Water vapor carbon dioxide temperature (warming) nonlinear feedback mechanism

In this Youtube video clip starting at 1:12:45 of the debate on the feedback mechanism of the CO$_2$-water-vapour warming effect Professor Richard Lindzen stated that the feedback mechanism is not controlled by the CO$_2$ concentration because of the non-linearity of the feedback mechanism and the heterogeneity of the water vapour distribution. Could someone explain that? It would be best if it is explained with the equations governing the feedback and it is pointed out where the breakdown of the simple monotonicity of temperature and CO$_2$ concentration occurs.

• You might want to edit the exact quote you are asking about into the question - because I believe they state "it is not settled that increase CO2 will increase global warming" which is a bit different than "there is a nonlinear mechanism" which is what you are claiming. – Floris Jun 4 '17 at 22:18
• @Floris: "it is not settled that increase CO2 will increase global warming" is the conclusion of "there is a nonlinear feedback mechanism ...". I claim the latter sentence is what Professor Lindzen has stated as the reason. Do you disagree and claim that he has said as much? I am interested in the detailed physics of that mechanism. – Hans Jun 4 '17 at 23:08
• @Hans, you had better have a lot of time on your hands. There are several facts to deal with, and a few(?) unknowns. Water vapor is the main greenhouse gas (GHG). CO2 is also a GHG. Both absorb IR, and there is some amount of overlap regarding the frequencies absorbed. Also, the IR bands that are absorbed are practically saturated, which means that a LOT of added CO2 adds a LITTLE bit of warming. Also, water vapor is a VERY good heat transfer mechanism, it forms clouds, clouds increase albedo and reflect IR back to earth's surface, etc. There are a LOT of interactions. – David White Jun 5 '17 at 1:50
• @DavidWhite: I suspect it is very complicated. Thank you for synopsis. Can you elaborate a little bit on the inhomogeneity and coupled nonlinearity that Professor Lindzen talked about? I suppose the nonlinearity is referring to the interaction you have mentioned, and it is a nonlinear dynamic process, is that correct? Do you have a good reference for that? – Hans Jun 5 '17 at 7:08
• I'm not familiar with Professor Lindzen's work, but his reference to inhomogeneity no doubt refers to the fact that the amount of water vapor in the atmosphere varies greatly with both time and location. Also, my guess is that "yes", he is referring to all of the interactions that I mentioned (and probably more). The effect of each variable (e.g., CO2 concentration, water vapor concentration, amount and type of clouds, etc.) on temperature is usually highly nonlinear, and all of these variables interact with each other. Such highly nonlinear, "interacting" problems are "hard". – David White Jun 5 '17 at 14:58