The area under the graph is growing slowly for each doubling.... therefore, the relationship is logarithmic.
Yes, but this is a graph of absorption, not temperature.
===
About the,
Originally Posted By: samwik
Exactly, as evidenced by the spectrum showing that very little is escaping into space anymore.
Anymore? Are you suggesting that this recently changed?"
...asked from your last post:
Think of the shape of the top of the (CO2 + water) peak that is cut off. It's a very ragged peak. Some of the valleys from that "ragged peak" are visible in your close-up of 15 microns (post #26570, "fig.3"). If this was lowered (lower concentration, i.e. 285 ppm), wouldn't there be some valleys (windows) opening wider, as the bottom of other valleys came into view?
===
...but back to the mechanism of heating.
That CO2 is effective at trapping IR heat quickly, over short distances (logarithmically, to extinction), only means that it is a better greenhouse gas than any gas that has a lower extinction coefficient.
The extinction coefficient doesn't mean that 'it can't absorb any more heat' (which is what some blogger has interpreted), but refers to how quickly a gas absorbs energy (in this case, IR heat). If it were "heated to extinction" with heat, and couldn't absorb more heat, then we'd be seeing some heat escape into space at that wavelength; but the graph shows that's not happening (anymore).
[next week: saturation....]
John, you said "I used Motl's formula (that he describes as a popular one for CO2) in my 26570 comment above."
[Here is a link to a physicist that discusses the relationship between CO2 and temperature as logathrimic.
Using his Temperature = Temperature0 + ln(1 + 1.2 x + 0.005 x2 + 0.0000014 x3) formula, I made the following spreadsheet:
This link was to Gary Novak, notable as a climatologically inclined "mushroom scientist."
Someone can't just take a formula for determining the Extinction Coefficient [Absorption = Absorption0 + ln(1 + 1.2 x + 0.005 x2 + 0.0000014 x3) ] and substitute "Temp." into the equation, in place of Absorption.
That is all someone [Motl or whomever] has done here.
There is no "logarithmic relationship for CO2 and temperature," except in the mind of some blogger, and those who have picked it up as a scientific-sounding fact.
Considering the logarithmic relationship for CO2 and temperature, I currently don't see how that is possible
I can see that you "currently" think this is a fact; but that is the very point we're debating here: Is the extinction coefficient (which has a well-established logarithmic relation to concentration), proportional to the temperature change?
The only thing I learned from that Gary Novak link was that "Steve McIntyre at climateaudit.org is trying to locate the provenance ;-) of the logarithmic formula [relating Temp. & concentration]...."
Gee, it oughta be in any chemical reference book, (Merck's CRC perhaps?) if it's not just a made up "formula."
I can understand how someone could hear that the absorption of IR is logarithmic and think that must apply to the heating also, but it just refers to how quickly IR heat is absorbed (or over what distance) at a given concentration.
But....
Absorption of IR quanta is a quantum process, and can be described by an equation containing 2nd, 3rd, 4th, etc.... order terms; leading to the logarithmic expression. There are some hints of what is involved in describing this process on the "climate surfings" link:
http://209.85.173.104/search?q=cache:2vN5elQF66wJ:www.hthpweb.com/hthp/fulltext/h34/htwu309.pdf+%22extinction+coefficient%22+%22heat+capacity%22&hl=en&ct=clnk&cd=20&gl=us
.... "The second and third terms characterise the increase of 'I' due to isotropic scattering and re-emission, respectively."
.... "A considerable fraction of photons can pass through the sample without being multiply scattered or absorbed, which causes a direct radiative exchange between the surfaces. Therefore, besides the conductive heat transfer, the radiative heat transfer and the interaction of both transfer channels have to be considered, too."
... "In the case of a cold sample the re-emission term in equation (3) vanishes and there is no interaction of radiation with other heat transfer modes. The part of the incoming radiation flux F which reaches the point t within the sample is described by an additional source term...."
...meanwhile....
Heating, via collisions, is a Newtonian process, and is described by simple linear equations; and so is directly proportional to concentration.
.
.
.
I wonder what the chances are of a CO2 molecule radiating its heat to either a water, space, or another CO2 molecule before it runs into either an oxygen (20.9463%), argon (0.93422%), or nitrogen (78.0842%) molecule and loses some of its energy.
Probably fairly low. Most likely, excited CO2 will collide with O2 or N2 as it "loses some of its energy." You've just described the mechanism that is defined as
heating of the atmosphere.
&
For the few heat quanta that are transferred to another CO2, or water, those also eventually are translated into heat, via collisions with the more abundant atmospheric gases, as you've suggested.
Thanks again,
