Climate Arindam Chakraborty · CAOS, IISc Bengaluru
Teaching tool

Radiative equilibrium in a grey atmosphere

Set the number of layers, the solar constant and the surface albedo, and the equilibrium temperature of every layer solves in the browser. Nothing to install.

Updated 2026-08-12

What the model does

Each layer is transparent to sunlight and absorbs all longwave radiation reaching it. Requiring energy balance at the surface and at every layer gives a linear system whose solution is the familiar result that the surface temperature rises with the number of absorbing layers while the topmost layer settles near the emission temperature 1. It is a caricature, and it is the right caricature to start from.

The model

Placeholder for the interactive model
Replace this figure with the model itself — see the comment in the source of this page for the two ways to do it.

Things to try

  • Add layers one at a time and watch how surface temperature grows.
  • Raise the albedo and find the value that brings the surface to freezing.
  • Compare the lapse rate the model produces with the observed one, and ask what is missing.
References
  1. Manabe, S., and R. T. Wetherald, 1967: Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci., 24, 241–259.