^{1}

Recently, Zhao and Shi have reviewed this topic. They point out that there are two limits for the D.F. The smallest possible value is unity for paths with large optical depths. The largest possible value is 2 for paths with small optical depths. These authors obtain a function which yields the optimum value of the D.F. for any path as a function of the optical depth of that path. ^{2} In this presentation I use various alternate formats by which I numerically obtain and check for accuracy the OLR obtained from the S.E. as corrected by the D.F. approximation. The paper by Zhao and Shi informs the choice of D.F. used in these computations. An U.S. Standard Atmosphere containing various single species of greenhouse gas is assumed. The only computational tool used is a spreadsheet.

- Raymond T. Pierrehumbert, “Principles of Planetary Climate”, Cambridge University Press, 2010, p. 191.
- Jian – Qi Zhao and Guang-Yu Shi, “An accurate approximation to the diffusivity factor”, Infrared Physics and Technology 56 (2013) 21-24