as output from a global storm resolving model. By understanding spectral overlap of greenhouse gases and clouds, we disentangle the effects of surface temperature, cloud top temperature, and relative humidity on Earth's longwave energy balance in cloudy columns.