Why is the greenhouse energy effect produced by CO2 logarithmic? Is it inevitably so for each of the other greenhouse gases? These are both good questions, and they are related. The whole concept of “sensitivity” as employed by climate scientists is based on a logarithmic understanding with respect to CO2, such that any one double of the atmospheric concentration of the gas will result in the same amount of effect on surface temperatures as any other double, no matter what the starting point may be. All models are tied to this understanding, and there is competition in search of an exact way to express the value of this effect for CO2, which tends to become more complicated when feedbacks are added to the picture. Science does not often produce a full explanation for why the effect is logarithmic, nor does it openly make any claim that all or any of the other greenhouse gases are known to be deserving of the same kind of numerical evaluation as that which is given to CO2, e.g., about 3C per double, including constant linkage to certain specified feedbacks, or about 1.2C per double for molecular CO2 alone, excluding feedbacks of any kind.
The work I have been doing, purportedly studying observations of greenhouse effects produced holistically by the atmospheric content of precipitable water (PW), which always includes a significant percentage of water vapor, a greenhouse gas, strongly suggests that a logarithmic understanding of its effects are applicable. The study also provides a rough numerical estimate (10C per double) of the value of the effect on surface temperatures from each double. This further suggests the idea that if both PW and CO2 adhere to the same logarithmic understanding, then that same understanding might very well apply to all of the greenhouse gases. Knowledge of the specific effect on surface temperatures for changes in each of those gases should be worth acquiring, given that we have excellent data available in each case regarding many aspects of past and present changes in their concentration.
Going back to the two questions I started with, I have been searching for clear and simple explanations of why this is so for molecular CO2, thinking that the same explanation must apply equally to all of the other gases, including water vapor, and possibly also by extension to PW in a more general way, after allowing for somewhat altered greenhouse effects ascribed to its non-gaseous contents. This post will lay out some thoughts about how the subject can be approached, providing an indication of its difficulties, with no end in sight.
The greenhouse effect does not apply to incoming photons of solar radiation that are ultimately captured by the dense materials making up the planetary surface. It does apply to outgoing photons, all of which are of longwave varieties, radiated from the surface and originally directed toward space by default. Earth has an atmosphere, and the atmosphere is full of stuff that can capture and swallow these photons. Some of this stuff is composed of the molecules of certain specific gases, each of which can capture photons of certain specific wavelengths, to the exclusion of all others. More of the stuff is composed of aerosols made up of small, densely-packed bodies of molecules in either a liquid or solid state. These bodies most likely have much broader, and perhaps more variable, capacities for capturing photons of many wavelengths.
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Surface capture of photons created by and delivered from sources existing in the atmosphere is a critical component of the greenhouse effect. It’s magnitude should ultimately depend on the amount of stuff in the atmosphere that can capture photons and head some of them back toward the surface, with the prospect that a certain number of these will at some point be captured at the surface. The central question is, how many will make it back to the surface relative to an increase in the total number of those that are trapped? It seemingly keeps diminishing in a statistically consistent manner, logarithmic on one side and linear on the other. I have no good answers to offer, but it is an interesting thing to think about.
(This post has been updated for clarity and brevity.)
Carl