A guest post by Spencer Weart, in collaboration with Raymond T. Pierrehumbert
The simple physics explanations for the greenhouse effect that you find on the internet are often quite wrong. These well-meaning errors can promote confusion about whether humanity is truly causing global warming by adding carbon dioxide to the atmosphere. Some people have been arguing that simple physics shows there is already so much CO2 in the air that its effect on infrared radiation is "saturated"— meaning that adding more gas can make scarcely any difference in how much radiation gets through the atmosphere, since all the radiation is already blocked. And besides, isn’t water vapor already blocking all the infrared rays that CO2 ever would?
The arguments do sound good, so good that in fact they helped to suppress research on the greenhouse effect for half a century. In 1900, shortly after Svante Arrhenius published his pathbreaking argument that our use of fossil fuels will eventually warm the planet, another scientist, Knut Ångström, asked an assistant, Herr J. Koch, to do a simple experiment. He sent infrared radiation through a tube filled with carbon dioxide, containing somewhat less gas in total then would be found in a column of air reaching to the top of the atmosphere. That’s not much, since the concentration in air is only a few hundred parts per million. Herr Koch did his experiments in a 30cm long tube, though 250cm would have been closer to the right length to use to represent the amount of CO2 in the atmosphere. Herr Koch reported that when he cut the amount of gas in the tube by one-third, the amount of radiation that got through scarcely changed. The American meteorological community was alerted to Ångström’s result in a commentary appearing in the June, 1901 issue of Monthly Weather Review, which used the result to caution "geologists" against adhering to Arrhenius’ wild ideas.
Still more persuasive to scientists of the day was the fact that water vapor, which is far more abundant in the air than carbon dioxide, also intercepts infrared radiation. In the infrared spectrum, the main bands where each gas blocked radiation overlapped one another. How could adding CO2 affect radiation in bands of the spectrum that H2O (not to mention CO2 itself) already made opaque? As these ideas spread, even scientists who had been enthusiastic about Arrhenius’s work decided it was in error. Work on the question stagnated. If there was ever an “establishment” view about the greenhouse effect, it was confidence that the CO2 emitted by humans could not affect anything so grand as the Earth’s climate.
Nobody was interested in thinking about the matter deeply enough to notice the flaw in the argument. The scientists were looking at warming from ground level, so to speak, asking about the radiation that reaches and leaves the surface of the Earth. Like Ångström, they tended to treat the atmosphere overhead as a unit, as if it were a single sheet of glass. (Thus the “greenhouse” analogy.) But this is not how global warming actually works.
What happens to infrared radiation emitted by the Earth’s surface? As it moves up layer by layer through the atmosphere, some is stopped in each layer. To be specific: a molecule of carbon dioxide, water vapor or some other greenhouse gas absorbs a bit of energy from the radiation. The molecule may radiate the energy back out again in a random direction. Or it may transfer the energy into velocity in collisions with other air molecules, so that the layer of air where it sits gets warmer. The layer of air radiates some of the energy it has absorbed back toward the ground, and some upwards to higher layers. As you go higher, the atmosphere gets thinner and colder. Eventually the energy reaches a layer so thin that radiation can escape into space.
What happens if we add more carbon dioxide? In the layers so high and thin that much of the heat radiation from lower down slips through, adding more greenhouse gas molecules means the layer will absorb more of the rays. So the place from which most of the heat energy finally leaves the Earth will shift to higher layers. Those are colder layers, so they do not radiate heat as well. The planet as a whole is now taking in more energy than it radiates (which is in fact our current situation). As the higher levels radiate some of the excess downwards, all the lower levels down to the surface warm up. The imbalance must continue until the high levels get hot enough to radiate as much energy back out as the planet is receiving.
Any saturation at lower levels would not change this, since it is the layers from which radiation does escape that determine the planet’s heat balance. The basic logic was neatly explained by John Tyndall back in 1862: "As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface."
Even a simple explanation can be hard to grasp in all its implications, and scientists only worked those out piecewise. First they had to understand that it was worth the trouble to think about carbon dioxide at all. Didn’t the fact that water vapor thoroughly blocks infrared radiation mean that any changes in CO2 are meaningless? Again, the scientists of the day got caught in the trap of thinking of the atmosphere as a single slab. Although they knew that the higher you went, the drier the air got, they only considered the total water vapor in the column.
The breakthroughs that finally set the field back on the right track came from research during the 1940s. Military officers lavishly funded research on the high layers of the air where their bombers operated, layers traversed by the infrared radiation they might use to detect enemies. Theoretical analysis of absorption leaped forward, with results confirmed by laboratory studies using techniques orders of magnitude better than Ångström could deploy. The resulting developments stimulated new and clearer thinking about atmospheric radiation.
Among other things, the new studies showed that in the frigid and rarified upper atmosphere where the crucial infrared absorption takes place, the nature of the absorption is different from what scientists had assumed from the old sea-level measurements. Take a single molecule of CO2 or H2O. It will absorb light only in a set of specific wavelengths, which show up as thin dark lines in a spectrum. In a gas at sea-level temperature and pressure, the countless molecules colliding with one another at different velocities each absorb at slightly different wavelengths, so the lines are broadened and overlap to a considerable extent. Even at sea level pressure, the absorption is concentrated into discrete spikes, but the gaps between the spikes are fairly narrow and the "valleys" between the spikes are not terribly deep. (see Part II) None of this was known a century ago. With the primitive infrared instruments available in the early 20th century, scientists saw the absorption smeared out into wide bands. And they had no theory to suggest anything different.
Measurements done for the US Air Force drew scientists’ attention to the details of the absorption, and especially at high altitudes. At low pressure the spikes become much more sharply defined, like a picket fence. There are gaps between the H2O lines where radiation can get through unless blocked by CO2 lines. Moreover, researchers had become acutely aware of how very dry the air gets at upper altitudes — indeed the stratosphere has scarcely any water vapor at all. By contrast, CO2 is well mixed all through the atmosphere, so as you look higher it becomes relatively more significant. The main points could have been understood already in the 1930s if scientists had looked at the greenhouse effect closely (in fact one physicist, E.O. Hulbert, did make a pretty good calculation, but the matter was of so little interest that nobody noticed.)
As we have seen, in the higher layers where radiation starts to slip through easily, adding some greenhouse gas must warm the Earth regardless of how the absorption works. The changes in the H2O and CO2 absorption lines with pressure and temperature only shift the layers where the main action takes place. You do need to take it all into account to make an exact calculation of the warming. In the 1950s, after good infrared data and digital computers became available, the physicist Gilbert Plass took time off from what seemed like more important research to work through lengthy calculations of the radiation balance, layer by layer in the atmosphere and point by point in the spectrum. He announced that adding CO2 really could cause a degree or so of global warming. Plass’s calculations were too primitive to account for many important effects. (Heat energy moves up not only by radiation but by convection, some radiation is blocked not by gas but by clouds, etc.) But for the few scientists who paid attention, it was now clear that the question was worth studying. Decades more would pass before scientists began to give the public a clear explanation of what was really going on in these calculations, drawing attention to the high, cold layers of the atmosphere. Even today, many popularizers try to explain the greenhouse effect as if the atmosphere were a single sheet of glass.
In sum, the way radiation is absorbed only matters if you want to calculate the exact degree of warming — adding carbon dioxide will make the greenhouse effect stronger regardless of saturation in the lower atmosphere. But in fact, the Earth’s atmosphere is not even close to being in a state of saturation. With the primitive techniques of his day, Ångström got a bad result, as explained in the Part II . Actually, it’s not clear that he would have appreciated the significance of his result even if he had gotten the correct answer for the way absorption varies with CO2 amount. From his writing, it’s a pretty good guess that he’d think a change of absorption of a percent or so upon doubling CO2 would be insignificant. In reality, that mere percent increase, when combined properly with the "thinning and cooling" argument, adds 4 Watts per square meter to the planets radiation balance for doubled CO2. That’s only about a percent of the solar energy absorbed by the Earth, but it’s a highly important percent to us! After all, a mere one percent change in the 280 Kelvin surface temperature of the Earth is 2.8 Kelvin (which is also 2.8 Celsius). And that’s without even taking into account the radiative forcing from all those amplifying feedbacks, like those due to water vapor and ice-albedo.
In any event, modern measurements show that there is not nearly enough CO2 in the atmosphere to block most of the infrared radiation in the bands of the spectrum where the gas absorbs. That’s even the case for water vapor in places where the air is very dry. (When night falls in a desert, the temperature can quickly drop from warm to freezing. Radiation from the surface escapes directly into space unless there are clouds to block it.)
So, if a skeptical friend hits you with the "saturation argument" against global warming, here’s all you need to say: (a) You’d still get an increase in greenhouse warming even if the atmosphere were saturated, because it’s the absorption in the thin upper atmosphere (which is unsaturated) that counts (b) It’s not even true that the atmosphere is actually saturated with respect to absorption by CO2, (c) Water vapor doesn’t overwhelm the effects of CO2 because there’s little water vapor in the high, cold regions from which infrared escapes, and at the low pressures there water vapor absorption is like a leaky sieve, which would let a lot more radiation through were it not for CO2, and (d) These issues were satisfactorily addressed by physicists 50 years ago, and the necessary physics is included in all climate models.
Then you can heave a sigh, and wonder how much different the world would be today if these arguments were understood in the 1920’s, as they could well have been if anybody had thought it important enough to think through.
For Further Reading
References and a more detailed history can be found here and here.
Some aspects of the "thinning and cooling" argument, and the importance of the radiating level are found in the post A Busy Week for Water Vapor, which also contains a discussion of water vapor radiative effects on the top-of-atmosphere vs. surface radiation budget. A general discussion of the relative roles of water vapor and CO2 is given in Gavin’s post on ths subject.
You can get a good feel for the way CO2 and water vapor affect the spectrum of radiation escaping the Earth by playing around with Dave Archer’s online radiation model here. It would help, of course, to read through the explanation of radiating levels in Archer’s book, Understanding the Forecast. A discussion of radiating levels for real and idealized cases, at a more advance level, can be found in the draft of Pierrehumbert’s ClimateBook; see Chapters 3 and 4.
The Monthly Weather Review article commenting on Ångström’s work is here, and Ångström’s original article is here.
All,
Ed Moran’s co-author, Dr. Tindall has provided an email address in the curve-manipulation thread. I suggest we take further discussion of this work off line and provide comments directly to the authors.
Hopefully, this will facilitate discussion in a civil manner and will serve to get discussions here back on track.
Tim while each LINE broadens due to collisional interactions (pressure effect) the BAND narrows as temperature falls and higher rotational levels in the ground state are depopulated. These two effects mean that the lower you go in the atmosphere the larger the range of wavelengths/frequencies that can absorb.
Densities at which you have to worry about the molecules that affect the molecules that affect the molecules are called liquids and the different layers are called solvation shells/nearest neighbors – next nearest neighbors, etc. For atmospheric effects you are pretty safely in the binary limit where one molecule only reacts with another at anytime. You can get some idea of this by calculating mean free paths.
Eli Rabett (#152) wrote:
So what this would seem to suggest is that the fine-level detail becomes less pronounced and less complex at lower temperatures and at lower pressures. At the same time, it isn’t just noise, but structured such that you will arrive at the same plot each time under the same conditions – much like the electron scattering of a crystal.
Anyway, my apologies for focusing on this aspect – it probably isn’t of that great an interest to others or perhaps of any interest at all. But it is something that I am curious about. I should really start trying to dig into the mathematics of it.
In any case, what you focus on – the broadening of lines due to pressure and the broadening of bands due to temperature – is obviously more important. Moreover, the fact that you distinguish between the two suggests that the phenomena is in no way scale-free – and that answers one of my questions. But as far as a recursive extended neighborhood goes, this would see to be a pressure effect rather than a temperature effect, so I would assume that this won’t reveal itself in terms of the structure of the lines since lines are by definition without structure.
Eli and/or Ray,
Perhaps you can help me with an area where my knowledge is a bit fuzzy. Once the greenhouse molecules absorb an IR photon, they can
a)emit another photon (not necessarily of the same wavelength, since fluctuations may alter energy levels in the interim) at a random angle
b)relax collisionally
The greenhouse gas has to be in equilibrium with the radiation field in the spectral region where it is sensitive. However, to what extent does the energy absorbed become thermalized with the other nongreenhouse gases in the atmosphere. Based on the Maxwell distribution, ~4% of CO2 molecules will have sufficient energy to excite the same vibrational band as the IR photons. I guess my question is to what extent does the energy absorbed by the ghgs thermalize to other components of the atmosphere (e.g. N2, O2…), and what are the processes by which it does so?
[Response: Here’s the answer to the simpler part of your question. The GHG is in thermodynamic equilibrium with the other gases, including the non-GHG’s like N2 and O2. The whole thing acts like a perfect gas in Earth conditions, and the equilibrium is maintained by collisions between molecules. Thus, there’s only one temperature for the whole system: the same temperature for CO2, H2O, N2, O2, etc. You can think of a GHG molecule at a given place in the atmosphere either emitting a bit more energy than it absorbs (on average), leading to a radiative cooling which is made up for by tapping the kinetic energy of the other gases, or emitting a bit less energy than it absorbs (on average) leading to a radiative heating which spreads to the kinetic energy of the other gases. For blackbody radiation, the photon gas is also in thermodynamic equilibrium with the molecules, in the perfectly usual sense. For real gases, the way the thermodynamics of interaction with the photon gas works is more tricky. Maybe Eli can help me out with a simple explanation here, but one crude (but not too wrong) way to think of it is that Maxwell’s equations are linear, Schroedinger’s equations are linear, and the interaction between the electromagnetic field and the wavefunction of the molecule is linear; this means that in some sense, you can look at the thermodynamic equilibrium “one wavelength at a time,” and then superpose to get the full solution. That’s in any event the usual way Kirchoff’s law is derived. Kirchoff did it “with mirrors,” but Hilbert did it with integral equation kernels. Same physical assumption either way. (Now if you want to really bend your mind, think about what the existence of nonlinear optical devices — like those frequency-doubling things used to make green laser pointers — does to Kirchoff’s law. It doesn’t have anything to do with any known kind of atmosphere, but it’s fun to think about) –raypierre]
This article goes well with RealClimate – Water zapour: feedback or forcing?
When surface temperatures change (whether from CO2 or solar forcing or volcanos etc.), you can therefore expect water vapour to adjust quickly to reflect that. To first approximation, the water vapour adjusts to maintain constant relative humidity. It’s important to point out that this is a result of the models, not a built-in assumption. Since approximately constant relative humidity implies an increase in specific humidity for an increase in air temperatures, the total amount of water vapour will increase adding to the greenhouse trapping of long-wave radiation. This is the famed ‘water vapour feedback’. A closer look reveals that for a warming (in the GISS model at least) relative humidity increases slightly in the tropics, and decreases at mid latitudes.
That article also discusses how fast the water vapor responds to changes in forcings – within two weeks – while greenhouse forcings have lifetimes on the scale of years to centuries.
Numerous reports agree with the prediction that temperatures will increase faster over land than over water. See Nature Runs Riot In Europe After Warm Winter, 2007
The general reasons for this seem to be that water has greater heat capacity, and can mix surface heat down into the ocean, which isn’t possible over land, and that there tend to be more clouds around the marine boundary layer. These clouds still seem to be the largest source of uncertainty in estimating the climate sensitivity: Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models, Bony&Dufresne GRL 2005
Right now, continental land masses all over the planet are experiencing record droughts – and while we think of a drought as a temporary diversion from normal conditions, these may be permanent changes brought on by new global circulation patterns in the atmosphere and oceans, as well as by vegetation changes (i.e. deforestation and increased industrial agriculture).
Radiative forcings change other variables like global circulation and water vapour feedback. Changes in global circulation and precipitation in turn have effects on the carbon cycle which seem to reduce the capacity of the system to absorb more CO2 – resulting in increased radiative forcings as more CO2 accumulates in the atmosphere.
I think we will see a future world pummled regularly by heat waves, droughts, floods, and storms, in which agricultural capacity will be reduced and water will be increasingly scarce. Just how fast and how far will this go? The cryosphere response still seems very uncertain.
Re #149: [Additionally, what method was used to determine…]
That’s a pretty big question. You might start by reading some of the other threads on this site, popular books such as Weart’s “The Discovery of Global Warming”, or introductory texts on climatology, depending on your level of interest.
But wait a minute. If you don’t already know how the “standard model” of AGW was developed, or the science that it’s grounded on, how can you possibly reject it on scientific grounds in favor of your hypothesis? It seems you must be relying on the egocentric approach: AGW would inconvenience me, therefore it can’t possibly be happening.
Rob B (#144) wrote:
I would expect you to know me a little better than that by now. I was explaining what I take to be their motivation, not mine.
Anyway, this is the last point at which I will be responding on topics not relevant to this article on this thread. I suggest others do the same simply as a matter of courtesy.
[Response: Thanks for the help in keeping things on-topic. So far, our moderation of these threads has been rather light and sporadic, largely because of lack of time. Thus, all of us here at RC rely on the readers to exercise some discipline and to keep the comments section from turning into a general climate chat-room. The cooperation is very much appreciated. –raypierre ]
The article says:
“The molecule may radiate the energy back out again in a random direction.”
Is this really a correct notion?
Assuming that there’s a upward flux of energy and all radiated photons should obey Bose statistics, then why there’s no increased probability for emitting new photon in the same quantum state as the rest of them?
“As we have seen, in the higher layers where radiation starts to slip through easily, adding some greenhouse gas must warm the Earth regardless of how the absorption works. ”
Now that is some GREAT science!
Re 158. I’ll take a stab. First, because there is no population inversion (i.e. there are still unexcited CO2 molecules, stimulated emission should be negligible. Second, the new photon is completely uncorrelated to the photon absorbed. It may have the same direction, spin, etc., but it need not. Indeed, as near as I can tell, it may not even have the same energy, as the energy levels of the molecule may be slightly different (due to collisions, etc.) at emission than at absorption. The important thing is, though, half the new photons will be heading back toward the surface, where formerly, virtually all the photons were outbound.
re 157: “…their motivation, not mine…..”
Fair enough.
“…last point….responding on topics not relevant…”
Fair enough.
A long time ago (like in the 1970s) Mike Mumma and Co at Goddard observed a population inversion in CO2 high in the atmosphere of Mars (and I think Venus). This involves excitation of the 2349 cm-1 001 level (asymmetric stretch). Suffice it to say this does not happen in the Earth’s troposphere and as far as I know the same thing has not been observed anywhere in the Earth’s atmosphere
153 Timothy, even isolated lines have (very narrow) structure, described by the natural line width. That structure is homogeneous (it is the same for each molecule).
154 Ray it is possible to calculate the probability of collisional energy transfer from one quantum state to another using first principles. OTOH it is very complex and can only be done for simple cases. These calculations can be compared to pressure broadening or state to state energy transfer measurements. An example is the CO2-He system. Another is C2H2-He.
Another approach is what are called power laws, scaling laws that calculate the collisional energy transfer probability in terms of the energy difference between states. These are linked back to simple models of the collision and have one or a few parameters which describe the average collision. This is one example and this is another.
Hope that helps.
From “A Saturated Gassy Argument”
This particular paragraph seems somewhat problematic to me, particularly beginning with the sentence, “Those are colder layers, so they do not radiate heat as well.”
Now by “heat” I would assume you are refering to the longwave radiation which is absorbed and re-emitted since gasses do not emit and blackbody radiation. But assuming this is the case, if they do not emit radiation that well, that also means that they let such radiation through quite well. But then what does it mean when you say “the high levels get hot enough to radiate…” This sounds like the oversimplified view that the greenhouse gases absorb and emit radiation at all frequencies – in essence – that they are black bodies. In this context, what does it mean for the higher levels to “heat up” enough to “radiate”?
Once again, if they are not “radiating,” by which I would assume you mean “re-emitting,” then it would appear that they aren’t absorbing, but if they aren’t absorbing, then they are transparent to the radiation which they would otherwise absorb due to being opaque.
Two Views of Greenhouse Gases
As a matter of fact, the first of these paints a picture of the higher levels of the atmosphere as having to warm up to the point at which they will radiate heat from below – which sounds like a “blackbody” view of greenhouse gases.
In contrast, the following is much closer to how I understand how greenhouse gases work.
Additionally, I would assume that the increased pressure and temperature of the lower layers of the atmosphere will broaden both the lines and the bands so of the greenhouse gases in those layers so as to increase the absorption and re-emission at those levels. Thus while additional CO2 “throws another blanket on top,” it will also “make the lower blankets thicker,” as it were.
I don’t think this is strictly accurate. For any part of the spectrum where absorptivity/emissivity is close to 1 (saturated?), the shape of the emission spectrum in that wavelength range will (I think) be the blackbody spectrum for that temperature. In the Archer Modtran calculator, if you set the altitude to zero, look up and vary the surface offset temperature (tropical atmosphere, other settings default) from 0 to 30 degrees (to increase the specific humidity) the IR emission spectrum looks more and more like a blackbody spectrum and is practically indistinguishable at an offset temperature of 30 degrees. Eli or anyone, comments?
DeWitt Payne (#166) responding to (#164, #165) wrote:
If the gas is actually is saturated at groundlevel at that part of the spectra, then it is neither absorbing nor emitting – except at those times that a given molecule drops back to ground state and is capable of becoming excited again. As such, the absorbtion and emission must be taking place in the “wings” neighboring that part of the spectra which is saturated, that is, where satuaration has yet to occur, or at a higher altitude where the spectra is not saturated.
Or so I would assume.
Misplaced System Inertia?
Given my limited knowledge, and as I have already suggested, the problem lies with this passage:
It seems almost as if the author is trying to explain the inertia of the system, that is, why it takes a while for the system to re-establish a state of equilibrium.
But it isn’t explained at this point. One of the obvious points at which the system has inertia would be the oceans, in fact, this would be the primary point. The oceans take a while to heat up. And they will even slow the rate at which the land heats up. This is the cause of the low pressures over land during the spring and summer which results in the upwelling of nutrients feeding algae blooms and resulting in hypoxia along the coastlines. (As a side point, this is what may have encouraged the growth of anaerobic sulfate-reducing bacteria during the major extinctions.)
But there is another point as well: the atmosphere. It takes a while for the atmosphere to heat up – which would also affect the spreading of the bands as explained by Eli Rabett in #152. The reason for this lies in the fact that it will take a while for the heat to become thoroughly mixed – and will also in part depend upon the inertia of the oceans.
There seems to be some confusion over the meaning of saturation. You are describing a population inversion, I think. In that case, absorption no longer follows the Beer-Lambert (IIRC) law and the ratio of transmitted light intensity to incident light intensity gets larger as the incident intensity increases. I don’t believe that a population inversion for CO2 or H2O can exist in the earth’s atmosphere at current temperatures. Otherwise you could build a CO2 laser in the open with no need for pumping. What I meant by saturation is the ratio of transmitted intensity to incident intensity in the wavelength region of interest is about 0.001 or smaller and is not a function of incident intensity.
DeWitt Payne (#169) wrote:
This quite possible.
I remember that Ray Ladbury had raised the question of whether I was equating saturation with population inversion a while back, although he wasn’t sure whether the two were different or not – from what I could tell. In fact, I suspect you are right: saturation wouldn’t be simply a function of whether all the molecules have reached an excited state, but whether they are sufficiently dense that over a relatively short distance all light at the peak frequency will be absorbed. More pieces to the puzzle, I suppose.
At the same time, I don’t quite see how gases could become blackbodies even within a given range of wavelengths. But it wouldn’t really resolve the problem of “atmospheric inertia” from what I can see since it is unlikely that the bands at which carbon dioxide reaches saturation would be unlikely to be where the temperature has risen to, at least within the upper atmosphere.
Additionally, that which is absorbed must be re-emitted, although it may be re-emitted in any direction, but that which is not absorbed will get through. Or at least this is how I understand it. Unless of course some of the energy is lost due to kinetic interactions, warming the atmosphere. But this latter point was raised by Raymond Pierrehumbert pointed out while stressing that it was fairly minor.
In any case, I am not actually arguing with either author, but simply pointing out what is opaque to me – which is I believe part of the reason why they post these essays in the first place. Moreover, even if someone does not consciously notice that a given part of the explanation is unclear, at a subconscious level, they will notice, and as in literature, this will make the narrative that much less psychologically powerful, reducing the degree to which they are convinced.
Or at least this is my understanding of human psychology.
Regarding #164, #165, #167, #168, #170
At this point I will limit myself to the issues I have raised so far. I suspect that I may have already shared more than enough of my confusion.
No need to address everything I have raised, but whatever light one might throw on these issues will be appreciated.
Timothy, Saturation simply means that all the radiation that is in the sensitive band is getting absorbed, so if you add more gas, the only radiation it can absorbe is the rediation in the wings of the spectral line.
WRT black body radiation, keep in mind that this is an abstraction–there are not true black bodies. Instead, the emissivity of a real gas becomes a function of wavelength. Thus, over the vibrational line, CO2 has an emissivity which varies from small in the wings to effectively one in the middle if I’m interpreting things correctly. So in the range where the emissivity is nonzero, it does indeed behave like a black (or gray) body. Keep in mind that the UV radiation that does escape is almost all coming from the upper atmosphere, so the region it is coming from really is that cold. Remember Eli’s comment about how the radiation from Venus makes it look as if it were cooler than Earth–it’s just because so little radiation escapes if I understand correctly.
It’s my understanding that anything that isn’t perfectly transparent or perfectly reflective, i.e. an emissivity/absorptivity greater than zero, is a blackbody. When the emissivity is less than one, the emission spectrum will show fine structure as the emissivity of each line varies with wavelength.
Re Ray Ladbury (#172)
I greatly appreciate the response…
I am going to have to chew on it a little, so I might not be able to respond until later today. But in any case this is obviously an area I am still trying to get a handle on, and I suppose reaching the point at which I am confused and aware of my confusion is itself a form of progress.
Hm. Ray says there are no true blackbodies, it’s a theoretical abstraction.
DeWitt says he understands everything except theoretically perfect zero emitter/absorbers are black bodies.
Cites, please, folks? ‘Sez whom’ so we can look at sources?
Ray Ladbury (#172) wrote:
This is my understanding as well. (Last paragraph of #165.)
I assume that this is still a function of column height, however, such that it follows a simple exponential decay law of the form 1-e^(-kh) where k is a constant and h is the height of the column.
Part of the problem which I was having with this point (second paragraph of #170) lay in my assumption that the temperature of the outermost layer of the atmosphere falls off to effectively zero, at least in comparison to the spectra of carbon dioxide. However, you raise a point in the following pertaining to the “effective temperature” of the earth which I hadn’t thought of in connection with this.
This is the mention of the effective temperature of Venus which is cooler (I would assume) than the surface of the earth. (I make this assumption because the thermal radiation going in at the outer mmost layer of the atmosphere must be balanced by the thermal radiation going out in both the case of Venus and the Earth, and I would assume that the outermost layer of the Earth’s atmosphere receives less radiation – unless this has something to do with the scattering of light at the outer layer of Venus’ atmosphere.)
In any case, the upper atmosphere will warm, and the degree to which it warms should be sufficient for it to emit grey body radiation within some parts of the spectrum where carbon dioxide is opaque to radiation. Additionally, lower parts of the atmosphere should warm still more so as to emit thermal radiation at shorter wavelengths where carbon dioxide is opaque as well.
One final note: if the above analysis is correct, then a layer will have to be a certain depth (or width) for it to become fully opaque at a given temperature. But at this point the mathematical analysis will become complex enough that it will be more difficult to put into words, particularly as the temperature varies with altitude.
DeWitt Payne (#173) wrote:
Understood and most certainly appreciated – particularly the finer details. All of this helps flesh things out considerably.
Correction to #176
I had written:
The scattering matters.
The effective temperature will be a function of the amount of radiation reaching the surface and being absorbed so that it becomes thermal radiation. Since so much light is scattered by the upper clouds of Venus (sulfuric acid, if I remember correctly) much less light will reach the surface. This lowers the effective temperature of Venus in all likelihood below that not only of the Earth’s surface, but below the effective temperature of the earth since the Earth scatters much less light before it reaches the surface and is absorbed so that it becomes thermal energy.
See:
http://www.atmos.washington.edu/2002Q4/211/notes_greenhouse.html
A Couple More Notes
1. The last sentence of the last paragraph of #168 was poorly phrased on my part:
The bit stating, “… it will take a while for the heat to become thoroughly mixed” if taken literally would suggest that the atmosphere reaches a uniform temperature throughout – which is obviously false. What it reaches is a state of quasi-equilibrium where the temperature will remain roughly constant at any given altitude.
2. For the purpose of mental imagery, I think of the opaqueness of the atmosphere as being similar to that of a fog such that it becomes more opaque the further an object is from the “observer.” Of course, if it is emitting radiation within that part of the spectra it is opaque to, this would make it a glowing fog. I suppose that might be a nice visual effect for a science fiction story.
Is not the physical process of black/graybody ala Planck radiation (primarily molecular/ionic acceleration/deceleration??) totally separate from the process of emission/absorption that goes on between the earth’s (blackbody) infrared radiation and gas molecules (molecular bond rotation and translation and electronic energy levels??)? Or did I snooze through part of this discussion??
[Response: I think maybe you’re confusing Planck radiation and Cerenkov radiation. It’s true that electromagnetic radiation and absorption (classically called “radiation reaction”) involved accelerations of charged bodies. However, it’s the motion of the charge distribution associated with molecular vibrations and rotations that results in the absorption and emission of infrared we’re talking about in connection with the atmosphere. It’s not acceleration and deceleration of ions or molecules as a whole that are involved. The Planck function describes the statistical properties of large numbers of molecular absorption and emission events of the former type, in a substance whose molecules are in thermal equilibrium at a given temeprature T. –raypierre]
[[It’s my understanding that anything that isn’t perfectly transparent or perfectly reflective, i.e. an emissivity/absorptivity greater than zero, is a blackbody.]]
No. A blackbody has an emissivity/absorptivity of 1. A body with 0 < e < 1 is a graybody. A body with e varying with wavelength is a realistic body.
I stand corrected. What I meant was that any thing with non-zero emissivity/absorptivity at the appropriate wavelengths will emit thermal radiation rather than is a blackbody. I think this was implied in the rest of my comment though:
But my statement as written was indeed technically incorrect as a true blackbody must have an emissivity identical to one and there is no such animal.
As long as we’re being trying to make technically correct statements:
Ray Ladbury stated in comment #172:
It isn’t all getting absorbed, that would imply an absorptivity identical to one or a true blackbody. The amount that gets through may be vanishingly small, but it’s not zero. So it’s nearly all, not all.
Can someone point to an explanation of how any molecule can bump into a GHG molecule so the GHG gas’s bonds get to vibrating and sometimes they will get rid of that energy when they emit a photon?
I realize that ‘bonds’ and ‘vibrating’ are imprecise words for whatever’s going on there, and that there’s not really a ‘there there’ —- and any nonmathematical explanation of the physics has to be closer to poetry.
Eli’s written about this enough for me to realize I don’t have words that explain how “sunlight heats Earth, Earth warms atmosphere, eventually photons depart into space, and GHG emitted will continue to change how that happens for a few centuries til an equilibrium is reached.”
raypierre (inline to #179) wrote:
I thought that “Cerenkov radiation” refered to the radiation emitted by a charge traveling faster than the speed of light within a medium, a bit like the sonic boom of something traveling faster than speed of sound. The radiation is a blue-green light, if I remember correctly. But I understand accelerating charges will typically emit radiation, too, although I remember there being some controversy over second and third derivatives involving Feynman (who argued for the third) and the principle of general relativity – for example, a charge being suspended in a gravity well won’t emit radiation. I don’t know what the current status of that one is, but it would be a little odd if they haven’t figured it out as of yet.
Then again, acceleration and gravity aren’t fully equivilent even locally (as Mach would have prefered and as Einstein originally intended) since the following will contain non-zero elements in any coordinate system if and only if space is curved:
Yes, Cerenkov radiation is probably not what Ray meant. The radiation from the acceleration/deceleration of charged particles is a much more general phenomenon, subsets of which include bremstrahlung, cyclotron and synchrotron radiation.
Way, way off topic, but funny: In the early days of nuclear physics, the way they used to find the beam from an accelerator was to move their head around until they saw the blue flash of Cerenkov radiation!
I think the way to understand blackbody radiation is to remember that the closest we actually come to it is the radiation emitted from a hole in a cavity. The radiation is emitted by the walls of the cavity, but it interacts not just with the walls of the material, but also with the radiation field itself and comes to equilibrium before it leaves the cavity. The Universe itself can be viewed as such a cavity–at a temperature of 3 Kelvins.
re raypierre’s response to 179: I don’t think I was confusing Cerenkov radiation. Actually I’m not smart enough to do that.
Let me see if I’m getting it. The earth radiates ala Planck black/graybody radiation in the infrared region as determined by the acceleration of molecular-sized charges caused by the collisions and course reversals which is based on the mv^2 energy — = temperature. But the absorption (and subsequent emission) by gas molecules is not Planck based. Rather the E-M energy is absorbed by certain gasses and stored in the intramolecular bonds by virtue of the bonds bending or stretching back and forth, or by electrons rising to a higher coincident energy levels. Now this latter process does not affect the temperature of the molecule, i.e. the molecule as a whole does not go any faster ala mv^2, nor does any of its neighbors, and the temperature of this slice of the atmosphere says the same. Then this molecule can “relax”, give up its bonding energy in the form of emitted E-M radiation at pretty much the same frequency that was initially absorbed. OR, before it re-emits, the molecule can crash into another and transfers some of its bond energy to kinetic energy in the collidee, raising its temperature. I suppose collidee can now become a collider, maybe even to the original molecule and transfer some of its kinetic energy to the original, but as kinetic energy not as bond replacement energy (or that, too????)
Is this accurate? Close? Thanks.
Hank Roberts wrote in #183
I’ll take a stab. You have two types of collisions, elastic and inelastic. In elastic collisions, no kinetic energy is lost by conversion to a different form like heat. Think pool balls or those rows of suspended ball bearings. In an inelastic collision some of the kinetic energy is converted to other forms of energy. Think car crashing into tree, things bend and stay bent. When molecules collide inelastically, the kinetic energy lost can excite internal modes in one or both of the molecules which then may return to their ground states by emitting photons. See here for a basic definition of elastic and inelastic collisions or google for more references. I wouldn’t begin to attempt a more detailed explanation of molecular collision theory here, even if I could.
SCM (#185) wrote:
I will have to ask you to explain the difference between those some time. As for the above, the farthest I ever got was being able to step through the derivation of Schwartzchild’s solution. Pretty stuff.
I recently posted a piece entitled “What Enhanced Greenhouse Gas Effect?” on the PhysOrg and the Environment Site forums, and a few days later Real Climate had an article called “A Saturated Gassy Argument”, which seemed to be an answer to my posts, although on a different site. Anyone who reads my posts will see that I am sceptical, at present, about the enhanced GHG effect. However, I am ready to be convinced otherwise by a properly reasoned physics explanation, which would require sufficient maths to be successful.
The “Saturated Gassy Argument” gave an interesting historical account of the GHG effect, and made an attempt at explaining how enhancement can occur at high altitudes, in spite of the fact that 100% absorption of power by CO2 at certain wavelengths occurs at lower levels. This argument was unconvincing because no numbers were given. It was left to the reader to establish for himself/herself whether the increased amount of absorption would be significant in view of the claimed high altitudes, and low densities involved. (And any other considerations like absorption cross section.) I want to have a go at this, but it will take time, and if anyone can post relevant information it would be greatly appreciated.
Part 2 of this RC post was called “What Angstrom didn’t know”, and did, indeed, try to give a little more by way of numbers, but I still found it to be confusing. In particular, the term “absorption factor”, was said to be the rate of decay of the exponential curve for absorption of infrared energy by increasing numbers of CO2 molecules. The appropriate curve for the atmosphere could, presumably, have been given, and the point on the curve for the present day could have been shown. This should have been done, because the numbers of CO2 molecules involved, and not the concentration per se, is what is relevant.
Again, the last paragraph on page 1 of Part 2 mentions the product of the absorption factor and the amount of CO2, but no explanation is given of how these parameters are handled. No units are given.
On the second page of this piece, a figure is shown for Absorption Factor (still unclear) against wavelength. This was said to be based on the Hitran data. I have not seen anything like this in the Hitran data, but it is obviously of great importance, and I should be very grateful if someone would please be kind enough to give me a web reference to this item. One astonishing thing about it is the vast dynamic range shown, from 10^5 down to 10^-5, a range of 10^10. These results were, presumably not measured. Indeed, the text mentions that the absorption results were computed for typical laboratory conditions, whereas what really matters is what is happening in the real atmosphere. What was the number of CO2 molecules in the calculation? Please can we have some numerical, physics explanation?
Aubrey E Banner
Cheshire, UK.
[[On the second page of this piece, a figure is shown for Absorption Factor (still unclear) against wavelength. This was said to be based on the Hitran data. I have not seen anything like this in the Hitran data, but it is obviously of great importance, and I should be very grateful if someone would please be kind enough to give me a web reference to this item. One astonishing thing about it is the vast dynamic range shown, from 10^5 down to 10^-5, a range of 10^10. These results were, presumably not measured. Indeed, the text mentions that the absorption results were computed for typical laboratory conditions, whereas what really matters is what is happening in the real atmosphere. What was the number of CO2 molecules in the calculation? Please can we have some numerical, physics explanation?]]
The absorptivities are calculated nowadays because we know what causes them; absorption lines are a quantum effect and can be predicted with extreme precision. That’s what HITRAN (and HITEMP) are all about. The number of molecules involved is one for any given isotope. That’s all you need.
Are you suggesting that there’s a discrepancy between the computed values and the observed values? What’s your source for the latter?
As for variation in the atmosphere, that’s been known for a long time from empirical data going back to the 1940s. In brief, the optical thickness of a given mass of gas in most circumstances varies directly with the ambient pressure and inversely with the square root of the temperature. The raw optical thickness is the product of the absorption coefficient and the specific mass (mass per unit area) present, or if you like, the absorption coefficient times the density times the path length, which gives the same answer.
I’ve been playing with the Archer Modtran calculator. It looks like increased water vapor actually enhances the effect of CO2, at least in a radiation only model. If you compare a high specific humidity case like the tropical atmosphere with a low surface temperature and corresponding low specific humidity case like subarctic winter, the sensitivity factor to doubling CO2 is more than twice as high for the tropical atmosphere than for the subarctic winter with both at constant relative humidity. This seems counter-intuitive until you look at the spectra and see what’s actually happening.
Thank you for your comments, #191, #192, but I am still not sure about the “Absorption Factor”. Is it the same as the absorption cross section, as in the HITRAN data? Again, is “absorptivity” the same thing?
No, I am not suggesting any discrepancy between computed and observed values. I just want the facts.
What I should really like to see is a physics analysis of the enhanced GHG effect, line by line, equation by equation, and diagram by diagram. Surely somebody can post this, or at least post a reference to the work, preferably a web reference?
Aubrey E Banner
Cheshire, UK.
Aubrey, it would depend greatly on what you already understand, and how much physics and math you’ve studied. Is it safe to assume you understand quantum mechanics and the work from the high altitude gas studies mentioned in the AIP History (first link under ‘Science’)? The cites there likely have much of what you want to know. This is a huge field widely distributed in the literature, not somethihng that can be put on a website in full mathematical detail.
In the AIP History, after reading the section on radiation physics, have you already responded there to the author’s request for people to comment on how they understood the presentation?
Mathematical physics without the math is poetry, at best.
Possibly you’re fully competent in radiation physics already, I dunno — I’m just a reader here. But it sounds like you’re asking for the Moon to be put on a plate so you can look at it close up, to me. Won’t fit.
#193 Aubrey,
As free resources you might want to have a look at Ray Pierrehumbert’s, work in progress which is available online (but only complete up to about Chapter 5):
http://geosci.uchicago.edu/~rtp1/ClimateBook/ClimateBook.html
The IPCC report AR4 is also available online, emphasis is more a thorough review of recent literature:
http://ipcc-wg1.ucar.edu/wg1/wg1-report.html
If you want to read the original papers on which it is based then Google Scholar is always worth a go:
http://scholar.google.com/
Personally, I’ve just ordered “The Physics of Atmospheres” by John T. Houghton which is an undergraduate text in the area. It’s a sufficiently large area that I don’t think any online resource is really suitable.
…and definitions for absorption coefficients are always fun…
“Erik” (12:23pm) is blogspam, please add to filters.
Aubrey, I looked at PhysOrg; nobody answered you because your posting there made clear you haven’t read the basic science,and can benefit from the threads posted here. I’m sure they weren’t posted as answers to you personally — but they may help.
At PhysOrg, you are stating your firm beliefs about what can possibly be true, and saying human activity can’t add to the natural greenhouse. Therre’s a lot to learn.
UCAR has a nice page, here:
http://www.ucar.edu/learn/1_3_1.htm
including this animation:
http://www.ucar.edu/learn/images/carbon.gif
I audited an undergrad physics course on “Radiation in planetary atmospheres” last term; the class notes are still online at http://www.atmosp.physics.utoronto.ca/people/strong/phy315/phy315.html
Lecture 18 is where the greenhouse effect comes in explicitly, but some of the earliest lectures spell out the underlying basic laws and the math involved: Beer’s Law, Schwartzchild and such; lots of PDEs. The prof derived a lot of the equations on the board but I think the class notes are more summary form. I’m afraid I can’t reproduce the derivations as I was just auditing. The homework for the real students stressed the math. Prof. Strong has contributed to the vast spectroscopy databases from lab measurements, but also taken field observations both via satellite and balloon sondes (including the infamous runaway balloon that RCAF couldn’t bring down) :-) The sonde data provides direct measurement of CO2 profiles by height; these are covered in the course notes.
I would definitely recommend Ray Pierrehumbert’s online book draft, cited above, as a good source for in-depth discussion of how all this fits together. His prose is quite readable yet you’ll also find the equations there.
Re: Comment 6: Response “The reason the stratosphere cools upon increase of CO2 is that the balance in the stratosphere is between absorption of solar radiation by ozone and cooling by infrared emission. As you increase the CO2, there is excessive radiative cooling, so the stratosphere has to cool down to come back into balance.”
Not sure I understand the mechanism as to why the stratosphere cools.
For a simple case, no CO2, the specific radiation frequency that stratosphere CO2 could block, passes through the stratosphere, unaffected. Adding CO2, causes a specific portion of the up coming radiation to be blocked which would seem to me to increase the temperature of the stratosphere.
The stratosphere CO2 after absorption of the up coming specific radiation frequency, would (statistically, if it strikes another molecule before re-emission) either transfer some energy to another stratosphere gas molecule (might not be CO2) as well as reemit, as you have stated, statistically up and down. As an number of the CO2 molecules will transfer energy to other stratosphere molecules, the stratosphere temperature should increase, as compared to the no CO2 case.
The other possible explanation for the decreasing stratosphere temperatures would be a reduction in low level clouds. A reduction in low level clouds would reduce the amount of up coming radiation (short) that ozone can absorb which would cool the stratosphere. If this mechanism is correct, I would expect the stratosphere would start to warm, as due to solar changes, it is my expectation that low level clouds will increase.
Mr. Astley, you’re reaching your conclusions by reasoning from your beliefs without checking them.
You can look this stuff up.
Try the first half dozen of these articles.
Does anything you read here change something that you believed to be true?:
http://scholar.google.com/scholar?q=cooling+stratosphere&hl=en&lr=&scoring=r&as_ylo=2002
“Try the first half dozen of these articles. Does anything you read here change something that you believed to be true?”
No.
As I said I have not seen an explanation of the mechanism, as how additional CO2 causes the stratosphere to cool. (See my comment 198). The links you provide are a shot gun of papers related to the stratosphere, none of which answers my question. A brief survey of the papers indicates that there are other concurrent changes that can explain a portion of stratosphere cooling such as a reduction in ozone.
I bring up the change in low level clouds as I believe, the 20th century changes in low level clouds has not been taken into account in the analysis.