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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Observed from a distance, Mr Eschenbach’s imaginary planet and shell would appear to be in equilibrium at 240 w/m2 in and 240 w/m2 out in the first part of his explanation. In the latter part of his explanation, with the shell opaque to LW, oberved from a distance the planet would appear to be in equilibrium at 240 w/m2 in and 240 w/m2 out. In other words, the distant observer would see both situations as the planet being the exact same temperature.
The only thing the observer might notice out of the ordinary is that if the imaginary shield went from “clear” to “opaque” to LW in an instant, there would be a perturbation (spelling not my strong point at best of times, so I’m pretty certain that’s wrong) to the outgoing energy until equilibrium was re-established. The distant observer would conclude that “something happened” but that the temperature of the planet as observed from space was the same before and after.
The energy conversion between the different forms of energy is not perfect, there is loss, entropy. No one has mentioned that yet.
“In physics, the term energy describes the amount of work which may potentially be done by forces or velocities (kinetic energies) within a system, without regard to limitations in transformation imposed by entropy. Changes in total energy of systems can only be accomplished by adding or subtracting energy from them, as energy is a quantity which is conserved, according to the first law of thermodynamics. According to special relativity, changes in the energy of systems will also coincide with changes in the system’s mass, and the total amount of mass of a system is a measure of its energy.
Energy in a system may be transformed so that it resides in a different state. Energy in many states may be used to do many varieties of physical work. Energy may be used in natural processes or machines, or else to provide some service to society (such as heat, light, or motion). For example, an internal combustion engine converts the potential chemical energy in gasoline and oxygen into heat, which is then transformed into the propulsive energy (kinetic energy that moves a vehicle.) A solar cell converts solar radiation into electrical energy that can then be used to light a bulb or power a computer.
The generic name for a device which converts energy from one form to another is a transducer.
In general, most types of energy, save for thermal energy, may be converted to any other kind of energy, with a theoretical efficiency of 100%. Such efficiencies may even occur in practice, such as when potential energies are converted to kinetic energies, and vice versa. Conversion of other types of energies to heat also may occur with high or perfect efficiency.
Exceptions occur when energy has already been partly distributed among many available quantum states for a collection of particles, which are freely allowed to explore any state of momentum and position (phase space). In such circumstances, a measure called entropy, or evening-out of energy distribution in such states, dictates that future states of the system must be of at least equal evenness in energy distribution. (There is no way, taking the universe as a whole, to collect energy into fewer states, once it has spread to them).
A consequence of this requirement is that there are limitations to the efficiency with which thermal energy can be converted to other kinds of energy, since thermal energy in equilibrium at a given temperature already represents the maximal evening-out of energy between all possible states. Such energy is sometimes considered “degraded energy,” because it is not entirely usable. The second law of thermodynamics is a way of stating that, for this reason, thermal energy in a system may be converted to other kinds of energy with efficiencies approaching 100%, only if the entropy (even-ness or disorder) of the universe is increased by other means, to compensate for the decrease in entropy associated with the disappearance of the thermal energy and its entropy content. Otherwise, only a part of thermal energy may be converted to other kinds of energy (and thus, useful work), since the remainder of the heat must be reserved to be transferred to a thermal reservoir at a lower temperature, in such a way that the increase in entropy for this process more than compensates for the entropy decrease associated with transformation of the rest of the heat into other types of energy.”
http://en.wikipedia.org/wiki/Energy_transformation
How this applies to the alleged greenhouse effect is an interesting question.
How it applies to the actual real planet Earth is an even more interesting question.
Is the effect significant? If so by how much and where does it take place?
I do believe that there are errors in figures 3 and 4. It is stated that the shells are at a temperature equivalent to 240 W/m^2, but the sum of the energy emissions is actually 480 W/m^2, because there is 240 W/m^2 towards earth and 240 W/m^2 out into space for both. This might be a source of confusion.
I’m interested in hearing where the failure is in the model. Nothing really sticks out to me.
I’m not sure what deficiency Willis is thinking of, but the one that occurs to me is that the main transfer of energy between the surface and the ‘shell’ in the real planet is not radiation but convection. There is enough GH gas in the atmosphere to absorb all the photons in the absorption bands within about ten metres. The main radiation layer is where the H2O ceases (the upper atmos. is dry) and the H2O radiation band gets a clear line of sight to outer space – that is the height corresponding to Willis’ shell. Hot air rising from the surface layer to the upper atmosphere is the main energy transport mechanism, and so the extra 240 Wm-2 is not needed to get the energy up there.
Also, people keep saying “multiple shells”. The above is the reason why that is not the reason.
Am going to hit the sack now but I just wondered if Willis’ query is perhaps related to the enthalpy of the system?
I’m going to have to agree with those who point out that the shell is not at thermal equilibrium. Our atmosphere is not made of a shell of Maxwell’s daimon’s radiating with a directional variance like that.
A further thought experiment…
I take a hot rock and place it outside where it’s zeroDeGC. The hot rock will cool down in a given period of time.
If I repeat the experiment, but this time place a 2nd hot rock alongside the first one, the first hot rock will take some time longer to cool down compared to the first experiment, BUT IT’S TEMPERATURE WILL NOT RISE. This we know to be true.
Hence this is the problem facing the proponents of the Enhanced Greenhouse Effect (EGHE) hypothesis. The EGHE should manifest itself in higher minimum temps. The proponents need to explain why we should rearrange our energy use and economies just because of higher minimum temps.
If they believe higher min T’s will eventually lead to higher max T’s, they then need to first prove this, and second, demonstrate empirically how long it will take before we reach these higher max T’s. Is it 1yr? 5yrs? 20yrs?
So far as I know, this hasn’t been done
The Earth itself is producing heat.
Firstly, your link to Judith Curry’s site is not correct (wrong format)
Now let try this by the Sherlock Holmes principle of eliminating the unnecessary.
Things which only affect the actual magnitude of the effect, and not its existence, are not necessary for a proof-of-concept model. So, I earlier suggested that the earth’s rotation was needed, but it is not, as that only affects the actual temperature, not the existence of warming. Likewise clouds – they affect albedo, but that does not matter. Oceans likewise – who says this model planet has oceans. Is an atmosphere needed? Well this provides extra mechanisms for heat transport i.e.convection but that does not seem to be essential.
Objections to the name “greenhouse effect” on the grounds that it is not a real greenhouse are just silly, and objections to the energy balance in figure 4 are also silly (figure 4 is correct).
What else – the shell in the model has to be infinitesimally thin otherwise you need convection to get heat through – is that it? You need several concentric shells of finite thickness in a real system?
I think the clue is given away in the question and that the simplification of a thin shell is the weak point. If you allow for a thick shell with a temperature gradient you can find a heat balance that allows different temperatures for the planetary surface. For example a planetary surface temperature of 35C (510 W/m2) and a temperature of -10C for the lower surface of the shell (270W/m2) would balance. The key then would be to find how the heat gradient can be calculated through the shell.
One thing for certain, is that there is no “barrier” separating the atmosphere from space as in the model presented.
I have observed that women like Dr. Curry have demonstrated that they can break through the gas ceiling. ;>)
I take back my remarks about the temperatures of shells. I missed the fact that the shell has twice the area since it has a top and a bottom, and so the per-area radiation is still just 240 W/m^2 for the shell.
Lets do a thought experiment on these shells of yours.
What happens if the shell is further away or closer. Does the temperature increase or decrease?
What happens if there are several shells? Does each lower level increase in temperature? Could we build a device that uses solar energy with say 500 shells that creates a temperature of say 25300 kelvin?
So if we look at what happens with the “greenhouse effect” we currently have, does moving the distance from say 10 feet off the ground to only 5 feet off the ground increase the temperature, because the bandwidth of the spectrum in question is fully absorbed within 10 of leaving the ground surface by CO2.
Does the fact that we are not in a vacuum change the temperature? My understanding is that as pressure increases, so too does the temperature. It has been shown that the density and weight of the Venusian atmosphere captures 100% the temperature one would expect without CO2 methane and other “greenhouse gasses” in the atmosphere.
To point, the 255 kelvin theoretical temperature of the Earths surface is as a black body with nothing surrounding it allowing the heat to escape back to space. But our Earth does not end at the surface, there is an ocean of air that extends this surface outward several miles. Thus, the temperature of 255 kelvin would be at the central point in the system from which the radiation is emitted, several miles above the surface of the Earth. Points below this position would increase in temperature and those beyond it decrease in temperature. So, is 30 degrees kelvin beyond the scope of this?
Basically, your whole idea is a joke original author, and while it can make sense, it is not compatible with what science shows.
AusieDan says:
November 27, 2010 at 3:51 pm
Roy generally knows what he is talking about. I say something similar, that there is both net negative feedback and also an active governor system that regulates the earth’s temperature. However, neither is the subject of this thread.
Thanks,
w.
James Delingpole has an interesting article that is somewhat pertinent here.
http://blogs.telegraph.co.uk/news/jamesdelingpole/100065683/why-i-now-deeply-regret-my-last-post/
@Eschenbach
> 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.
The Earth’s atmosphere is not completely opaque to longwave. There is a transparent transmission band extending from 8 to 13 microns, in the center of the terrestrial thermal black body curve. This allows up to 30% of the longware to escape.
http://clivebest.com/blog/wp-content/uploads/2010/01/595px-atmospheric_transmission.png
The rest of the longwave is absorbed by the atmosphere, mostly by water vapor.
Note that CO2 has 4 absorption bands, but the 2,3 and 5 micron bands are not in the main part of the thermal curve and don’t have much effect. The 15 micron band is the largest and is centered in the 310K thermal curve.
CO2 is a powerful absorber of longwave energy. Though present in only “trace” amount (380 ppm), it completely absorbs 100% of the 13-16 micron longwave emitted from the surface, all within the few hundred meters above the surface.
But adding more CO2 does not make this band “more opaque”. Water (in all of its states) is doing all of the “heavy lifting” here on Earth, in terms of warming and regulating Earth’s climate. CO2 has a relatively small “greenhouse effect”.
To see this, consider Mars, whose atmosphere is 95% CO2. Though much thinner, it contains almost 30 times as much CO2 per surface area unit, than Earth. Yet it has virtually no greenhouse warming effect: the mean surface temperature is very close to the theoretical black body temperature of 210 Kelvins.
Mars Facts http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html
Visual geometric albedo 0.170 (Earth 0.367)
Solar irradiance (W/m2) 589.2 (Earth 1367.6)
Black-body temperature 210.1 K (Earth 254.3 K)
Average temperature: ~210 K (Earth 287 K)
6 hrs worth of guesses…. BZZZZZZZZZ time’s up!
Thierry says:
November 27, 2010 at 12:36 pm
I’m glad no one else has commented on this, and I probably shouldn’t too. I thought this had been put to bed long ago.
Lunar conditions don’t apply due to many things beyond the lack of CO2. Lunar soil is a poor heat conductor, in part because its dry. That’s one reason why some deserts, e.g. the high deserts of Oregon or Arizona, cool off so quickly at night. (Basalt walled canyons in Oregon will bake you all night.) Worse, a lunar night is 14 days long – that’s a lot of time for radiational cooling to cool!
Also, the effect of real greenhouse is achieved by locking convection so that warmed air doesn’t rise and leave the greenhouse. There’s no convection in a real greenhouse. As Willis noted, he’s talking about the “Greenhouse Effect,” which is unfortunately very different from real greenhouse physics.
Some folks upthread have said that what is missing is rotation. 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.
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.
The approximately 70% water does not absorb/reflect the same as the remaining 30% land.
Or was that said already?
Sorry, but figure 4 is incorrect. The 240 going into space comes from nowhere. I don’t know what kind of games Willis Eschenbach is playing, but this flaw is really trivial. And the outgoing energy is not the only flaw. It’s not about energy balance. It’s about the description. It’s wrong. You cannot have outgoing energy without that energy coming from somewhere. But nowhere in the graph is it shown how that energy can pass through a shell that doesn’t allow that kind of energy to pass through it.
> … I still have not seen anyone point to it.
Are you perhaps thinking of “convection”, which is a major transporter of heat in the Earth’s atmostphere?
The atmosphere is the shell. For climate we meaurse the temperature of the shell not whats is encased in the shell. That is why the greehouse effect does not reflect the real world.
Answer:- Chaos squared
PS. People in glass planets should not get as cold as I am.