One claim made by climatologists is that each doubling in the concentration of CO2 will cause the same increase in the Earth's surface temperature. So far as we can tell, the basis for this claim is that the absorption of radiation by greenhouse gases is "logarithmic". See Nelson, Earthguide and Wikipedia for examples. We never understood this "logarithmic" argument. We have never seen any calculations to back it up.
The greenhouse effect in our Planetary Greenhouse example is the result of logarithmic absorption by a greenhouse gas. The atmosphere contains a hypothetical gas that is opaque to some, but not all, long-wave radiation. As we showed in our previous post, successive doublings in the concentration of this gas do not cause the same increase in surface temperature. Indeed, the graph produced by our computer program shows that each successive doubling causes half as much warming as the previous doubling.
Thus logarithmic absorption alone is not sufficient justification for the existence of a "CO2 Doubling Temperature".