Why logarithmic? A note on the dependence of radiative forcing on gas concentration

Line-by-line radiative transfer computations show that the logarithmic dependence of radiative forcing on gas concentration not only applies to broadband irradiation fluxes such as in the well-known case of the CO₂ forcing, but also applies to the spectral radiance change due to both CO₂ and other gases, such as H₂O. The logarithmic relationship holds for monochromatic radiance requires an explanation beyond the conventional ideas based on the spectroscopic features of the gas absorption lines. We show that the phenomenon can be explained by an Emission Layer Displacement Model, which describes the radiance response to gas perturbation under normal atmospheric conditions such as temperature linearly varying with height and gas concentration exponentially decaying with height.