Any body with a temperature above absolute zero emits electromagnetic radiation. This radiation spans a range of wavelengths, the distribution of which depends on the surface temperature of the emitting body.
This relationship is described by Planck’s law, which defines the spectral distribution of radiation emitted by a black body as a function of wavelength and temperature (Figure 1) [1].
Figure 1: Blackbody radiation at different temperatures, calculated using Planck’s law. The area under each curve represents the total energy emitted at a given temperature.
In this representation, the ordinate corresponds to the spectral radiance (power emitted per unit area and per unit wavelength), while the abscissa represents the wavelength. The total energy emitted by the body is given by the area under the curve.
The interaction between the Sun and the Earth can be understood through radiative balance. The Sun continuously emits radiation that reaches the Earth. However, the Earth does not indefinitely warm up because it also emits radiation back into space. At equilibrium, the incoming solar radiation (heat gain) is balanced by the outgoing terrestrial radiation (heat loss).
Taking into account that part of the incoming solar radiation is reflected by the Earth’s surface and atmosphere (albedo effect), the Earth absorbs on average approximately 240 W/m².
At radiative equilibrium, the Earth must therefore emit the same amount of energy, i.e., 240 W/m².
The total emitted flux of a body is more directly described by the Stefan–Boltzmann law, which relates the emitted energy to temperature. Using this relationship, a planet emitting 240 W/m² would have an effective temperature of approximately −18°C. This corresponds to the theoretical temperature of the Earth in the absence of greenhouse gases [2].
Figure 2.3 illustrates the case of an Earth with greenhouse gases. In this situation, greenhouse gases absorb and re-emit infrared radiation, reducing the efficiency of radiative cooling. As a result, to emit the same outgoing flux of 240 W/m², the surface temperature must increase to approximately 15°C, which corresponds to present-day average conditions.
Figure 2: Outgoing radiation as a function of temperature. Without greenhouse gases, an emitted flux of 240 W/m² corresponds to a temperature of −18°C. When greenhouse gases are present, they reduce radiative cooling, requiring a higher surface temperature (~15°C) to maintain energy balance.
In other words, greenhouse gases act by limiting the Earth’s radiative cooling, thereby increasing the equilibrium surface temperature.
Bibliography
[1] Daniel, V. (2003, October 21). Le rayonnement thermique et la loi du Corps Noir — Planet-Terre. Planet-Terre.ens-Lyon.fr. https://planet-terre.ens-lyon.fr/ressource/bilan-radiatif-terre1.xml
[2] Dufresne, J.-L., & Treiner, J. (2024). L’effet de serre atmosphérique : plus subtil qu’on ne le croit ! Ens-Lyon.fr. https://perso.ens-lyon.fr/fenril.montorier/fichiers/LP21%20BUP%20Profil%20temp%C3%A9rature%20atmosph%C3%A8re