A Quasi-Linear Relationship between Planetary Outgoing Longwave Radiation and Surface Temperature in a Radiative-Convective-Transportive Climate Model of a Gray Atmosphere

In this study, we put forward a radiative-convective-transportive energy balance model of a gray atmosphere to examine individual roles of the greenhouse effect of water vapor, vertical convection, and atmospheric poleward energy transport as well as their combined effects for a quasi-linear relationship between the outgoing longwave radiation (OLR) and surface temperature (TS). The greenhouse effect of water vapor enhances the meridional gradient of surface temperature, thereby directly contributing to a quasi-linear OLR-TS relationship. The atmospheric poleward energy transport decreases the meridional gradient of surface temperature. As a result of the poleward energy transport, tropical (high-latitude) atmosphere-surface columns emit less (more) OLR than the solar energy input at their respective locations, causing a substantial reduction of the meridional gradient of the OLR. The combined effect of reducing the meridional gradients of both OLR and surface temperature by the poleward energy transport also contributes to the quasi-linear OLR-TS relationship. Vertical convective energy transport reduces the meridional gradient of surface temperature without affecting the meridional gradient of OLR, thereby suppressing part of the reduction to the increasing rate of OLR with surface temperature by the greenhouse effect of water vapor and poleward energy transport. Because of the nature of the energy balance in the climate system, such a quasi-linear relationship is also a good approximation for the relationship between the annual-mean net downward solar energy flux at the top of the atmosphere and surface temperature.