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 opaque shell example seems nonsensical. If the shell is opaque at all wavelengths there is no albedo and the shell absorbs near total TSI and would radiate half that to the surface, But if the shell is opaque to LW, the energy reradiated by the planet couldn’t escape and would build up in the interstice between shell and planet.
Matthew Sullivan says:
November 27, 2010 at 6:35 pm
Vorlath: The 240 W/m^2 outwards is thermal radiation from the shell, not the radiation from the earth somehow passing through the shell.
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Thermal radiation from what energy source? And why doesn’t fig 3 show this if what you say is true? Also, Willis Eschenbach disagrees with you. He’s saying it does come from the Earth and it’s passing through the shell.
I’m seeing a lot of goalpost movement here. The math is flawed. Plain and simple.
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Willis Eschenbach says:
November 27, 2010 at 6:55 pm
Baa Humbug says:
November 27, 2010 at 4:27 pm
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.
The key to understanding the effect is to remember that the shell has two sides. It radiates energy from both sides equally.
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If so, then it’s no longer opaque. Here’s the definition of opaque as it relates to energy.
2. not transmitting radiation, sound, heat, etc.
So please stop changing the goalpost, or at the very least stop using better terms to describe your models.
Willis. My answer [guess] to your question.
The posited globe receives much less energy at the higher latitudes than at the equator.
This would make for an energy imbalance and [consequently] an energy flow between the low latitudes and the poles.
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.
On the incoming side, about 70 W/m2 of the incoming solar energy is absorbed by the atmosphere. In addition, there are losses from convection and from evapotranspiration. These losses move energy directly from the planetary surface to the shell. These are estimated at another 100 W/m2. Finally, about 40W/m2 goes straight to space from the surface. Total loss is about 210 W/m2.
So out of the 480 W/m2 from our theoretically perfect system, we end up with only about 270 W/m2 for the surface temperature, and the rest goes up in losses.
And 270 W/m2 is a blackbody temperature well below freezing … the system pictured is simply not powerful enough to heat the surface given the real-world losses.
This means that at a minimum a system to model the earth must have two separate and distinct shells. One shell is not enough to concentrate enough energy to satisfy the known constraints.
With two shells, you end up with a theoretical maximum of three times the incoming W/m2. For the earth this is 720 W/m2. That is enough to allow for known losses and to still have enough to warm the surface to the Earth’s 15°C.
People may have gotten the erroneous idea that I am opposed to models. To the contrary, I use them and write them myself. I am particularly interested in what I call “Tinkertoy models”. These are the models which contain the absolute minimum information necessary to model a system.
For radiation/convection/evapotranspiration models of the earth, the absolute minimum configuration is two shells. My iterative Excel model of the two-shell system is here (I hope, server hassles lately). All models are wrong. Some models are useful.
Grrr … no iterative model, it gives me “Forbidden” to my public iMac folder.
Onwards.
As always Willis, a great, thought-provoking post.
Judging by the responses, so far, you’ve hit the odd raw nerve!
Nice demonstration of just how shaky the application of the adjective “Greenhouse” is to the”consensus” that “underpins” CAGW.
I would say the missing component is convection from the surface to TOA.
typo in my last message: stop = start
Here’s the corrected version:
So please stop changing the goalpost, or at the very least *start* using better terms to describe your models.
Also, if you’re letting the shell transmit energy, is this happening in figure 3 as well? So it’s not truly opaque. But even so, you’ve got a delay that doesn’t show up even if the totals do add up eventually with a continuous supply of energy. If half the energy from the beam goes back into space, then that’s 120W/m2 leaving 120W/m2 going to the planet surface and back to the shell where half again goes to space. So we’re at 60W/m2. On and on until all of it is sent back into space. It will add up to 240W/m2. But the description of opaque is completely off.
‘Willis Eschenbach says:
November 27, 2010 at 7:50 pm
Why The Thought Experiment Can’t Represent Earth’
Well throw another log on the fire, I’ll get the beer and popcorn. This sholud get interesting.
Well, I’ll take a stab at the ‘bonus’ question: I would say in short because the earth’s climate system of predominately the amosphere and the oceans move heat around the earth (convection, latent heat of vaporization from the oceans, and ocean currents) to locations they can more easily escape, in essence ‘negating the shell to some extent.
The oceans absorb heat, and ocean currents move the heat towards the poles, where it can radiate the heat into space, without being ‘reheated’ the same as at the equator because of lower angle of incidence of the sun (thus the poles are acting as a ‘heat outlet’ of the earth.
The atmosphere transports a lot of heat in water vapor from the oceans (the latent heat of vaporization) higher in the atmosphere, where when the water vapor condenses, it gives up its heat higher into the atmosphere, where it is radiated into space quicker (due to the thinner atmosphere) than heat radiated at a lower level in the atmosphere.
. . is this explanation on the right track . . ?
Willis Eschenbach;
For radiation/convection/evapotranspiration models of the earth, the absolute minimum configuration is two shells.>>
So when I said one shell of o mass and o thickness was unrealistic, that much better would be a shell of 1 km thickness resulting in a temperature gradient from earth surface to TOS, that would be different how? You proposed two shells as being the minimum and I proposed (in effect) a near infinite number of shells of near 0 thickness stacked to a depth of one kilometer. Your two shell minimum is better than one shell, but an infinite number of shells is far superior to both, easily described by calculus, and much much more accurate than two shells. Or three. Or 10.
Great thread by the way, provoked a very interesting discussion. But your two shell minimum isn’t much better than your original one shell.
Here goes Willis again wandering off into the never never land of naively simplistic science. This post if I can understand it correctly deals with Greenhouse effect which most people will interpret as the greenhouse GAS effect. It has already been pointed out correctly that there is no shell but a continuum of atmosphere from the surface to the TOA.
Now the facts are that CO2 can only interact with about 7% of the outgoing radiation and H2O somewhat more than that but the majority of the incoming and outgoing radiation interacts with the particulate in the atmosphere which is not resonant frequency sensitive as are the gasses. Particulate is defined as water droplets and solid particles such as volcanic ash carbon and fly ash etc.
Clearly the vast majority of the particulate is water droplets or clouds. Therefore the so called greenhouse gas effect is a very small contributor to the general warming produced by our atmosphere.
The debate over whether clouds have a net positive or net negative forcing effect has raged for years IPCC claim net positive thus the effect of an increase in temperature is an increase in humidity which produces more cloud therefore warms the earth Drs Lindzen, Christie and Spencer feel the reverse is true and that clouds have a net negative forcing effect which creates an equilibrium.
The cloud cover according to satellite data has varied from 62% to 69% over the last 30 years which has had a significant effect on temperatures.
To get back to Willis’s childish illustrations there is never a 100% transparent or 100% opaque atmosphere and to cite a “global average” radiation is even more ridiculous than trying to compute a “global average temperature” from a bunch of computer generated statistics.
Basically the clouds do tend to smooth out the average radiation budget although they will reduce the average as they increase and increase the average as they decrease.
Paul Birch says:
November 27, 2010 at 2:00 pm
A transparent shell would not be at 0K. If it were perfectly transparent (which is physically unreal, but never mind) it would retain whatever temperature it had when you first put it there, because it is neither absorbing nor losing any heat. If it were merely very nearly transparent (which is the physically realisable case) , then in this example it would be at a temperature ~ 255K. The temperature would be somewhat higher or lower than this, depending as the emissivity were higher or lower in the visible or thermal.
This model implicitly assumes uniform insolation, which is not valid for a sphere illuminated from one direction. Steady state requires that the planet does not rotate (relative to the sun), or has negligible heat capacity; the temperature would then range from a factor 4^1/4 higher (ie 361K) at the subsolar point, through ~73K around the terminator, to ~0K on the dark side. There would be no meaningful average or global temperature at all. The greenhouse effect of the shell would be the same factor of 2^1/4 (for the visibly transparent, thermally opaque case). Add diurnal rotation and finite heat capacity and thermal conductivity, and things become much more complicated. There is no steady state, and the temperature curve for a given latitude is messy to compute. The thermal capacity of the shell has to be considered too. The general effect of thermal capacity and rotation is to transfer (some) heat between the day and night sides.
Useful analysis. So even this (supposedly) extremely simplified scenario results in thermal complexity and a non-equilibrium thermal state, with all the non-equilibrium implications of nonlinear dynamics etc.
Does this not make it even more absurd to make any attempt to analyse earth’s real climate in terms of linear, equilibrium physics? OK there is always a heat in – heat out equation. But a complex chaotic system can respond in complex including adaptive ways…
There is no greenhouse effect because the greenhouse effect assumes all energy is transfered radiatively. Your model shows only radiative energy transfer.
I highly doubt that it is even possible to reliably model all the seperate modes of energy transfer in the earth-atmosphere system, conduction, convection, radiation, evaporation, condensation and mass transfer(i.e. wind and precipitation)
Here’s a couple thought experiments on heat transfer:
1. You have a really hot cup of hot chocolate and you want to cool it down do you A. Drop an ice cube in it (conduction), B. blow on it (convection) or C. hold it up to the clear night sky (radiate)
2. Thermoses use a vacuum for their insulation, because purely radiative energy transfer is slower then conduction and convection when a gas is present.
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.
Vorlath: The shells aren’t transmitting the radiation. All of the radiation leaving the shell is thermal radiation originating from the shell, the same way the energy going up from the modeled planet is thermal radiation originating from there.
Bill Illis says:
November 27, 2010 at 2:36 pm
Bill, can you give a quantum explanation of why the CO2 “greenhouse” or IR radiative heat trapping effect does not saturate in a few hundred meters?
The mean free path and radiative balance scenario that you describe could surely be turned on its head by missing out just one subtle feedback somewhere.
1) The earth has multiple shells of insulation.
2) The earth is not a black body- it is a grey body.
Just another comment on Willis’s article.
Go to Climate4you.com select global temperature and go down to the top of atmosphere radiation section.
You will see a wild variation in TOA radiation from 216 W/m2 to 238 W/m2 with a mean around 230 W/m2, not exactly what Willis was promoting, The CO2 curve v’s TOA radiation is also very instructive.
Willis Eschenbach says:
November 27, 2010 at 6:55 pm
Baa Humbug says:
November 27, 2010 at 4:27 pm
Willis I’m having trouble with fig.3
Yes thnx Willis.
The model does not work in that if you make the ‘shield’ distance to the earth surface thinner and thinner until it is actually AT the surface you are in fact at the same condition as either figure 2 or 3. This cannot be if the model is to be consistent.
Roger
The glass sphere is uniform but greenhouse gasses(water vapour,clouds and co2) are not uniform around the earth,they are variable over time.
I posted the thought experiment to provoke discussion, so success on that front.
I’m looking for the simplest model that will give me earthlike results. That model contains two shells. Yes, you can model it with four, or four hundred. I’m looking to simplify, not complicate.
Thanks,
w.
Barry, my planet with a 100% transparent shell is not the real world. It is a THOUGHT EXPERIMENT. These have been used throughout the history of physics. In a thought experiment, one can imagine such things as a perfectly clear shell. It is useful because it helps us to understand our mysterious universe, not because it is correct in the details.
Willis,
You still haven’t replied to several posts that say you can’t add the two 240 W/m2 downward radiation element and get 480 W/m2 upward.
Geoff Sherrington says:
November 27, 2010 at 7:36 pm
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.
Thickness will only affect the response time for a change in input. Near 0 = fast response, thick = slow response. As small at 1 atom thickness would still be in equilibrium.