Greenhouse effect and Earth's surface temperature

[DrStupid]

My understanding is that the absorption and re-emitting of IR photons is not thermal because the re-emission is much faster than the time for the molecule to interact with another molecule and covert the internal excited state energy into kinetic energy.

I can't follow that argumentation because IR absorptions and intermolecular interactions are independent from each other. I would expect a probability of

1 - \exp \left( { - x} \right) \approx x

for an interaction after IR absorption and before IR emission, where x is the ratio between the mean lifetime of the excited state and the mean time period between two interactions. Low values of x make such interactions less likely but not impossible. This just increases the time required to reach the thermal equilibrium resulting in some kind of low-pass filter for the impact of IR radiation to temperature. In order to exclude impact of thermal re-emission you need to show that the relevant variations of IR radiation are too fast to be followed by temperature.

 

[DrStupid]

The spectrum of the re-emitted radiation form CO2 does not match the Planck black-body distribution.

As CO2 is not a black body this isn't very surprising. Do I miss something?

 

[BillyT]

Hi Billy: ... The spectrum of the re-emitted radiation form CO2 does not match the Planck black-body distribution. ...

No one with even the slightest understanding that spectrial line radiation has the energy of the diference between two discrete energy states would think it should be a continuum distribution that Planck BB radiation is.

At high density gases do show an effect of collisions - the spectral lines are not as "sharp" (have slightly wider spacing of the line profile between it half intensity points) This is called "collisional broading." It is caused by the fact that the energy levels of two atoms (or molecules) that are separated by only "atomic distances" are distrubed / not exactly the same as for the isolated radiator.*

The extreme case of this is a hot radiating solid - there the collisional broading is so great that distinguable lines no longer exist, and the the radiation is a continuum.

* My experimental Ph.D. thesis concerned this collisional broading for radiation from a plasma. Mostly Argon ions and electrons. There it is a little more complex and Hans Griem at Un of Md had just worked out a model, which I tested. The near approaching and not too hot (fast) electron does not pass by the ion on a straight line trajectory as a neutral atom would pass by another neutral. The electron path is bent by the net positive ion. So the collision lasts longer and the collision broading is more extreme. Even the peak of the line can be displaced and the line shape is no longer symetical about the peak. - In one line case the peak was shifted by more than an Angstrom.

 

[klimatos]

Re-radiation and Re-emission: A Cautionary Note:

Throughout this series of posts, I have noted a somewhat careless use of the terms “re-radiation” and “re-emission”. It is almost as if the writers were somehow implying that the photons absorbed by a molecule and the photons later emitted by that molecule were somehow identical. This may occasionally be the case, but I think that it is not common. Unless you can prove that the second photon has exactly the same energy level as the first, it is not logically “re-emission”. For example, an atmospheric water molecule may readily absorb a high-energy photon of solar radiation (this accounts for about 83 Wm-2 of the atmosphere’s heat budget), but that molecule is extremely unlikely to emit such a photon. Instead, it is more likely to emit one or more photons of lower energy levels. I would argue that photons are neither re-radiated or re-emitted by either the Earth’s surface or its atmosphere. Both of these entities emit radiation and both of them absorb it. Since both the Earth’s surface and its atmosphere undergo temperature changes due to both emission and absorption, it is obvious that some conversion of internal electronic energy to and from external kinetic energy takes place. Hence, emitted energy does not equal absorbed energy in most atmospheric situations. I think that the use of the “re-“ prefix is both erroneous and misleading. Instead of saying “the later re-emission of a photon”, why can’t we just say “the later emission of a photon”?

 

[rootone]

It's a note about semantics rather than the physics here, but yes 'the later emission of a photon' leaves less room for misunderstanding.
're-emission' might lead some to conclude that what is being emitted is the exact same photon that was originally 'captured'/absorbed, but that photon of course no longer exists.

 

[BillyT]

It's a note about semantics rather than the physics here, but yes 'the later emission of a photon' leaves less room for misunderstanding.
're-emission' might lead some to conclude that what is being emitted is the exact same photon that was originally 'captured'/absorbed, but that photon of course no longer exists.

Agreed. The photon which is emitted after one has been absorbed will be traveling 99.9% of the time in a significantly different direction - certainly is not the absorbed photon "re-emitted"

Also if an energetic photon is absorbed and produces a higher than least excited state of the absorber, it is very likely that the decay of that excited state will be via emission of two or more lower energy photons. This is because, crudely speaking the transition probably for a state to a lower state is greater when the two states (upper and lower) are less separated.* I. e. when a high state is excited, the result is usually a cascade down thru several intermediate states, not a single radiative transition down to the ground state.

For example, in deep space most of the hydrogen atoms are just protons, but they do occasionally become neutral atomic hydrogen by capture of a passing electron into a very high bound state. To even do that there needs to be some "third body" to take up the electron's greater than binding energy. Thus it is very improbable that the "third body" can absorb all the energy the free electron had (More than 13.6 ev) so it "falls" directly into the ground state. It might for example be captured into the n = 23 excited state, then "drop down" with IR radiation to the n = 22, 21, or 20 state, from which it will drop down in cascade fashion thru more lower states still. Eventually (after a fraction of a second) it may emit some visible light of the Balmer serie and then a UV photon of the Lyman serie as it become part of a hydrogen atom in the ground state.

* This is because closely spaced quantized energy level wave functions overlap much more than pair with greater difference in energy levels. Again crudely speaking the radiative transition probabily between two state is proportional to the overlap of their wave functions. (Assuming, of course, that such transitions are "permitted" - obey the "selection rules.")

 

[Buzz Bloom]

Hi Billy:

Thanks for your post explaining my misunderstanding.

No one with even the slightest understanding that spectrial line radiation has the energy of the diference between two discrete energy states would think it should be a continuum distribution that Planck BB radiation is.

The extreme case of this is a hot radiating solid - there the collisional broading is so great that distinguable lines no longer exist, and the the radiation is a continuum.

* My experimental Ph.D. thesis concerned this collisional broading for radiation from a plasma.

Not being well educated on the topic, I had the misunderstanding that the "broadening" due to the range of the kinetic energy of molecules caused the shape of radiation from a gas to approximate a Planck distribution, as you say it does for a solid, and I am guessing it does also for a liquid. Can you suggest a reference that discusses the degree of broadening by a gas or plasma as a function of temperature?

Regards,
Buzz

 

[Buzz Bloom]

Hence, emitted energy does not equal absorbed energy in most atmospheric situations.

Hi klimatos:

I understand that there are very many excited states of electrons bound to nuclei, and that the energy absorbed which excites an electron to a higher state than the minimum excited state has more than one way to release energy while returning to a lower energy state. I gather from what you are saying that for the excited molecular states of such molecules as CO2, these states also show the same behavior of as bound electrons' states. This seems a bit odd to me since the physical changes in the molecular shape when it it is in an excited state do not seem to have the quantum mechanical characteristic of electrons bound to a nucleus, in which an electron does not actually have a moving position in an orbit, but rather a probability distribution of its position. Is this also true of the position of the carbon and oxygen nuclei relative to each other in defining the molecule's excites states? Do all excited states of a molecule have multiple transition paths to lower states as do bound electrons?

I have no access to a technical library, and limited access online to more than abstracts of articles. Can you recommend any reference that I might be able to access that describes the excited energy states and transitional possibilities of those states for CO2?

Regards,
Buzz

 

[Buzz Bloom]

Hi @BillyT:

Here is one more thought about themeasured CO2 IR spectrum not being thermal, and what this means.

Even if the spectrum is not continuous, that is it is a collection of spikes at discrete frequencies, I would expect that the spectrum will be different than that of CO2 gas at a controlled fixed temperature, or a combination of such spectrums for several fixed temperatures. My thought is that the CO2 in our atmosphere is mostly concentrated at a few distinct levels, and that the temperature at these levels depends mostly on altitude, although there are variations due to latitude and season and time of day. I would expect the measured distribution to be more like that of CO2 at the Earth's surface temperature (rather than the temperatures atr the altitudes of CO2 concentrations) adjusted for the variations of the absorption coefficient for different frequencies.

AFAIK, this analysis of the data in the http://www.leif.org/EOS/2012GL051542.pdf paper has not been done. What would you expect such an analysis to show?

Regards,
Buzz

 

[Buzz Bloom]

Throughout this series of posts, I have noted a somewhat careless use of the terms “re-radiation” and “re-emission”. It is almost as if the writers were somehow implying that the photons absorbed by a molecule and the photons later emitted by that molecule were somehow identical.

Hi @klimatos:

It was my intention to imply that the IR photon emitted by a CO2 molecule would be have the same energy as the photon it had recently absorbed. I did not intent that it was the same photon. What not-too-wordy vocabulary would you suggest for expressing this idea?

I understand that the recent posts have suggested that this intent of mine is incorrect, but that is a separate issue which I am trying to resolve.

Regards,
Buzz

 

[Buzz Bloom]

I can't follow that argumentation because IR absorptions and intermolecular interactions are independent from each other. I would expect a probability of

1−exp(−x) ≈ x​

for an interaction after IR absorption and before IR emission, where x is the ratio between the mean lifetime of the excited state and the mean time period between two interactions. Low values of x make such interactions less likely but not impossible. This just increases the time required to reach the thermal equilibrium resulting in some kind of low-pass filter for the impact of IR radiation to temperature. In order to exclude impact of thermal re-emission you need to show that the relevant variations of IR radiation are too fast to be followed by temperature.

Hi @DrStupid:

Thank you for your discussion about "x". I apologize for being careless in my exposition in ignoring what I believe (based on email correspondence with an expert) is a very small value of x.

Regards,
Buzz

 

[DrStupid]

I apologize for being careless in my exposition in ignoring what I believe (based on email correspondence with an expert) is a very small value of x.

Very small values of x just mean, that the time to reach the thermal equilibrium is very long compared to the life time of the excited state. What you need for your argumentation is a comparison of the time to equilibrium with the rate of IR variations.

 

[klimatos]

I have no access to a technical library, and limited access online to more than abstracts of articles. Can you recommend any reference that I might be able to access that describes the excited energy states and transitional possibilities of those states for CO2?

Sorry, Buzz, my field is the atmosphere. You need a QM guru for that task.

 

[klimatos]

It was my intention to imply that the IR photon emitted by a CO2 molecule would be have the same energy as the photon it had recently absorbed. I did not intent that it was the same photon. What not-too-wordy vocabulary would you suggest for expressing this idea?

Why not just say, "emits a photon of the identical energy level"? As you went on to note, I'm not sure how often this happens except for lowest excitation level.

 

[klimatos]

Some More-or-Less "Hard" Numbers

NASA’s Global Observatory has released some interesting numbers relevant to this thread:
1) 1880 to 2014 global near-surface temperature increase is 0.75°C (1.35°F)
2) October 2015 mean global carbon-dioxide level is 401.58 ppm
3) Rise in world mean sea level:
Satellite measurements: 1993 to 2015: 3.24 mm per year (about a foot per century)
Tide gauge data: 1880-2014: 1.87 mm per year (a bit over seven inches per century)

http://climate.nasa.gov/vital-signs/

 

[Devon Fletcher]

Of course, the 'average' temperature of anything is a rather nebulous concept, and, in the case of the Earth, things like the albedo, relative temperatures, and radiated energy, are constantly changing, and vary widely across the globe.
As the atmosphere absorbs some of the radiation coming from the Sun, that energy is not all being re-radiated back to Space, but some of it hangs around, warming things up down here.
For a really comprehensive look at all this stuff, I can't recommend highly enough 'Experimenting on a small Planet', Wm. W. Hay, Published by Springer.
It's a great read, includes a comprehensive history of Science, a self-indulgent memoir, and lucid, entertaining explanations of all this climate stuff.
This may have been mentioned before. I'm new here, and haven't read all the threads... but, get it if you haven't already.

 

[Buzz Bloom]

Why not just say, "emits a photon of the identical energy level"? As you went on to note, I'm not sure how often this happens except for lowest excitation level.

HI klimatos:

Thank you for your post responding to my questions.

You suggestion "emits a photon of the identical energy level" is excellent, except that it has eight words. I think this would be inconvenient to repeat multiple times in a long discussion about the concept.and its implications. I would prefer to continue using "re-emits" with a one time additional sentence using your suggested language to explain what "re-emits" is intended to mean.

I am also not "sure" about the relative frequency of re-emits compared with the emitting a photon of a different energy than the one absorbed. I have been trying to get more information about this for some time, but it extremely difficult for me with my limited access to a technical library. My belief that CO2 IR re-emitting is quite frequent is a conclusion I came to from a brief email correspondence with a professor of atmospheric physics at MIT. As you can see from the unanswered questions I have asked in this thread about this topic, easy answers don't seem to exist.

Regards,
Buzz

 

[Buzz Bloom]

For a really comprehensive look at all this stuff, I can't recommend highly enough 'Experimenting on a small Planet', Wm. W. Hay, Published by Springer.

Hi Devon:

Thank is for the recommendation. The book is not available in my local library, nor in the inter-library network to which my local library belongs. I will request the help of my library's research librarian to get a copy for me from some other source.

Regards,
Buzz

 

[Buzz Bloom]

What you need for your argumentation is a comparison of the time to equilibrium with the rate of IR variations.

Hi DrStupid:

Thank you for responding to my post. I acquired some understanding about the non-thermal emission of IR photons by atmospheric CO2 molecules from a brief email conversation with an expert. My qualitative understanding that the time between the absorption of a IR photon by a CO2 molecule and the subsequent emission of a similar photon is very much less than the time for the molecule to interact with another molecule. I also came to understand that it is molecule-to-molecule interactions that transforms the absorbed energy from a photon into kinetic energy, and thereby to a rise in temperature of the gas.

Since that conversation I have been trying to acquire some specific quantitative information about this topic, including asking multiple questions on this topic in the Physics Forum, and so far I have been unsuccessful. Can you help me?

Regards,
Buzz

 

[Devon Fletcher]

According to Hay, the CO2 (and other) molecules can have an electron 'promoted' to a higher orbit (and therefore capable of an emission), by a photon of the appropriate ...or slightly higher...energy. The energy excess to the promotion is absorbed as translational (temperature).energy.
All these emissions occur at very specific frequencies, but with multi-atomic molecules, the number of possible appropriate photon energies are many, and, as a result can virtually blanket whole swathes of the spectrum.

Here is a graph of the various greenhouse gases and theirabsorption spectra. It is from the Wm Hay book, and is typical of the many illustrations therein.