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Greenhouse Effect Basics: Warm Earth, Cold Atmosphere

Posted on 29 February 2012 by Tom Curtis

Heating and Heat Flow

Some physics, everyone knows.  In our daily lives we encounter the effects of physics all the time, and as a result, we know what physics predicts in those circumstances at a gut level.  We may not be able to put it into numbers.  We may not be able to apply it in novel situations.  But we know it all the same.

One example is as simple as putting on a blanket.  We know that if we want warm something up, we can increase the supply of heat - or we can reduce the escape of heat.  Either is effective.  If you have a pot that is simmering and you want to bring it to the boil, you can turn the heat up, or you can put on the lid.  If we put on the lid, the pot will go nicely from simmering to boiling, and we don't need to turn up the heat even slightly.  Indeed, if we are not careful to turn down the heat, the pot may well boil over.

Likewise, if you have two identical motors running with an identical load and speed (Revolutions Per Minute), one with the water pump working and one without, we are all physicist enough to say that the second one will run hotter.  It does not matter that the energy supplied as fuel is identical in both cases.  The fact that heat escapes more easilly with water circulating through the radiator will keep the first cooler.  The consequence is that stopping the the water from circulating will lead second motor to disaster.

Nor do we find people who doubt this.  Suppose somebody told us their water pump was broken, but that the Second Law of Thermodynamics prohibited transfer of heat from a cooler place (the water) to a hotter place (the engine block), so they'ld be fine so long as they didn't rev any faster than normal, we'ld look at them in complete disbelief.  Or we would if we were too polite to burst out laughing.  And if they set out cross country confident in their belief, it doesn't matter what destination they claim they're heading for.  Rather, as we all know,  they're really heading for a breakdown!

(Image copyright to iStock, and not to be reproduced without their permission.)

Heat Flow to Space

This physics that everyone knows is not only true of pots and radiators.  It is true of the Earth as well.  The Earth is warmed by our remarkably stable Sun.  As a result, the Earth's surface radiates energy to space, and over time the incoming energy balances the outgoing energy.  The process is made more complicated, however, by the existence of Infra Red (IR) absorbing molecules in the atmosphere.  

Without those molecules, Infra Red radiation from the Earth's surface would travel directly to space, cooling the Earth quickly and efficiently.  At certain wavelengths of Infra Red radiation, however, those molecules absorb many, or all, of the photons emitted from the Earth's surface.  That energy is often redistributed among other molecules by collision, but eventually some of the redistributed energy will be reradiated by the Infra Red absorbing molecules.  This process absorption, redistribution and then re-emission may occur many times before the energy escapes the atmosphere, but eventually it will either by being emitted to space, or back to the surface.

Intuitively, the energy that goes through multiple stages of absorption, redistribution and re-emission will not escape to space as fast that which is emitted directly to space from the surface.  This intuition is sound, but it depends essentially on one factor, the temperature of the atmosphere.

We can see this by considering a fundamental law that governs the radiation of energy, the Stefan-Boltzmann Law:

In words, that is J-star equals epsilon sigma T to the fourth power, but we don't need to worry about that.  What we need to notice is that J-star, which is the energy radiated over a given time from a given area, is proportional to the fourth power of T, ie, temperature.  If the temperature doubles, the energy radiated increases sixteen-fold.  If it triples, it increases eighty-one- fold.  And so on.  So, if the temperature of the atmosphere is different from that of the surface, the absorption, redistribution and re-emission of IR radiation by molecules in the atmosphere will certainly change the rate at which heat escapes to space.

Higher is Colder

There is another piece of physics everyone knows.  It is that as you go higher in the atmosphere, the atmosphere gets colder.  That is the reason why some mountain peaks are snow covered while their bases are still warm.  This is not a universal law.  It is not true, for example, in the stratosphere where the absorption of UltraViolet radiation from the Sun causes temperatures to rise with increased height.  But eighty percent of the Earth's atmosphere is in the troposphere (the lowest layer of the Earth's atmosphere), and most radiation leaving the top of the troposphere escapes to space.  And in the troposphere, as you get higher, the temperature gets lower.  On average, the temperature drops by 6.5 degrees C for every thousand meters of altitude you climb.  That means, for example, that the temperatures fall by about 24.5 degrees C as you climb to the summit of Mount Fuji, and by 50 to 100 degrees as you rise to the top of the troposphere.

We have already seen that temperature significantly effects the radiation of heat.  Colder objects radiate less energy, and the Infra-Red absorbing molecules in the atmosphere are colder than the surface.  Therefore it is no surprise that the Infra-Red absorbing molecules in the atmosphere radiate less energy to space than they absorb from the warmer surface.  That difference is the essence of the greenhouse effect.

No More Arm Waving

It would be helpfull to recapitulate at this point.  So far we have noted four simple facts:

  1. That if you reduce the escape of heat, but do not reduce the incoming heat, things warm up;
  2. That the atmosphere contains molecules that absorb Infra-Red radiation;
  3. That radiated energy depends on the temperature of the radiating object; and
  4. That the atmosphere gets cooler as you get higher, so that the Infra-Red absorbing molecules in the atmosphere radiate less energy to space than they absorb from the surface.

These four facts imply the existence of an atmospheric greenhouse effect, ie, that the presence of Infra-Red absorbing molecules in the atmosphere results in the surface being warmer than it otherwise would be.

In science, however, purely verbal reasoning like this is considered suspect.  The reason is that sometimes odd effects occur that render verbal reasoning moot.  So in science, there is no substitute for putting the theory into a mathematical form.  It gets rid of the arm waving.

Fortunately for us, scientists have already put this theory into mathematical form, at a very detailed level.  We can access this work, free of charge, by using the Modtran Model.  The Modtran Model shows the radiation up or down over a column of atmosphere under particular conditions.  By changing the conditions, you can explore the predicted effects of those changes on upward or downward radiation at any level of the atmosphere from 0 to 70 kilometers altitude.  Setting the altitude to 70 kilometers effectively shows the radiation upward to space from the top of the atmosphere, or downward from space at the top of the atmosphere.  Setting the altituded to 0 kilometers effectively shows the radiation upward, or downward at the surface.

Using Modtran, I determined the energy output looking downwards from an altitutude of 70 kilometers using the US Standard Atmosphere (1).   The result can be seen on the following graph as the green shaded area.  I repeated the model run, but this time with the altitude set at 0 km.  The result is shown by the outer curve defining the red area in the graph below.  That means that the red area itself, which is the upwards radiation from the surface minus the upward radiation to space, is the reduction in energy radiated to space because of the presence of Infra-Red absorbing molecules in the atmosphere.  That is, it is the greenhouse effect.

Settled Science

We have all heard how inaccurate models can be.  Therefore the fact that a particular model predicts this difference in radiation only shows what the theory predicts.  It does not show what is actually happening.

Scientists are not happy with theories whose only support is a model.  So in 1969, Conrath and associates compared the results of model calculations of radiation to space with the actually observed radiation using the IRIS instrument on the Nimbus 3 Satellite.   The following graph shows the result of their comparison.  The dotted line shows the modelled values, while the solid line shows the observed values:

The effect of a particular Infra-Red absorbing molecule, Carbon Dioxide, is clearly visible.  With the publication of this data in 1970, the greenhouse effect ceased to be theoretical.  It was an observed fact.



(1)  Default settings except for adjusting surface temperatures (Ground T offset, c) to approximately match the Earths Global Mean Surface Temperature (about -10 degrees C offset).

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Comments 51 to 70 out of 70:

  1. dunc461 @49, there are no such things as stupid questions. I can understand how you reached your conclusion in that for CO2, nearly all absorption and nearly all radiation is in the wave number 600-700 band shown in the Modtran graph. However, it does not follow. Energy absorbed by CO2 (or any other green house gas) is likely to be transferred to other molecules by collisions long before it is reradiated. From there it may be transferred to water vapour, methane, ozone, or some other greenhouse gas, and radiated in an entirely different part of the spectrum. Of course, much of it is reradiated by CO2, but a significant proportion of the energy radiated by CO2 molecules may well have been carried to those molecules via absorption by other GHG molecules, or even be convection or transfer of latent heat. What is important, therefore, is not the individual paths of any given packets of energy, but the statistical effect of the overall process. That is governed by the fact that in certain frequency bands, nearly all energy radiated from the surface is absorbed in the atmosphere, and that the atmosphere radiates in those frequency bands from much higher altitudes, and hence at much cooler temperatures. The result is a significant reduction of the IR radiation to space from those bands, which must be compensated by higher intensity in those frequencies where radiation can escape to space, which is achieved by a warmer surface. The distinction between tracking individual packets of energy, and the statistical approach may seem like hair splitting to you. Not recognizing the difference does, however, lead to genuine confusions, some of which have motivated some persistent so-called skeptic "myths". In one case I know of, the fact that radiation from individual layers of the atmosphere is in fact half up and half down has led to the mistaken assumption that IR radiation to space must equal the back radiation in those parts of the spectrum absorbed by GHG. That is, of course, false. In fact, downward radiation at the surface is often much larger than the radiation to space because it comes from warmer, lower layers of the atmosphere, while that to space comes from the cooler, higher layers. On a related issue, when you follow the statistical approach, it becomes evident that the back radiation is not necessary for the green house effect (although it does exist, and is significant for some climate effects). In particular, because the lapse rate is independent of radiative transfer in the troposphere, even if there were no back radiation, a greenhouse effect could still exist by modulating the rate of energy transfer by convection to the upper atmosphere. I will be exploring this, and other issues in forthcoming posts in this series. In the meantime, I hope this has been helpful. Finally, I apologize if I was too abrupt in my first response to you. Regulars here can develop a hypersensitive alert system for trolling. The result is we sometime react to legitimate questions as though they were attempts at trolling. We should not do it, but we are human. If you ever read the full sequence of comments in the 2nd Law of Thermodynamics thread linked @48 above, you will understand why. So, if you think you have asked a silly question, it actually means I have just given a poor answer, for which I apologize. I hope this one is more helpful.
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  2. Tom, when you say "atmosphere radiates in those frequency bands from much higher altitudes, and hence at much cooler temperatures" Is that true across the CO2 absorption spectrum or just at the wings (e.g. see end of p. 4643 in My other question is how much is "much"? Are there satellite measurements of effective radiation altitude?
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  3. Eric (skeptic) @52, this post is solely about the greenhouse effect itself, not about how the greenhouse effect will change with increasing CO2 (or other Green House Gas) concentrations. So, although it is true for CO2 that most of the change will be in the wings, as you put it, the absolute effect of current concentrations is strongest in the center of the band. Looking at the last diagram in the OP (from Conrath), you can see the lowest portions of the CO2 trough are about 70 degrees C cooler than the surface. Given the standard lapse rate, that means the effective altitude of radiation to space in those frequencies are is about 10 km. The small spike in the center is from even higher in the atmosphere, and in fact from the stratosphere which is why it is warmer than the surrounding trough. Working our way up the right hand side of the trough, we find small ledges at about 240 and 260 K, indicating the effective altitude of radiation for these frequencies are about 7 and 5 km respectively. Further to the right, at about a wave number of 800, there are two very small troughs that are also caused by CO2. (At least, I am certain the larger is, and I think the smaller is as well.) Clearly for these troughs, the effective altitude of radiation is 1 or 2 km at most. Working to the left, the very uneven series of troughs from wavenumber 350 to 550 are caused by water. The average altitude of effective radiation for these frequencies is 3 - 4 km, but highly variable depending on the exact frequency. These values are fairly representative. The effective altitude of radiation averaged across all frequencies in the IR spectrum is about 5 km. It should be noted that the "effective altitude of radiation" should be understood as (approximately) the average altitude from which radiation reaches space. It has a more technical definition, but for lay purposes treating it as an average is probably accurate enough. (Chris Colose can correct me if he thinks the technical definition is important.) As such, radiation at a given frequency may come from several kilometers above or below the effective altitude of radiation. Measurement of the effective altitude of radiation from space can be done much as I have just done, but using more accurate temperature measurements from radiosondes to calibrate the altitudes. It can also be done by determining the altitude of cloud features visible at particular frequencies. And, as scientists are usually very clever people, it may well have been done by other means I am not familiar with as well. I will leave discussion of how the green house effect changes with increasing CO2 to a later post on the subject, although for CO2, you are correct that the change in intensity (but not the effective altitude of radiation) is primarily on the wings.
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  4. Tom Curtis @36: "The most fundamental fact about the greenhouse effect is that if the energy escaping to space exceeds the energy entering the system, then the temperature will rise until they balance again. If the energy escaping is less than the energy entering system, temperatures will fall until they balance again." Don't you have the two cases backwards there? If energy escaping exceeds energy entering, the temperature will fall, not rise.
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  5. (continuing my preceding comment) The most logical correction is probably to interchange "escaping to space" and "entering the system" wherever they appear. This reversal doesn't seem to have affected any subsequent argument. @38 seems not to have noticed, and writes as though your statement in #36 were corrected to the proper sense.
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  6. ribwoods @54 and 55, thankyou for picking up on my error. Of course, I know this backwards, so I am at a loss to explain how I got it backwards when writing that comment, other than that it underlines the need for me to proof read my comments. I have corrected the original with due acknowledgement.
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  7. Questions on this post 1) What would happen if you put more absorbers of high energy radiation (sunlight) and warmed the upper atmosphere, since it is no longer as cold? More generally how can you change the vertical temperature rate of decline to change the greenhouse effect? 2) In the MODTRAN model, adding more and more CO2 increases the emission to space right at 667 cm^-1 (the blip that continues to go upwards, all the more at very high concentrations. Is this accounted for since it seems to reduce the CO2 effect?
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  8. Anthony C @57: 1) If you add sufficient absorbers of high energy radiation to the upper atmosphere, the result will be a reverse greenhouse effect in which a warm upper atmosphere results in a surface cooler than 255 degrees K. It would be very difficult, however, to bring about that situation on Earth. Titan actually experiences this effect, but is the only body in the solar system known to do so SFAIK. 2) Yes, as the blip in the center does show increased emissions with increased CO2 concentrations because its effective altitude of radiation rises higher into the stratosphere. The effect in real life is not as strong as shown on Modtran because: a) Increased CO2 levels cool the stratosphere, counteracting the effect; and b) Increased CO2 levels cause the tropopause (the boundary between the troposphere and stratosphere) to rise, thereby increasing the altitude to which the lapse rate continues as in the troposphere. Because Modtran uses standard temperature profiles which do not adjust with changes of forcing, it cannot show these effects. However, they will show up in Global Circulation Models (GCM) and are therefore accounted for. Whether this aspect in GCMs is robust, or an area of uncertainty I could not say.
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  9. Anthony, In general, the greenhouse effect depends intimately on the vertical temperature profile. Models of snowball Earth have a rather isothermal atmosphere (especially in winter) much like modern Antarctica, and this makes it difficult to generate a strong greenhouse effect. Tom is right about Titan, which has an organic haze upper layer (though the greenhouse effect wins out on Titan, this anti-greenhouse only partially cancels) and the problem is similar to the nuclear winter issue as well. As far as the CO2 "blip" in the center: as Tom notes, the stratopshere cools which somewhat offsets this effect (not seen in MODTRAN) and the decrease in emission toward the wings more than offsets the increase in the center. This is all accounted for in line by line radiative transfer studies.
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  10. Tom Curtis @51 Thanks, I really appreciate your help and look forward to your future posts. It really didn’t make sense to me that the energy absorbed would only be emitted at certain wavelengths. That is why I was looking for higher "window" rates at the top of the atmosphere. Lapse rate is a new term for me. My current understanding is that lapse rate is defined as “The rate at which air temperature falls with increasing altitude.” and it is effect of the GHCs on lapse rate that causes the ”greenhouse” effect. In simple terms, am I correct in saying that the temperature of given layer in the atmosphere (except the top and bottom layers) is the temperature at which the sum of the following is equal to zero. BBR = Black Body Radiation 50% BBR Generated in the layer below + BBR that passed through the layer below + 50% BBR Generated in the layer above + BBR that passed through the layer above + Heat of absorption by GHC +/- Sensible Heat gain or loss by convection */- Latent Heat gain or loss - Heat of adiabatic expansion - Portion of pass through BBR from layer above to layer below - Portion of pass through BBR from layer below to layer above - 50% BBR Generated to the layer below - 50% BBR Generated to the layer above = 0
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  11. dunc461: Again,a review of some "first principles". Gases do only emit and absorb at certain wavelengths (aka wave numbers), and this is a basic principle of spectroscopy. In Planck's law, emissivity is a function of wavelength. More so, Kirchhoff's Law says that emissivity equals absorptivity at the same wavelength (all other factors being equal), so if CO2 is absorbing at a particular wavelength, it should also emit at that wavelength. ...but as Tom has pointed out, energy absorbed by one molecule can be transferred to other molecules, so the bulk radiation emitted from a layer of the atmosphere has properties that are a mix of the bulk atmospheric constituents, not the single (or few) gases that do the absorbing. In your last post, I think you've roughly got the idea, but the way you are looking at it is a bit unusual, and you have missed one extremely important thing. The unusual part is that in radiative transfer, you usually just think of the upward-directed and downward-directed fluxes as individual values that occur (or can be measured) at a point in the atmosphere - not "generated by the layer below" - because it doesn't matter if is was emitted by the layer below, or whether it just passed through the layer below having been emitted from other layers further down. The usual way of describing this process is to use Beer's Law. Thus, the heating due to IR absorption is (upward IR)*(portion absorbed) + (downward IR)*(portion absorbed). This is just mathematical arrangement, however, and is done that way because it is easier to see what is going on and arrange things for computer calculation. The error is that you've forgotten about solar radiation. It is also being absorbed (according to Beer's Law), and needs to be included in the energy balance.
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  12. Bob Loblaw @61 Thanks for your post. You have to forgive my approach. As an old Chemical Engineer, I tend to compare this process to a distillation column where back in day we used Theoretical Stages and did Heat and Material Balances. I used the generated BBR to designate the full spectrum radiation and the pass through BBR to represent the radiation where the energy in the GHC bands had been partially depleted. You are of course right about the solar radiation. I thought about that just after I completed the post.
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  13. dunc461: Note that I said it was unusual, not wrong (except for the lack of solar). In essence, the real atmosphere works as a continuous function, not a series of layers, so the "best" way is to use calculus and analog solutions to describe the system. We almost invariably end up breaking things into layers (or a series of discrete points that kind of look like layers) for practical purposes, however - e.g., finite difference methods for solving differential equations. Beer's Law is a fun example: there is an integrated form (e.g., I/I_0 = exp(-tau*m)) that I used to teach, but a chemist might be more familiar with it in a differential form (e.g, dI/dz = ...) because that's how it is commonly used in a lab when measuring concentrations of solutions by optical methods (sodium comes to mind). Neither is "wrong", but one may be more familiar depending on a person's background, and one may be more convenient, depending on the usage.
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  14. dunc461 @60, your itemization of the relevant processes is basically correct, excepting (as noted by Bob Loblaw) absorption from the sun and (in GCMs and the real atmosphere) lateral heat transfer. More important than those omissions is that it omits the fact that heat loss or gain by convection is governed by the difference between the existing lapse rate at a particular place and time (the environmental lapse rate) and the lapse rate at which convection with consequent loss of pressure involves no loss of heat (the adiabatic lapse rate, or if their is moisture in the air, the moist adiabatic lapse rate). For non-chemical engineers who are reading this, "adiabatic" processes are processes in which there is no net transfer of energy. The result is that if other effects make the lapse rate greater than the moist adiabatic lapse rate, convection will increase until the lapse rate returns to the moist adiabatic lapse rate. Conversely, if other processes cause the lapse rate to be less than the moist adiabatic lapse rate, convection will weaken thus tending bring the lapse rate back to the moist adiabatic lapse rate. The result is that for much of the Earth, in the troposphere the lapse rate can be taken as being determined by the moist adiabatic lapse rate. There are limits on this process, notably at the poles and the tropopause (and above) where convection is weak so that other factors dominate. This is the subject of my intended next post in this series.
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  15. Tom Curtis and participants on this tread: I studied the last six months climate change and then had a holiday leave. This tread was one of the first I worked through to restart my study. And indeed a very effective one! Thanks for all your effort and time. Many thanks to the SkS-team
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  16. This is a response to Tarcisio José D from another thread. In response to my explanation, he asks:
    "My question is, which quality of your atmosphere makes it only absorbs IR radiation that rises in the atmosphere and free passes IR radiation that the atmosphere emits more toward the ground."
    In fact nothing I wrote suggests the gases within the atmosphere act as a diode. Each IR active gas will absorb IR radiation with equal facility from all directions, and emit it with equal probability in all directions. However, the atmosphere as a whole acts as a diode. That is, it emits more IR radiation upwards to space than it does towards the ground. It does this because the emission to space comes from higher, and cooler layers within the troposphere as explained in the article above, and also in my posts 36, 51, and 58 above. Importantly, Line By Line (LBL) models, which calculate the IR emission and absorption in the atmosphere at each wave number, and which require each layer of the atmosphere absorbs IR radiation with equal facility whether the radiation comes from below or above, or from the atmosphere or the surface, and which requires that each layer radiates equal amounts of IR radiation upwards and downwards, produce this diode like effect, provided that the atmosphere is cooler at higher altitudes. You can see this for yourself with Modtran. If you run the model on default settings, the outgoing IR radiation equals (Iout) 287.844 W/m^2. Altering the settings to sensor altitude = 0 km, and "looking up" shows the downward long wave radiation from the atmosphere (Iout) is 348.226 W/m^2. The accuracy of these LBL models is shown in the section "Settled science" in the main article, and in my post number 43. It should be noted that the observed upward IR radiation from the top of the atmosphere is 239 W/m^2, while the observed downward IR radiation at the bottom of the atmosphere is 333 W/m^2, amply illustrating this diode like quality of the atmosphere as a whole, even though no individual component (gas molecule) of the atmosphere acts like a diode. I understand that Tarcisio José D is facing a considerable language barrier in communicating in English, and is to be commended for his efforts to overcome that barrier. I recommend that he read carefully this post, the main article above, and the posts linked to in my response. If he is having difficulty in understanding the issue, I also recommend he enlist the aid of a technically proficient friend who is fluent in both English and his native language (which I assume is Spanish or Portuguese). Google translate is not up to translating technical discussions accurately, and will only lead to ongoing confusion. Finally, the issue he needs to address is, why should we prefer his hand waving explanation to the detailed results of LBL models which have proven remarkably accurate in predicting the observed radiation in the atmosphere, whether sampled from satellites, the ground, or aircraft at intermediate levels of the atmosphere?
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  17. I think it's worth adding to this discussion that the rectifying properties of a diode are due to a voltage barrier or gradient inside the material. Following this analogy (not a good one I think), it's the temperature gradient in the atmosphere that causes the its "rectifying" properties. Indeed, the greenhouse effect depends on the lapse rate (temperature gradient) and there would be none if the atmosphere was isothermal. The OLR would be the leakage current of the "atmospheric diode", luckly not a good one :)
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  18. In the above nice graph by Conrath, et al, there is that cental up going spike that appears at the maximum absorption wavelength for the CO2 bending mode. The same thing shows up using Modtran and the spike varies in an interesting way with the simulated altitude of the satellite. If I show this to an audience someone will ask about that spike. I could guess but don't want to. Can someone explain?
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  19. curiousd, What is it exactly that you are asking about the hole (the inverted spike)? Yes, that is the region of CO2 absorption, but what don't you understand? Without knowing that answer, just taking a shot and hoping this answers your question: Within that range of wavelengths (or wave numbers or frequencies, depending on whichever measure is being used), CO2 strongly absorbs radiation. In the dense troposphere, such absorbed energy is usually quickly transmitted, through a collision, to another molecule, most likely O2 or N2 (those being by far the most common). This leaves the CO2 molecule capable of absorbing (and transmitting) IR once again, and also heats the atmosphere (given that the temperature of a gas is primarily a measure of the translational kinetic energy of its component molecules). At higher altitudes, where the altitude is less dense (and cooler), the CO2 molecule has more of a chance of re-emitting the absorbed radiation before passing that energy on to another molecule by collision. Even so, while it is more likely to have absorbed the energy from the warmer parts of the atmosphere below than the cooler parts above, it may radiate it away in any direction, with equal chance, so that some of the radiation arriving from from the planet below, through the atmosphere, may be radiated back down where it is more likely to be absorbed by the atmosphere and transmitted to another molecule. Eventually, of course, some of this radiation escapes into space -- but much less of it within this band than in other bands, due to all of the interference along the way. So there are two ways that you can explain this. One is to visualize the various photon-and-molecule interactions along the way, which prevent energy in that band from proceeding through unscathed (as it does in most, but not all, other bands). Another, broader way to look at it is that the energy in the IR band is dimmed, much as lighted is partially blocked, scattered and dimmed when passing through a fog. But in the case of the radiation in this band, in the atmosphere, there is eventually a point in the atmosphere where that band of radiation is being emitted and the atmosphere is rarefied enough to allow it to escape, unhindered, into space. Since this altitude is higher, that area of the atmosphere is also cooler, therefore it emits at a lower temperature and therefore it emits less total radiation (in that band). In a nutshell, then, this means that for other bands, the degree of emission (the strength in that band) conforms to the temperature at the surface of the earth (since the radiation makes it through, unhindered, from surface to space). [Study the Stefan-Boltzmann law.] The band in the absorbed-by-CO2 range, however, is hindered, and so is emitted from an area near the top of the troposphere. That area is, of course, much cooler, and so the radiation of emission represents that of a body of a much lower temperature, i.e. radiation in that band is weaker. Taking this one step further and increasing the CO2 concentration can, among other things, show that eventual transmission into space, while unaffected and so unchanged in other bands, will occur from a higher altitude in the CO2-absorption bands. This means that total energy emitted from the surface, which has warmed due to the effect, will be higher, but emission into space within the CO2 band will from an even higher, cooler altitude, and so will be reduced. [There are other details here, such as pressure and doppler broadening, which marginally widen the bands being discussed, but these details aren't strictly necessary to understanding the "hole" or "window" under discussion.]
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  20. curiousd @68, I take it that you are asking about the small upward spike at the center of the CO2 absorption band rather than the large notch in the outgoing radiation caused by CO2 absorption and re-emission that Sphaerica has explained. The upward spike occurs in the point of strongest absorption by CO2. Because it is the point of strongest absorption, it requires less CO2 to absorb all (or most) of the upwelling radiation from below at that wavenumber. Consequently, CO2 at a higher altitude is able to absorb all upwelling radiation than is the case at neighbouring wavenumbers. Conversely, of course, there is stronger emission from higher altitudes at that wavenumber than from neighbouring wave numbers. These facts, together with the temperature profile of the atmosphere have interesting consequences: If you look down at 5km on the modtran program (default settings), you will see no central spike. That is because the high density is such that the greater absorptivity only makes a small difference in the average altitude of emission of upwelling radiation at that altitude. A small difference in altitude means a small difference in temperature, and hence little difference in the energy emitted. At 10 km there is a small downward spike at that wavenumber. Because 10 km is below the tropopause, higher means cooler, so emission from a higher altitude emits less energy. Again, however, because of the reasonably high density, the altitude difference is small. At 18 km, the small downward spike disappears again, although it was present at 17 km. The reason it disappears is that 18 km is the tropopause, so the small difference in altitude makes no difference in temperature, and hence emissions. At 20 km, a small upward spike appears. That is because the average altitude of emission for the wavenumber of strongest absorption is now in the stratosphere, and has a higher temperature than the neigbouring wavenumbers, whose average altitude of emission are still in the tropopause. At 30 km, the central spike is much taller. That is because the less dense atmosphere at this altitude results a greater altitude difference from the greater emission/absorption at that wavenumber, so the average emissions are from significantly higher. You will also notice, however, that the emissions from neigbouring wavenumbers are also higher than those at 20 km, indicating that the average altitude of emission to space at those wavenumbers has risen above the tropopause into the stratosphere. Despite this, total upward radiation has fallen nearly 1 W/m^2 compared to at 20 km. That is partly due to increased absorption by ozone, and partly because the average altitude of radiation to space in the wings of the CO2 notch is sill rising within the troposphere, resulting in reduced upward radiation. As move the look down altitude further up, upwelling radiation increase again, by about 1.5 W/m^2; but the basic shape of the CO2 absorption spectrum remains the same. It is important to note that the modtran model does not respond dynamically to increased CO2. Increasing CO2 increases the effective altitude of radiation to space. A simplistic understanding of this might suggest, from the fact that increased altitude shows increased upward radiation above 30 km, that increased CO2 will not decrease TOA IR radiation. In fact, that is not the case, even with no dynamic response, as can be shown by doubling CO2 in a modtran experiment. Further, increasing CO2 increases the height of the tropopause slightly, and significantly cools the stratosphere and hence the increase in emissions in the central regions of the CO2 notch with altitude above the tropopause. That means the Modtran model underestimates the reduction in IR radiation to space with increased CO2. Note also that different latitudes and seasons have very different temperature profiles, which makes a significant difference to the effect of change in lookdown altitude.
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  21. I have been directed to this thread but could not even start to question it, there are too many lacunae in the reasoning starting from the car engine analogy. The engine boils even if the pump keeps pumping because the heat is transported by the pump and has to be dissipated by conduction/convection through the vanes of the 'radiator' - where radiation is irrelevant, just stop the fan to find out. Radiator is a misnomer for a domestic device for conduction and convection of heat - physicists should know that.

    I cannot get my head round  3 kgs of CO2 molecules accepting and re-emitting 300 watts of radiant energy in the presence of three thousand more numerous molecules of N2 O2 H2O etc - do they all agree not to collide with them so as not to convert the energy to kinetic?

    I cannot get my head round the 2.9 w/m2 said to be the surplus greenhouse heating - that equates to raising the atmosheric weight of air through10 degrees p.a. - I think we would have noticed it somehow.

    It's time someone addressed their energies to the way spectrographs are calibrated.



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  22. old sage - Yes, GHGs share energy back and forth with the surrounding atmosphere. 

    The electron relaxation time for a CO2 molecule is on the order of 10-6 seconds before radiating a photon, while at sea level pressures each gas molecule will collide ~109 times per second - meaning that a CO2 molecule will average roughly 1000 collisions before it can radiate. Therefore the GHG molecules and the surrounding atmosphere are at the same temperature. 

    The thing is, at thermal equilibrium the absorption spectra of an object (including a volume of gas) is equal to the emission spectra - and as much energy leaves as enters. Note that this doesn't mean the same molecules radiate as absorb, just that statistically as much energy is radiated as absorbed by radiatively active molecules in that volume. And those that radiate do so becase they have the energy to do so, because they are warm enough. 

    Again, you are presenting Arguments from Incredulity, in contrast to facts, to measurements. Your personal inability to get your head around those facts does not invalidate them. 

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  23. Old Sage @7, this initial comment is just to clear up some (frankly silly) arguments so as to not distract from the main substance.

    1)  The radiator analogy:  A radiator of a car in motion will not boil if it has sufficient coolant and the water pump is working.  It is only if the car is stationary that disconnecting the radiator fan is sufficient to cause the radiator to boil.  Further, pointing out that radiators do not loose most of their heat by radiation is irrelevant.  "Radiator" remains their name, and the analogy merely points out that if you maintain a constant energy input, but decrease the energy output, the system will warm.  A significant number of AGW deniers deny that basic fact.  

    2)  The CO2 concentration in the atmosphere is measured in parts per million by volume (ppmv), not parts per million by mass.  The atmospheric concentration is now 400 ppmv, so it is 4 moles of CO2 for every 9996 moles of other gases; or if you like 1 molecule of CO2 for every 2499 molecules of other gases.

    3a)  Your quotation of 2.9 W/m^2 forcing ignores the forcing from aerosols, which is negative.  Therefore it overstates the total forcing by nearly a factor of two.  Further, it is the forcing, which is the difference in top of atmosphere (TOA) radiative imbalance for a given change of radiative conditions prior to any responses to that change, including increases in temperature.  Feedbacks and increases in temperature will further alter the TOA energy imbalance, with positive feedbacks increasing it, and negative feedbacks and increases in temperature reducing it.  As it happens, the increase in temperature since 1750 (the reference date for forcings) has reduced the TOA energy imbalance to 0.6 W/m^2.

    3b) The energy increase caused by the greenhouse effect is distributed among all Earth's surface components.  That includes the upper few meters of soil, the melting of snow and ice, the increase of temperature of the ocean and the increase in temperature of the atmosphere.  It even includes any increase of storage of chemical energy resulting from the CO2 fertilization effect, although that amount is (comparitavely) too small to consider.  Of these components, the atmosphere absorbs around 2% (1.4% according to Church et al, 2011) of the heat, while the ocean absorbs over 90%.

    If you want to pursue this line of argument, this link leads to an appropriate thread.

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  24. old sage


    see my comment here

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  25. Old Sage @71, IMO, whether or not CO2 radiates at normal atmospheric pressures and temperatures is the crux of your argument.  In fact, that CO2 does radiate in the IR at normal atmospheric temperatures and pressures is resoundingly confirmed by experiment.  

    Line by Line and broad band radiation models model the transfer of radiation within the atmosphere.  For line by line models, the atmosphere is divided up into a number of layers.  For each layer radiative transfer is calculated, with the total upward radiation at the top of that layer being the total upward radiation at the top of the next lower layer, less the radiation absorbed by the layer, plus the upward emissions by that layer.  For line by line models, this is calculated seperately for each wave number.  For broad band models, it is calculated seperately for groups or wave numbers (ie, the bands).  All such models assume that each layer emits an amount based on their emissivity times the radiation expected for that wave number (or band) by a black body of the same temperature of the layer.  The emissivity, of course, equals the absorptivity.  

    If CO2 did not radiate at normal atmospheres and pressures, such models would be massively inaccurate.  Instead, they are stunningly confirmed by observations (see the section "Settled Science" in the main article, and my comment number 42).  These models have not just been confirmed by observations from space, but also by observations by aircraft looking both upwards and downwards at various altitudes.  Indeed, they have also been confirmed by aircraft observations looking sidewards, as the original research was done in the interests of developing accurate Infrared guided air to air missiles.  They have also been confirmed by observations looking upwards from the ground.  Here (courtesy of Science of Doom) is a comparison between modelled and observed back radiation:

     Science of Doom has more graphs of measurments of back radiation on this page.

    The back radiation is particularly devestating to your theory.  As I understand it, you claim that CO2 absorbs, but does not reradiate IR radiation, except in the "electromagnetic soup" at the top of the atmosphere, ie, the ionosphere.  If that were the case, there would be no IR back radiation.  Any IR back radiation from the ionosphere would be as completely absorbed by the intervening atmosphere as would IR radiation from the surface.  With no intervening radiation (according to your theory), the result would be a complete lack of IR radiation at the surface at bands where CO2 was strongly aborbing.  Instead, we see the opposite, with the strongest IR back radiation at those wavelengths where CO2 is most strongly aborbing:

    Further, nearly all of that back radiation comes from the lowest km of the Earth's atmosphere.  For that reason, typically, the brightness temperature, ie, the incoming energy normalized by black body radiation curve, closely matches the surface.  The exceptions are when the upper troposphere is signicantly warmer than the surface (as with Antarctica in the winter) which results in warmer wings (where CO2 is less absorptive, and hence originates from higher in the atmosphere in the case of back radiation) then does the more strongly absorbing center:

    In contrast to your theory, the theory that CO2 radiates IR at normal atmospheric temperatures and pressures results in not just accurate predictions of the total energy radiated, but accurate predictions of the detailed profile of the emission spectrum given knowledge of the atmospheric temperature profile.  (For the upward case, see the section "Settled Science" in the main article.

    In contrast to this mass of detailed prediction and confirmation, you offer us a counter theory which has not even reached the back of envelope calculation stage.  There is a reason that it has gone no further.  If you take it further it immediately breaks down and is shown to be contradicted by the evidence.  Given that, your choice at the moment is very clear.  Embrace science by rejecting the nonsense you are currently espousing - or show clearly that it is pseudo-science you love and expouse by repeating the same old nonsense yet again.

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  26. @72 

    KR, Please help me understand which excited electronic states are playing a role in the greenhouse effect. I only familar with the IR vibrational quantum states. 

    Much appreciated. 

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  27. MThompson - Those IR active vibrational quantum states are exactly what is involved in the greenhouse effect. [ For those not familar, nothing like the classics as a starter: Martin and Barker 1932, The Infrared Absorption Spectrum of Carbon Dioxide, is a good place to look ]

    Those IR active vibrational states (which exclude lengthwise compression/expansion vibrations, as they don't change the electronic moment of the molecule and hence don't absorb/radiate) absorb/emit thermal range EM, with multiple wavelengths in each from different excitation states. These are further expanded by various spectral broadening effects (too many to briefly list)

    Beyond that, I'm not certain what you are asking. Any IR active gas can and will act as a greenhouse gas, restricting radiation to space to an altitude where the remaining gases above have something less than a 50% chance (to a first approximation) of absorbing a particular upward photon - and due to the lapse rate, that altitude will be cooler than the surface atmosphere, meaning less energy radiated to space than would be the case in an atmosphere transparent to that wavelength. The overall effect is just a reduction in effective emissivity of the surface to space, and hence a higher temperature required to radiate the incoming energy back out, to maintain conservation of energy. 

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  28. KR and MThompson,

    The excited electronic states of CO2 do not play a particular role in the Greenhouse effect. Any molecules that are in excited electronic states will have slightly different vibrational frequencies and so will add to the breadth of a vibrational band. However the fraction of molecules in excited electonic states will be small (as given by the Boltzmann distribution)


    I wonder whether MThompson was refering to KR's comment about "electron relaxation time" @72 which I must admit does seem out of place

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  29. Phil @78,

    Thank you for your answer. I was indeed inquiring about KR@72 statement that "The electron relaxation time for a CO2 molecule is on the order of 10-6 seconds ..."

    Furthermore, it seems that 10e-6 seems much too slow for relaxation of electronic states, and rather too fast for IR vibrational states.

    Gratitude for furthering my education on this,



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  30. Mea culpa, I often work with electronic state changes and that is my default vocabulary (in error in this case). Those are more visible/UV in range. 

    Vibrational (near/far IR), rotational (far IR/microwave) and combinational modes are involved in thermal IR. Radiation times for these modes are on the order of 7-15*10-6 seconds at 1atm.

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  31. Many thanks to Phil and KR for educating me on this topic. Naturally I have done considerable reading online, but many times the explanations are not clear to me because of the misapplication of concepts and poor analogies.

    From my reading it seems that asymmetric stretch is the primary vibrational mode for CO2 and is some 13x more intense than the two bending modes combined. So in my understanding from this discussion and other reading is that CO2 is capturing the blackbody radiation of the earth at these wavelengths. Additionally there is some broadening of the lines that allows more than just the two primary “peaks” to be absorbed, and that broadening increases the total energy stored in vibrational modes of C02.

    Please let me know if I have a good mental image of the process.

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  32. MThompson @81. I think you are both right and wrong. The asymmetric stretch is stronger than the bend, however the important fact you are missing is the distribution of IR radiation emitted by planet Earth. This is a (near) black body distribution, and the peak (at 288K) almost co-incides with the CO2 bend. Thus the bend plays a more important role simply because there is more radiation in the Earths emission spectrum to absorb.

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  33. It might be helpful to visualize the various vibrational modes of CO2 with these animated GIFs:

    Asymmetric  Asymmetric

    Bending  Bending 

    Symmetric  Symmetric

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  34. Molecular visualizations of CO2 from the GIF's (from Timothy Chase's website):

    Ground State Mode

    Ground State


    Pure Symmetric Stretching Mode

    The pure symmetric stretching mode v1 of CO2. While this is a mode that may gain and lose energy collisionally it is not infrared (IR) active as there is no transient electric dipole.



    Bending Mode V2

    The bending mode v2 of CO2, responsible for the 15.00 μm (wavenumber 667 cm-1) band -- the mode dominating the enhanced greenhouse effect and that primarily used by AIRS. This is infrared (IR) active due to a transient dipole: bending results in charge being asymmetrically distributed with net positive near the carbon atom and negative near the two oxygen atoms.





    Asymmetic Stretching Mode V3

    The asymmetric stretching mode v3 of CO2 is responsible for the 4.26 μm (wavenumber of 2349 cm-1) band. The asymmetic stretch result in a net positive charge near the carbon atom and a net negative charge with the isolated oxygen atom, creating an electric dipole and making it infrared (IR) active. Given the range of atmospheric temperatures and concentrations of CO2 the bending mode v2 plays a greater role in climate change.


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  35. KR @80

    Can you give a reference for your stated radiative lifetimes? I thought spontaneous emission in the mid IR (at the CO2 bending mode) had lifetimes on the order of milliseconds, not microseconds.

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  36. Phil @82

    Daniel @84 

    Thanks for pointing out how the energy distribution factors into this. After reading your comments I did quite a bit of poking around online to refine my understanding. The big CO2 peaks may overlap some with molecular water, but the CO2 components seem to span a wavelength range of roughly 13-18 microns. Does this range correspond to higher quantum number states of the bending mode? It seems transitions between asymmetric stretch and bending mode have wavelength of about 9.5 microns.

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  37. MThompson @86,

    At atmospheric temperatures only a few percent of CO2 molecules are in the first vibrationally excited state. All the rest are in the vibrational ground state. Thus, vibrational transitions to higher levels are not involved. The broadness of the bending mode comes from the fact that each vibrational state has a large number of rotational levels populated, and vibrational transitions can be from a lower to a higher rotational level ("R-branch" transitions) or from a higher to a lower rotational level ("P-branch" transitions). The rotational component of the one vibrational transition can broaden the spectral absorption band by hundreds of wavenumbers. These ever more wide-spread transitions, by the way, are why the CO2 absorption band (and water bands, for that matter, never fully "saturate" with increasing levels of water and CO2 in the atmosphere.  

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  38. tcflood @87

    Thank you for the clear explanation of how the rotational modes broaden the primary transitions. I am still trying to understand how the bending vibrational mode of CO2 gets populated. I see from the Maxwell-Boltzman distribution that about 6% to 15% of gas molecules at earth temperatures have enough kinetic energy to excite the CO2 bending mode. Now my question is: “Do photons from the earth’s blackbody spectrum in the range of 13-18 microns ( 770 to 560 cm-1) pump ground-sate CO2 molecules to the bending mode?”

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  39. MThompson @88;

    How black body-like the earth's emission is depends on the details of the specific piece of surface, but on the average I think the consensis is that it is about 90% BB-like. So, yes, the earth's IR emission in the region around 700 cm-1 is absorbed efficiently by the CO2. The key point here, though, is that in the troposphere that excited CO2* (* means excited state) undergoes about 10^10 collisions each second and the excitation energy is transferred at about that rate to all the gases in the immediate vacinity, thus, contributiong to the thermal pool. The rate of spontaneous emission in the mid IR range tends to correspond to lifetimes of the excited state on the order of milliseconds, which is way too long for the specific originally excited CO2* (lifetime of a few hundred picoseconds) to have any probability of just emitting the photon directly back out.  Thus, the low equilibrium percentage of CO2* in the atmosphere can essentially be thought of as coming entirely from the Boltzmann thermal equilibrium and this is the population from which re-emission of the IR occurs.

    It sounds like your population of from 6-15% of CO2* may have been calculated assuming the ground state is singly degenerate. I think the ground state and excited state are both doubly degenerate for the bending mode so the percentages may be half of that. I'm not sure on this point. Maybe someone else can comment.

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  40. tcflood,

    You are Way over my head.  I'm but an interested dilettante in this man-made global warming stuff.  Still, I have some observations which may or may not be pertinent to anything.  Consensus:  Who was polled to establish the so-called Consensus?  Climatologists?  Weathermen?  Physicists? Sociologists?  Petroleum Engineers?  Volcanologists? Ecologists?  Paleontologists?  Archaeologists?  Pathologists?  Dentists?  For sure, nobody polled me.

    Also, science isn't about consensus.  Science is the effort--sometimes the painful effort--to get at something approaching the truth.  At one time "consensus" had it that the four humors were responsible for health and disease.  At one time "consensus" had it that the sun revolved around the earth.  At one time "Consensus" had it that most cancers started with one great mutational 'hit'.  "Consensus" is a misleading term if there ever was one.

    So much for my soap box.  The other day I was watching a TV show--the source of most of my scientific information.  The Journalist was interviewing scientific types.  One was a young woman digging away in the melting Alaska permafrost.  They filmed impressive looking sink-holes caused by melting ice.  She climbed down into a sink-hole [looked risky to me] and showed melting frozen earth, 2-4 feet deep, containing clusters of roots from "plants that died hundreds or thousands of years ago."

    Hmmm.  Either these were the roots of plants that could grow in solid ice OR climate was a lot warmer in the far North way back then. [Little Climatic Optimum?].  How could it have been warmer 'hundreds of thousands of years ago, when it's supposed to be warmer NOW than since, if not before, the last interglacial? What do you think?

    I know.  The exception proves the rule.  Still, they went on to claim that, at the present rate, by the end of the century, atmospheric CO2 would be twice that of today and the fish would boil in the sea [that's a joke].  Anyway, I googled it and did some high school arithmetic.  Maybe I made a couple of systematic errors but, looks like, if we burned All petroleum and natural gas tomorrow, we would increase the tonnage of CO2 in the atmosphere by .001%.  Note, this isn't saying that the % in the earth's atmosphere would go up that much.  It means that atmospheric CO2 would go up a tiny fraction--IF--we burned it all at one time.  Of course, all that petroleum-produced CO2 might hug the ground  and heat up the surface a lot because, as we know, manmade CO2 is a lot different from 'natural' CO2.

    Also, I worry a lot about carbonates.  I live on a hill loaded with sea shells, ammonites, snails etc. that died tens of millions of years ago.  The 'turn-over' rate is pretty slow and my guess is that they'll be locked in the rock another 65 million years.  It occurs to me that the same thing is happening in the sea today.  Sea life--especially those with shells--must be locking up plenty, plenty of carbonates.  Once locked, they are generally fixed unless cooked and vaporized by volcanoes.


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    Moderator Response:

    [DB] In addition to the sage advice already given you below, please read The Big Picture thread for background...and familiarize yourself with this site's Comments Policy.

  41. Spoonie,

    At this site we like people to post on topic to the thread.  Since you have so many points you are off topic on most threads.  Pick the one ot two you feel most strongly about and ask about that.

    I noticed your high school math teacher was way off base.  The atmosphere is currently 400 ppm CO2 and went up 3 ppm last year.  That is about a 1% per year increase at current rates of emission.  About half the emitted CO2 is absorbed so about 2% per year is emitted.  There are several hundred years of supply at current rates of emission.  You are off by about a factor of 1,000,000.  I suspect the rest of your information is about as current as your CO2 emissions.  Ask questions about what you do not understand and people will try to help you.  If you get your information from the denier blogs you will stay a million times off.

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  42. spoonieduck,

    As Michael suggested, you should identify the appropriate thread for each of your varied comments so that they can be addressed individually in the correct place. For your questions about Consensus, for example, you could go to the top-left of the page, where the thermometer graphic lies under the heading "MOST USED Climate Myths and what the science really says...", and you'll see that number 4 is "There is no consensus". Click on that link and it will take you to a post with Basic, Intermediate, and Advanced levels that answer your questions before you even asked them.

    For the question about whether it was a lot warmer in the far North "way back then", you could start with number 1, "Climate's changed before", and learn how it's precisely that which helps us predict what the consequences will be this time. (Note that being warmer "hundreds of thousands of years ago" is not inconsistent with it being warmer now than since the last interglacial.) You might also want to read the series of posts starting with The Last Interglacial - An Analogue for the Future?

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  43. tcflood @89

    So if I understand correctly, the CO2 bending mode is continuously populated by the earth's blackbody radiation in the range of 13-18 microns (770 to 560 cm-1) plus, to a lesser extent, collisions with other atmospheric gasses that have sufficient kinetic energy to activate the bending mode. Of course the most probable speed of the atmospheric gasses does not have enough energy to excite the bending mode, but some small number of atmospheric gas molecules do because of the Maxwell-Boltzmann tail.

    Once the CO2 bending mode is activated (by either mechanism) it will relax primarily through collisions with N2, O2 and Ar, thus raising their kinetic energy. The probability of CO2* emitting a photon in the range of 13-18 microns (770 to 560 cm-1) is very small because of the high collision frequency of atmospheric air molecules in the troposphere. 

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  44. MThompson at 93;

    The rate of emission of IR photons from the excited bending mode of CO2* in the atmosphere is a property of the bulk steady-state concentration of that state regardless of the lifetime of the state for any single molecule. By my calculation using the Boltzmann equation, at 80 F about 4% of the CO2 molecules are excited in the bending mode.  The rate of spontaneous emission from the sample depends on that number.

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  45. tcflood at 94, 

    Thanks very much. My percentages were for the energy of all gas molecules that had enough energy to excite CO2, but your steady-state 4% number is more direct and to-the-point.

    Now to continue developing my mental image, the photons from the earth's surface blackbody radiation in the range of 13-18 microns (770 to 560 cm-1) are pumping the CO2->CO2* transition. The CO2* relax in one of two ways: by colliding with other atmospheric gas molecules and thus raise their kinetic energy, or the CO2* relax by releasing photons in the range of 13-18 microns. Is this a good visualization?


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  46. MThompson at 95;

    I don't know that this is all going to matter in understanding the greenhouse effect, but to get the clearest physical picture of what is going on, it is probably best to separate the two phenomena of (1) IR pumping of the CO2 bending mode which has the effect of heating the surrounding atmosphere and (2) the temperature-dependent equilibrium between the vibrational groundstate (v0) and the first excited state (v1) which leads to a steadystate concentration of v1 from which IR emission occurs.

    In (1) photoexcitation forms a v1 CO2* in a single specific molecule which then has a lifetime of only picoseconds because it undergoes collisional energy transfer reforming v0 CO2 and distributing the energy into the local atmospheric vicinity.  Photoexcitation can be thought of as only causing atmospheric warming.


    In (2) the thermal pool of all the atmospheric gases has enough energy to cause, say, 4% of the total CO2 population to persist as a constant concentration of v1 excited state species in accordance with the Boltzmann equation.  Now, spontaneous emission is a strictly first-order kinetic phenonenon so that the rate of emission depends on a constant times the concentration of the excited state. The rates at which individual molecular excited states are thermally produced or thermally quenched don't matter -- only the concentration matters for photon emission.

    If you are able to view the system as having two independent processes in this way, it may be easier to understand. 

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  47. MThompson;

    It just occurred to me that a good example might be to suppose that the GHG of concern were benzene.  Let's suppose that the molecular vibration of interest were the C-H stretching mode at about 3000 cm-1.  Let's say the earth somehow naturally emitted significant IR energy at that frequency.  The benzene C-H stretch would be excited and that energy would be immediately transferred to the surrounding O2 and N2 thermal bath. Suppose that the ambient atmospheric temperature were about 40 C. The Boltzman distribution for that vibrational mode would be ~100 % v0 and 1 x 10^-6 %  of v1. With no significant concentration of v1 at equlibrium, no emission of IR at 3000 cm-1 would be seen (say, back-radiation toward earth) from this system.

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  48. tcflood from comments 96 and 97,

    Thanks. The explanations that you have given are helping me a lot. Now I see that without CO2 the earth’s blackbody radiation in the range of 13-18 microns (770 to 560 cm-1)  would be able to escape to space, instead of pumping the v2 CO2* state and quickly distribute the energy into the local atmospheric vicinity.

    Digging into this a little more, I found a nice calculator online that shows the earth’s BB radiation in the bandwidth of interest is about 3x1022 photons per second per square meter. I estimate that near the earth’s surface there are about 1x1022 C02 molecules per cubic meter. I have not yet had time to delve into the photoabsorption cross-section of CO2, but I’d guess that a few tens of meters would be sufficient to absorb all the earth's photons in the wavelength band of interest. This guess of course assumes that the lifetime of v2 C02* is much shorter than one second.

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  49. MThompson at 98:

    You are now getting into more detail than I have, but a few tens of meters is exactly the kind of distance that I have heard or seen mentioned many times. 

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  50. MThomson,

    you appear to inching toward this myth. If you are, you should take the conversation to that thread.

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