The observed quasi-linear OLR-TS relation manifests a climate footprint of radiative (such as the greenhouse effect) and non-radiative processes (poleward energy transport). The former acts to increase the meridional gradient of surface temperature and the latter decreases the meridional gradient of atmospheric temperatures, causing the flattening of the meridional profile of the OLR. Radiative processes alone can lead to a quasi-linear OLR-TS relation that is more steeply sloped. The atmospheric poleward energy transport alone can also lead to a quasi-linear OLR-TS relation by rerouting part of the OLR to be emitted from a warmer place to a colder place. The combined effects of radiative and non-radiative processes make the quasi-linear OLR-TS relation less sloped with a higher degree of linearity. In response to anthropogenic radiative forcing, the slope of the quasi-linear OLR-TS relation is further reduced via stronger water vapor feedback and enhanced poleward energy transport.

