Guest post By Tom Vonk (Tom is a physicist and long time poster at many climate blogs. Note also I’ll have another essay coming soon supporting the role of CO2 – For a another view on the CO2 issue, please see also this guest post by Ferdinand Engelbeen Anthony)
If you search for “greenhouse effect” in Google and get 1 cent for statements like…
“CO2 absorbs the outgoing infrared energy and warms the atmosphere” – or – “CO2 traps part of the infrared radiation between ground and the upper part of the atmosphere”
…you will be millionaire .
Even Internet sites that are said to have a good scientific level like “Science of doom” publish statements similar to those quoted above . These statements are all wrong yet happen so often that I submitted this guest post to Anthony to clear this issue once for all.
In the case that somebody asks why there is no peer reviewed paper about this issue , it is because everything what follows is textbook material . We will use results from statistical thermodynamics and quantum mechanics that have been known for some 100 years or more . More specifically the statement that we will prove is :
“A volume of gas in Local Thermodynamic Equilibrium (LTE) cannot be heated by CO2.”
There are 3 concepts that we will introduce below and that are necessary to the understanding .
- The Local Thermodynamic Equilibrium (LTE)
This concept plays a central part so some words of definition . First what LTE is not . LTE is not Thermodynamic Equilibrium (TE) , it is a much weaker assumption . LTE requires only that the equilibrium exists in some neighborhood of every point . For example the temperature may vary with time and space within a volume so that this volume is not in a Thermodynamic Equilibrium . However if there is an equilibrium within every small subvolume of this volume , we will have LTE .
Intuitively the notion of LTE is linked to the speed with which the particles move and to their density . If the particle stays long enough in a small volume to interact with other particles in this small volume , for example by collisions , then the particle will equilibrate with others . If it doesn’t stay long enough then it can’t equilibrate with others and there is no LTE .
There are 2 reasons why the importance of LTE is paramount .
First is that a temperature cannot be defined for a volume which is not in LTE . That is easy to understand . The temperature is an average energy of a small volume in equilibrium . Since there is no equilibrium in any small volume if we have not LTE , the temperature cannot be defined in this case.
Second is that the energy distribution in a volume in LTE follows known laws and can be computed .
The energy equipartition law
Kinetic energy is present in several forms . A monoatomic gas has only the translational kinetic energy , the well known ½.m.V² . A polyatomic gas can also vibrate and rotate and therefore has in addition to the translational kinetic energy also the vibrational and the rotational kinetic energy . When we want to specify the total kinetic energy of a molecule , we need to account for all 3 forms of it .
Thus the immediate question we ask is : “If we add energy to a molecule , what will it do ? Increase its velocity ? Increase its vibration ? Increase its rotation ? Some mixture of all 3 ?”
The answer is given by the energy equipartition law . It says : “In LTE the energy is shared equally among its different forms .”
As we have seen that the temperature is an average energy ,and that it is defined only under LTE conditions , it is possible to link the average kinetic energy <E> to the temperature . For instance in a monoatomic gas like Helium we have <E>= 3/2.k.T . The factor 3/2 comes because there are 3 translational degrees of freedom (3 space dimensions) and it can be reformulated by saying that the kinetic energy per translational degree of freedom is ½.k.T . From there can be derived ideal gas laws , specific heat capacities and much more . For polyatomic molecules exhibiting vibration and rotation the calculations are more complicated . The important point in this statistical law is that if we add some energy to a great number of molecules , this energy will be shared equally among their translational , rotational and vibrational degrees of freedom .
Quantum mechanical interactions of molecules with infrared radiation
Everything that happens in the interaction between a molecule and the infrared radiation is governed by quantum mechanics . Therefore the processes cannot be understood without at least the basics of the QM theory .
The most important point is that only the vibration and rotation modes of a molecule can interact with the infrared radiation . In addition this interaction will take place only if the molecule presents a non zero dipolar momentum . As a non zero dipolar momentum implies some asymmetry in the distribution of the electrical charges , it is specially important in non symmetric molecules . For instance the nitrogen N-N molecule is symmetrical and has no permanent dipolar momentum .
O=C=O is also symmetrical and has no permanent dipolar momentum . C=O is non symmetrical and has a permanent dipolar momentum . However to interact with IR it is not necessary that the dipolar momentum be permanent . While O=C=O has no permanent dipolar momentum , it has vibrational modes where an asymmetry appears and it is those modes that will absorb and emit IR . Also nitrogen N-N colliding with another molecule will be deformed and acquire a transient dipolar momentum which will allow it to absorb and emit IR .
In the picture left you see the 4 possible vibration modes of CO2 . The first one is symmetrical and therefore displays no dipolar momentum and doesn’t interact with IR . The second and the third look similar and have a dipolar momentum . It is these both that represent the famous 15µ band . The fourth is highly asymmetrical and also has a dipolar momentum .
What does interaction between a vibration mode and IR mean ?
The vibrational energies are quantified , that means that they can only take some discrete values . In the picture above is shown what happens when a molecule meets a photon whose energy (h.ν or ђ.ω) is exactly equal to the difference between 2 energy levels E2-E1 . The molecule absorbs the photon and “jumps up” from E1 to E2 . Of course the opposite process exists too – a molecule in the energy level E2 can “jump down” from E2 to E1 and emit a photon of energy E2-E1 .
But that is not everything that happens . What also happens are collisions and during collisions all following processes are possible .
- Translation-translation interaction . This is your usual billiard ball collision .
- Translation-vibration interaction . Here energy is exchanged between the vibration modes and the translation modes .
- Translation-rotation interaction . Here energy is is exchanged between the rotation modes and the translation modes .
- Rotation-vibration interaction … etc .
In the matter that concerns us here , namely a mixture of CO2 and N2 under infrared radiation only 2 processes are important : translation-translation and translation-vibration . We will therefore neglect all other processes without loosing generality .
The proof of our statement
The translation-translation process (sphere collision) has been well understood since more than 100 years . It can be studied by semi-classical statistical mechanics and the result is that the velocities of molecules (translational kinetic energy) within a volume of gas in equilibrium are distributed according to the Maxwell-Boltzmann distribution . As this distribution is invariant for a constant temperature , there are no net energy transfers and we do not need to further analyze this process .
The 2 processes of interest are the following :
CO2 + γ → CO2* (1)
This reads “a CO2 molecule absorbs an infrared photon γ and goes to a vibrationally excited state CO2*”
CO2* + N2 → CO2 + N2⁺ (2)
This reads “a vibrationally excited CO2 molecule CO2* collides with an N2 molecule and relaxes to a lower vibrational energy state CO2 while the N2 molecule increases its velocity to N2⁺ “. We use a different symbol * and ⁺ for the excited states to differentiate the energy modes – vibrational (*) for CO2 and translational (⁺) for N2 . In other words , there is transfer between vibrational and translational degrees of freedom in the process (2) . This process in non equilibrium conditions is sometimes called thermalization .
The microscopical process (2) is described by time symmetrical equations . All mechanical and electromagnetical interactions are governed by equations invariant under time reversal . This is not true for electroweak interactions but they play no role in the process (2) .
Again in simple words , it means that if the process (2) happens then the time symmetrical process , namely CO2 + N2⁺ → CO2* + N2 , happens too . Indeed this time reversed process where fast (e.g hot) N2 molecules slow down and excite vibrationally CO2 molecules is what makes an N2/CO2 laser work. Therefore the right way to write the process (2) is the following .
CO2* + N2 ↔ CO2 + N2⁺ (3)
Where the use of the double arrow ↔ instad of the simple arrow → is telling us that this process goes in both directions . Now the most important question is “What are the rates of the → and the ← processes ?”
The LTE conditions with the energy equipartition law give immediately the answer : “These rates are exactly equal .” This means that for every collision where a vibrationally excited CO2* transfers energy to N2 , there is a collision where N2⁺ transfers the same energy to CO2 and excites it vibrationally . There is no net energy transfer from CO2 to N2 through the vibration-translation interaction .
As we have seen that CO2 cannot transfer energy to N2 through the translation-translation process either , there is no net energy transfer (e.g “heating”) from CO2 to N2 what proves our statement .
This has an interesting corollary for the process (1) , IR absorption by CO2 molecules . We know that in equilibrium the distribution of the vibrational quantum states (e.g how many molecules are in a state with energy Ei) is invariant and depends only on temperature . For example only about 5 % of CO2 molecules are in a vibrationally excited state at room temperatures , 95 % are in the ground state .
Therefore in order to maintain the number of vibrationally excited molecules constant , every time a CO2 molecule absorbs an infrared photon and excites vibrationally , it is necessary that another CO2 molecule relaxes by going to a lower energy state . As we have seen above that this relaxation cannot happen through collisions with N2 because no net energy transfer is permitted , only the process (1) is available . Indeed the right way to write the process (1) is also :
CO2 + γ ↔ CO2* (1)
Where the use of the double arrow shows that the absorption process (→) happens at the same time as the emission process (←) . Because the number of excited molecules in a small volume in LTE must stay constant , follows that both processes emission/absorption must balance . In other words CO2 which absorbs strongly the 15µ IR , will emit strongly almost exactly as much 15 µ radiation as it absorbs . This is independent of the CO2 concentrations and of the intensity of IR radiation .
For those who prefer experimental proofs to theoretical arguments , here is a simple experiment demonstrating the above statements . Let us consider a hollow sphere at 15°C filled with air . You install an IR detector on the surface of the cavity . This is equivalent to the atmosphere during the night . The cavity will emit IR according to a black body law . Some frequencies of this BB radiation will be absorbed by the vibration modes of the CO2 molecules present in the air . What you will observe is :
- The detector shows that the cavity absorbs the same power on 15µ as it emits
- The temperature of the air stays at 15°C and more specifically the N2 and O2 do not heat
These observations demonstrate as expected that CO2 emits the same power as it absorbs and that there is no net energy transfer between the vibrational modes of CO2 and the translational modes of N2 and O2 . If you double the CO2 concentration or make the temperature vary , the observations stay identical showing that the conclusions we made are independent of temperatures and CO2 concentrations .
Conclusion and caveats
The main point is that every time you hear or read that “CO2 heats the atmosphere” , that “energy is trapped by CO2” , that “energy is stored by green house gases” and similar statements , you may be sure that this source is not to be trusted for information about radiation questions .
Caveat 1
The statement we proved cannot be interpreted as “CO2 has no impact on the dynamics of the Earth-atmosphere system” . What we have proven is that the CO2 cannot heat the atmosphere in the bulk but the whole system cannot be reduced to the bulk of the atmosphere . Indeed there are 2 interfaces – the void on one side and the surface of the Earth on the other side . Neither the former nor the latter is in LTE and the arguments we used are not valid . The dynamics of the system are governed by the lapse rate which is “anchored” to the ground and whose variations are dependent not only on convection , latent heat changes and conduction but also radiative transfer . The concentrations of CO2 (and H2O) play a role in this dynamics but it is not the purpose of this post to examine these much more complex and not well understood aspects .
Caveat 2
You will sometimes read or hear that “the CO2 has not the time to emit IR because the relaxation time is much longer than the mean time between collisions .” We know now that this conclusion is clearly wrong but looks like common sense if one accepts the premises which are true . Where is the problem ?
Well as the collisions are dominating , the CO2 will indeed often relax by a collision process . But with the same token it will also often excite by a collision process . And both processes will happen with an equal rate in LTE as we have seen . As for the emission , we are talking typically about 10ⁿ molecules with n of the order of 20 . Even if the average emission time is longer than the time between collisions , there is still a huge number of excited molecules who had not the opportunity to relax collisionally and who will emit . Not surprisingly this is also what experience shows .
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Thanks to Jeff for finding the hole in this argument and debunking the seemingly illogical conclusion in a more recent blog entry. I guess it was Tom who got tied up in the theoretical intricacies and neglected the check the conclusions against common sense. I’m glad it wasn’t me, but next time it might just as well be me.
“”” Chris de Freitas says:
August 5, 2010 at 5:49 pm
The focus is on the gas (CO2) rather than on the radiation budget. The greenhouse gases affect the allwave radiation budget of the Earth’s surface as well as the allwave radiation budget of the atmosphere. For the Earth as a whole and on average, the atmosphere is in radiation deficit, whereas there is a surplus at the surface. Surface-to-atmosphere sensible and latent heat fluxes bring about equilibrium. If there is an increase in CO2, say, the surface-atmosphere budget changes. We get a higher air temperature (i.e. by increased sensible heat flux) and increase in evapotranspiration (i.e. increased latent heat flux). “””
Nice to see your post here Dr de Freitas to give some of your insights. Particularly to remind us of the other transport mechanisms such as Latent Heat.
I’m always aware that evaporative and convective cooling near the surface is contributing to the heating of the atmosphere; but do tend to push it aside, to concentrate on what the purely EM radiative effects are.
Trenberth’s energy budget schematic appears to claim a quite assymmetrical atmospheric radiation distribution; since he gives an outgoing longwave flux of 235 W/m^2 of which 40 W/m^2 is actually a direct path from the surface; not an atmospheric radiation. But he has 324 W/m^2 “back radiation” from the atmosphere to the ground, which is hugely in excess of the 195 W/m^2 outgoing from the atmosphere.
It would seem that any layer of the atmosphere should be emitting isotropically, so that the downward and outgoing amounts are about equal. After that; my back of the envelope thinking is that the outgoing escape path should be favored over the back radiation downward path; because both the Temperature lapse rate and the density gradient should lead to a narrowing of the GHG absorption lines at increased altitude; but broadening of those lines for lower layers. So upper layers should allow more wavelenghts to escape the GHG traps, while the downward radiation has to run the gauntlet of an increasingly widening blockage, leading to a greater probablility of recapture going down than going up.
So I would expect more than 50% of the total atmospheric Radiation to escape, and less than 50% to return to the surface; which is totally at odds with Trenberth’s schematic.
If you have a simple answer to this quandrary, It would be nice to know where the truth lies. Trenberth’s 40 W/m^2 escape via the atmospheric window, also seems too low to me; implying almost complete absorption of the surface emission by the atmosphere whereas spectral plots would seem to allow capture of a much smaller fraction of the total energy.
George
“”” TomVonk says:
August 6, 2010 at 9:42 am
Henry Pool
……………………………..
The reason of 50% is not in the position of the molecules but in the isotropy of the emission .
While there is a non isotropic flow of IR (from ground up) as long as it is not absorbed , it is isotropically reemitted . So in a plane approximation you can say that statistically over a large number of reemissions , half will be up and half will be down . “””
Tom, I agree with you that the atmospheric emission from any layer ought to be isotropic leading to a 50-50 up/down split.
However, I have argued elsewhere, that because of both temperature and density gradients, the escape path to space is favored over the return path to the surface; because of re-absorption in subsequent atmospheric layers.
A higher layer is both cooler and less dense, so both the Doppler, and Collision broadening of the GHG absorption lines are reduced fro the higher layer but increased for a lower denser and warmer layer.
So the atmospheric layer below some arbitrary layer is even more (spectrally) absorptive, while the layer above is less absorptive, and so allows more of the spectrum to escape. So I believe the escape route is favored over the return route; since every recapture (in the atmopshere) event leads to another 50-50 split of subsequent emissions; and less returns to the surface than escapes to space. My mathematics has gotten just a bit too long in the tooth to do the necessary computations of this multiple cascade of absorptions and emissions along with computing the Doppler and Collision broadening of the absorption lines to compute the degree of assymmetry; but I do believe there is one.
“”” Nasif Nahle says:
August 6, 2010 at 9:46 am
Look over this graph at http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
There is an atrocious omission and flawed data there. Have you got it? The vertical axis says: “major” components (of the atmosphere); nevertheless, they omitted Argon. Argon mass fraction in the atmosphere is more than 20 times higher than CO2 mass fraction. Argon’s totabs and totemiss is 128% higher than CO2 totabs and totemiss. The absorption spectrum of Argon is wider than CO2 absorption spectrum. What’s the reason the author omitted such important component of the atmosphere, i.e. Argon, and included CO2, which mass fractions and totabs and totemiss are so insignificant? “””
So Nasif; it would seem you have the rest of us at a disadvantage; in that you appear to have data on the Infra-Red absorption spectrum of Argon. I wasn’t previously aware that Argon, even had an IR absorption spectrum or that any Noble gas could absorb at LWIR wavelengths.
Can you point us to a location where we can find this Argon LWIR spectrum ?
“”” cba says:
August 6, 2010 at 5:44 am
================
Spector says:
August 5, 2010 at 11:11 pm
………………………………………………Izapped
======================
That’s because of several factors. First off, The HITRAN database itself consists of single frequency ( or wavelength) line descriptions. The bands like co2 15 um are nothing but a tremendous number of lines close together. To use HITRAN in a spectrum, one must create a line width based upon temperature, pressure, including partial pressures of the molecule of interest and the ‘other molecules present’, and the line data associated with width. For instance, there’s pressure broadening along with wavelength shift due to pressure corrections to be made. “””
So –cba– you hit a nerve somewhere or lit up my alarm board somehow.
I have used some other molecular spectra program that Phil graciously pointed me to; but I began to wonder just what they were calculating the spectrum of.
Obviously the IR or any spectrum of say CO2 or H2O in isolation will be way different from what happens in a real atmosphere. Phil has pointed out both CO2 and H2O spectra to me (and anyone else who wanted it) that look as similar as the warts on a wart hog are to the feathers on a bald eagle. Those spectra immediately had me screaming insanely for some information on just what the sample being modelled (computed) were; and how they were related to a real atmospheric sample.
So your comments on what needs to be done pre-HITRAN modelling are most appropriate.
I assume that HITRAN is one of those things that is available to institutionalized folks; but beyond the reach of us peons.
Thanks for bringing up the issue of a real world sample to model.
I also see very little discussion of the result of Doppler and Collision broadening on the up/down split of the atmospheric LWIR emission.
I have argued that escape is favored over return to surface, since higher layers are colder and lower density, and so must exhibit narrower GHG absorption lines; while lower layers must have broader absorption lines; so recapture is more likely going down than going up. Each recapture of course then leads to another 50-50 up/down split of subsequent emissions.
Sorry Tom. I don’t follow you.
The paper that confirmed to me that CO2 is (also) cooling the atmosphere by re-radiating sunshine is this one:
http://www.iop.org/EJ/article/0004-637X/644/1/551/64090.web.pdf?request-id=76e1a830-4451-4c80-aa58-4728c1d646ec
they measured this radiation as it bounced back to earth from the moon. So the direction of the radiation was:sun-earth-moon-earth. Follow the green line in fig. 6, bottom. Note that it already starts at 1.2 um, then one peak at 1.4 um, then various peaks at 1.6 um and 3 big peaks at 2 um.
Obviously this also happens as 4-5 um and at other absorbative wavelenghts of CO2 that were not included in this investigation. As to what is happening here: do you not see this as cooling?
And would the opposite – i.e. the trapping of (IR) radiation- not also cause warming?
So which is it?
Your theory does not explain my simple observation that humidity (water vapor) reduces heat – which is why coastal areas are always cooler than more inland (where it is drier)
George E. Smith says:
August 6, 2010 at 10:24 am
Hi George,
Are you willing to think along the lines of momentum conservation as far as isotropy claims go?
I say that isotropy exists in the center of mass system of the molecule, BUT, when the molecule absorbed a photon it also got a momentum impulse of h*nu/c and thus it is no longer in the center of mass system. This is true for the “average” molecule absorbing a photon. When it emits a photon, again on the average the real quantum mechanical solution should show the asymmetry that the conservation of momentum imposes on the gas.
Now if all this momentum does not escape as other photons with different energy distributions, the H2O and CO2 etc that are involved in this absorption business would end up in the stratosphere, imo. There is a finite number of molecules but a practically infinite number of infrared photons impinging continuously on them.
Julio says:
August 6, 2010 at 5:56 am
Reed Coray says:
August 5, 2010 at 7:38 pm
Reed, let me try to explain how it works.
Suppose you make money at the rate of 100 dollars a day. Your money bin is full, so you want to get rid of this annoying cash inflow. You consider giving it away to the federal government, but because of some bizarre tax rule they are obligated to give you back 20% of everything you give them. How do you ensure a net zero flow?
Answer: you give them 125 dollars a day, $25 more than what you make from your other sources. They give you back 20% of 125, which is $25, and they use the rest cheerfully for their own nefarious purposes. Your net cash flow is now zero.
Again, thank you for taking the time to respond to my comments. Continuing the discussion, I believe your federal government tax analogy doesn’t apply to radiation from an object enclosed by a glass shield. Here’s why. In your federal government analogy, the federal government equates to the glass shield. As such, I believe you are saying that the 20% of the energy radiated from the enclosed object that does not pass through the glass is returned to the enclosed object. If any of this “unpassed” energy is not returned to the emitting object, then the emitting object (in your analogy, my “money bin”) loses energy (money) with time. E.g., (a) my employer deposits $100 dollars per unit time into my “money bin”, (b) from my “money bin” I’m giving to the government $125 per unit time, and (c) the government is returning to my “money bin” less than $25 per unit time–say for the sake of argument, $20 per unit time. Using these numbers my “money bin” is being depleted at a rate of $5 per unit time.
I believe that only for special geometries and special “reflection conditions” can it be shown that all of the energy not passed by the glass is returned to the emitting object. Specifically, I believe all “un-passed” energy will be returned to the emitting object only for (a) a spherical glass shield, (b) specular reflection off the glass, (c) a spherical emitting object, and (d) the centers of the spherical emitting object and the spherical glass sphere are collocated.
Taking these one at a time.
(a) Spherical glass shield. If the glass shield is not spherical, with the exception of (i) a spherical enclosed emitting object co-centered with a surrounding glass sphere and (ii) specular reflection off the glass shield, I believe a point on the surface of the emitting object can always be found such that radiation emanating from that point that encounters the glass shield will not return to the emitting object; but rather will be directed towards a different part of the surface of the glass shield. Since the glass shield passes 80% of the energy incident on it, 80% of such energy will pass through the glass–never to be returned to the enclosed emitting object. As such, only a fraction of the “20% energy initially not passed by the glass shield” will return to the emitting object.
(b) Specular reflection off the glass shield. If the “20% energy initially not passed by the glass shield” is returned to the interior of the glass shell with directionality other than specular reflection–say either Lambertian (amount proportional to the cosine of the angle between the radiated direction and the normal to the surface of the glass) or isotropically in the interior half-plane (which I believe is the model the AGW community uses), then a portion of the energy emitted from the enclosed object when encountering the glass surface will be directed towards another portion of the glass surface. 80% of such energy will pass through the glass shield never to be returned to the enclosed radiating object.
(c) The enclosed object must be a sphere. If energy is spectrally reflected from a spherical glass shield, I believe the only emitting-object shape for which the reflected energy is guaranteed to strike the emitting object before striking the glass shield is a sphere, and the center of that sphere must be coincident with the center of the spherical glass shield. [Note: I’m almost positive that energy leaving the surface of a spherical object that is specularly reflected from the surface of a co-centered larger spherical object will be returned to the emitting object. I’m not positive other geometries don’t exist with these properties, but I doubt it. In any event, I can find geometries for which energy leaving a non-spherical object reflected from a spherical glass shell will not be directly returned to the emitting object.] For these cases, some of the “20% unpassed energy” will encounter the glass shield before encountering the emitting object, and 80% of that portion of the “20% unpassed energy” will never return to the emitting object.
(d) The center of the spherical emitting object must be coincident with the center of the spherical glass shield. If the two objects are not co-centered (say the enclosed sphere is offset where at one point the two surfaces almost touch, then energy from the “almost touching point” on the enclosed sphere radiated tangent (or nearly tangent) to the surface of the enclosed sphere when specularly reflected by the surface of the larger sphere will be reflected towards the larger sphere and not back towards the emitting sphere. As such, some of this reflected energy will pass through the glass shield never to be returned to the emitting objects.
Bottom line, for your “tax analogy” to apply to energy passing through a glass shield, I believe you must prove that the 20% of the energy that doesn’t initially pass through the glass shield is returned to the emitting object. With the exception of the special case mentioned above (and maybe a few other special cases, but definitely not the general case), I don’t believe this can be done.
“”” cal says:
August 6, 2010 at 2:36 am
Bill Illis says
Here is a nice chart showing the effective temperature that is being radiated across the IR Earth spectrum.
http://cimss.ssec.wisc.edu/goes/sndprf/spectra.gif “””
A very interesting graph Bill; but I am having a hard time trying to understand what it really means.
For a start, I would ask, is this a calculated spectrum from some model or other of the atmosphere or is this actual measured earth emission observed from outer space.
I don’t understand your comment that some bands are emitting at a higher temperature than they should be; (296 versus 288). Clearly they are emitting at exactly the temperature they should be.
I have long argued that the earth is doing it’s most efficient cooling from the hottest desert surfaces during the heat of the day; where surface temeprature can get over +60 deg C or 333 K which is even higher than your 296. Because of the sigma. T^4 effect, the hotter surfaces radiate much more proportionately than do the colder surfaces so basing a radiation budget on some fictional global average temeprature of 288 K is clearly not real. And at the other end; at cold places like Vostok, the radiant cooling is more than an order of magnitude lower than from the hottest deserts.
But back to this brightness Temperatures business. What I am hearing, seems to be that it is assumed that ALL of the surface radiation is absorbed in the lowest atmosphere layers EXCEPT Trenberth’s ridiculously small 40 W/m^2 that escpaes immediately via “the amosheric window”. Then that lowest atmosphere layer emit and a 50-50 split sends it half up and half down; and the up ward is again absorbed by a higher and now cooler layer; which in turn emits but now at a lower temperature; until finally some much higher and much cooler layer gets to emit radiation that actually escapes to space and that radiating temperature is the one that must balance with the incoming TSI insolation rate.
And that is where I get hung up. It seems to me that any layer from the surface to the highest limits of the atmosphere is radiating some roughly blackbody looking spectrum corresponding to its own Temperature; and much of that spectrum exits directly to space (assuming cloudless skies for the moment) with a spectrum corresponding to the emission temperature of that surface; but now with holes in it from absorption by GHG molecules or the atmospheric gases themselves.
Each higher and cooler layer in turn emits thermal radiation corresponding to its temperature; and much of that also escapes directly to space around the absorption bands of the higher atmosphere layers; and so on; so that the total LWIR emission from the earth should then be a composite of roughly BB spectra but with source temepratures ranging ove the entire surface Temeprature range, as well as the range of atmospheric emitting Temperatures.
Observations of earth emission spectra seen outside the atmosphere from satellites should co0ntain components that are emitted from surface that are 333 K or even higher; and this is important since the Wien displacement Law, would shift these emission peaks even further away from the CO2 15 micron nand as the spectral peak moves from its nominal 10.1 microns at 288 K down to about 8.7 microns at 333 K.
I’m having a hard time keeping straight what people are citing as actual emissions from the earth apart from what some computer model is calculating that satellites should be able to see (but maybe aren’t).
The earth’s surface SHOULD be emitting at a higher effective Temperature than 288 K because the hotter surfaces far more than make up for the laziness of the colder surfaces.
TomVonk says:
August 6, 2010 at 9:26 am
Paul Birch says: We don’t. Really. We have an approximation to LTE. We have an approximation to equipartition. But it is the departures from LTE, caused by and causing superimposed radiative fluxes at different temperatures etc
Tom Vonk says: “There are 2 methods to answer that .
One is to put a dozen of links showing that this is the working hypothesis especially in all radiative transfer models .”
It is a useful approximation for some of the analysis. Not when taken to your absurd extreme.
“I prefer the second which is to ask you to specify what you mean by approximate LTE”
A state in which only a small proportion of molecules at any one time belong to a population with a significantly different temperature to the majority, or in which the temperature difference between populations is only slight.
“You know , a system not in LTE can only be treated by QM .”
Not true. One can for example treat radiative systems using classical absorption, scattering and transmission coefficients. One can consider mean lifetimes of the various populations against energy transfer to other populations. Quantum mechanics may ultimately lie behind the physics, but bulk macroscopic parameters are fine for most practical thermodynamic analysis.
“There is a rather sharp distinction between the 2 states . As I have written LTE is a statement about a neighborhood of a point . It doesn’t say how large it must be , it only says that it must exist . And questions of existence are not “approximate” , they have mostly binary yes or no answers .”
If you really want to get this pedantic, then the answer is that LTE does not exist in the real universe, and if it ever did exist it could not be observed. It is a mathematical fiction. A limiting case never actually achieved.
http://wattsupwiththat.com/2010/08/05/co2-heats-the-atmosphere-a-counter-view/#comment-449799
Sorry.
A theory must describe what we see happening. Otherwise it is no good.
If it were not for the ozone and the water vapor and the CO2 and the oxygen in the air then we would all fry….the extra 30% radiation or so would make us toast….
Unfortunately some of these gases also cause warming…. by re-radiating some earthshine at certain wavelengths. But what is the net effect of the cooling and warming of each the gases in the atmosphere (including the noble gases)???
Where is the research on that? If you don’t have anything on that, then what is the use discussing any of these so-called theories?
Cheers…
Henry
Reed Coray says:
August 6, 2010 at 11:49 am
Hi Reed,
Please don’t take this wrong, but I think you are tying yourself up in knots unnecessarily.
To go back to my silly example, it doesn’t matter the exact amount the government gives me back, as long as it is a fixed percentage of my donation. If it only gives me back $20 a day for every $125 I donate, that means the rate of return is only 16%, and my “equilibrium donation rate” then has to be 100/(1-0.16) = $119.05; 16% of this is $19.05, and I’m in business again (or not, of course, depending on your perspective).
Back to the Earth: it radiates upward, and without an atmosphere all that radiation would just go out into space. With greenhouse gases, some of it comes back to the Earth, some of this goes up again, etc. In steady state, you still have to have that the net amount going out into space equals the amount coming in, or else the Earth + atmosphere system would just keep getting hotter and hotter. So what you end up with is some amount of radiation “trapped”, kind of bouncing back and forth between the upper atmosphere and the earth, like the $19.05 above: every day I give the government $119.05, and it gives me back $19.05; the next day I get a fresh $100 in dividends from my bank, add the previous day’s $19.05, and give it to the government; by the evening, the $19.05 is back, and so on.
Back to the atmosphere: you’re saying that you don’t believe that the back-reflected flux plus the transmitted flux equals the total upward flux. Well, what else is the energy to do? Think of the glass example. The energy could go back; it could go through; or it could–what, continually build up inside the glass until the glass melts? That’s not what happens in real life. Check out any real greenhouse. The glass gets hot, up to a point, and then it reaches its own optimal equilibrium temperature where it radiates out (in both directions) as much as it is getting.
You just have to imagine a steady state in which energy just flows through without building up anywhere, although there may be large, constant pools of it in various places–like a lake in the course of a stream; that would be the equivalent of the “trapped energy.”
George E. Smith says:
August 6, 2010 at 10:30 am
“”” Nasif Nahle says:
August 6, 2010 at 9:46 am
Look over this graph at http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
There is an atrocious omission and flawed data there. Have you got it? The vertical axis says: “major” components (of the atmosphere); nevertheless, they omitted Argon. Argon mass fraction in the atmosphere is more than 20 times higher than CO2 mass fraction. Argon’s totabs and totemiss is 128% higher than CO2 totabs and totemiss. The absorption spectrum of Argon is wider than CO2 absorption spectrum. What’s the reason the author omitted such important component of the atmosphere, i.e. Argon, and included CO2, which mass fractions and totabs and totemiss are so insignificant? “””
So Nasif; it would seem you have the rest of us at a disadvantage; in that you appear to have data on the Infra-Red absorption spectrum of Argon. I wasn’t previously aware that Argon, even had an IR absorption spectrum or that any Noble gas could absorb at LWIR wavelengths.
Can you point us to a location where we can find this Argon LWIR spectrum ?
There cannot be any data on IR absorption by Argon because Argon is transparent to IR, more transparent than the CO2. Argon is a major component of the atmosphere which is in a higher concentration than CO2.
TomVonk,
Thank you for your piece of the puzzle on CO2 in the atmosphere. It was concise and lucid.
The more pieces of the puzzle that are offered and discussed the better we are to be able to recognize the picture/pattern of the total puzzle even before all the pieces of the puzzle are available and fitted in.
I read your original post and all of your responses to comments so far and most of the commenters posts.
Question: Given your conclusion with its caveats, and that they basically apply to other gases in the atmosphere beside N2 then please address the possibility of another case during the period of the detla CO2 conc/dt (time) or the time of transition from one CO2 conc to another. Does the rate of change of CO2 conc affect the situation? Of course I am assuming there is a situation where there is not a fundamentally an LTE situation.
Anthony and team, you guys sure know how to give us all great learning episodes : ) Thanks.
John
Spector,
I’m not totally sure what you’re driving at with ‘quantized classical vibration’ but I did not see anything wrong with your statement. It is the effect of the total spectrum for transmission or absorption with contributions from all lines of all molecules involved.
The HITRAN database includes parameters for each line that include the starting and ending energy states for a line plus information about line width and the effects of ‘other’ molecules upon the particular line. You might want to continue reading below.
George E. Smith,
HITRAN is not a spectrum nor does it generate one as is. You have to generate your own – which is what I had to do. The papers they provide on their website include details on how to accomplish that effort – Rothman et al 1994, appendix. What I did was to create a program that reads an output file from their javahawks program (supplied) that permits selection of molecules (&isotopes) along with temperatures and pressures and frequency ranges (I use wavelength ranges). My program then takes the partial extracted database and corrects for the temperature and pressures and permits further selection of molecules. It then builds a set of transmission parameters in an array of wavelengths for the number of layers being used. A layer has concentrations for molecules, a temperature, and a pressure.
Once the output file is prepared, I import it into excel where I have a series of transmission arrays. The lines have widths and heights and the contribution for a wavelength range for each line is added together. Each array is for a 1cm thickness of the gas for that layer. Actual transmission and absorption is determined for a layer is the exponential of that value times the thickness of the layer in cm. 1-transmission fraction gives the absorption fraction.
depending on what I’m doing, I can do straight attenuation or do radiative transfer where there is both absorption and emission in a layer.
The absorption occurs when a BB like spectrum enters the layer and it is multiplied by the layer’s attenuation. Emission from the layer is the multiplication of the BB spectrum for a black body at the temperature of the layer with the absorption factors. The entire atmosphere is modeled by typically using over 50 layers.
My program system is limited to between about 0.1 um and 75um. The resolution is variable, permitting me to look with high resolution at very narrow ranges or lower resolution at much wider ranges. For validation, I compared my results to some medium and ultrahigh resolution measured spectrums in the visible spectrum (not associated with climatology). It works pretty good for its intended application (which is not climatology).
To get HITRAN, one must request it. As I recall, when I requested access, I was not associated with an institution nor had I been involved with one or with basic scientific research for decades. When I requested it, my purpose was primarily to play with atmospheric studies on my own. Only later did I start to apply my work to any actual (non climatological) research effort. Note- I don’t recommend this approach to anyone else. Going to this resolution doesn’t really offer improved accuracy as one is really dealing with over 50% cloudy skies and variations that are significant.
as for one molecule or all, I use all and subtract out a single molecule for determining the effects. What I’ve used most recently is rather low resolution and has the ability to adjust co2 and h2o levels. There isn’t a lot of actual power absorption overlap but there is several percent difference.
“”” Nasif Nahle says:
August 6, 2010 at 2:18 pm
George E. Smith says:
August 6, 2010 at 10:30 am
“”” Nasif Nahle says:
August 6, 2010 at 9:46 am
Look over this graph at http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
There is an atrocious omission and flawed data there. Have you got it? The vertical axis says: “major” components (of the atmosphere); nevertheless, they omitted Argon. Argon mass fraction in the atmosphere is more than 20 times higher than CO2 mass fraction. Argon’s totabs and totemiss is 128% higher than CO2 totabs and totemiss. The absorption spectrum of Argon is wider than CO2 absorption spectrum. “””
Well there I have cut and pasted just what you said:- “”” The absorption spectrum of Argon is wider than CO2 absorption spectrum. “””
So is the argon LWIR absorption spectrum wider than that of CO2 or is it non-existent; I’m having a hard time getting your point.
If Argon is a totally raiatively inert component of the atmosphere then it is not unlike a mountain or a building that is also not part of the active atmosphere.
They have also omitted helium and xenon that also are parts of the atmosphere having no effect on climate.
Tom Vonk,
Tom, I think there may be a problem in the area of LTE or not LTE with molecules and with radiation. It looks like you are dealing with the condition of LTE assumption for both molecules and with radiation. This is clearly not the case overall as there is radiation coming from the Earth’s surface at a higher BB emission temperature than one finds in most of the atmosphere.
The atmosphere essentially has LTE with molecules. The LTE example region is going to have all of the molecule types at the same temperature after a small time has expired from the last change in energy transport. This condition will have the energy transferred to and from the n2 and o2 molecules at the same rate and will not have a net transfer of energy. This also assumes no convection or conduction occurring in or out of the LTE example region. If there is total LTE, molecules and radiation included, then there will be the same amount of power radiated as absorbed with none going to the other molecules.
If there is an increase in the radiation amount (in the spectral area of the ghg molecules), then there will be additional absorption by the CO2 but the emission is temperature dependent. For energy balance, there must be an increase in the CO2 temperature if more power is being absorbed to permit more power to be emitted. During this transient time, the co2 molecules must heat up and become hotter than the n2 and o2. In order for LTE to be restored, the co2 must heat up the n2 and o2 to the new temperature. Once LTE is restored, then one returns to the condition that n2 and o2 no longer receive or give back net power to the co2. Also, the co2 must be in radiative equilibrium, giving off as much radiation energy as it receives.
Nasif,
argon is a noble gas. It isn’t interested in forming any molecules and so requires high energy uV to excite it to higher levels before it is capable of absorbing and emitting in the visible and infrared. The only way you’re really going to get much IR is to have a molecule where you can have low energy states without having to raise the lower state well above the ground state.
Tom Vonk’s QM analysis may be correct, in a narrow pre-defined technical sense, but its relevance to the real-world problem of dynamic temperature levels seems very limited.
We know empirically that backradiation has no diurnal cycle. This is a strong indicator that it doesn’t come from GHG emissions alone. The bulk constituents of the atmosphere do heat heat up as result of all the the heat-transfer processes, not just radiation. What the usual explanation of the “greenhouse effect” usually misses, moreover, is that the backradiation is simply part of a nearly null-net exchange between the surface and the base of the atmosphere. With the surface being more than 70% water, which evaporates in response to IR rather than raising its temperature, there is no radiation-only algebra that can determine temperatures. While HITRAN and similar codes do an excellent job of determining the transmitivity of signals through the atmosphere for remote sensing, they do not solve any thermodynamic problem that involves convective transfer of latent heat. Observations of the Bowen ratio show that the latter is the principal mode of heat transfer to the atmosphere. Ths science is not settled–it hasn’t even been done!
High five Tom! It’s a long time since we spoke on the, now defunct, CA Forum.
Unfortunately, I’m still unconvinced on the ‘microscopic’ ideology. I still only see this as an ‘insulation’ factor for ‘radiative theory’ and an ‘interpretation’ of GHE (greenhouse effect) WRT altitude.
Best regards, Ray Dart.
Julio says:
August 6, 2010 at 1:55 pm
Reed Coray says:
August 6, 2010 at 11:49 am
Hi Reed,
Please don’t take this wrong, but I think you are tying yourself up in knots unnecessarily.
Julio, I don’t take your comment “wrong”; in fact, I kind of like it. I’ve tied myself in knots before and I may be doing so now. I accept the idea that for a system surrounded by a vacuum when radiation-rate-equilibrium is reached, the amount of energy per unit time leaving a system via radiation is equal to the amount of energy per unit time entering the system. In fact, this is the definition of radiation-rate-equilibrium. For a “system” to be in radiation-rate-equilibrium, I believe all subsystems of that system must also be in energy-rate-equilibrium–not radiation-rate-equilibrium because the subsystems may exchange energy via convection and conduction.
I also believe a body surrounding a second body that possesses an internal energy source will affect the temperature of the second body. For example, (a) Assume a black body exists internal to which is an energy source supplying a fixed amount of energy per unit time. (b) Assume the temperature of the surface of that black body is everywhere the same, T Kelvins. (c) In radiation-rate-equilibrium with a vacuum at 0 Kelvins, the temperature of the black body surface will be such that A*sigma*T^4 is equal to the rate of internal energy supplied to the black body (where A is the black body radiator’s surface area and sigma is the Stefan-Boltzmann constant). (d) If you surround this black body with another black (or grey) body which has no internal energy source, the presence of the surrounding black/grey body will likely alter the surface temperature of the emitting black body. So, I agree that the temperature of the emitting black body can be affected by a surrounding body.
However, I’m uncomfortable with descriptions that say heat is “trapped”, and it is the “trapping of heat” that produces the rise in temperature of the emitting black body. Any physical material with a non-zero specific heat capacity “traps heat”. “Trapping heat” is not limited to “greenhouse materials.” In fact, adding material that “traps heat” may even lead to cooling. Before you say, “now he’s off his rocker”, consider the following. A black body, spherical, Earth has an internal energy source deep within its core that is supplying energy at a fixed rate, H. The radius of Earth is R. In radiation-rate-equilibrium with a vacuum at 0 Kelvins, the temperature, T of the Earth’s surface is given by the equation:
T = { H / (4*pi*R*R*sigma) }^(1/4)
where sigma is the Stefan-Boltzmann constant. If we increase the radius of the Earth to R0 by adding “black body material” that is devoid of an internal energy source, the added material will “trap heat”, but the temperature of the Earth surface will decrease. The latter happens because the formula for the Earth surface temperature has the same form as above, but the radius R is replaced with a larger radius, R0. Thus, we are “trapping heat” and the temperature of the body decreases.
In addition, isn’t it true that the CO2 surrounding the Earth will “trap heat” independent of the temperature of the surface of the Earth? If so and if “trapping heat” causes the temperature to rise, then the “trapping of heat” doesn’t stop when the black body’s temperature rises, and the black body’s temperature will continue to rise until the CO2 reaches a temperature where its molecular motion has sufficient speed to escape the gravitational pull of the Earth.
I believe a better way to state what is happening is the following. If a black body with a fixed-rate energy source is in radiation-rate-equilibrium with the vacuum of space at 0 Kelvins, placing additional material separate from but surrounding the black body will likely cause the temperature of the surface of the black body to change in such a way that energy-rate-equilibrium is re-established for the black body. Only now heat can leave the black body via conduction and convection as well as radiation, so I don’t want to say the black body reaches radiation-rate-equilibrium, rather it reaches energy-rate-equilibrium. Furthermore, once energy-rate-equilibrium is established, it holds for any subsystem. That is, it holds for the CO2 as a whole, any “block of atmosphere”, etc. In particular, I believe the temperature of the surface of the Earth would be altered by a pure Nitrogen or Argon or Helium or any atmosphere. Although greenhouse gases may affect the temperature of the surface of the Earth differently than non-greenhouse gases, I don’t agree with the claim that it’s the presence of greenhouse gases that causes the Earth’s temperature to be on the order of 33 Kelvins than it would be in the absence of greenhouse gases. (I even question the number 33, but that’s another story.) I think any atmosphere will alter the Earth’s surface temperature. How much is altered by greenhouse gases versus non-greenhouse gases, I don’t know. It’s a problem I would like someone more knowledgeable than I am to answer.
I’d appreciate it if you’d answer a few questions. Assume the Earth is devoid of water, the Earth has an internal energy source providing energy at a constant rate, and the Earth’s surface temperature without any atmosphere is everywhere T.
(1) When a CO2 atmosphere is added, does the CO2 “trap heat”?
(2) If yes, does this “trapping of heat” cause the temperature of the Earth to rise–i.e., can it be said that the “trapping of heat in the atmosphere” is the cause of the Earth’s surface temperature rise?
(3) If yes, is the CO2’s ability to “trap heat” a function of the Earth’s surface temperature? That is, will the CO2 trap heat for all Earth surface temperatures, or is there an Earth surface temperature at which CO2 ceases to “trap heat?”
(4) If there is an Earth surface temperature at which CO2 ceases to “trap heat”, what roughly is that temperature?
You can see where I’m going with this [I’m tying bigger and more complicated knots :)] If the premises that (a) “CO2 trapping heat” causes the temperature to rise, and (b) CO2 traps heat independent of the temperature of the Earth’s surface are valid, then a CO2 atmosphere should cause the Earth surface temperature to rise without bound.
About five months ago I got interested in developing from first principles equations for radiative energy flow between two “grey bodies” in a vacuum where one grey-body completely surrounds the other grey body. For most geometries, the mathematics is too unwieldy (at least for me) to generate a closed-form equation for the rate of energy transfer. However, for the geometry of two spherical, co-centered, grey-body shells, the mathematics is tractable. I wrote a paper providing all the mathematics. If you’re interested, I’d be happy to send you the paper (microsoft word 2007) for your review and comment. I don’t know your E-mail address, but I’m sure we can get Anthony to either send you my E-mail address or have him send me your E-mail address.
Final note. I’ve enjoyed our exchange of comments. Thank you for your time.
Icba says:
August 6, 2010 at 5:26 pm
Nasif,
argon is a noble gas. It isn’t interested in forming any molecules and so requires high energy uV to excite it to higher levels before it is capable of absorbing and emitting in the visible and infrared. The only way you’re really going to get much IR is to have a molecule where you can have low energy states without having to raise the lower state well above the ground state.
Please, read my post at Nasif Nahle. August 6, 2010 at 2:18 pm
stevengoddard says:
August 5, 2010 at 10:57 pm
Ric Werme,
Sorry Steven, you make it so easy to be knee jerk sarcastic. It would help if you were truly interested in sharing some stuff that you don’t. BTW, I did think about length of day – the areas just poleward of the arctic circles get a bit more daylight thanks to refraction of the atmosphere, though that’s not germane.
So, implications of slightly more insolation for a couple weeks on either side of midsummer at the SP and PHX:
1) Peak insolation at the SP is sin(23.44)N where N is solar flux in w/m^2 on a surface perpendicular to the Sun – about 40%, but good for all day. At PHX, latitude 33.43, at local noon the Sun will be at altitude 90 – 33.43 + 23.44 = 80°, sin(80.01) is 0.985, more than twice as much, but falling off quickly more than a few hours before and after.
Implication 1) Phoenix’s temperature likely has a bigger diurnal variation than the south pole.
2) The SP has greater insolation for only a few weeks. The seasonal lag in New Hampshire between peak insolation and peak daily temperatures is about five weeks.
Implication 2) The many weeks where the SP has less insolation than PHX has a significant effect on temperature differences between the two places.
3) The altitude of the SP is 2,835 m. The altitude of PHX is 340 m. That’s good for some 23°C in adiabatic lapse rate. Possibly more given the dense polar air.
4) The albedo at the SP is much higher than at PHX. I’m sorry, I can’t estimate the temperature differential that’s good for.
5) CO2 concentration in ppm should be about the same since rain doesn’t take much CO2 out of the air on its way to the SP, but H2O will be quite a bit less, thanks to the low dew point.
Implication 3+5) the air above PHX has quite a bit more CO2 and H2O thanks to the extra 777 m of air LWIR has to navigate.
So, given all that, I’m disappointed that you ascribed the temperature difference between the two sites as solely due to humidity without giving the merest mention to all the other variables.
Oops – stupid math error (actually, number error)
Implication 3+5) the air above PHX has quite a bit more CO2 and H2O thanks to the extra 2500 m of air LWIR has to navigate.
On Antarctic receiving more solar radiation than Phoenix in mid-summer.
The math is a little difficult for Phoenix, but it can be shown it receives more than
the equator at the equinox (when the sun goes overhead there), so I would say it is plausible for Phoenix.
In Antarctic mid-summer the sun stays at 23 deg above the horizon for 24 hours. sine 23 deg = 0.4. Average daily flux = 0.4 times the overhead value.
At the equator equinox the sun goes up over ahead and down in 12 hours. 24-hour average value of sine (positive part only) is 1/pi. Average daily flux is 1/pi= 0.32 times the overhead flux.
So, strange but true. In a clear sky, the mean daily flux reaching a horizontal surface is greater for Antarctica than the equator at equinox.