The Earth's global radiation budget depends critically on the relationship between outgoing longwave radiation (OLR) and surface temperature (Ts). Above 270 K, which represents 89% of the surface of Earth, we find that linearity poorly represents the OLR-TS relationship. Although the AMIP runs of CMIP6 models largely capture the linearity of OLR and Ts, there is considerable variation in how they represent this departure from linearity.

In this study, we investigate physical mechanisms that control the OLR-Ts relationship seen in ERA5 reanalysis and CMIP6 models by using accurate radiative transfer calculations. Our study identifies three key mechanisms to explain both the linearity and departure from linearity of OLR-Ts relationship. The first is the total infrared opacity of the atmosphere, which accounts for 60% of the observed OLR-Ts linear slope. The second is changes in atmospheric emission induced by a foreign pressure effect on absorption lines (of water vapor and other greenhouse gases) and continuum absorption of water vapor, which accounts for 30% of the linear slope. The third is changes in atmospheric emission induced by variations in relative humidity, particularly in the mid-troposphere (250 to 750 hPa), which determines the non-linearity in the OLR-Ts relationship and adds to the remaining 10% of the slope. Furthermore, we find that inter-model spread in mid-tropospheric relative humidity explains a large fraction of the differences in OLR across CMIP6 models at given surface temperatures. Our research also shows that the humidity-induced clear-sky OLR curve is synergistically enhanced by clouds owing to a strong correlation between cloud and humidity.