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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Could it be that the model results in a equilibrium temp of 303 k? Way too hot for me.
Ben
I’m going with spherical chickens in a vacuum…?
Our average radiation is based on our average temperature. I don’t believe 390PPM of CO2 contributes anything measurable to our average temperature. I think the difference between the calculated black body temperature and our actual temperature is because we don’t live on a black body disk, we live on a gray, spinning sphere with lots of integrating thermal mass and a homogenizing atmosphere.
Want to see some negative feedback? Try increasing radiation by the fourth power of a temperature difference. Mother Nature does not want us to be warm!
Jimmi says:
November 27, 2010 at 5:24 pm
Thanks, Jimmi, fixed. WordPress changed their default, I missed it.
There is a “greenhouse” effect in a greenhouse, although it is less important than trapping the warmer air inside. Like CO2, glass is transparent to the sun’s shortwave energy. Also like CO2, the glass absorbs IR and then reemits it in all directions. The half that goes back into the greenhouse helps heat the greenhouse. Having two panes of glass means, in a very crude sense, that only 1/4 of the IR makes it out.
Vorlath: The 240 W/m^2 outwards is thermal radiation from the shell, not the radiation from the earth somehow passing through the shell.
Willis Eschenbach;
Even with that, there is still something that prevents this single-shell planetary “greenhouse” in our thought experiment from representing our real planet in even the simplest way. I still have not seen anyone point to it.>>
There are so many defficiencies in this model Willis that you’re probably going to have to throw out a hint. You’ve so oversimplified things that there are dozens of simple things wrong with it. What perspective are you looking at this from?
o An outside observer would see the temperature of the planet as identical if the shell is opaque or clear to LW. Both radiate 240 w/m2.
o For the shell to radiate 240 w/m2 it must have some sort of mass that heats up to emitt 240 w/m2. Depending on what material you presume the shell to be made of, that could be a very large amount of energy, or very small.
o For the model to be vaguely accurate, it cannot presume a shell of 0 thickness. Per above, the shell must have mass to function, and therefore some sort of thickness. If we were to change the model to presume the shell surface is one kilometer above the earth surface, and that the shell thickness is 1 km, then the model breaks down entirely. Both the clear and opaque to LW shells would then have a temperature gradiant between earth surface and TOS (Top of Shell). The distant observer would still see 240 w/m2, but it would be EFFECTIVE black body temperature that exists somewhere between planetary surface and TOS. The difference between the clear and opaque models would then be that the effective black body temperature is identical, but the altitude at which it occurs is different. Further, the earth surface in this case would NOT double its radiance as it must in a o thickness 0 mass shell model.
o The sun emitts considerable LW though mostly SW. An opaque shell would absorb and re-emitt LW from the Sun, and I expect this would be measurable.
o Though you postulate the Sun as some sort of cloud emitting constant radiance to earth surface at all times, the earth surface is not constant. Even assuming constant 240 w/m2 constant over entire surface, land and water will react differently. In the case of a presumed vacuum between shell and earth surface, I presume also that we have oceans that don’t boil, but otherwise have identical properties. In that case, LW only penetrating a few microns of water, the water surface would heat up enormously with the hot water rising to the top and becoming a barrier to mixing. Land would heat up less as it does not flow and conductance would carry some heat to some depth. This is the reverse of the real world where land would heat up faster than ocean surface. If we presume instead that the shell is again 1 km thick and touches the earth surface, then the top few microns of ocean would heat up and transfer the bulk of the energy back into the shell without appreciable changing the heat content of the ocean at all.
I could go on, but I think you’ve got to narrow the scope somewhat.
Sorry Willis… but you have just added to the rather large chunk of climate science junk.
You said “In the situation shown in Fig. 4, the sun directly warms the planet. In addition, the planet is warmed … by the radiation from the inner surface of the shell. … As a result the temperature of the surface of the planet is much higher than in the previous Figures.”
NO, No and No.!!! The colder inner surface of the shell can not warm the warmer surface of the Earth (Second Law of Thermodynamics). However, if the colder shell surface was slightly less cold (due to the absorbed infra-red radiation from the surface of the Earth) than the loss of heat from the surface of the Earth would be less due to the lower temperature differential. This in effect would lead to increase in the minimum temperature readings at the Earth’s surface (as stated by Baa Humbug above). I think there is evidence that there is an increase in minimum temperatures leading to an increase in the average surface temperatures ( Can someone verify this?). If so then this may be evidence of an increased “greenhouse” effect?
Water, clouds and wind is missing from this simple model…??
Willis can we have your answer please? I’m exhausted trying to keep up
Willis,
Add one more variable to your thought experiment. Add a layer of 100% IR transparent atmosphere to the model. Assume very high gravity so that even with a thin layer, the atmosphere is extremely dense at the surface, say, 100x earth’s, yet near zero at the outer diameter that you considered, like ours. Now some energy will be transferred by conduction and diffusion from the surface to the atmosphere at the lowest levels so that the lowest layer will be the same temperature as the surface. The temperature profile will decrease via the usual adiabatic lapse rate for whatever gravity we choose (this might take some time as conduction and diffusion are both slow, but we will wait for equilibrium). The highest level will be near absolute zero, due to near zero pressure. What happens? Now what happens when the density at the surface is 1000x? 1 million x? By failing to consider temperature simply due to pressure, and the atmosphere whose molecules are also emitting IR (even though they are IR transparent), the greenhouse effect by greenhouse gases is overstated, while the effect simply due to pressure rise with depth is understated or ignored. Forget convection for this small addition to your model.
Willis,
I normally find your posts very interesting, but this ‘bonus question’ lark is a bit too juvenile. There are a whole host of reasons why your model is inadequate to represent the climate system of the earth – earth has an atmosphere, no hard shell, with convection, water that changes state, and with oceans, and with a hot core, etc, etc, etc, etc, etc.
This strikes me as a bit like a weird game of ‘one of these things is not like the others’ where the question-poser eventually reveals the fact that the odd one out is obviously the one which has a different penultimate letter, and no other differences count.
I get accused of believing some odd things, but I’m not the one denying that N2 and O2 molecules have temperatures. 781,000PPM of N2 has no thermal capacity or thermal mass? 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. Stefan-Boltzmann says things radiate based on their temperature, not whether they’re made of CO2 or water vapor.
The earth is round and it’s not a black body.
NASA Abandoned Flawed Climate Calculations in 1960’s
“Lunar Temperatures Cast Doubt on Climate Theory
NASA had found that daytime temperatures on the lunar surface were lower than expected because planetary bodies also conduct heat to their inside rather than radiating it all into space – an empirical fact that challenges the GHG theory. Computer models supporting GHG theory had predicted that such heat energy would be ‘blanketed’ above a planet’s surface.”
The key to understanding the effect is to remember that the shell has two sides. It radiates energy from both sides equally.
The planet has one side. If it is receiving 240 W/m2, it must radiate at 240 W/m2 to stay in balance.
A shell, on the other hand, has two sides. Suppose it is heated from one side at a given rate, say 480 W/m2. With twice the surface area, the must radiate at half the rate per square metre to maintain the balance. Half goes out to space, half goes in to the planet. And the rate of radiation is what determines the blackbody temperature.
Not sure if that is clear. If not, ask in a different way.
Thanks,
w.
The m^2 of the shell is greater than the m^2 of the earth’s surface.
Morris Minor:
The second law of thermodynamics is about the net flow of heat. In Figure 4, the net heat flow between the warm planet and cooler shell is still towards the shell, so there is no violation.
You’re killin’ me Willis. People say, it’s missing this or it’s missing that and you say, well, all models miss stuff. The obvious rejoinder being, if it’s missing something important, than it’s not much of a model, is it? And you say, even if it included everything, it still wouldn’t provide a workable model of the “greenhouse effect” on our planet.
I was hoping by the time I got to the end of the comments, you’d spill the beans, but not yet. So out with it! Put an end to this infernal guessing!
In our world the atmosphere has a temperature, that’s why it radiates some photons to earth. The model has but a vacuum and a shell of presumable infinite thinness so there is nothing there to have a temperature and thereby radiate energy.
Do I get some sort of prize?
I think it’s the fact that you are showing us a simplified model of a “perfect” system, sort of in the spirit of the ‘ol college physics 101 “assume there is no friction”.
In your model, the shells operate at 100% efficiency and the “earth” is a perfect blackbody for exactly what you are modeling.
Nothing is perfect or works at 100% efficiency. Iskandar hit on this a little earlier up in the posts.
Did anyone mention the bottom line? Two additional watts of forcing at the surface from all anthropogenic GHGs together for a total of 242 watts per square meter temporarily until equilibrium is reestablished. New equilbrium temperature will be close to 2 degrees higher if nothing else changes.
There’s barely a third of that surface warming actually observed if we can trust the instrumental record. Therefore Trenberth’s “missing heat”.
I suspect the missing heat is being rejected by higher speed water cycle which means more convection and higher albedo from more clouds. Humans still emit aerosols along with their CO2 and methane and aerosols have a surface cooling effect so some of the 2 watt GHG forcing is negated by those. Nothing is missing. Trenberth should relax about it.
Earth does not receive ALL of it’s energy from the sun. Their is an additional source from within the earth radiating heat away from it’s active core.
Morris Minor;
NO, No and No.!!! The colder inner surface of the shell can not warm the warmer surface of the Earth (Second Law of Thermodynamics).>>
No violation of 2nd Law occurs. Consider a similar thought experiment. A house is heated by a 10,000 watt heater and exists in a -40 C atmosphere. At equilibrium, the temperature inside the house is higher than -40, and the house radiates 10,000 watts to the oustide. Double the thickness of the walls from say R2o to R40. At equilibrium, the house radiates exactly 10,000 watts to the outside. But the temperature in the house is higher. Why? Because the layer of extra insulation added must heat up until the house as a whole is radiating 10,000 watts to the outside. But since it radiates in two directions, not one, the interior temperature of the house must increase until the amount of extra energy it radiates balances the energy absorbed by the extra insulation and radiated back into the house.
I’m a hardcore skeptic and I don’t have a single problem with this. My problem is with all the other factors in a chaotic system that physics requires to be a mitigating factor that the climate alarmists conveniently ignore. Well I have two problems. The second is trying to stay awake long enough to find out what the heck Willis is getting at.
The blue down arrow on your figure 4 disappears in the case of a vanishingly thin transparent sphere. This is because the mass of the transparent sphere affects its capacity to capture and reradiate energy.
The shell as proposed is a constant, and does not allow for any feedbacks due to, for example, that pesky water vapor.
Interestingly, I think that both Miscolskzi and Hansen would agree with me on this.