Proof of the Atmospheric Greenhouse Effect: Arthur Smith
Posted by jennifer, October 10th, 2008 - under Opinion.
Tags: Climate & Climate Change
Arthurs Smith does not explain the specific contribution of carbon dioxide to global warming, nor does he deal with the issue of convective overturning, but in ‘Proof of the Atmospheric Greenhouse Effect’ he elegantly explains the greenhouse effect in harmony with “the scientific standards of theoretical physics”. In particular he first defines basic terms and relevant equation for energy flow, considers a planet with no infrared-absorbing atmosphere, and then shows that by adding a simple infrared-absorbing layer it is possible to explain why we are not all freezing here on planet earth.
Read more here: http://arxiv.org/abs/0802.4324
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687 Responses to “Proof of the Atmospheric Greenhouse Effect: Arthur Smith”
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Not the case with the earth.
http://www.cliffsnotes.com/WileyCDA/Section/What-is-thermal-equilibrium-.id-305406,articleId-27116.html
SJT: “Not the case with the earth”
The earth is not in thermal equilibrium and therefore cannot have a temperature by definition, sensu-strictu.
SJT: “You want to attribute a single temperature to the earth? We’ve just had a whole million pages of posts from deniers saying you can’t do that.”
It doesn’t bother me in this issue, it’s what Arthur’s model requires and it is internally inconsistent.
Some quotes from it
The only “observables” in this set up are the constant temperature and the zero sum flux.
Here \dot E refers to time derivative so internal energy and observables cannot change so we have equilibrium specifically mentioned and in equations 13 14 and 15 that follows we find an albedo term but no emissivity term.
Even if the planet isn’t in thermal equilibrium it does not as a whole radiate as black body nor does it absorb as a black body. It’s simply a nonsense to assume in the face of certain knowledge to assume a black body radiation when it isn’t so.
I thought Jan was arguing it is :$
SJT: You thought wrong.
One final comment about the spurious commutivity objection to what Motl did with Tafe and Teff to prove that GMST is a fallacy; NT at 10.34 am above says that commutivity applies to equations, not numbers; the Pielke Snr paper which raises the lack of correlation between Tafe and Teff does so in relation to the IPCC equation for climate sensitivity;
(1)dH/dt=f-T’/^
Where H is the heat content of the land-ocean-atmosphere system, f is the radiative forcng, T’ is the change in global average surface temperature in response to the change in H, and ^ is the climate feedback parameter which defines the rate at which the climate system returns forcing to space as IR and/or as changes in albedo. Thus the IPCC equation marries Tafe and Teff from the outset; Pielke objected to this equation because of its inadequacy in spatially representing Teff or SB as represented by H. Lucia in an elegant solution, refuting eli’s objections in the bargain, accommodated Pielke’s concerns by extending the equation so that it no longer represents a single point but the multiple SB points on the globe;
(1)dH/dt=f-(T’/^+(3/^)/)
Where is the absolute value of the GMST in the REFERENCE CASE, 0~To is the difference between a local surface temperature and the GMST in the REFERENCE CASE, and 0~T’ is the difference between the local surface temperature and the GMST at the current time (t). The extended equation maintains the order of the key variables but qualifies them in that context; no objection on the basis of commutivity is possible. Lucia confirms the Pielke calculated variation between Tafe and Teff of at least 20% and up to 46% for f (the measure of CO2 forcing, or in Arthur’s case, the greenhouse effect); that being the case, not only is GMST a crock to base AGW on but the 33K greenhouse can be reduced by 20-46%.
The formula again:
(1)dH/dt=f-(T’/^+(3/^)/)
And is the absolute value of the GMST in the REFERENCE CASE; the rest as follows above.
The equation is not transposing but is at point 1 at lucia’s post;
http://rankexploits.com/musings/2008/spatial-variations-in-gmst-eli-rabbett-vs-dr-pielke-sr/
(1)dH/dt = f-( T’/^ + (3/^) / )
“And is the absolute value of the GMST in the REFERENCE CASE;
just testing.
Cohenite, I’ll quote Pierrehumbert again, just for the hard of hearing.
SJT: “I thought Jan was arguing it is ”
how long have been following this thread? How many times do you need to be told that the problem is entirely within Smith’s model which is inconsistent.
More generally I actually agree with Louis hat in a strict sense earth has no definable single temperature.
So what?
Refer post above.
<blockquote.how long have been following this thread? How many times do you need to be told that the problem is entirely within Smith’s model which is inconsistent.
Now you’ve got me. It seems to be quite consistent, he has explained what it is and why as far as I can tell. You seem to be hung up on thermal equilibrium, when he has made no claims to depends on such a thing.
SJT: “You seem to be hung up on thermal equilibrium,”
This is also not correct I would be the last to claim that planet earth is in equilibrium it never is. However one dimensional Energy Balance Models are in fact equilibrium models and can be useful if used with self consistent parameters Arthur’s model is an equilibrium model but not consistent.
My response to Smith March last year. I haven’t change my views much except to mellow a little on the issue of the utility of EBMs but you’ll see even there I agree the world is not in equilibrium but that is not the case in the model.
http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=161&st=0&sk=t&sd=a&start=30#p3047
All I’m saying is that if he or anyone else wants to use an equilibrium model then the model should be consistent and Kirchoff’s law must apply.
oops I stuffed that one up
Jennifer is it possible to get a preview function going?
Will; you can go line-dancing with Pierrehumbert as far as I care; I rebutted him about 4000 posts ago; any one who can claim that Earth has uniform temps when the record range is 147.6C belongs in a barn.
He says it’s a steady state, not an equilibrium. About ten times. After that, I think he wondered why he bothered.
He didn’t.
SJT” “He says it’s a steady state, not an equilibrium. About ten times. After that, I think he wondered why he bothered.”
That’s right he thinks repetition makes it true it doesn’t.
How many times have I needed to remind you of this?
you are right he shouldn’t have bothered because it does not change the fact that he set up an eqilibrum model not just a steady state one. Finally how many times do you need to be also told that too I irrelevant poor absorbers make poor emitters regardless of whether they are in thermal equilibrium or not. It is therefore also inconsistent with the more general case to assume an absorptivity of .7 and an emissivity of 1.
My stainless steel urn while I can hear the water boiling inside registers 37C (body temperature) with a non contact thermometer can I invite you to come over and grab it and pick it up by the sides when it is boiling?
I distinctly remember him saying “steady state”. It’s his model, not yours.
“It’s his model, not yours.”
So what?
So what?? It’s a steady state model. It’s not a thermodynamic equilibrium one. It’s a simple one, but it’s enough to illustrate the GHG effect.
The irony, of course, is the Mikolczi’s model is a one dimensional, “Equilibrium” model.
SJT: “So what?? It’s a steady state model. It’s not a thermodynamic equilibrium one. It’s a simple one, but it’s enough to illustrate the GHG effect.”
Who is talking about thermodynamic equilibrium just radiative or thermal equilibrium as he expressly stated in his paper and denied outside.
It’s hardly the first time someone has built a kite that didn’t fly.
His model doesn’t work based on it he should pick up my urn while it’s boiling do you think he’ll be that silly?
What do you think think the contact thermometer says?
Reminder the non contact one says 37C
Hmmm, does that explain Jan’s confusion?
Jan Pompe – Kirchhoff’s law, as you have been applying it (where the emissivity that applies to the actual emitted radiation is equal to the absorptivity applied to the actual absorbed radiation), is true only in the case of *thermodynamic equilibrium* (which is the same thing as the *thermal equilibrium* I have been talking about, but evidently not the same as the thermal equilibrium you have been talking about). I will repeat again my quote from Riedi, which uses the term “thermal equilibrium” as I have been using it, to mean the final equilibrium state of an isolated body in thermodynamics:
P.C. Riedi’s “Thermal Physics”, 2nd Edition, Oxford Science (1988) – p. 3
“When the properties of a thermally isolated system become independent of time the system is said to be in thermal equilibrium. [...] The approach to equilibrium would depend on the nature of the experimental system but the properties of all systems in thermal equilibrium are contained in the laws of thermodynamics. The simplicity and the universal character of the thermal equilibrium state makes it of great theoretical importance although it is clear that only carefully prepared experiments are in general in thermal equilibrium with their surroundings.
The equilibrium state should be distinguished from the ’steady state’ often considered in the study of transport properties such as thermal conductivity. In Fig. 1.1 the thermal reservoirs are at temperatures T_R1 and T_R2 and the temperature along the metal rod will quickly seem to become independent of time. The rod is now in a steady state – the simplest type of transport situation – but the only possible equilibrium state for the isolated system of reservoirs and rod is when T_R1 is equal to T_R2.”
Once again, I ask you, consider a point on the rod in Riedi’s example, connecting two systems at different temperatures. Do you believe this spot to be in “thermal equilibrium” because its temperature is steady and unchanging, and the heat energy entering from the left side (let’s say the left side is hotter than the right) is equal to the heat energy leaving through the right side of this spot on the rod?
If so, you are wrong, according to Riedi (and any other text book on the subject) – this is steady state, not “thermal equilibrium”.
Steady state conditions are quite insufficient to ensure equal emission and absorption, as the many examples (bodies, lights, lasers) I’ve provided above show.
Arthur Why don’t you come cuddle my hot water urn when it’s boiling the radiative measure says it’s only 37 C.
“Once again, I ask you, consider a point on the rod in Riedi’s example, connecting two systems at different temperatures. ”
It’s am irrelevant example your model is suspended in space the only energy source for climate is space and the only sink is to space. By integrating over the sphere you in effect average the source over the whole sphere effectively removing the degrees of freedom such that (if not in reality) surround the planet with a virtual unchanging source and sink at the same temperature. You do away with the reservoirs at different temperatures but that is the way with one dimensional equilibrium models like the one you have created. You can call it a steady state all you want it isn’t. I agree the real world is in quasi steady state but in one dimensional equilibrium models it isn’t.
Wait, so you don’t claim that Riedi’s rod is in thermal equilibrium? Then you are making no sense whatsoever.
“you in effect average the source over the whole sphere effectively removing the degrees of freedom such that (if not in reality) surround the planet with a virtual unchanging source and sink at the same temperature. You do away with the reservoirs at different temperatures”
This is simply wrong.
(A) I do not treat the incoming radiation as if it were averaged over the sphere. The model in my paper specifically assumes there is a “sun angle” along which the incoming radiation appears, for example the angle given in eq. 17 for the simple rotating planet. Outgoing radiation does of course go in all directions – but it is also not assumed to be uniform, rather it is at the specific rate associated with the temperature at any given time and latitude and longitude – i.e. this is a 2+1 dimensional approach to the problem.
(B) Even if I were assuming incoming radiation came uniformly from all directions, it is still short-wavelength radiation – in particular, it could not be thermal radiation from a “virtual unchanging source at the same temperature” because that source would have to look like the surface of the Sun in all directions, to provide that spectrum of light. In particular, total intensity would be 10′s of thousands of times higher in such a case, in order to have the same spectrum from a uniform surrounding source – and of course Earth’s equilibrium temperature would end up at 5000 K like the surface of the Sun, if that were the actual assumption I made. Just cutting the intensity of thermal radiation by a factor of 10,000 or more while leaving the spectrum the same is a very different thing from having a “virtual unchanging source at the same temperature”.
Arthur:
Why are you saying the rod it is in thermal equilibrium? Reidl says it isn’t I agree with him. You isolate the rod an the temperature gradient will disappear do it’s not a case of thermal equilibrium.
You map the solar constant (a single value) to a single number that allows no room for gradients either vertically, horizontally or temporally i.e. it’s an average and with no temperature gradients with your assumption of a zero sum radiation it’s in thermal equilibrium because if you isolate the earth in your model no flux enters no flux leaves the zero sum doesn’t change and since there is no gradient like Reidls rod there is no gradient to equalise so nothing changes and there has been and remains thermal equilibrium.
B is not even wrong.
Why do have a problem with it?
Did you notice everyone who makes the same mistake as you do the Nathan (NT) posted up including the wikipedia explicitly say their model assumes thermal equilibrium.
http:en.wikipedia.org/wiki/Black_body#Assumptions
Assumption thermal equilibrium but absorptivity != emissivity as required by Kirchoff’s law.
http:en.wikipedia.org/wiki/Thermal_equilibrium#endnote_Barbieri2007
Formula given for “Equilibrium temperature” by Barbieri 2007 fails to equate absorptivity and emissivity.
http:en.wikipedia.org/wiki/Stefan-Boltzmann_law#Temperature_of_the_Earth
Surprise here one that gets it right recognise the equation? They don’t say the assume equilibrium but absorptivity=emissivity in that one.
So the articles pointed to by NT actually support me NT thought the supported you goes to show how much he understands this so do you think I should pay him any attention?
I may not be too bright, but the “black body” model is not the one that Arthur is using, his is more complex.
SJT: “I may not be too bright, but the “black body” model is not the one that Arthur is using, his is more complex.”
it just looks that way to you because you are not too bright.
Pompe’s law
The observed complexity is inversely proportional to the brightness of the observer. It’s really a subjective measure.
No, Jan. Like I have said before, I’m aware of my limitations. Other people don’t appear to be.
SJT: “No, Jan. Like I have said before, I’m aware of my limitations”
The evidence is that you are not aware of your limitations you have been most vocal in you pretence that you understand it despite the fact that neither you nor the person you are defending have ever done any work in heat management and control nor have any knowledge of or experience in systems identification. Smith doesn’t even correctly identify system in his own model and tries to shoehorn parameters from a different (potential divider) model into an equilibrium model and gets wrong results.
Like I said, I’m aware of my limitations.
cohenite…I heard back from Ralf Tscheuschner but he doesn’t want to get into the blog scene. I think the nonsense at realclimate and deltoid has put him off, and who can blame him.
He has graciously invited questions on his paper and I plan to ask for some clarification. If you have any questions, pass them on, or I’ll send you info on how to do it.
Gordon; well done; Jennifer has my details; if our good host doesn’t mind feel free to contact me through Jennifer; I think we must persuade G&T to do a post; for my part I am interested in the approach taken by Pielke, Motl, Lucia, Essex and McKitrick amongst others; my posts at 7.55pm and 8.08pm above on 24 OCT sum up my position; pity the equation wouldn’t transpose.
Hey, Cohenite, your famouse
rabett.blogspot.com/2008/10/believing-ten-impossible-things-before.html
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