At radiative equilibrium, the solar flux that is absorbed by the Earth, , equals the infra-red radiation emitted by the Earth, (figure 8):
Fluxes and are expressed in .
depends on the planetary albedo:
is the Earth albedo, which depends on the ice sheet extent. It is computed as detailed in section 2.4.
is the global-mean, annual-mean incoming solar flux at the top of the atmosphere. Since at any time, the Sun lights up only a quarter of the Earth, we have , where is the solar constant.
depends on temperature according to Stefan-Boltzmann's law, and is modulated by the greenhouse effect:
where:
is the greenhouse effect: it is the fraction of infrared radiation emitted by the Earth that is retained by the greenhouse effect and fails to escape to space;
is Stefan-Boltzmann's constant.
This relationship is illustrated for different concentration in figure 9.
We calculate at each time step , assuming radiative balance:
Graphically, corresponds to the intersection point between and curves (figure 9).
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The temperature simulated by SimClimat follows the equilibrium temperature , but with some delay to represent the effect of the thermal inertia of the oceans (section 5.1).