Saturday, April 02, 2016

It's the Number Density Not the Mixing Ratio


If Eli had a unit in any devalued paper currency for each time some fool uttered

even when they get it right,
he would be swimming in carrots.

However, this being Rabett Run, Eli would like to show the bunnies a way of dealing with this.

There is a cute little number called Loschmidt, the number of molecules in a cubic meter of air at 1 atm and 0 oC, 2.686 7774(47) x 1025 molecules/m3

CO2 is now at 400 ppm, so the number of CO2 molecule in a cubic meter of air is 1.07 x 1022 CO2 molecules/mat the surface.

The average volume occupied by each CO2 molecule is just the inverse or ~9.30  x 10-23 m

The spacing between CO2 molecules will be of the order of the cube root  ~4.5 x 10-8 m or 0.045 microns.  Anybunny who wants can model this as a sphere rather than a cube.  4/3 π: to you

The wavelength of a photon that is absorbed by a CO2 molecule in the bending vibrational band is 15 microns,

Comparing the two the wavelength of the photon is about 330 times larger than the average spacing between CO2 molecules in air.

Not every CO2 molecule is going to absorb that photon, but there are an awful lot of CO2 molecules that can.

On average a 15 micron photon at the surface will travel a couple of meters before it is absorbed,

14 comments:

Sou said...

Thanks for this Eli. I'd occasionally wondered about this but never put my mind to it. Will probably quote lots.

Tom Curtis said...

Bear in mind that the Galileo Movement in Australia (Dragon Slayers to the last man) started with just this calculation. They then argue that:
1) Clearly the CO2 effect is saturated;
2) As a result heat is not taken to the top of the atmosphere by radiation, but by convection; and
3) The only practical effect of CO2 is to cool the top of the atmosphere by radiation to space, thereby cooling the Earth.

Wonderful non-sequiturs all, and the basis of my fairly constant mantra that most AGW denial starts from the determined misunderstanding of how the greenhouse effect works.

I bring this up just so you know what bus you might be walking into.

Russell Seitz said...

Thanks for confirming Tyndall , who used a ~ ten foot pipe full of CO2 for his Victrian demo of heat-blocking by a gas.

Hank Roberts said...

Thank you Eli, for the numbers.

So throwing an infrared photon into the outer dark is like throwing a bolo through a picket fence ....

> Galileo ... Slayers
Refute them thus: https://www.aip.org/history/climate/co2.htm

" The logic is rather simple once it is grasped, but it takes a new way of looking at the atmosphere — not as a single slab, like the gas in Koch's tube (or the glass over a greenhouse), but as a set of interacting layers...."

Barton Paul Levenson said...

May I recommend:

http://bartonlevenson.com/Saturation.html

Chase Stoudt said...

I have a legitimate science question (or at least I hope so) that has probably already been covered in the literature, at what altitude is the CO2 greenhouse effect the strongest? I know it's not at the top because lack of atmosphere and not at the bottom because it's had all the chances to be absorbed. I assume it depends on the air column makeup, and that gcms take this into account in some way? The radiative transfer codes?

Brandon R. Gates said...

Chase Stoudt,

I know it's not at the top because lack of atmosphere and not at the bottom because it's had all the chances to be absorbed.

That sounds like the saturation argument in disguise. It's CO2s all the way down. Figure from Wu and Liu (2010), A new one-dimensional radiative equilibrium model for investigating atmospheric radiation entropy flux.

I get similar results from a free version of MODTRAN hosted by U. of Chicago.

Brandon R. Gates said...

Chase, PS:

I should note that the real troposphere is more complicated. Image from Grant Petty (2006). Science of Doom explains in more detail.

Chase Stoudt said...

Brandon, thanks. I knew it was more complicated than the simple model I had in my head. SOD and Petty pretty much answered the question I hadn't really thought out. I didn't realize that most of the atmosphere is cooling via longwave except for the top of the tropical tropopause (duh, you have to balance out the absorbed short wave somehow). I think the first sentence in the last paragraph of Wu said it for me

"It is noteworthy that the results obtained from this study reveal that the atmospheric net radiation entropy flux at all altitudes is intrinsically connected with the overall atmospheric LW optical depth, which further implies the sensitivity of the atmospheric net entropy flux (or production rate) to greenhouse gases (i.e. increased overall atmospheric LW optical depth)"

Or as you put it, "CO2's all the way down".

Hank Roberts said...

Perhaps you followed the fun over at
http://hannahlab.org/climate-skeptics-peter-wards-ozone-depletion-theory/#comment-12440
(comments there now closed, so no need to get all wound up reading from the top)

I did wonder if Eli had ever commented on the Bill Nye experiment mentioned therein, and the WTF critique of that experiment that PLW found so convincing?

If so, bump it to where Google can find it by searching, eh?

(It would seem unlikely any comments will make emeritus geophysicist P.L. Ward doubt his revision of quantum physics. Be nice.)

EliRabett said...

HAnk,

Eli hates you for not letting him know when that nonsense was live.

Eli

Hank Roberts said...

Hm. How about a water molecule, at whatever altitude?

This is getting banged around various places (quote from NotWithABang)


http://scienceblogs.com/startswithabang/2016/04/09/comments-of-the-week-105-from-the-movie-gravity-to-the-most-astounding-fact/

-----excerpt follows-----
Q: "... statements made by Dr Roy Spencer of UAH, John Cook of Skeptical Science, and Carl Mears of RSS all acknowledging the falling humidity, its impact, and the collective failure of the climate science community to definitively explain it.
It is important because all of the climate models require a positive water vapor feedback to create their predicted warming signal. The predictions are all high largely because water vapor is stubbornly refusing to cooperate.”

A: "This is potentially important, and potentially a game-changer, depending on how things turn out. There is a not-necessarily-crazy theory that as CO2 rises, the amount of water vapor in the atmosphere — something which varies tremendously, is a strong greenhouse gas and is of order ~1% of our atmosphere (rather than being measured in hundreds of ppm like CO2) — falls. Falling humidity is an observed correlation with rising CO2, and so, the argument goes, water vapor may fall as well. This is potentially important, potentially interesting, and would represent a new line of inquiry in the field of climate science...."

-------end excerpt------

Hank Roberts said...

Oh, sorry about my untimely question, I only came across that one a few days before I asked you about it. I do try to be prompt reporting my puzzlements.

Hank Roberts said...

Er, I mean, the Bill Nye one.
The Peter L. Ward thread (where Bill Nye was mentioned) -- well, guilty. It closed quickly, but the host invited email if one has further thoughts.

I'd mentioned it in a comment at Stoat, I'll give you the next one.
Or did I already?