Energy Balance Model with Greenhouse Parameterization

A simple energy balance model determines the surface temperature of the Earth by balancing the incoming solar energy flux with the outgoing blackbody energy flux . The greenhouse effect is parameterized by a single number, , which reduces the outgoing energy flux by the factor . The greenhouse parameter includes the direct and indirect effects of all of the processes that result from changing greenhouse gas concentrations in the atmosphere.

The incoming solar energy flux is , where is the solar constant, m is the radius of the Earth, and is the albedo of the Earth. The outgoing energy flux is , where is the greenhouse parameter and is the Stefan–Boltzmann constant. The equilibrium temperature is the temperature at which .

References:

M. I. Budyko, "The Effect of Solar Radiation Variations on the Climate of the Earth", Tellus21, 1969 pp. 611–619.

L. R. Kump, J. F. Kasting, and R. G. Crane, The Earth System, Upper Saddle River, New Jersey: Pearson Education, 2004.