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?
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Willis, I’m curious about the effect of a high mass, 100% IR transparent atmosphere as posed in my first question above… Not sure if you saw it. Thanks, Mike S.
Willis
How does the glass shell radiate twice as much energy as it receives? Inquiring minds would really like to know.
Ken Coffman says:
November 27, 2010 at 6:53 pm
“I get accused of believing some odd things, but I’m not the one denying that N2 and O2 molecules have temperatures.”
Individual molecules will have wildly varying temperatures if you could somehow find a way to measure them individually.
“781,000PPM of N2 has no thermal capacity or thermal mass?”
Of course it has thermal mass and as a group of molecules will have a measurable temperature which is the average of the group.
“I don’t care how many degrees of freedom your fantasies have, the temperature of 781,000PPM N2 has nearly nothing to do with anything 390PPM of CO2 can do.”
This is where you’re wrong. Imagine two thick sheets of copper sitting out in the sun. On one we put a put a very thin coat of black paint and on the other we put a very thin coat of white paint. The paint weighs next to nothing compared to the weight of the metal. Will the paint cause a difference in the temperature of metal as it sits out in the sun? I think you know the answer to that.
“Stefan-Boltzmann says things radiate based on their temperature, not whether they’re made of CO2 or water vapor.”
That is correct. But what governs absorption? The key is that CO2 absorbs infrared radiation at characteristic infrared frequencies while N2 is completely transparent in infrared. In a dense mixed gas (air is “dense” in this context) of N2 and CO2 when a CO2 molecule absorbs infrared radiation it translates to kinetic energy – the molecule is moving and vibrating faster as a result. The motion is what registers on a thermometer. Since it’s in a dense gas it almost immediately bumps into a neighboring molecule and transfers some of its kinetic energy to the molecule it bumps into. In that manner CO2 acts to absorb infrared energy emitted from the earth’s surface and raises the temperature of all the molecules surrounding it. Without the CO2 the radiation would have passed straight though the N2 and the N2 would not have been made warmer.
Hello all,
To Ric Werme’reply, November 27, 2010 at 6:03 pm
1/ Everytime you see a reference to -18°C in the climate debate, you have to remember this value comes from the use the other way around of the Stefan-Boltzmann’s law as related in the peer-reviewed paper “Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics” (Gerlich & Tscheuchner). Therefore, this -18°C value means absolutely nothing and should never be used in the climate debate.
2/ Since the wrong calculation is usually done for a non rotating and atmosphere free planet, the comparison with the moon do apply here since in the same situation, earth would end up with the same desert-like surface anyway. The moon low rotation motion (14 days) is slow enough to reach a surface temperature steady state.
3/ The whole point is that a pure radiative approach of earth climate is meaningless as pointed out by G&T.
@Ken (con’t)
The “greenhouse effect” (a poor term but we have to live with it) is physics that was known theoretically 200 years ago. About 150 years ago John Tyndall demonstrated it expermentally in literally thousands of different experiments with various gases under various pressures irradiated at various frequencies. He published his results in a seminal tome titled “Heat: A Mode of Motion”. You can read the book in its entirety on Google Books:
http://books.google.com/books?id=eZEAAAAAMAAJ&dq=john%20tyndall%22%20heat%20motion&pg=PP1#v=onepage&q&f=false
For ease of reading I suggest downloading the PDF file.
The bottom line is the greenhouse effect was demonstrated experimentally over 150 years ago. Anyone claiming it isn’t real is sorely lacking in understanding of introductory level physics.
Others may be interested in the related discussion starting here and particularly the following comment on the shell model, and also here. The general idea was covered further at greater length here.
Willis
A simple question for you. Recognizing that your analogy is extremely simplistic to prove the existence of the “greenhouse affect”, what happens if you make the shell only 80% opaque to long wave radiation and then increase that gradually to 80.1%?
My guess, it results in an unmeasureably small change in the planets temperature!
Please feel free to enlighten me at 2billyarber@Gmail.com
Bill Yarber
It stands to reason that heating a globe who’s core has been cooling overall since it’s formation would be an intensive matter. And because of our size and shape, we don’t capture much of the Sun’s infrared. If the Earth fails to capture and hold onto longwave, we roast during the day and freeze at night.
The premise here is to layer up. One blanket does not trap heat nearly as well as multiple blankets. And a single opaque blanket may lead to cold damp conditions. So it’s a good idea to have a bit of flow-through in each of these layers. Which equates to the idea of the shells being not absolutely opaque but nearly opaque to longwave.
TimM says:
November 28, 2010 at 3:24 am
“I assume that the amount of heat humans create is known to some degree and accounted for in climate modelling (unless it is considered trivial)?”
Yes and no. It isn’t trivial when a thermometer is located in close proximity to an artificial heat source! Averaged over the entire surface of the earth it is indeed a trivial amount of heat. Also trivial is the amount of heat from the molten hot core of the earth that is emitted from the surface due to the crust being a very good insulator.
Willis: “OK, let’s assume that the sun is some form of luminous cloud that illuminates the planet evenly with 240 W/m2 of solar radiation.”
Then the planet heats up to the same temperature as the luminous cloud. Luminous cloud is a simplifcation too far, principles need to be argued from point source.
Flow of energy is then crucially determined by geometry. A disc (facing into the point source) has much the same issue as luminous cloud. I’d say it is essential to stick to a sphere.
Even a highly idealised spherical model needs to be detailed enough to integrate incoming radiation distributed over the sphere (or one side of a sphere at any time), conduction over the surface, and differentials of OLR at different coordinates.
I’m not going to try to do that because it relies on too many assumptions (that I’m not in the best position to deal with). However I supect that the combination of assumptions, integrals and application of S-B will introduce some significant numerical factors not evident in the simple “vertical line” diagrams above.
(BTW, before you answered the question set at the top of the thread, my answer was going to be “no angles”.)
It seems there should be some time considerations that should play into a “greenhouse gas” model. I imagine that on the gasless moon radiation strikes the surface, heat is created in the atoms at the surface and some short time later the heat is available to be re-radiated (at a longer wavelength), but if there were no “short time later” you would have a reflective surface and presumably there would be no heating. Likewise the time needed for radiation to be absorbed and re-radiated within the atmosphere should have a bearing on what equilibrium temp is achieved. In other words the atmosphere can be thought of as hindering or slowing the passage of radiation from the surface, and how quickly that happens helps determine how much warming occurs – with less warming occurring when radiant energy passes more quickly.
Does the atmosphere have an R-factor? Shouldn’t a blanket or insulation be part of this awkward, inapt greenhouse metaphor? Maybe an electric blanket where the electricity coming in on a wire in an electric blanket is akin to the shortwave sunlight passing freely through the atmosphere to warm the surface?
@Dave Springer says:
“The bottom line is the greenhouse effect was demonstrated experimentally over 150 years ago. Anyone claiming it isn’t real is sorely lacking in understanding of introductory level physics”
Nobody is saying that there is no backradiation. The point is that backradiation emitted by a layer with -55 Celsius cannot transfer heat to a surface much warmer that -55 Celsius. This is the second law of thermodynamics. This second law is true for all of us: Being realists, physicist or oekofascist…
Willis,
If it is the simplest possible model you want that is USEFUL then I think I already suggested it. A shell one km thick being in contact with earth surface and a resulting temperature gradient from earth surface to Top Of Shell. Still no where close to reality, but sufficient to model re-radiance of energy based on varying amounts of CO2.
As for those who are jumping on Willis because they don’t get how the shell winds up doing what it does, I’m sad to say that this hard core skeptic agrees 100%, that is EXACTLY what happens. In the real world the “effect” is distributed across the thickness of the atmosphere, and it seems counter intuitive when you look at the drawing, but that is what happens. As upward bound photons are absorbed by CO2 molecules and then re-emitted in a random direction, the amount of energy they absorb gets re-emitted 1/2 upward and 1/2 downward. For conservation of energy to take place, the earth surface mut heat up enough to create upward bound photons that balance the re-emitted downward bound photons.
Which is why a “shell” of a given thickness with a temperature gradient from bottom to top is usefull. It isn’t the surface temp per se we are interested in, it is the change in the gradient. If you do it that way you will find that doubling co2=3.7watts=+1 degree AT SOME POINT ON THE GRADIENT and that surface temp of earth only goes up about 0.6 degrees and the observed temperature of earth from space goes up…. O.
Sorry, model doesn’t work. In figure 2 the temperature of the shell is given as 0 Kelvin. Since energy is either transmitted perfectly or reflected perfectly, that temperature doesn’t change. As a result in figure 4 it has to radiate at 0 Kelvin.
Another way of going about it, after going opaque we change the suns output from 240W/m^2 to, say, 500W/m^2. What happens on the inside? The answer must be that nothing changes. The shell is opaque and all energy is reflected. Inside the numbers stay at 240W/m^2 and on the outside the numbers are now 500W/m^2. Does the shell now have two temperatures?
– – – – – –
Dave Springer,
I agree. The name ‘GHG effect’ is a terribly misleading and very unscientific name. So let us forthwith not use it. I suggest something like Atmospheric Effects of Molecular Dipole Moment Gases is much much better.
Also, regarding the GHG effect being proven, yes, but a simplified demonstration in laboratory does not mean the earth atmosphere effect when mixed with actual atmospheric processes has always the same effect as the laboratory at all altitudes and in all regions. It is simple in lab principle is all we can conclude.
John
The actual surface temperature does not follow the Radiation Theory Explanation.
The Earth should get much, much hotter during the day and much cooler at night. Basically, the Earth absorbs just an extremely tiny amount of the solar energy received during the day and releases back that tiny amount at night.
It absorbs only 0.00026% of the energy received by the Sun during the 12 hours of sunshine and then releases back that 0.00026% at night (give or take some small daily seasonal change).
In other words, 99.99974% of the solar energy received during the day is sent back up to the atmosphere and eventually to space every second that the Sun is up.
A given square metre of Earth Surface receives 20,736,000 joules of solar energy during the day but the surface temperature only rises by 54 joules during that period.
You could think of it as, over time, the Earth has accumulated a tiny differential in outgoing versus incoming radiation and if the Sun didn’t come up tomorrow, it would all be gone in 86 hours (give or take a lag from the ocean and land – it might take a few decades to fall to -270C but it would fall to -75C in just a few days).
This is a fairly typical 24 hours of measured Radiation Flows for a given location. The explanation does not match reality. Table Mountain Colorado on November 17th, 2010.
http://img12.imageshack.us/img12/3225/tablemountainnets.png
http://img140.imageshack.us/img140/4109/tablemountainall.png
Good post! You addressed both greenhouse effect and zero greenhouse effect. You overlooked a third possibility. On Titan, the atmosphere absorbs some frequencies directly from the sun, and is transparent to some of the longwave frequenices from the planet, resulting in a possible ” anti- greenhouse effect.
How about this fundamental problem…
In figure 4 the blue arrow is radiating energy from a low energy black body (the glass) towards a higher energy black body (the earth). Isn’t this a violation of entropy?
Furthermore, this can’t happen unless work is somehow applied to the model and there isn’t any in the model is there?
Thierry’s G&T objection is not completely off the wall. The simplistic global warming models assume an instantaneous adjustment in temperatures. In practice, you’ve got to apply Newton’s law of cooling.
I plugged in Newton’s cooling law on my July 24, 2010 post here:
http://scienceofdoom.com/2010/07/24/the-amazing-case-of-back-radiation-part-two/
bessokeks,
“But transfering heat energy from “cold” to “warm” violates the second law of thermodynamics.
There is no way around that.”
There is a lot of misunderstanding surrounding the second law of thermodynamics. The original formulation of this law says approximately what you attribute to it. This was applied to heat transfers in conducting bodies. The modern formulation is in entropy and states that in a closed system, the total entropy must always increase. The application to heat transfer has been changed to refer to net heat transfers. The implications to conduction of heat have not changed. However, we know that radiative transfers do indeed take place in both directions.
In order for the second law to be obeyed, the net transfer must always be from warmer to cooler. This should be intuitive – even a cool body emits photons of energy which must travel at the speed of light regardless of the fact that they may impinge on surfaces that are warmer. The net transfer argument should make it plain that more photons will be emitted from the warmer surface.
A modern version of Maxwells demon thought experiment is to imagine a demon sitting between the cool and warm surfaces. The demon is supposed to allow the photons from the cooler surface to reach the warmer surface, but prevent the flow in the opposite direction. The action of the demon would cause the cool surface to become cooler and the warm surface to become warmer. This is clearly in violation of the second law. The Maxwell demon paradox was solved when it was realised that the demon needs information to sort the photons and this prevents the system from being closed.
In practice, although photons from the cool surface carry energy to the warm surface, a higher flow occurs in the opposite direction. The result is that the warm surface cools and the cool surface warms. Ie, they equilibriate and their entropy increases. Thus, back radiation does not violate the second law.
Thinking a bit further. in figure 4 the temperature of the planet has to rise until it radiates 240W/m^2 at and above the short wavelength where the shell is transparent. The radiated spectrum will look a bit unnatural but that’s to be expected when working with miracle matter.
John Bowman says:
November 28, 2010 at 6:02 am
“It should more properly be called ” the insulation effect” as the atmosphere limits the transmission of heat energy by its attenuation within a material.”
Exactamundo!
That should be enough said and it’s a shame when it isn’t. Most people at least intuitively understand the effect of insulation if not the physical mechanism by which it works.
willis,
can you explain why the temperature of the shell in figures (3) and (4) is only 255K rather than 303K? It seems to be absorbing and radiating at 480W per m2 – the same as the planet in figure (4).
thanks
nige
I agree that thought provoking hypothesis can generate discussion amongst discerning individuals but they must be accompanied with caveats which clearly state that the thought presented is a special case and on its own has no practical implications in the real world except it is one of a long list of interdependent variables which make up the final result.
My concern is that some will take such a presentation too literally and form a wrong impression.
The assumption that 100% of the absorbed radiation is reemitted back from the earths surface is incorrect since the plant life of the world absorbs radiation energy to generate carbohydrate from CO2 and H2O.
The grossly oversimplified diagrams showing radiation from the gasses or particulate in the atmosphere has a free ride back to the earths surface is nonsense since radiation downward will have the same degree of absorption as radiation upwards. Further to this point with regard to gasses they absorb resonant frequencies very quickly ( try doing a Beer’s law calculation) however the close neighbors to the resonant frequencies are absorbed much slower so reach higher into the atmosphere, when a molecule reradiates however it does so at exactly its resonant frequency so its return path is much shorter. Thus none of this energy can return to the surface. I note that in one comment an exception was made to the transfer of energy by collision this is not a viable argument since the time taken by a molecule to reemit IR energy is about 10 000 times longer than the time taken to collide with another molecule thus there is virtually no reemission.
One last point, to assume the atmosphere of the entire world contains some mix of components which forms a 100% opaque screen to all the outgoing radiation is a worthless hypothesis I think a number of shells representing all the different components with their contribution to the warming effect of our atmosphere would be far more instructive.