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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It would be difficult to have an earth model with only two shells. You would need one for the gasses (which are mostly uniform), one for the water vapour (which is not uniform, although can be persistant in some areas), and one for the clouds (which are not uniform, although can be persistant in some areas). These ‘shells’ overlap, for the most part, but are distinctive in their responses. You could also include the ozone layer and thermosphere. But I would not calculate the earth as a black body.
Vorlath,
I don’t see what’s wrong with the third diagram. Shortwave radiation comes through shield (transparent to shortwave) hits planet (opaque to SW) and heats it, where upon planet emits LW. LW radiation hits shield (opaque to LW) heating it, where upon it begins to emit LW in both directions, further heating the planet surface, and losing LW to space. Just because a material is opaque (non transparent) to a wavelength doesn’t mean it can’t emit that wavelength. I would suggest that white light won’t pass from a source behind the tungsten filament in an incandescent globe to the other side, even when the incandescent light bulb is on.
Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?
Without reading the comments, I would venture to guess that the energy in the system you are postulating doesn’t do any work.
Okay, my guess. A lot of incoming shortwave radiation is absorbed by LIFE on the planet, it is not immediatly reradiated as longwave radiation?
Braddles says:
November 27, 2010 at 2:13 pm
The comments that dispute Willis’ excellent post highlight some of the problems with the AGW sceptic arguments. Those who argue that the greenhouse effect does not exist do the sceptics’ side a disservice, by arguing an untenable position. It creates a weakness in the sceptical position, which warmists focus on to try to discredit all sceptic arguments.
True, then on the other hand, warmists occupation with this self-created strawman does a devastating disservice to its side. It exposes its rage as being unfocused, not centering on the strong skeptic gems in there. Informed minorities on both sides should ignore both the untenable and the rage.
In for a penny, in for a pound. Had to read the lot and hope I did not miss any points. Several made great store on their observation that the Earth was not an emitter.
Really
Its a humungus ball of molten rock at about 2,000 degrees with a very thin layer of colder rock on top. Space is about zero degrees and if i am correct hot moves to cold, I.E. the earth emits. Volcanoes, hot rocks, hot springs, geothermal vents, it emits all the time and is a very effective means of warming the oceans and thus the air.
It is not a black body like the moon
Ok, Willis, so I have a really stupid question relating to the thought experiment.
You posited a shell and the implied assumption was that the shell was unchanging over time. Obviously this was to restrict the experiment to simply defining the upper boundry of radiation.
The real shell (atmosphere) is created by life, which is constantly replenishing it. We’re now at 390 ppm of CO2. An increase in CO2 ought to result in an increase in O2, although the climate community doesn’t seem to have accounted for this. As such the shell ought to be somewhat thicker now than 1890. Maybe not by much, but thicker all the same. Moreover, the assumption of CO2 being (n)% of the atmosphere and growing seems off. If plants are also emitting more O2 then the (n)% isn’t growing as much as it may seem at first blush. As such this would imply that much of the apparent temp increases are more related to land use etc than CO2 (or natural recovery from the LIA, etc.) since it appears that the AGW argument is that CO2 is rising whereas all else is purely static.
So… my question. Am I missing something really basic here? Thanks…
Hi Willis; these types of thought experiments are interesting and serve a purpose. If I may point out an aspect to do with your figure 4; in the first instance only 240 w/m2 reaches the surface in the form of SW so only 240 w/m2 is reemitted to the disc in the form of LW; of that 240 w/m2 isotropic effect causes 120 w/m2 to be reemitted from the disc back to the surface and 120 w/m2 outwards to space; so in the next instance the surface has 240 w/m2 SW + 120 w/m2 LW for a total of 360 w/m2 and so on; in short this is, of course, a limiting sum geometric series:
Sn=a/1-r where a=1 and r=0.5; or 1/n^2 for n=1 to infinity is 2.
In otherwords the surface will only receive 480 w/m2 at infinity.
Willis Eschenbach says:
November 27, 2010 at 2:51 pm
but my thought experiment is in a vacuum.
So standing your Glass Thermos Flask in the sun at mid-day will slow down the cooling during the daytime… but by mid-night the contents will be cool… and probably cold just before dawn…
On a more constructive note it would be wonderful if you could create, based upon the very intelligent comments you have received so far, a revised version of your diagram that is technically correct and isn’t based upon a vacuum… because I remember being taught: Nature abhors a vacuum
Willis:
Please forgive the abruptness of this post which O am fitting in between duties I have today.
At November 27, 2010 at 8:20 pm davidmhoffer said to you:
“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.”
You have replied to that at November 27, 2010 at 10:12 pm saying:
“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.”
OK. I understand that, but it can be misleading to simplify beyond the physical process being modelled: an analogue is not a model of a mechanism but may be an accurate model of the behaviour of that mechanism.
GHG molecules in the atmosphere absorb IR photons from the Earth’s surface then (ignoring collisional energy exchange) release that energy by emitting photons in all directions. So, the molecules emit half the energy in upward directions and half in downward directions.
Thus, the GHG molecules act like half-silvered mirrors transmitting visible light. They accept radiation from below, then emit half of that energy upwards and half downwards.
Ignoring effects of collisional energy exchange, the number of ‘half-silvered mirrors’ to model the observed GHG effect is 7.
So, I suggest that your “simplest model that will give me earthlike results”is 7 spheres each with 50% transmittance and 50% reflectance. And a more realistic model would include energy extraction by molecular collisions from each shell.
Richard
I also found the following passage very interesting…
see http://www.newton.dep.anl.gov/askasci/env99/env223.htm
The flow of heat through the sandstone and limestone overlying Wind Cave’s passages is extremely slow. Temperature fluctuations of over 60°F between day and night are not uncommon on the surface, but if we were to monitor the temperature only two feet below the surface on such a day, the fluctuation in temperature would be only about 1°F. Therefore, it does not stay warm long enough during the day, nor does it stay cool long enough during the night, to significantly change the temperature
of the rock only two feet underground. The same principle holds true for seasonal temperature fluctuations as well, although the depth at which temperatures begin to stabilize is greater. Seasonal temperature fluctuations of 80°F are reduced to only l°F at a depth of about 50 feet.
So does the temperature gradient look like from the earth’s core up to ground level?
Is the earth internally generating heat or just simply cooling down?
Sorry to be throwing another spanner into the works….
You can solve this with one shell. No problem.
But You must add little bit of reality.
The energy balance between surface and your shell is NOT a radiative balance.
In real world is it a heat balance driven by convection. Then You get the height of the real world “shell”. 33K/6 Kk/km = 5,5 km
6 K/km are average lapse rate.
I’m no scientist, but how about uh… barbecues, campfires, air-conditioners, billions of cars, motorcycles, ships, airplanes, heaters, stoves, buildings on fire, industries, power stations, nuclear stations, Borneo, Russia & Sumatra forest fires, geysers, electricity, volcanoes, lava streams, E=MC2, energy and heat produced by nature, earth and man? Doesn’t that add substantially and explain a fraction of a degree rise of temperature perhaps? Do I get at least a bonus?
Willis,
Are you calculating the earth as a black body, because it behaves like a black body?
I am puzzled by the long wave radiation out to space of 240 W/m2 (top RHS of figure 4)
If the boundary does not allow long-wave radiation out then where does this radiation come from?
Under steady state conditions (equilibrium)
Outflow must equal Inflow. Outflow=Inflow (1)
Under these conditions storage has no effect on the result
i.e. S dT/Dt is zero where S is storage and T temp and t time.
As far as I can see the components don’t obey equation 1 in Figure 4.
Willis,
Please take a look at Fig 3b here: http://realplanet.eu/atmoseffect.htm
A surface temperature of 15 degrees is achieved with a single shell, simply by adding gravity and a circulating atmosphere. This seems more realistic than your 2 shell model.
“Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?”
================================
Assuming you wanted the simplest answer and noting that you said ‘planetary’, I posted at 2:58 pm;
“Day/night cycles are not considered. Day: outgoing is less than incoming. Night: outgoing is greater than incoming. The change (raising) of surface temperature is the difference between these two budgets.”
You first need two conditions, not two shells, for your construct to work. When I was at school (1960’s), a greenhouse was explained to work because glass is semi-transparent to IR. Therefore, when the sun is shining, its internal temperature increases as less IR escapes than is received. When the sun is not shining, its internal temperature decays to ambient more slowly (than without glass) because of the same phenomenon – the semi-transparency. Convection losses are present at all times but vary as delta T changes – applicable to a greenhouse but not a planet.
I claim my $5!-)
Willis Eschenbach says:
November 27, 2010 at 7:50 pm
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.
Damn. I started to reply that the atmosphere is made of an almost infinite number of ‘shells’ but didn’t submit because you said it was a simple model.
I’d like you to expand though. How do you think your insight relates to the real world? The path lengths of longwave radiation go from about 10^-27m near the surface (due to the density of the atmosphere) to around 1m at the top of the ionosphere. Radiation becomes more important than convection as a transporter of heat somewhere near the tropopause.
Humidity near the tropopause has been falling since 1948 on the average. I think this will have negated any rise in co2. Specific humidity near the tropopause mysteriously mimics solar activity levels: http://tallbloke.files.wordpress.com/2010/08/shumidity-ssn96.png
So what caused the warming? Reduced cloud cover and high solar activity. ISCCP data shows a drop in tropical cloud cover from 1980-1998: http://tallbloke.files.wordpress.com/2010/11/isccp-temp.jpg My calcs show this was causing an extra 4W/m^2 forcing on the surface in the 1993-2003 decade.
Simples. 🙂
More junk science.
The problem with thought experiments is that there are always factors left out to simplify. Climate Science has already left out too much science. Leaving out more simply proves the thought experiment is worthless for this application.
Try your thought experiment again with a reasonable figure for the energy flux within the earth. Then keep adding the other factors left out and viola, no NET greenhouse effect!!!
Capiche??
Robert Weber says:
November 27, 2010 at 10:25 pm
Not sure what you are referring to. The energy flows are exactly balanced, at all levels and in all three figures (Figs. 2, 3, 4). Perhaps you could explain what you see as the problem. There have been several posts that I did not understand, such as the one that said:
Sometimes I think I understand that, but then it slips from my grasp again.
In any case, if you could restate what you think the problem is with my thought experiment, I will see if I can explain it.
w.
Between Willises post here and J Currys “Skeptics make your best case”, my brain is frazzled.
If I’ve got it right, Willis says at 7:50pm “It’s not powerful enough…..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.”
At 2:42 pm I gave a simple short answer to the simple question thus:
Baa Humbug says:
November 27, 2010 at 2:42 pm
Layer upon layer upon layer
So, do I get a cyber prize or a cyber kick up the backside?
The only stupid question is the one you don’t ask.
I don’t follow that. If anything, it seems like making more CO2 should decrease the amount of O2 in the atmosphere. Oxygen makes up about 21% of the atmosphere, or about 210,000 ppmv. Every CO2 requires one O2. So for the CO2 to go from 280 to 390 ppmv, the O2 might go down to 209,890 ppmv. Of course, this doesn’t include any feedbacks, sources, or sinks … just a rough number. In any case the change in O2 concentration is on the order of five hundredths of a percent (0.05%), so the difference would be trivial.
kuhnkat says:
November 28, 2010 at 1:53 am
Thought experiments have a long and distinguished history in science. They are used to explore things that are difficult to explore experimentally.
I have done exactly that in my Excel model referred to above. I still find a net warming effect. Here is a more complete view of a two-shell system, with the other factors included. The two shells are shown as horizontal gray bands:
Finally, your claims would have more weight if they were accompanied by numbers.
Willis, see
Can I have a virtual banana please?
The Greenhouse Effect is a ridiculous name for an effect that has been used as blame for climate. Greenhouses do not act like the atmosphere. Greenhouses are heated by visible light and the energy loss of that light to become IR energy. Glass does not transmit IR, or UV for that matter, but greenhouses still get warmer than ambient. Incoming visible light is transmitted and this warms the interior and suffers energy loss so that some if that light becomes IR which remains inside the greenhouse because the glass traps it inside. The temperature will build and build until someone opens a vent to let in cooler air and expel the hot air.
The atmosphere is transparent to IR, and some UV light, as well as visible light. Yes water vapour and CO2, as well as other misnamed GHG’s, do warm up by adsorbing this energy, but this heat is not stored to be re-radiated later because the 2nd law of thermodynamics does not let this happen. The adsorbed heat is immediately conveyed to the other atmospheric gasses by convection, conduction or radiation to cooler areas. (Heat will only be transferred from hot to cold never in the other direction). So some of this heat will be transferred back to space because the lower atmospheric layers will be warmer!
The whole idea that something can ‘store’ heat violates the laws of thermodynamics and so makes the GHG warming hypothesis a failure.