The Komabayashi-Ingersoll limit was the first to be analytically derived and only considers a grey stratosphere in radiative equilibrium. A grey stratosphere (or atmosphere) is an approach to modeling radiative transfer that does not take into account the frequency-dependence of absorption by a gas. In the case of a grey stratosphere or atmosphere, the Eddington approximation can be used to calculate radiative fluxes. This approach focuses on the balance between the outgoing longwave radiation at the tropopause,formula_1, and the optical depth of water vapor, formula_2, in the tropopause, which is determined by the temperature and pressure at the tropopause according to the saturation vapor pressure. This balance is represented by the following equationsformula_3Where the first equation represents the requirement for radiative equilibrium at the tropopause and the second equation represents how much water vapor is present at the tropopause. Taking the outgoing longwave radiation as a free parameter, these equations will intersect only once for a single value of the outgoing longwave radiation, this value is taken as the Komabayashi-Ingersoll limit. At that value the Stefan-Boltzmann feedback breaks down because the tropospheric temperature required to maintain the Komabayashi-Ingersoll OLR value results in a water vapor optical depth that blocks the OLR needed to cool the tropopause.