Could increasing CO2 be its own positive feedback?

Question

Please bear with me; this will need a little in the way of explanation.

What follows isn’t about the usual feedbacks that are discussed here; water vapour, Ice albedo, methane etc; what I am asking about is a possible feedback solely from the increase in CO2 itself!

… a positive feedback which, for a doubling of CO2, would be the equivalent of an additional increase of 59%!

Now, I think it would be highly unlikely that I have found anything new; far more likely that what follows is either already known and accounted for, or that my reasoning is flawed.  Whatever the answer, I’m sure it will improve my understanding of this area of the AGW subject and hope others will find this an interesting and helpful question.

Now for the details.  I’ll keep it as simple as I can; please let me know if any clarification is required.

Starting with the question of CO2; its absorption and emission of radiation in the atmosphere, in particular, how this would change with increasing altitude.  As a thought experiment, lets divide the atmosphere into an arbitrary number of layers of equal mass and CO2 content.  Each layer is compressed by the weight of  all the layers above, so if we were to ascend through the atmosphere, we would observe the pressure dropping and the volume increasing in each layer with respect to the layer below.  The uppermost layers would be many times the volume of those near the surface.
 
Now that’s pretty basic; I assume you’re all with me so far.

Next imagine two CO2 molecules separated by an average distance within a given layer.  Call one the emitting molecule and the other the absorbing, or ‘target’ molecule.  If  it is to be absorbed, the photon must pass within the absorption cross-section of the ‘target’ molecule (imagine a circle drawn on a plane at right angles to the direction of the photon. If the photon passes within the circle, it is absorbed.  The circle is the ‘target’).
  
Now consider the angular size of the target measured from the emitting molecule and how this would vary with altitude.  Near the surface the angular size of the target would be relatively large; at altitude, much smaller, because the ‘target’ molecule is much further away.  This would mean that the probability of absorption, therefore the efficiency of CO2 as a greenhouse gas, would decrease dramatically with increasing altitude.  A photon traveling vertically from the surface would almost certainly be absorbed, while a similar photon entering the top layer would have a good chance of escaping to space.

And how is this a positive feedback?  Well, if increasing the distance between molecules reduces the efficiency, then reducing the distance would increase the efficiency.  Obviously, this won’t be done by an increase in pressure, but by increasing the proportion of CO2 in the atmosphere, you would get the same effect.   Since CO2 is well mixed, this increase in efficiency would apply to the whole atmosphere.

So , if the above is reasonable, how strong would the effect be?  The two main points are as follows:

1 )  For a given pressure; In order to halve the average distance between molecules, you need eight times the mass of CO2.

2 )  There is an inverse square relationship between the distance between molecules and the size of the ‘target’. So halving that distance would mean four times the probability of absorption.

Combining these, then a doubling of CO2 would result in a ‘cube root squared’ increase in its efficiency; about 59%!  Or, to put it another way, a doubling of CO2 would effectively be the equivalent of a 3.17x increase over the original amount.  (this subject to the usual logarithmic approximation)

--------------------------------------

As I said at the start, I think it unlikely that I have come up with anything new; far more likely that the above is already allowed for, or there is an error in my reasoning.  Whatever the answers, I hope to learn from this question.

Thanks in anticipation …

d/dx+d/dy+d/dz · Accepted Answer

The optical thickness of a given mass of CO2 does not change with density. In a gas where molecules have random orientations, photons are emitted isotropically.  Consider a spherical EM wave traveling outward through an absorbing gas with density p.  The number of CO2 molecules in a sphere of radius r is N = 4pi p r^3/3.  Let s be the absorption cross section for one molecule.  The probability of absorption within the volume of radius r is Ns = 4 pi p s r^3/3.  If the density is halved the probability of absorption is halved. This is Beer's Law.  

Now for the more subtle points. The probability of a molecular collision is proportional to pressure.  When molecules collide, the quantum state might change and this means that the lifetime of a quantum state is shorter at a higher pressure.  By the Heisenberg Uncertainty Principle, a shorter lifetime means more uncertainty in the energy and this is manifest in broadening of spectral lines.  The total absorption integrated over the breadth of the line does not change much, but the distribution does.  The spectrum of CO2 at ground level is not identical to the spectrum of CO2 in the stratosphere.  There is a bandwidth expansion with increasing CO2 concentration, but this is not a feedback.

The effect of temperature is very slight and actually a negative feedback. The direct effect of CO2 is a small increase in temperature as measured by molecular kinetic energy. At any time, there is a small probability (about 0.1%) that a CO2 molecule is in a vibrationally excited state due to collisions (thermal energy).  These molecules are transparent to the 0->1 transition.  If the temperature rises by 0.8 C, the fraction of molecules in the excited state rises by approximately 2E-5.  That is, as a gas becomes hotter, it becomes more transparent.  When the sun enters the red giant phase and engulfs the earth raising temperatures to 6000 K, more than 70% of the  remaining CO2 will be in an excited state and the greenhouse effect will be diminished.

Anonymous · Answer

Up until now, the oceans have been absorbing carbon dioxide. However, increasing temperatures and ocean acidification will reduce the solubility of carbon dioxide in the water, perhaps to the point where the oceans outgas, rather than absorb carbon dioxide. This would be a positive feedback.

Percussim

The Medieval Warm Period was not warmer than today.
http://www.meteo.psu.edu/~mann/shared/research/ONLINE-PREPRINTS/Millennium/mbh99.pdf

Some places were warm, but other places were cool.
http://www.meteo.psu.edu/~mann/shared/articles/MannetalScience09.pdf

Grapes are grown in Scotland today.
http://www.johnstoa.co.uk/blackgrape.htm

David · Answer

I'm going to take a wild uneducated guess and say that the effect of the decrease in *horizontal* distance between molecules is canceled out by the decrease in *vertical* distance between the molecules that lie below those in question (i.e., band saturation). This should mean that less radiation hits those molecules in question, and so the net result (through this effect, anyway) in any given volume of atmosphere is nil.

Interesting question though, I'll be interested to hear from the experts.

Climaticsman · Answer

Many times the volume but equally reduced density. CO2 is denser than air. Water vapour is by far the most prevalent greenhouse gas and it hasn't increased. No the feedback is neither positive nor negative in the context you mention. The inverse square law applies so long as progress is not impeded, which in the case of solar radiation is true, but the greenhouse gases do impede terrestrial radiation, so in that context it is not.

Greenhouse gases are absolutely essential to you and me and they govern the planets temperature brilliantly in a delicate balance. That delicate balance is not affected much by the claimed increase in CO2 and the evidence for global warming is real but not man made and not unusual. There has been periods in the recent history of the world that have been much colder (known as the Little Ice Age) and just before that, a period that was much warmer, when we had grape vines in Scotland, called the Medieval Warm Period. Polar bears survived both, as did we, and neither had anything to do with power stations or cars or aeroplanes.

By the way, when you see power stations filmed on a news or documentary item to do with climate change, they always show you the cooling towers, with lots of clouds spewing out - that is the purest water you could ever get, and not smoke at all, or a greenhouse gas. They also show large wide bodied jets taking off - they use less fuel per passenger mile than your car - its very much drama to impress, but very unscientific, even untrue. It is designed to get you on their side and is dishonest.

I have added a link below, but I have studied this subject for many years, was a Principal Climatics Engineer and wrote papers on solar and terrestrial radiation in the 80s before CO2 became famous for the wrong reasons. Take a cool look at the facts.

ChemFlunky · Answer

I'm... pretty sure that what you're talking about is what scientists calculate as the direct effect of CO2 in terms of warming, and it doesn't count as a feedback.

Remember, to act as a positive feedback, you need something like this:
A causes B, B causes C, C causes more A
(for example: heat causes evaporation, evaporation causes increased greenhouse effect from water vapor, increased greenhouse effect causes heat)

For CO2 to be a direct feedback, more atmospheric CO2 has to either cause more atmospheric CO2, or cause more of something that causes more CO2.  There are relatively direct *negative* feedbacks from CO2 (for example, more atmospheric CO2 leads to increased CO2 absorption by bodies of water, which leads to less atmospheric CO2), and there are some fairly indirect anthropogenic feedbacks (more CO2>more warming>more AC use>more CO2), but I'm not aware of any natural positive feedbacks directly from atmospheric CO2

Rio · Answer

No just use the specific gravity charts and you will have an (ah ha) moment.

< d/dx, in his 2nd para explained it to you. But this has been reiterated many times: http://answers.yahoo.com/question/index;_ylt=AlRTubJdE77ft5sczUDTKsXty6IX;_ylv=3?qid=20110919211537AAL6DYL
Either your asking about standardized distribution or using a constraint. Make up your mind.

Hey Dook · Answer

I saw something along these lines once somewhere, but I can't remember where. I would try realclimate or IPCC or a textbook. Or google. Probably one of the climate scientists posting here here knows, but their appearance can be spotty.

PS: Dawei is spot-on re Percussim. Don't waste your time helping train the incurably dishonest to become less obviously so.

bravozulu · Answer

You have to ignore the climate history of the earth to believe the fantasy that climate is unstable.

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Could increasing CO2 be its own positive feedback?

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