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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Your model assumes a transparent shell and a vacuum within. These are not true for the earth since clouds can reflect or scatter the short wave radiation and the atmosphere is not a vacuum.
I am intrigued by this thread.
Perhaps I have missed some glaring fundamental principle but the only answer to the bonus question that I can come up with is the scale of complexity of the model.
For any realistic calculation to be made the model would have to include all the goings on of the many layers of the shield as well as other factors like convection , cloud formation etc.
I think it is safe to say that once the radiation has arrived on Earth it can never again be emitted as short wave so the question is whether the long wave emissions can maintain the energy balance. It occurs to me that the long wave opacity of the atmosphere might have gaps in it which will affect the numerical calculations but I do not see any holes in the principle.
In summary: My guess is the inability of the basic model to cover all necessary parameters.
Molecules, like air, do not reflect energy. If they absorb, and then retransmit, it is not directional, but in all directions from the molecule, as a tensor, not a vector.
It’s the impervious nature of a shell. Like the glass in a real greenhouse. It traps and elevates heat. Our atmosphere does not resemble glass or a shell.
If it did we would all be cooked.
Statistically in all directions, I meant.
Our atmosphere is multishell
Willias,
I forgot to add: The higher value of the ground temperature results in a higher radiation out level from the ground than if the ground were not as hot. However, the atmospheric radiation from just above the ground (due to the local atmospheric temperature acting on a radiating gas) is omnidirectional, and the downward component, called back radiation, almost equals the upward radiation from the ground, resulting in a greatly reduced NET radiation heat transfer. It is convective heat transfer that carries most of the energy from absorbed solar radiation in the ground to the upper atmosphere. Thus the higher radiation level up and back radiation do not cause the heating, they are a result of it.
I think Paul Birch got it. The earth is a sphere, with a “point” source of energy in the sun a single 1D model can’t capture the system.
Earth’s ‘shell’ is not fixed.An atmosphere can expand/contract.
I’ll just say it again as clear as I can since I and others have mentioned it several times. The last figure. Figure 4. The math is wrong. If the shell is opaque to longwave, then you have two possibilities for the 240W/m2 radiating out into space from the shell.
1. Longwave is coming from space or the Sun.
2. Shortwave is coming from the surface of the Earth and converting to longwave as it passes through the shell.
Neither of those are shown in your graph. You have all of 240W/m2 going to the surface of the Earth. So option #1 is no good. Second, you have blue lines indicating longwave radiation on the inside of the shell. So option #2 is no good. Option #2 has another issue that makes it wrong is that the line of radiation from the Sun is shown to go all the way through to the surface of the Earth without any conversion. So if there is no conversion going in, then there is no conversion possible going out either.
IOW, the math is critically wrong in figure 4. Please fix this before continuing.
Well this looks as if it will be an interesting thread.
I am not sure what the most important missing factor is, but would vote for the fact that the earth rotates. This means that on average the incoming radiation only warms some of the time, but the outgoing is present all the time. However this only affects the average temperature, and the basic principle that warming occurs is still correct.
The Earth is vastly more complicated than the model, and has many known and unknown feedback mechanisms.
Most of these must be negative feedbacks, or we’d have had a runaway greenhouse or freezer effect eons ago and life would not have arisen.
Willis – Roy Spencer claims that there is a net negative feedback which more than counters the CO2 effect.
He claimes that this is not just theory but that he has measured it from observations.
Please comment.
The “greenhouse effect” is, if I remember, only a PR definition that was used to simplify stuff for the policy makers or something.
Secondly the greenhouses isn’t used to trap heat per se (if they were they’d be padded down with loads and loads of insolation) but to control the inside environment for maximum growth using sunlight, artificial light and heat (for night time and winter), humidity, CO2 and Nitrogen levels, pesticides, and of course water flow and nutrients. CO2 is of course not used to trap heat or to add to the heat because if it were that much of a problem plants getting heat stroke would be a real problem and you’d end up spending more money on cooling systems, so the trace gas is simply used as nutrient in a controlled environment.
So the analogy that gases acts with a “greenhouse effect” is just bad since the greenhouse is to control a balanced environment.
I get the feeling I’ll be slapping my forehead and exclaiming; Doh! I shoulda thoughta that one!
Let me be the first (?) to state that I am in fact a blathering blowhard, and a stuffed shirt! I take what little I know and make up the rest! I pass wind at your silly little mystery question! Hahahahahahahahahahaha… I’m dressed like a turnip!
Willis,
I see the following as a being a problem with your model:
The incoming energy (from the sun) you express in w/m^2, lets simplify it even more and say that energy is delivered in truckloads.
Lets say we get 2 truckloads per hour.
With your transparent shell, we end up with 2 truckloads in and two truckloads out, things are balanced.
But when we come to your semi-transparent shell, you are still getting two truckloads per hour, but you say that these two truckloads are delivered to both the earth and to the shell — that makes 4 truckloads/hr.
Where did the extra two truckloads come from?
You then make things even worse, by saying that the magical two extra truckloads that are delivered to the shell are again magically multiplied, with two going out to space, and two more going to the earth.
Where do these magical extra truckloads of energy come from?
“There is a vacuum both inside and outside the transparent shell. ”
=======
A vacuum inside ??
Not my kind of planet.
The sun does not hit the earth on all sides at once. There is no night and day in your model.
Willis I’m having trouble with fig.3
If the shell is radiating 240Wm2 to space AND 240Wm2 to the planet, it must therefore be receiving a total of 480Wm2, which is what fig.3 shows.
IF it is receiving 480Wm2, how can it be the same temp as the planet surface i.e. 255K or -18C? The planet surface is receiving only 240Wm2.
Maybe I’m not comprhending this situation too well. To put it another way..
Take an energy source radiating 240Wm2 and point it at a black body object. This object will reach 255K.
Now, if we add a SECOND energy source of 240Wm2 from the opposite direction, according to fig.3 this object will stillbe at 255K???
If it is not the cloudy thingies, could it be that the basic theory is a load of dung beetles raison d’etre?
“Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?”
Because the oceans also have their own “greenhouse effect”. They allow downward shortwave radiation (visible light) to warm the oceans to depths of 200 meters (with the warming diminishing with depth), but only release heat at the surface. John Daly made the argument that a planet that was all ocean would be warmer than a planet of all land. Refer to the following post inder the heading of “The oceans also behave this way”:
http://www.john-daly.com/deepsea.htm
” … it does not give enough energy to allow for the known losses in the climate system.”
“Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?”
When your shell absorbs the blackbody radiation from the planet, it heats up to a lesser temperature than the planet’s surface, so it will emit a lower frequency blackbody radiation than it received. CO2 re-emits the same frequencies it receives.
Wait. Your figure 3 is wrong. 480 W go up to the shell, it must reach the same temperature as the planet’s surface, otherwise it can’t re-emit 480 W. (Again, this is not the case with CO2 in the atmosphere, as it re-emits the frequencies it receives due to absorption bands, not blackbody spectra)
DirkH says:
November 27, 2010 at 4:53 pm
“Wait. Your figure 3 is wrong. ”
Sorry, i mean figure 4