How Clear-Sky Spectral Overlap Shapes Radiation in Cloudy Atmospheres

Abstract 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 CO 2 and H 2 O to understand how spectral overlap between gases and clouds impacts the longwave cloud radiative effect (CRE) and cloudy-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 the surface temperature but predominantly because they are masked by H 2 O and CO 2 . Spectral decomposition of feedbacks reveals that the changing emission temperature of greenhouse gases stabilizes the climate even in fully cloudy columns and that 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 the 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. Significance Statement The spectral distribution of outgoing longwave radiation (OLR) is determined by which atmospheric constituent first becomes optically thick when viewed from above. Using pencil-and-paper models for the spectral variation of OLR, we disentangle the effects of surface temperature, cloud-top temperature, and relative humidity on Earth’s longwave energy balance. Our expressions yield an understanding of physical phenomena, illustrating that the cloud radiative effect (the difference in OLR in an atmospheric column with and without a cloud) is linear in the difference between surface and cloud-top temperature because clouds and gases share the longwave spectrum. Additionally, changes in water vapor and CO 2 emission temperature can provide a stabilizing response to warming surface temperatures even in cloudy columns with unchanging clouds.