Earth’s outgoing longwave radiation linear due to H₂O greenhouse effect

Earth’s climate is set by a balance between incoming solar and outgoing infrared radiation. The physical processes that influence this balance are complex and nonlinear, yet models and satellite measurements counterintuitively show that Earth’s infrared radiation is simply a linear function of surface temperature. Here we explain why: Linearity is due to the cancellation of two nonlinear processes and always arises in an atmosphere dominated by a condensable greenhouse gas. Our work explains a fundamental property of Earth’s climate and has implications for climate change as well as the climates of extrasolar planets with exotic greenhouse gases.

Satellite measurements and radiative calculations show that Earth’s outgoing longwave radiation (OLR) is an essentially linear function of surface temperature over a wide range of temperatures ($\gtrsim$60 K). Linearity implies that radiative forcing has the same impact in warmer as in colder climates and is thus of fundamental importance for understanding past and future climate change. Although the evidence for a nearly linear relation was first pointed out more than 50 y ago, it is still unclear why this relation is valid and when it breaks down. Here we present a simple semianalytical model that explains Earth’s linear OLR as an emergent property of an atmosphere whose greenhouse effect is dominated by a condensable gas. Linearity arises from a competition between the surface’s increasing thermal emission and the narrowing of spectral window regions with warming and breaks down at high temperatures once continuum absorption cuts off spectral windows. Our model provides a way of understanding the longwave contribution to Earth’s climate sensitivity and suggests that extrasolar planets with other condensable greenhouse gases could have climate dynamics similar to Earth’s.