Saturday, 9 September 2017

Questions of the greenhouse gas effect

Reblog: http://sealevel.info/Happer_UNC_2014-09-08/Another_question.html

Ref: http://www.sealevel.info/Happer_UNC_2014-09-08/


Subject: Another dumb question from Dave

From: David Burton Wed, Nov 12, 2014 at 10:48 PM
To: William Happer
Dear Prof. Happer,

At your UNC lecture you told us many things which I had not known, but two of them were these:

1. At low altitudes, the mean time between molecular collisions, through which an excited CO2 molecule can transfer its energy to another gas molecule (usually N2) is on the order of 1 nanosecond.

2. The mean decay time for an excited CO2 molecule to emit an IR photon is on the order of 1 second (a billion times as long).

Did I understand that correctly?

You didn't mention it, but I assume H2O molecules have a similar decay time to emit an IR photon. Is that right, too?

So, after a CO2 (or H2O) molecule absorbs a 15 micron IR photon, about 99.9999999% of the time it will give up its energy by collision with another gas molecule, not by re-emission of another photon. Is that true (assuming that I counted the right number of nines)?

In other words, the very widely repeated description of GHG molecules absorbing infrared photons and then re-emitting them in random directions is only correct for about one absorbed photon in a billion. True?

Here's an example from the NSF, with a lovely animated picture, which even illustrates the correct vibrational mode:

(Aside: it doesn't really shock me that the NSF is wrong -- I previously caught them contradicting Archimedes: before & after.)

If that NSF web page & illustration were right, then the amount of IR emitted by CO2 or H2O vapor in the atmosphere would depend heavily on how much IR it received and absorbed. If more IR was emitted from the ground, then more IR would be re-emitted by the CO2 and H2O molecules, back toward the ground. But I think that must be wrong.

If 99.9999999% of the IR absorbed by atmospheric CO2 is converted by molecular collisions into heat, that seems to imply that the amount of ~15 micron IR emitted by atmospheric CO2 depends only on the atmosphere's temperature (and CO2 partial pressure), not on how the air got to that temperature. Whether the ground is very cold and emits little IR, or very warm and emits lots of IR, will not affect the amount of IR emitted by the CO2 in the adjacent atmosphere (except by affecting the temperature of that air). Is that correct?

Thank you for educating a dumb old computer scientist like me!

Warmest regards,
Dave


From: William Happer Thu, Nov 13, 2014 at 11:29 AM
To: David Burton

Dear David,

Some response are entered below in square brackets and upper case.  Thanks for your interest!

Will

From:David Burton
Sent: Wednesday, November 12, 2014 10:49 PM
To: William Happer
Subject: Another dumb question from Dave

Dear Prof. Happer,

At your UNC lecture you told us many things which I had not known, but two of them were these:

1. At low altitudes, the mean time between molecular collisions, through which an excited CO2 molecule can transfer its energy to another gas molecule (usually N2) is on the order of 1 nanosecond.

2. The mean decay time for an excited CO2 molecule to emit an IR photon is on the order of 1 second (a billion times as long).

Did I understand that correctly? [YES, PRECISELY.  I ATTACH A PAPER ON RADIATIVE LIFETIMES OF CO2 FROM THE CO2 LASER COMMUNITY. YOU SHOULD LOOK AT THE BENDING-MODE TRANSITIONS, FOR EXAMPLE, 010 – 000. AS I THINK I MAY HAVE INDICATED ON SLIDE 24, THE RADIATIVE DECAY RATES FOR THE BENDING MODE ALSO DEPEND ON VIBRATION AND ROTATIONAL QUANTUM NUMBERS, AND THEY CAN BE A FEW ORDERS OF MAGNITUDE SLOWER THAN 1 S^{-1} FOR HIGHER EXCITED STATES. THIS IS BECAUSE OF SMALL MATRIX ELEMENTS FOR THE TRANSITION MOMENTS.]
 

You didn't mention it, but I assume H2O molecules have a similar decay time to emit an IR photon. Is that right, too? [YES.  I CAN'T IMMEDIATELY FIND A SIMILAR PAPER TO THE ONE I ATTACHED ABOUT CO2, BUT THESE TRANSITIONS HAVE BEEN CAREFULLY STUDIED IN CONNECTION WITH INTERSTELLAR MASERS. I ATTACH SOME NICE VIEWGRAPHS THAT SUMMARIZE THE ISSUES, A FEW OF WHICH TOUCH ON H2O, ONE OF THE IMPORTANT INTERSTELLAR MOLECULES.  ALAS, THE SLIDES DO NOT INCLUDE A TABLE OF LIFETIMES. BUT YOU SHOULD BE ABLE TO TRACK THEM DOWN FROM REFERENCES ON THE VIEWGRAPHS IF YOU LIKE. ROUGHLY SPEAKING, THE RADIATIVE LIFETIMES OF ELECTRIC DIPOLE MOMENTS SCALE AS THE CUBE OF THE WAVELENTH AND INVERSELY AS THE SQUARE OF THE ELECTRIC DIPOLE MATRIX ELEMENT (FROM BASIC QUANTUM MECHANICS) SO IF AN ATOM HAS A RADIATIVE LIFETIME OF 16 NSEC AT A WAVELENGTH OF 0.6 MIRONS (SODIUM), A CO2 BENDING MODE TRANSITION, WITH A WAVELENGTH OF 15 MICRONS AND ABOUT 1/30 THE MATRIX ELEMENT SHOULD HAVE A LIFETIME OF ORDER 16 (30)^2 (15/.6)^3 NS = 0.2 S.
 

So, after a CO2 (or H2O) molecule absorbs a 15 micron IR photon, about 99.9999999% of the time it will give up its energy by collision with another gas molecule, not by re-emission of another photon. Is that true (assuming that I counted the right number of nines)? [YES, ABSOLUTELY.]


In other words, the very widely repeated description of GHG molecules absorbing infrared photons and then re-emitting them in random directions is only correct for about one absorbed photon in a billion. True? [YES, IT IS THIS EXTREME SLOWNESS OF RADIATIVE DECAY RATES THAT ALLOWS THE CO2 MOLECULES IN THE ATMOSPHERE TO HAVE VERY NEARLY THE SAME VIBRATION-ROTATION TEMPERATURE OF THE LOCAL AIR MOLECULES.]
 

Here's an example from the NSF, with a lovely animated picture, which even illustrates the correct vibrational mode:

 
Am I correct in thinking that illustration is wrong for about 99.9999999% of the photons which CO2 absorbs in the lower troposphere? [YES, THE PICTURE IS A BIT MISLEADING. IF THE CO2 MOLECULE IN AIR ABSORBS A RESONANT PHOTON, IT IS MUCH MORE LIKELY ( ON THE ORDER OF A BILLION TIMES MORE LIKELY) TO HEAT THE SURROUNDING AIR MOLECULES WITH THE ENERGY IT ACQUIRED FROM THE ABSORBED PHOTON, THAN TO RERADIATE A PHOTON AT THE SAME OR SOME DIFFERENT FREQUENCY.  IF THE CO2 MOLECULE COULD RADIATE COMPLETELY WITH NO COLLISIONAL INTERRUPTIONS, THE LENGTH OF THE RADIATIVE PULSE WOULD BE THE DISTANCE LIGHT CAN TRAVEL IN THE RADIATIVE LIFETIME. SO THE PULSE IN THE NSF FIGURE SHOULD BE 300,000 KM LONG, FROM THE EARTH'S SURFACE TO WELL BEYOND A SATELLITE IN GEOSYNCHRONOUS ORBIT. THE RADIATED PULSE SHOULD CONTAIN 667 CM^{-1} *3 X 10^{10} CM S^{-1}*1 S  WAVES OR ABOUT 2 TRILLION WAVES, NOT JUST A FEW AS IN THE FIGURE.  A BIT OF POETIC LICENSE IS OK.  I CERTAINLY PLEAD GUILTY TO USING SOME ON MY VIEWGRAPHS. BUT WE SHOULD NOT MAKE TRILLION-DOLLAR ECONOMIC DECISIONS WITHOUT MORE QUANTITATIVE CONSIDERATION OF THE PHYSICS.]
 

(Aside: it doesn't really shock me that the NSF is wrong -- I previously caught them contradicting Archimedes: before & after.)

If that NSF web page & illustration were right, then the amount of IR emitted by CO2 or H2O vapor in the atmosphere would depend heavily on how much IR it received and absorbed. If more IR was emitted from the ground, then more IR would be re-emitted by the CO2 and H2O molecules, back toward the ground. But I think that must be wrong.[YES, THE AMOUNT OF RADIATION EMITTED BY GREENHOUSE MOLECULES DEPENDS ALMOST ENTIRELY ON THEIR TEMPERATURE. THE PERTRUBATION BY RADIATION COMING FROM THE GROUND OR OUTER SPACE IS NEGLIGIBLE.  CO2 LASER BUILDERS GO OUT OF THEIR WAY WITH CUNNING DISCHARE PHYSICS TO GET THE CO2 MOLECULES OUT OF THERMAL EQUILIBRIUM SO THEY CAN AMPLIFY RADIATION.]
 

If 99.9999999% of the IR absorbed by atmospheric CO2 is converted by molecular collisions into heat, that seems to imply that the amount of ~15 micron IR emitted by atmospheric CO2 depends only on the atmosphere's temperature (and CO2 partial pressure), not on how the air got to that temperature. [YES, I COULD HAVE SAVED A COMMENT BY READING FURTHER.] Whether the ground is very cold and emits little IR, or very warm and emits lots of IR, will not affect the amount of IR emitted by the CO2 in the adjacent atmosphere (except by affecting the temperature of that air). Is that correct? [YES, PRECISELY.  WE HAVE BEEN TALKING ABOUT WHAT CHANDRASEKHAR CALLS AN “ABSORBING ATMOSPHERE” AS OPPOSED TO A “SCATTERING ATMOSPHERE.”  ASTROPHYSICISTS ARE OFTEN MORE INTERESTED IN SCATTERING ATMOSPHERES, LIKE THE INTERIOR OF THE SUN. THE BLUE SKY DURING A CLEAR DAY IS AN EXAMPLE OF SCATTERING ATMOSPHERE.  VERY LITTLE HEATING OR COOLING OF THE AIR OCCURS WITH THIS “RAYLEIGH SCATTERING.”]


Thank you for educating a dumb old computer scientist like me! [YOU ARE HARDLY DUMB.  YOU GET AN A+ FOR THIS RECITATION SESSION ON RADIATIVE TRANSFER. ]


2 attachments
Statz67-lifetimes.pdf  2090K
H2O-masers.pdf  396K

From: David Burton Thu, Nov 13, 2014 at 11:46 AM
To: William Happer
Wow, thank you very much, Prof. Happer!

I feel like I've just gotten a taste of Princeton education, for free.  You are very, very generous with your time, and I am very grateful.

Warmest regards,
Dave
[...snip...]


From: David Burton Thu, Nov 13, 2014 at 12:53 PM
To: T
Dear T,

I think you will find the discussion below very interesting. Prof. Wm. Happer is one of the world's top experts on CO2's emission and absorption of radiation. He's a colleague of America's most illustrious living scientist, Prof. Freeman Dyson. Prof. Happer's reply to me is in [BLUE] below.

Note that the NSF has got it wrong (again)!

Here's an audio recording + powerpoint of Prof. Happer's lecture at UNC, which prompted this discussion:
Sorry, there was no video recording made, but you can view the powerpoint slides while listening to the audio, which is almost as good.

Warmest regards,
Dave
[...snip...]


From: T Thu, Nov 13, 2014 at 1:03 PM
To: David Burton
Dave,

That is interesting, but not sure what the significance is to the discussion.

If greenhouse gases warm the atmosphere due to absorption of photons, and emission is dependent only on temperature, isn't the net effect the same? A warmer atmosphere emits more LW radiation.
[...snip...]


From: David Burton Thu, Nov 13, 2014 at 1:31 PM
To: T
Hi T,

To me it is interesting for three reasons:

1. It means that the amount of LW IR which is emitted by the CO2 & H2O in the atmosphere, and absorbed by the ground, is independent of the amount of IR emitted by the ground (except that warm ground helps warm the air, through both IR emissions & convection, and the temperature of the air controls the amount of IR that it emits).

2. It means the common description of IR being emitted by the ground, absorbed by the CO2 & H2O vapor, and re-emitted (in a random direction) -- i.e., what the NSF describes -- is wrong.

3. It means my own understanding of how the GH effect works was wrong.

I don't like being wrong. It is uncomfortable. But I like learning, and I learned something new!

Warmest regards,
Dave
[...snip...]


From: T Thu, Nov 13, 2014 at 1:46 PM
To: David Burton
Dave,

I'm not sure that functionally there is any difference. If the ground emits more LW, the atmosphere warms and responds by emitting more LW. So they aren't independent.  That is why the air warms during a sunny day, because of increased IR emissions from the ground.
[...snip...]


From: David Burton Thu, Nov 13, 2014 at 1:56 PM
To: T
T,

The way the NSF describes it (and the way I mistakenly thought it worked), the amount of IR which the ground absorbs from the atmosphere depends almost entirely on the amount of IR which the ground emits. It might not be the very same photons, but it might as well be: the photons the ground receives are just a fraction of those which it emits. But that's wrong.

The reality is that the amount of IR the ground absorbs from the atmosphere depends almost entirely on the air temperature & composition, and not at all on the amount of IR which the ground emits.

The two aren't completely independent, because IR emissions from the ground do affect the air temperature, which, in turn, affects the IR emissions from the air, but the linkage is weak, because other factors (like convective heat transfer) affect air temperature more.

Dave
[...snip...]


From: Robert G. Brown Thu, Nov 13, 2014 at 5:29 PM
To: David Burton
On Thu, 13 Nov 2014, David Burton wrote:

Dear Prof. Brown,
I think you might find the discussion below interesting. Prof. Happer's
reply to me is in [BLUE] below.

Yeah, I already know most of that stuff, and I'm pretty sure I have his
powerpoint presentation slides as well. I wasn't aware that there were
levels with lifetimes as long as 1 second -- that's actually pretty long
as atomic/molecular lifetimes go -- but those particular levels are then
going to be very sharp and not terribly responsive to non-resonant IR.
Either way, CO_2 doesn't "scatter" LWIR radiation, it absorbs it
(typically within a few meters, the mean free path at atmospheric
concentrations) and the energy is almost instantly transferred to the
surrounding air.

That doesn't mean that they don't radiate. It just means that their
radiation temperature is in equilibrium in the surrounding air, and it
isn't reradiating of a photon it absorbed, it is radiation initiated by
e.g. a collision with an air molecule.

That's why the greenhouse effect is basically logarithmic at this point.
It is long ago and overwhelmingly saturated. The atmosphere is
basically totally opaque in the CO_2 aborptive bands from sea level up
to maybe 8 or 9 km. Somewhere up there, where the air is much colder,
the molecules get far enough apart that LWIR emitted from the colder air
have a good chance of escaping without being reabsorbed. Increasing
CO_2 basically causes a very small variation of the average height and
-- due to the adiabatic lapse rate, which has little that is directly
due to the GHE itself -- therefore the temperature at which the
atmosphere becomes effectively transparent. The rate at which the
energy in this band emerges from the atmosphere is hence much less than
the rate at which it was originally emitted at the surface in this band.
Given constant average SWV (visible) delivery of radiation into the
system from the Sun, the ground temperature has to warm a tiny bit in
order to compensate for the loss of outgoing power in the CO_2 band.

Here is a curve indicating just how much explanatory power CO_2 has as
far as the temperatures over the last 164 years are concerned. Quite a
lot, actually. Happer might be interested in this curve. I think he
passed on the reference to Wilson and Gea-Banacloche in AJP (2012) which
reviews the CO_2-only no-feedback GHE and ends up concluding that the
no-feedback total climate sensitivity on doubling CO_2 ought to be
around 0.9 to 1.1C. I get an excellent fit to all of HadCRUT4 with TCS
around 1.8C,

If I add an entirely heuristic (but obvious) harmonic correction to the
fit to account for the 67 year whatever is causing the systematic
variation, the fit is even better, but the direct fit to the physically
motivated log only has enormous statistical explanatory power with a
residual standard error of 0.1 on 163 degrees of freedom and only two
fit parameters, one of which does nothing but line up the (arbitrary)
scale of the anomaly with that of the fit. There is, in fact, almost
nothing left to explain but noise and the harmonic term. Hard to see
why we need to bother with the world's most expensive, difficult,
chaotic, nonlinear, horribly underresolved models at all, if they cannot
beat a one parameter physically motivated radiative model that ignores
everything but CO_2.
 
rgb
[...snip...]
 
Robert G. Brown http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567 Fax: 919-660-2525


2 attachments
Toft-CO2-PDO.eps  108K
(or converted by ZamZar to Toft-CO2-PDO.png 202K)
Toft-CO2-vs-MME.eps  58K
(or converted by ZamZar to Toft-CO2-vs-MME.png 226K)

From: David Burton Tue, Jan 20, 2015 at 11:52 PM
To: William Happer
Dear Prof. Happer,

I just stumbled across someone else discussing the same topic, and he came to a "similar" conclusion, sort of. Dr. Joshua Halpern, who blogs under the pen name of Eli Rabett, calculated that 1 in 10^5 rather than 1 in 10^9 IR-stimulated CO2 molecules will give up that energy by re-emisison of an IR photon, rather than collision with another air molecule. He gets about the same radiative lifetime as you, but a collisional lifetime of about 10 microseconds rather than one nanosecond.

A difference of four orders of magnitude suggests to me that he goofed, but I don't understand this well enough to understand how. Here's the article:

Warmest regards,
Dave
[...snip...]
 

From: William Happer Wed, Jan 21, 2015 at 10:05 AM
To: David Burton

Dear David,

Thanks for bringing this to my attention. Measurements show a broadening of order B = 0.1 cm^{-1} = 3 GHz for CO2 lines at 1 atmosphere and 300 K. For example, see Fig. 1 of the attached paper. This would imply a "time between collisions" of t = 1/(2*pi*B) = 50 ps = .05 ns.

The "about a nanosecond" I mentioned was an estimate of the lifetime for velocity changing collisions that go in to the spatial diffusion coefficient. Here are typical numbers:

Density of air molecules at ground level = Loschmidt's number = N = 2.69 x 10 {19} cm^{-3}

Kinetic cross section = sig = pi*(10^{-8})^2 =3.14 x 10^{-16} cm^{2}

Mean relative velocity (roughly sound speed in air) = v = 3.43 x 10^{4} cm s^{-1}

Lifetime = 1/(N*v*sig) = 3.45 ns

On a quick read of Joshua's reference he seems to have assumed that only other CO2 molecules in the air cause deexcitation, but not N2 and O2 molecules. It is true that the "self-quenching" rates for CO2-CO2 collisions are much larger, typically a factor of 10 if my memory serves, than the rates for CO2-N2 collisions, but there are thousands of times more N2 and O2 molecules so they dominate the deexcitation.

I will try to be more careful in my wording in the future. I appreciate the feedback and I hope you will keep it coming.

Will


1 attachment
Rothman-etal92.pdf  2481K

 

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