Guest Post by Willis Eschenbach
Dr. Judith Curry notes in a posting at her excellent blog Climate Etc. that there are folks out there that claim the poorly named planetary “greenhouse effect” doesn’t exist. And she is right, some folks do think that. I took a shot at explaining that the “greenhouse effect” is a real phenomenon, with my “Steel Greenhouse” post. I’d like to take another shot at clarifying how a planetary “greenhouse effect” works. This is another thought experiment.
Imagine a planet in space with no atmosphere. Surround it with a transparent shell a few kilometres above the surface, as shown in Figure 1.
Figure 1. An imaginary planet surrounded by a thin transparent shell a few kilometres above the surface (vertical scale exaggerated). The top of the transparent shell has been temporarily removed to clarify the physical layout. For our thought experiment, the transparent shell completely encloses the planet, with no holes. There is a vacuum both inside and outside the transparent shell.
To further the thought experiment, imagine that near the planet there is a sun, as bright and as distant from that planet as the Sun is from the Earth.
Next, we have a couple of simplifying assumptions. The first is that the surface areas of the planet and the shell (either the outside surface or the inside surface) are about equal. If the planet is the size of the earth and the transparent shell is say 1 kilometre above the surface, the difference in area is about a tenth of a percent. You can get the same answer by using the exact areas and watts rather than watts per square meter, but the difference is trivial. Assume that the shell is a meter above the surface, or a centimeter. The math is the same. So the simplification is warranted.
The second simplifying assumption is that the planet is a blackbody for longwave (infra-red or “greenhouse”) radiation. In fact the longwave emissivity/absorptivity of the Earth’s surface is generally over 0.95, so the assumption is fine for a first-order understanding. You can include the two factors yourselves if you wish, it makes little difference.
Let’s look at several possibilities using different kinds of shells. First, Fig. 2 shows a section through the planet with a perfectly transparent shell. This shell passes both long and shortwave radiation straight through without absorbing anything:
Figure 2. Section of a planet with a shell which is perfectly transparent to shortwave (solar) and longwave (“greenhouse”) radiation. Note that the distance from the shell to the planet is greatly exaggerated.
With the transparent shell, the planet is at -18°C. Since the shell is transparent and absorbs no energy at all, it is at the temperature of outer space (actually slightly above 0K, usually taken as 0K for ease of calculation). The planet absorbs 240 W/m2 and emits 240 W/m2. The shell emits and absorbs zero W/m2. Thus both the shell and the planet are in equilibrium, with the energy absorbed equal to the energy radiated.
Next, Figure 3 shows what happens when the shell is perfectly opaque to both short and longwave radiation. In this case all radiation is absorbed by the shell.
Figure 3. Planet with a shell which is perfectly opaque to shortwave (solar) and longwave (“greenhouse”) radiation.
The planet stays at the same temperature in Figs. 2 and 3. In Fig. 3, this is because the planet is heated by the radiation from the shell. With the opaque shell in Fig. 3, the shell takes up the same temperature as the planet. Again, energy balance is maintained, with both shell and planet showing 240 W/m2 in and out. The important thing to note here is that the shell radiates both outward and inward.
Finally, Fig. 4 shows the energy balance when the shell is transparent to shortwave (solar) and is opaque to longwave (“greenhouse”) radiation. This, of course, is what the Earth’s atmosphere does.
Here we see a curious thing. At equilibrium, the planetary temperature is much higher than before:
Figure 4. Planet with a shell that is transparent to shortwave (solar) radiation, but is opaque to longwave (“greenhouse”) radiation.
In the situation shown in Fig. 4, the sun directly warms the planet. In addition, the planet is warmed (just as in Fig. 3) by the radiation from the inner surface of the shell. As a result, the planetary surface ends up absorbing (and radiating) 480 W/m2. As a result the temperature of the surface of the planet is much higher than in the previous Figures.
Note that all parts of the system are still in equilibrium. The surface both receives and emits 480 W/m2. The shell receives and emits 240 W/m2. The entire planetary system also emits the amount that it receives. So the system is in balance.
And that’s it. That’s how the “greenhouse effect” works. It doesn’t require CO2. It doesn’t need an atmosphere. It works because a shell has two sides, and it radiates energy from both the inside and the outside.
The “greenhouse effect” does not violate any known laws of physics. Energy is neither created nor destroyed. All that happens is that a bit of the outgoing energy is returned to the surface of the planet. This leaves the surface warmer than it would be without that extra energy.
So yes, dear friends, the “greenhouse effect” is real, whether it is created by a transparent shell or an atmosphere.
And now, for those that have followed the story this far, a bonus question:
Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?
Lets start with the infamous woods experiment:
As with all climate science I like to review the ACTUAL paper and get the data. Wood’s “paper”
R. W. Wood: Note on the Theory of the Greenhouse
The following text is from the Philosophical magazine
XXIV. Note on the Theory of the Greenhouse
By Professor R. W. Wood (Communicated by the Author)
THERE appears to be a widespread belief that the comparatively high temperature produced within a closed space covered with glass, and exposed to solar radiation, results from a transformation of wave-length, that is, that the heat waves from the sun, which are able to penetrate the glass, fall upon the walls of the enclosure and raise its temperature: the heat energy is re-emitted by the walls in the form of much longer waves, which are unable to penetrate the glass, the greenhouse acting as a radiation trap.
I have always felt some doubt as to whether this action played any very large part in the elevation of temperature. It appeared much more probable that the part played by the glass was the prevention of the escape of the warm air heated by the ground within the enclosure. If we open the doors of a greenhouse on a cold and windy day, the trapping of radiation appears to lose much of its efficacy. As a matter of fact I am of the opinion that a greenhouse made of a glass transparent to waves of every possible length would show a temperature nearly, if not quite, as high as that observed in a glass house. The transparent screen allows the solar radiation to warm the ground, and the ground in turn warms the air, but only the limited amount within the enclosure. In the “open,” the ground is continually brought into contact with cold air by convection currents.
To test the matter I constructed two enclosures of dead black cardboard, one covered with a glass plate, the other with a plate of rock-salt of equal thickness. The bulb of a themometer was inserted in each enclosure and the whole packed in cotton, with the exception of the transparent plates which were exposed. When exposed to sunlight the temperature rose gradually to 65 oC., the enclosure covered with the salt plate keeping a little ahead of the other, owing to the fact that it transmitted the longer waves from the sun, which were stopped by the glass. In order to eliminate this action the sunlight was first passed through a glass plate.
There was now scarcely a difference of one degree between the temperatures of the two enclosures. The maximum temperature reached was about 55 oC. From what we know about the distribution of energy in the spectrum of the radiation emitted by a body at 55 o, it is clear that the rock-salt plate is capable of transmitting practically all of it, while the glass plate stops it entirely. This shows us that the loss of temperature of the ground by radiation is very small in comparison to the loss by convection, in other words that we gain very little from the circumstance that the radiation is trapped.
Is it therefore necessary to pay attention to trapped radiation in deducing the temperature of a planet as affected by its atmosphere? The solar rays penetrate the atmosphere, warm the ground which in turn warms the atmosphere by contact and by convection currents. The heat received is thus stored up in the atmosphere, remaining there on account of the very low radiating power of a gas. It seems to me very doubtful if the atmosphere is warmed to any great extent by absorbing the radiation from the ground, even under the most favourable conditions.
I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention to the fact that trapped radiation appears to play but a very small part in the actual cases with which we are familiar.”
Why is his second to last paragraph wrong?
Comments and correction to this section are welcome!
Firstly, note that unlike the experiments described earlier, this paragraph merely expresses his opinion.
1. he expresses an OPINION
2 He neglects the stratosphere which is not subject to convection.
3. the troposphere is largely opaque to IR. Thus convection plays a large role
in moving heat up from the surface, but since the stratosphere has very little water vapor and is largely transparent to IR it is instrumental in the propagation of heat via radiation to space.
and we would need to discuss line broadening at some point
So, willis needs another shell,
‘Mike Lorrey says:
November 28, 2010 at 12:33 pm
Ok for those of you who keep claiming fig 4 is wrong, here is why its not:
Solar energy to the planet: 240 w/m^2
Energy reradiated by the atmosphere back to the planet: 240 w/m^2
Add the two together: 480 w/m^2, which is what the planet radiates back.’
Sorry, You can’t do that in accounting. That violates accounting principles. You deposit $240 into your checking account. If you transfer $240 into your saving account then transfer back into your checking account. You still only have $240 not $480. It does not make a difference if you do it in one lump sum or a dime at a time. Part or all of the money is going to be in of three places. your checking account, cyberspace or saving account. The only way to reach $480 is to add $240 to the system.
“Of course, the air really is in contact with the surface, and it really has an exponential temperature gradient as altitude rises caused by gravity, at least up to the tropopause, but it sounds like these are not the problems you have in mind.”
You mean a linear gradient. It would only have an (approximately) exponential gradient if the purely radiative model was correct.
“So other than this, what is wrong with the good old Planet Dewar model?”
That it neglects convection and the adiabatic lapse rate?
Chico sajovic said “3. Argon gas is used in insulated windows becuase of its low thermal conductivity and co2 isn’t used because the greenhouse effect isn’t real.”
True on thermal conductivity. Putting CO2 between glass would be like putting glass between glass. But CO2 is exactly like having shards of glass in the atmosphere, it absorbs heat and spreads it to the rest of the atmosphere (including O2 and N2).
John Marshall said “…light becomes IR which remains inside the greenhouse because the glass traps it inside.”
Glass absorbs IR and re-emits it. CO2 does exactly that and conducts heat to the O2 and N2 around it.
Steve Mosher’s post @2:50 pm above is paraphrased from Jan Schloerer, who states: “Caveat: This is not my field.”
Schloerer does a credible job, but at the end his preconceived conclusions show that his mind was already made up:
Schloerer wrote that almost 14 years ago, and it is another good example of why the scientific method must be followed, rather than panicking over scary what-ifs. Fourteen years on, and after spending many billions of dollars on a non-problem, it is clear that the climate is, if anything, even more benign.
“If you transfer $240 into your saving account then transfer back into your checking account. You still only have $240 not $480.”
You pay the $240 from your employer and another $240 from your savings account into your checking account. At the same time, you transfer $480 from your checking account to your savings account, and $240 from your savings account to the grocery store.
Hu McCulloch says:
November 28, 2010 at 1:34 pm
Thanks, Hu, good to hear from you. In theory there is no limit to how much you can concentrate energy (slow down its loss) in this manner. I don’t see why people think there should be a limit. Take an electric heating element. Put it in a Dewar flask. The heating element reaches a higher temperature. Put the Dewar in a larger Dewar. Higher temperature. Repeat ad lib., you can achieve a very, very high temperature … why is that seen as being so impossible?
old construction worker says:
November 28, 2010 at 3:06 pm
If I understand you, you seem to be confusing total (net) flows with individual flows. The net flow from the planet to the shell in Fig. 4 is 240 W/m2. The individual flow from the planet to the shell is 480 W/m2. Fig. 4 shows only individual flows, and not net flows. It is the individual flow from the planet to the shell that determines the blackbody temperature.
PS – among my other skills, I am an accountant. I assure you that no accounting principles were violated in any of the Figures.
Greenhouse effect doesn’t exist just because Al Gore believe it does.
old construction worker;
Sorry, You can’t do that in accounting. That violates accounting principles. You deposit $240 into your checking account. If you transfer $240 into your saving account then transfer back into your checking account. You still only have $240 not $480.>>
Physics isn’t accounting. But if it were, it would go more like this.
I send You a check for $240.
You send Me a check for $240.
Every day for many days.
Insert Willis.
I send you a check for $240.
You send Willis a cheque for $240.
Willis sends Me a cheque for $120 and you a cheque for $120.
You now have an extra $120, so the next day…
I send you a cheque for $240.
You send Willis a cheque for $360.
Willis sends me a cheque for $180 and you a checque for $180.
First day you wound up with $120, extra and second day $180, so on 3rd day…
I send you a cheque for $240.
You send Willis a cheque for $420.
Willis sends me a cheque for $210 and you a cheque for $210
And so on and so forth until every day (at equilibrium) you are sending Willis a cheque for $480 every day, and he is sending you and me a cheque for $240 each every day. My cheque to you still goes straight to you for $240. The books still balance. The only difference is that Willis started out with $0 and now on any given day has $480.
If we were back to physics, that would be the “shell” and it would be retaining how ever much energy is required to make it radiate 240 w/m2 in each direction.
Hi, Willis. You seem to have some German gene inherited. The one that makes Germans say,”why make things simple if we can make it complicated”, a gene that those who worked in electronics are quite aware of. 🙂
Your explanation of why the Climate Model you devised doesn’t work is OK, technically. But I see it as a close look to the tree. Walking away from the tree and having a better view of the forest, I would say that given the fact that there is a tremendous amount of variables working in the climate system, and that feedbacks are positive as well as negative, and because there is no way to calculate how interaction of ALL those feedbacks will work our, the Climate System is CHAOTIC.
So the simplest explantion would be: “The model is useless because we cannot model chaos”.
Still in Salomon islands? Please scubba down and bring me one bolt from a Japanese Zero sunk off the coast… 🙂
So are you saying that in my Planet Dante example, the surface really could be heated indefinitely (until incandescence started leatting the heat through)?
On another matter, did you get my e-mail of 10/23 regarding our Tanganyika piece? I first sent it 10/19, but it didn’t seem to go through so I sent it again, both times using your taunovobay address. Please e-mail me either way.
Willis Eschenbach says:
November 28, 2010 at 3:35 am
Hi Wll, thanks for the reference to Zeno; however I think your reference to the real world confounding the application of a a limiting sum geometric series to Figure 4 so that the final amount of flux is never received misses the point that this effect in the real world prevents a runnaway situation from occuring; to that extent your comment that “In theory there is no limit to how much you can concentrate energy (slow down its loss) in this manner.” I think is wrong and it is the mistake the IPCC makes with its climate sensitivity formula. There is no evidence for this. The IPCC attributes ACO2 as being the forcing agent, F, for this scenario, with water vapor the feedback, f, and temperature, t, the parameter for the change; the interaction of these variables is measured by the state vector, S, which would itself change if F has the effect the IPCC alleges. IPCC represents this dynamic thus:
dS/dt=S/f+F
IPCC assumes that f is +ve so if we intergrate by dividing both sides by fS+F, and multipling both sides by f*dt we get:
(S2+F/f)/(S1+F/f)=exp(f*(t2-t1))
The problem with this is because it predicts that as the final value of t, t2, approaches infinity, the value of S2 becomes infinite. This is wrong because if there is a climate forcing in operation, at infinite time, the temperature anomaly should approach its finite equilibrium value even if there is positive feedback. This is shown by Venus which is paraded by AGW supporters as being the inevitable result of AGW; but, if there was any greenhouse effect on Venus it has now stopped despite high levels of CO2 and obviously its equilibrium was less than infinity. The correct formula for measuring feedback is done by Spencer and Braswell:
http://www.drroyspencer.com/Spencer-and-Braswell-08.pdf
Their equation 2 is:
Cp*T/*t=-^T+N+f+S
The difference with S&B’s equation is that it introduces a term for the stochastic properties of clouds, N and breaks F into -^T and f; f is ACO2 and -^T is a total feedback term which must be negative so that an infinite equilibrium is impossible.
On another point with your figure 4 it seems to me that not just Zeno’s arrow would apply but Zeroth’s law; if you assume that between the shell and the surface there will be an equilibrium then an isothermal state must be reached; that is if the flux is equivalent everywhere then temperature must be equal everywhere. Of course even in a hypothetical situation like yours that can’t be because gravity would produce a gradient with pressure higher at the bottom; even allowing for a vacuum that would impact on temperature so that a disequilibrium between the surface and the shell temperature would occur?
Smokey,
The woods experiment is a farce. Now to be sure until the 1950s we did not understand that the stratosphere was dry. It took the airforce to figure that out. The results of that research and the effects of C02 at that altitude are now gratefully better understood. As I have explained to you before, if we did not understand how C02 interacts with IR throughout the air column (not in an enclosure) we would not have been able to build satellites that actually work in sensing the earth and clouds.
Stealth aircraft would not be stealthy. IR missiles would not work as they do.
If you want to argue about feedbacks, that’s fine. That question is open for debate. If you want to argue that known working physics doesnt work, well then there is no debate. TWO entirely different questions. I would suggest that you will get more respect from people if you read what Anthony, Willis, Lindzen, Spencer, Christy, Monkton, say about C02 and radiation. None of them deny the basic physics. I would guess because they either have worked with the physics or understand it. Once you do, then you’ll stand on BETTER skeptical ground.
On reading the comments in more detail, I see that I was overlooking your proposal of a multi (2) shell Dante model, on the 27th at 750PM.
But this doesn’t make the 1-shell model wrong as an insight into how the GHG effect works — as you say, it just isn’t strong enough, given leakages.
I like the example of a heating element inside a Dewar. But when it comes to the atmosphere the heating element (the sun) is outside. What does that do to the results?
I have greatly enjoyed this thread which tries to answer a question. I would like to see a similar thread that seeks to answer the question as to why the warmest temperatures on earth occur where there are the least amount of green house gases. That is arid areas. I do not have the answer, but I would enjoy the attempts to answer that question.
Willis Eschenbach says:
November 27, 2010 at 7:50 pm
“Why The Thought Experiment Can’t Represent Earth
It is not powerful enough.
What I have illustrated above is the energy balance in a theoretically perfect single shell planetary “greenhouse”. It shows that the maximum amount that such a system can produce is a doubling of the input. Not one Watt per square metre more. It is not a magical system. At best, it can double the input.
Since the real Earth receives about 240 W/m2 (after albedo reflections), the most the system could theoretically produce is 480 W/m2.
At first glance, that seems like plenty. I mean, blackbody temperature for 480 W/m2 is 30°C, and the Earth only averages around 15°C. But in the real world there are losses. …”
There was a reply that you seem to have skipped over, which was on the money. The shells you are talking about don’t model the lapse rate.
Will Nelson says:
November 27, 2010 at 12:33 pm
“Adiabatic lapse rate?”
How can the troposphere, the imaginary shell(s), at -65 c warm the surface at +15 c?
“Second law of thermodynamics: Heat cannot spontaneously flow from a colder location to a hotter location.”
http://en.wikipedia.org/wiki/Second_law_of_thermodynamics
Hi Steven Mosher,
If you re-read my post you’ll see that I wasn’t commenting on Wood’s experiment at all, nor about feedbacks, although your response indicates tht’s what you believed. I simply pointed out where your own comment came from, and the fact that when preconceived assumptions were made by Schloerer, they were typically alarming – but wrong. None of what he feared and expected happened. In fact, just the opposite.
Maybe you were inadvertently responding to Bryan?
And your comment…
“Why is his second to last paragraph wrong?
Comments and correction to this section are welcome!”
…was apparently lifted directly from Jan Schloerer’s very similar statement here.
Just sayin’, that’s all.☺
Carry on.
Steven Mosher;
If you want to argue about feedbacks, that’s fine. That question is open for debate. If you want to argue that known working physics doesnt work, well then there is no debate.>>
Oh yes there is. There is a huge debate. Massive in fact. Because the known physics is not what is being argued by the alarmists. The IPCC reports gloss over the fact that CO2 is logarithmic. Known physics. They gloss over the exponential negative feedback response (T to the power of 4) of the planet surface. Known physics. They extrapolate temperature increases from economic scenarios that would require 10 to 100 times current consumption to achieve. Known physics. They predict +1 degree from CO2 doubling, but fail to mention that it is the effective black body temperature they are calculating against, not the much lower average surface temperature. Known physics. They highlight large temperature increases at the pole as if they are a harbinger of things to come planet wide while they know full well that increases at the equator will miniscule. Known physics. They present the temperature increases at the high latitudes as of they are uniform over the course of the year when they know full well that the bulk of the rise is in the depths of winter and the summers are very little warmer. Known physics. They talk incessantly about daily averages, glossing over that the day time highs change little but the night time lows increase. Known physics. They predict higher total energy in the system resulting in more severe weather though the result of most of the warming happening in the coldest places at the coldest times results in more uniform temperatures globaly, and it is temperature differentials that cause extreme weather, meaning less extreme weather in a warmer world, not more. Known physics.
They misrepresent the physics repeatedly, and when one attempts to engage them in a proper discussion of the physics, what happens? Well look at this temperature record. Well look at these tree rings. Well look at these tidal gauges. Well look at this ice extent. Anything, absolutely ANYTHING to get the topic off the physics and turn the discussion to secondary or even more removed proxy data that they then claim proves the physics. But discuss the physics? Not a chance. They haven’t the kahonies to have a real discussion of the physics. If they did, they would have to admit:
o CO2 is logarithmic and the amount of oil we would need to burn to get to the catastrophic temperature increases they predict is nearly astronomical.
o Using effective black body exagerates the actual surface temperature change
o Averages are meaningless because most of the temperature increases that make up the average will be in the coldest climates, in the depths of winter, and at night time lows.
o A warmer world is more uniform temperature wise, and hence less severe weather.
No debate about the known physics? Are you kidding me? The arguments of the alarmists rest on everything EXCEPT the “known physics”. They want to debate temperature records and species extinction and temperature reconstructions from 7 trees in Siberia to prove the physics. Except it isn’t the “known physics” that they are trying to prove, it is “their physics”, a “special physics”, physics proven by proxy, mythology, and photoshop. The “known physics” says, point blank, NO PROBLEM, so they have set about replacing it with tree rings, polar bears on ice floes, and tidal gauges on sinking islands.
The known physics you speak of and the known physics of the alarmists are two different things, which is why there IS in fact a debate. If you were being honest Mr Mosher, you would excoriate the alarmists for glossing over the actual physics and when being critical of statements like Smokey’s you would include the physics that mitigates and limits the effects of CO2 along with your argument that the warming effects of CO2 are known and not debatable.
One variable in isolation does not a physics equation make.
Miswording above:
They predict +1 degree from CO2 doubling, but fail to mention that it is the effective black body temperature they are calculating against, not the much lower average surface temperature.
Should have read “…not the much higher average surface temperature (meaning much lower change at surface)”
DavidmHoffer, http://wattsupwiththat.com/2010/11/27/people-living-in-glass-planets/#comment-538654
You should make clear that the HEATER never increases in temperature!! The room also can never exceed the temperature of the heater!!
Sorry smokey, I thought I was responding to him.
I think william connelly is the one who actual found the document in the stacks. Could be wrong about that. We discussed it a while back on lucia’s site.
Willis,
the real problem with these models is that they use the wrong form of the energy equations. When you have two bodies radiating against each other you have to use the form that takes into account the temperature of the body being radiated against. In the case of GHG’s, since their radiation is based on molecular bond instead of temperature, how would you do that??
Using the form of the RTE which computes energy radiated to 0K simply does not do it and is one of several reasons why climate science is so unphysical. Simply put, it ignores the fact that photons also have wave properties and waves can interact. These interactions can cancel and interfere with wave propagation so that your 120 down does NOT all get to the ground and your 240 up does not all get up!!! What happens to the energy?? Maybe you can find some physicist to tell us!!