In a recent post Claes Johnson attempts to answer the following question from Roy Spencer:

*How does the surface 'know' how opaque the atmosphere is before it 'decides' at what rate it should emit IR?*

There is one point which I would like to make here which seem to have escaped many GHE-skeptics. In a previous post I constructed a simple radiation model, which does not necessarily come close to the real situation, but which nevertheless highlights something important. In the model in question no part of the system 'knows' what goes on anywhere else, the only things each part knows is its own temperature and absorptivity. The model also contains 'backradiation'. Moreover, the 'backradiation'

*taken alone*does in fact slow down the rate of cooling in the system. The question is now:*Does the model reproduce anything like the greenhouse effect?*The answer is:*It doesn't.*In the model the temperature lapse rate flattens as the absorptivity/emmisivity increases with the consequence that the system cools, which is a clear deviation from the so called GHE.The reason for this is probably the following: The amount of backradition can never exceed the radiation that at the same time is lost to outer space. Thus the backradiation cannot trap energy in the system since it is always associated with an 'out-radiation' that is equally big.

The real difference with the GHE and reality is thus probably much more subtle than both Roy and Claes wants it to appear. To be honest, I have not quite understood the supposed mechanism of GHE although I have tried, but maybe I will succeed in the future to completely disentagle the mathematical structure of it. I very much encourage the mathematically inclined audience to also make such an attempt, since the present 'wordy' discussion on 'backradition' has not managed to clear the confusion.

My

*suspicion*though is that the greenhouse effect is based on a mechanism of**reflection**rather than**absorption-thermalization-thermal reemission**. Hence it is formally more akin to radiation pressure, but that remains to be clarified. Good luck.
Hi Anders,

SvaraRaderaPlease accept a note from the 'mathematically-inclined audience'.

Your 'model' has more than one fatal flaw. It shows a complete lack of comprehension of the difference between radiation and diffusion, and tacks no account of the thickness of the atmosphere (in your model a molecule in an atmosphere one molecule thick or one at the bottom of an infinitely thick atmosphere will still radiate the same amount of heat 'directly into space', a plainly absurd result).

So, as it stands your 'model' is no more meaningful than any other quasi-random string of numbers and letters with arbitrary values assigned to them, and thus the conclusions you draw from it are, to be polite, unsupported by your data.

Hi Alien Technician,

SvaraRaderaI see that you have made quite a number of comments, I will see if I can respond to them in some compact form in the future. Having skimmed them through I do get the impression that you think that I present fully developed models when I in fact only construct simple models to pinpoint certain specific issues. In this case the main point was that a layer which thermally back-radiates a certain amount of radiation would at the same time radiate outwards the same amount. Thus there is no energy-trapping in the system and I demonstrate that the temperature gradient would instead flatten with a toy-model.

Moreover, regarding the stratophere which you commented on before you made some interesting remarks, but again I didn't propose any 'model', I merely analyzed some different opinions regarding the temperature gradient commonly expressed. These differences taken alone should indicate that the general understanding of what is really at stake is rather modest.

AT

SvaraRaderaI responded to some (but not all) of your previous comments. To further clarify some of your concerns:

I fully acknowledge that a varying thickness of the atmosphere must be taken into account. I highlight that issue in "A note on thermal diffusivity", and it is true that it is not taken into account here.

The word "diffusion" I use only because the second derivative looks formally like a diffusive heat transport term.

Please focus on the discrete model. Can you argue that by taking into account varying thickness, then main conclusion, that is a flattening lapse rate, would suddenly change to a steepening lapse rate as A increases.

Hi Anders,

SvaraRaderaI appreciate your responses, and your sincere efforts to come to grips with the physics through your own reflections.

However, I still more or less respectfully suggest that you are overreaching when you challenge the laws of physics on the basis of an understanding that is still developing.

So my point regarding what you call your 'toy model' remains. Your argument is not in any shape to say anything meaningful about the lapse rate. I have already mentioned two obvious flaws that would invalidate the reasoning you give. Now let's look at your algebra.

(A - A^2)U(n) - 1/2*A^2(U(n+1) - 2U(n) + U(n-1)) = 0

First, it's not immediately clear how your equation is to be used. You wish to model a dynamic process, but give what appears to be a static description. To me it looks more like a spreadsheet calculation than a physical model.

Still, we can try to work with it, and see what, if anything, it is actually telling us about the temperature in any given layer of the atmosphere, a temperature which you designate U(n).

So, once again, your equation is

(A - A^2)U(n) - 1/2*A^2(U(n+1) - 2U(n) + U(n-1)) = 0

and, rearranging and simplifying, we get

U(n) = A * (U(n+1) + U(n-1))/2

In other words, your 'model' simply asserts that the temperature at any arbitrarily defined 'layer' is the average of the adjoining undefined values scaled by A.

And I'm afraid it's hard to see how this unfounded assertion might have any physical meaning.