## Tuesday, September 20, 2005

### Latent heat II

This exchange is kind of funny. A serious calculational error of a well-known promoter of the global warming theory - an error described below - shows how weak intuition the climate folks have about the order-of-magnitude estimates of the basic processes in nature. They obviously never discuss technical things that require actual numbers.

In his new text meant to humiliate the latent heat

William Connolley decided to show how trivial it's to defeat the latent heat. It is becoming completely obvious that he actually believes that the latent heat can indeed be neglected. In the original version of his article, he wrote the following sentence:

• Long-wave-down (not net) at the sfc in January is about 135 w/m2 so it would melt about 30m of ice in a day. Of course that neglects the long-wave up.

Yes, this is what he thinks. Don't get confused by his pretentious terminology - his point is very simple. He thinks that the solar radiation above the Arctic is enough to melt 30 meters of ice a day! This is how the "mainstream" climate scientists visualize the heat budget. This is how they do calculations that are meant to justify investments of trillions of dollars. It can't be surprising that they conclude that a "catastrophe" is imminent if they expect ice to melt so quickly. Note that William Connolley is not a random person who has nothing to do with ice; he is paid as a "senior scientific officer" and "climate modeller" of the British Antarctic Survey. You may expect that such a person has some idea about ice; you would be completely wrong. You would be wrong by 3 orders of magnitude.

Of course that Connolley's statement is complete rubbish; the correct answer is not 30 meters but 30 millimeters. He's wrong by three orders of magnitude. Most healthy children would be able to figure out that the Arctic Sun can't melt 30 meters of ice a day. Do you think that a climate modeller focusing on Antarctica should have no idea how much heat one needs to melt ice? His error is like confusing the height of Mount Everest with your house. It's like predicting that the year 3005 will arrive next year. It's like a string theorist who believes that the critical dimension is 10,000. It's like a particle physicist who believes that the size of the nucleus is the inverse electroweak scale. It's just unforgivable ignorance. For pedagogical reasons, let me do this calculation properly.

Let's be very cavalier and multiply those 135 Watts per meter squared by the number of seconds per day, 86,400, which will certainly lead to a huge overestimate. We obtain 11,664,000 Joules per day and per squared meter. Let's call the units "meters times Joules per day and cubic meter". If we divide it by the density of water or ice, namely 1,000 kilograms per cubic meter, we obtain 11,664 meters times Joules per day and kilogram. If we divide this number by the latent heat of ice which is 355,000 Joules per kilogram, we obtain roughly 0.03 meters or 3 centimeters. Yes, indeed, he can only melt 1 inch a day instead of the 30 meters that he argued.

No doubt, the climate arguments and models are robust against such changes by 3 orders of magnitude. They're permanently safe because what they actually rely upon are not calculations but human bigotry and political fanatism. Folks like William never solve actual scientific questions that require rational reasoning or a calculation like this one. Whenever someone wants to help them to do some reasoning properly, they will attack him (the biggest insult being that the person is connected with the commercial sector) ;-) because they are, by definition, the only experts in the world.

Ocean circulation

The sea ice is important as a heat sink not only because of the latent heat whose relevance I have probably sufficiently demonstrated. It is also critical because the sea ice, whenever it exists, drives the circulation of the ocean. Normally, 90% of the ocean mass is below "thermocline" which is 100-400 meters below the surface. Within this region, the temperature is dropping very quickly. Below thermocline, the temperature only drops slowly, towards those 0-3 degrees Celsius of the very deep ocean. What's important is that the ocean below thermocline does not exchange heat efficiently. When we talk about the heat exchange and about the ocean as a heat sink, only the upper 100-400 meters of water are important.

Sea ice is important not only because the large latent heat of the 2 meters of ice is enough to compete with the specific heat of 100 meters of "active" water. Ice is also critical for ocean's being a heat sink because ice drives the circulation, and it actually decides about the height of the water column that is able to store the heat.

I just can't understand how someone may think that he is able to say anything about the future climate if he neglects things like that - that are much more important than some greenhouse effect involving not-the-most-important greenhouse gas. But everyone knows the reason: it's because they are allowed do it like that by the environment. There is almost no one - or at least almost no one in the scientific world - who would have the courage to tell them that what they're doing is completely silly.

Although it has always been the case that the weakest students of physics chose climate science, in our bizarre world such people are apparently gaining a divine status. But they are still the very same people; poor students who can't distinguish meters from millimeters. And these people indirectly suck one half of the GDP growth of our planet.

1. I still don't quite get your point. Before I read part II I did my own calculation and used all of the 1.6kW/m^2 of sunlight (a number I remembered from highschool where we actually measured it) to estimate that your two meters of ice have a latent heat that is equivalent to about a month of sunshine (let's not worry about a factor of 10 here).

So what are you arguing? When it comes to climate we are not talking about months. We are talking about decades and centuries. Doesn't the above numer show that melting all the ice or freezing a simimlar amount of water is roghly like one month of sunlight in that time period? Are you suggesting that on the long run the earth should take up more of the sun's radiation by melting all the ice? My friend, let me assure you that this will not last very long.

For 100% absorbtion it lasts one month and that only covers the radiation incident on the arctic. For higher reflection it lasts longer but pretty soon you have to come up with another one of these great ideas.

2. Dear Lumos,

"Let's be very cavalier and multiply those 135 Watts per meter squared by the number of seconds per day, 86,400, which will certainly lead to a huge overestimate. We obtain 11,664,000 Joules per day and per squared meter. Let's call the units "meters times Joules per day and cubic meter". If we divide it by the density of water or ice, namely 1,000 kilograms per cubic meter, we obtain 11,664 meters time Joules per day and kilogram. If we divide this number by the latent heat of ice which is 355,000 Joules per kilogram, we obtain roughly 0.03 meters or 3 centimeters. Yes, indeed, he can only melt 1 inch a day instead of the 30 meters that he argued.

"No doubt, the climate arguments and models are robust against such changes by 3 orders of magnitude. They're permanently safe because what they actually rely upon are not calculations but human bigotry and political fanatism."

Lumo, if you read Kahn's "On Thermonuclear War" you find the crackpot idea that the Russians could flood everyone. Kahn quotes von Neumann suggesting, I think, that someone sprinkles soot over the antarctic to melt the ice and flood cities.

This is so absurd it reminds me of the sort of errors you find. Anything dark coloured placed on ice warms up and simply melts a small hole for itself down a few millimetres into the ice until it has no effect. The soot particles sink, the ice remains. I've tried it.

Anyhow, near the poles the daily rotation has no effect on the elevation of the sun in the sky so you have 6 months of darkness then 6 months of light, which is not strong since it goes through a long slant distance of atmosphere. Any melting in the 6 months of light would result in re-freezing in the 6 months of darkness.

God alone knows what the climatic scientists put into their computer models to deal with this. The big error for a long time was what happens to carbon dioxide which dissolves in the oceans. Because of nuclear testing which put a known amount of measurable C-14 into the atmosphere, it was easy to work out the net rate at which the carbon went into the ocean, but the experts still got the details of the model wrong, because they guessed the partition between how much was taken up by land vegetation and how much went into the ocean.

You know how much carbon a tree takes up a year because its mass increases as it grows, taking in CO2. The kinds of errors in climatic science are just dumb. I don't agree with you regarding the cause, I think it's due to the committee politics.

You get a bunch of them writing their papers or computer programs, and they have to reach a consensus on the methodology in a meeting, so they all vote for what superficially looks nice at the time, and nobody is personally responsible for anything.

Global warming will be a benefit when you consider Canada and Siberia, where a small increase in the number of frost-free days leads to a vast increase in agricultural potential. The only drawback is the increase in hurricanes and tornadoes in tropical areas, due to increased sea temperature.

It is very sad that climatic politics is locked into making scare-story predictions instead of planning to deal with the problems objectively.

Best wishes,
Nigel

3. Dear Robert,

in Arctic you would need something closer than a year than a month to melt 2 meters, using all sunshine that you actually receive.

You say that we are talking about decades. No, one is only talking about decades when he uses 1000 times faster meltdown of ice, like the "climate modeller focusing on ice" William Connolley.

Otherwise we would be talking about centuries and millenia before the climate is changed really substantially so that it affects people and likes and everyone would understand that this debate is totally silly.

The fact that we're talking about decades is used as a permanent justification. In 20 years, everyone will know that these theories in 2005 were just idiotic, much like all of their predecessors - like Ehrich's mass starvation theories. But no one will remember the names of various Connolleys, and therefore no one will be really able to convict them and arrest them for the trillion-sized damages that they caused to the whole civilization. Which is why they have a complete freedom to invent ever more idiotic theories and steal ever larger amounts of money for their perverted political plans.

Moreover, they're not the only guilty ones. It's also thousands or millions of other people who uncritically believe their nonsensical deductions.

This is no science, and it is not fair politics either. The people who are behind the massive spending from taxpayers' money should be responsible for their acts.

Best
Lubos

4. And no, my friend Robert, I am not proposing to melt all ice on the planet. It's "them" who argue that ice is gonna melt instantly. I don't even know whether the total increase of ice on our planet is positive or negative, especially because of the massive increase in Antarctica.

I only demonstrated that these conclusions about imminent tragedies are always based on their totally failing intuition about physical processes important for the climate.

If one needs a year to melt the two meters with the full power of the Sun, it does not mean that the ice will actually melt in one year. In reality, the ice is pretty close to the equilibrium, and the equilibrium is only slightly violated so that it naturally takes about a century to melt significant masses of ice such as sea ice.

Now, all of "our" CO2 changes this equilibrium at most by a few percent, so this is about changes of the trend of meltdown that could remove it in something like 1,000 years. It's just completely ridiculous to plan a protection against such things before some bad consequences actually start to occur. And of course nothing wrong is happening with the climate right now. And the same thing will hold for centuries. If the climate will be a bit different in 50 years, everyone will also be more accomodated to the new conditions.

We can't be paying air-conditioning for our grand-grand-grand-grand-sons because they would immediately throw it into trash. The later we pay for whatever related to the climate - and I am not sure what is exactly the thing that we should shoot for - the better (and cheaper).

Saying that one type of weather is moral and another type of weather is immoral is simply dumb.

5. Lubos... don't you think it was just the teensiest bit dishonest to base an entire post around a sentence I deleted before you even read the blog?

6. Robert:

The solar radiation, at the top of the earth atmosphere, if straight down, is 1369 Watts/M^2, not 1.6KW/M^2.

And certainly, in the polar area, you do not have sunshine directly overhead. It's got to come down at a tilted angle, reducing the amount of radiation per square meters.

The fact that it comes down at an angle also means it will go through much thick atmosphere at an angle, so it will lose considerably before reaching the ground. You notice the same phenomena when you watch the sun set on the beach. It loses so much power when going through the atmosphere at a highly tilted angle that the sun becomes reddish and you can actually star at it.

And don't forget that the surface of the earth constantly radiate heat to outer space as well. We all know the outspace is a vast super cool heat sink at 2.725 K CMB background temperature. Whether the polar ice will melt or not depends on the balancing temperature at which point the heat radiated away and that received from the sun are in equilibrium.

And of course, in the dark half of the year in the polar area, where there will be no sun shine 24x7, such equilibrium is not possible since it only lose heat to the space heat sink, and gain nothing from the sun shine. So the polar ice grows some what during the winter and melt some what during the summer. And largely remain intact over centuries.

So really, for polar area, the only time scale that matters is half year, not centuries.

Quantoken

7. Beletter:

You've got to understand that while casual typos like I accidentally add a "r" to your name. Or sometimes you mean mm (milimeter), but typed it as nm (nanometer). Those are trivial. But getting an order-of-magnitude quantity wrong by 3 orders of magnitude, that reflects a complete lack of intuition of physics quantity, and is absolutely unforgiveable. Too bad you made such an error and by all means Lubos can jump onto it. Some times Lubos makes similar low level mistakes and I jump onto him as well whenever I can catch him. So it's a fair game.

Another lack of intuition, reflected on most global warming clima-to-logists, is the fact that they fail to recognize that CO2 is much heavier than water, H2O. The molecular weight of CO2 is 44 while that of water is 18. In thermal dynamics that means the distribution of CO2 is much closer to the lower layer of the atmosphere, while that of H2O is much higher?

Does it matter? It sure does!!! The vast majority of solar heat reaching the ground, is absorbed by the ocean by evaporating the water. The H2O molecules are lighter than air and they raise very high, well above the bulk of CO2, on the top of atmosphere they radiate the heat away and condense back to water and form cloud.

You see the heat is thus release to outer space, totally bypass the CO2 in the atmosphere. Therefore largely defeating the green house effect of CO2.

Quantoken

8. Dear Belette,

accidentally, I've seen your brave statement about those 30 meters before you scratched it. It was shocking but because I did not know what sfc was, I did not want to reply something that had a probability to be missing an important point.

As you can say, I did the calculation and knew what was the right result.

But this history does not matter. As a person paid for climate, you should know how much ice can the Sun melt before someone looks at your blog, and you should also know if after someone looks at your blog. You should simply know it all the time, and whether or not I saw your craziness earlier or later makes absolutely no difference.

Best
Lubos

9. 1.3 or 1.6 doesn't matter for order of magnitude estimates.

As far as the angle goes: If alpha is the angle between the spin of the earth and the orbit (23 degrees roughly) then what you have to compute for the pole is

1/2pi int_0^pi dphi cos(phi) sin(alpha)

=

0.12

so if you want that shaves of another factor of 10.

However, I agree that it's not clear that if the world average temperature increases the amount of polar ice gets less. You could also imagine that more water from the oceans evaporates and eventually falls as snow in the arctic regions where it will still be way beyond freezing temperature.

10. Robert:

How could you make two mathematical conceptual errors in a row. I thought string theoretists, if not decent in general physics intuitions, should at least be sharp in mathematics.

You said:
"the angle between the spin of the earth and the orbit (23 degrees roughly)"

By spin you mean the spin axis? The angle between spin axis and the orbital plane would be the complemental angle of 23.5 degree. The 23.5 degree should be the angle between the rotating plane, and the orbital plane, not between the spin axis and the orbital plane.

And I do not know what you make of the integration you cited:

1/2pi int_0^pi dphi cos(phi) sin(alpha)

But looks to me you integrate cos(phi) from zero to PI, you should get zero, and the sin(alpha) part is just a constant. Check your math again.

Quantoken

11. Dear Quantoken,

Robert probably meant the angle between the spin axis and the axis of the orbital angular momentum which is 23.5, much like the angle between the two planes - the plane of the orbit and the equatorial plane (which is perpendicular to the axis of spin).

Hi Robert,

once you agree that the whole Antarctic ice is unlikely to disappear (and after averaging some fluctuations, the same thing is probably be true for the Arctic - why not), then it's pretty clear that there can't be any truly "global warming" tragedies awaiting us.

The icebergs can't quite melt, the ice will still regulate the oscillations of the temperatures, and so forth. So does the global warming theory predict meltdown of all ice and higher fluctuations or not?

Best
Lubos

12. Yeah I know Robert probably knew what he meant to say if not for the wrong selection of terminology.

But his integration is clearly wrong. When the sun is below the horizon you really can not count it and integrate it as negative sun shine :-)

I tried to figure out the right calculation, and find it actually is not trivial at all.

This will be a challenge to see who can first come up with a correct calculation of the percentage of sun shine the polar area receives, averaged over a year. Polar Area is defined as the area with altitude 67.3 or above. And NO, Robert's integration is not right, even if he removes the genative part.

Quantoken

13. QT: you provide a perfect example of why doing arithmetic isn't enough. The atmosphere (or at least the lower layes, including all the bits we're talking about) isn't sorted by mass (obviously, or we'd be living in the unbreathable soup of heavy noble gases and CFCs and stuff at the bottom). This is (a) obvious and (b) measurable, if you won't believe the obvious.

That applies to all the well-mixed quantities. Water vapour is a bit different, because it condenses out in some circumstances. But it still isn't sorted by mass.

14. Belette:

I can not believe that a researcher like you could be SO POOR in basic physics knowledge and basic intuition regarding quantities.

It is a fact that air molecules of different mass DO get segregated under gravity field, so heavier molecules tends to take up a larger percentage at lower altitude than high altitude. But certainly it is not a clear cut segregation that you find 100% noble gas at one layer and 100% CO2 at a different layer. There is a distribution, over the scale of several kilometers or more. See this for a picture how the air compositions change versus altitude.

Ths segregation is decided by the fundamental laws of thermal dynamics and three factors play out in balancing act:
1.Entropy: Molecules tend to diffuse evenly to gain maximum entropy. This would make the air composition the same ever where, when gravity is absent.
2.Energy: Under gravity pull, molecules tend to concentrate on lower positions to lower the gravitational potential energy. The more heavier molecules are more likely to be found at lower altitudes.
3.Temperature. This decides what is more important: lowering energy, or increasing entropy, in reaching a equilibrium.

As a result, the volume density distribution of mulecules is given by this formula:

n(h) = n0 * exp(-mgh/kT)

Any one who has taken a physics 101 should be more than familiar with the above formula.

Based on their difference of molecular weight (O2 is 32, N2 is 28, and CO2 is 44), you would expect that the volume density of O2 will be reduced by half for every 5KM altitude gain. And N2 is halfed for every 5.7KM. The two numbers are close enough that we say that in the breathable part of atmosphere (no more than 10000 feet) O2 and N2 has about the same composition every where. But for CO2 since it's much heavier, it's halfed for every 3.65 KM gain of altitude. So for the water vapor that goes up to 8KM height, the CO2 is only 22% in volume density compare to sea level.

That is to say, for the water vapor at 8KM height, 78% of the atmospheric CO2 will be in the layer below it, not above. The water will be evaporated from the surface of the earth, raise high above in the atmosphere, release heat there and radiate to space. And come back down in the form of rain or snow, colling the surface temperature. This process TOTALLY by-passes the CO2 layer, 78% of which lay no more than 8KM above the ground. Therefore the green house effect is by-passed.

You can not even deny it that the process is actually happening. Every single drop of surface water that goes in the air at all, was vaporized absorbing huge amount of heat, when they come down, they come down either as water that's cooler than the surface, hence colling the surface, or come down as snow, colling down the surface even more.

This process is actually happening every day, because surface evaporations and rain falls are natually observed, and you notice the temperature cools whenever there is rain fall or snow fall. That is a huge heat exchange process supplementing any direct heat radiation from the ground, rendering the green house effect irrelevant at all.

The so called 0.6 degree average temperature raise over the century, is nothing more than the data bias due to the fact that you prefer to measure your temperature on a nice sunny day, when it's hotter, rather than take the measurement on a rainy day, or a snow day, when it's colder and wet. I bet if you average those rainy days in, the 0.6 degree data bias will be gone or you may even find some cooling going on.

Quantoken

15. I might also add that the segregation of molecules of different mass under gravity field indeed happens. The strong evidence is that nuclear weapons are real, not fictional. The same segregation process is used in cetrifugal force devices that enrich U235 out of the natural U238. Einstein told us it's really the same thing, since the centifugal force, which is an acceleration field, has the same effect as the gravity field. And U235 and U238 are segregated due to their slight difference in mass.

Quantoken

16. QT: oh dear, you are unteachable. One last try, not really for you, but for the lurkers. The very link you quote sez "The highest layers of the atmosphere, the mesosphere, the thermosphere, and the exosphere, differ significantly in composition from the lower regions"... in other words, down in the troposphere, and even up in the stratosphere, things don't separate by gravity.

Lubos (are you watching your comments?): it would be fun to see you comment on this; either to commit yourself to QTs mistake, or to correct her.

17. Dear William,

I enjoy your discussions with Quantoken - it's a fair discussion between two peers. ;-) (Is it she? Why do you think so?)

Well, I don't believe in complete segregation; the Maxwell-Boltzmann distribution (exponentially decreasing) for individual gas components (they have different rates of the decrease) is more realistic. Of course, this distribution is mostly constant in the "lower troposphere". And it's the first time I hear that gravity does not decide about the concentration of molecules in upper stratosphere. Could you teach us more about this surprising statement?

Best
Lubos

18. Hi Lubos, hedging your bets I see. Try http://www.faqs.org/faqs/ozone-depletion/intro/, section 1.3.

19. Dear Belette,
Actually I read sec. 1.3 of what you suggested Lubos. However, I don't see any kind of argument for
the "fact" that in the earth's troposphere and stratosphere,

1) *most* stable chemical
species are "well-mixed" (i.e. their mixing ratios are independent of altitude).

2) molecules do not segregate by weight in the troposphere or stratosphere (here he was just repeating himself, I guess).

3) and that the relative proportions of Helium, Nitrogen, and Krypton are unchanged up to about 100 km.

4)and that the "...vertical transport in the troposphere takes place by convection and turbulent mixing. In the stratosphere and in the mesosphere, it takes place by "eddy diffusion" - the gradual mechanical mixing of gas by motions on small scales".

I would believe in all these statements if you could direct me to a source where 1)-4) are explained by some well-known physical principles...They could - in principle - just be empirical facts? At any rate, I cannot disagree with his statement, that:
"if a species' mixing ratio changes with altitude, some
kind of physical or chemical transformation is taking place", since I don't see, that the concept of "transformation" means a lot here. Could the "transformation" - in principle - be the identity-"transformation", i.e. the trivial one?

Best, Kasper

20. Belette:

Thanks for the link. I know the exponential Maxwell-Boltzmann distribution is only valid when it's in equilibrium. After reading the link you provided, I concede that I was wrong about the mass segregation part. It makes sense that when the free path is short, the turbulance of air transportation and mixing dorminates over the diffusion. So the conclusion as given by the link is right.

But that does NOT change the main point of my argument, which is that the process of water evaporate from the ground, and subsequently fall down as rain or snow. That process brings out a huge amount of heat from the ground, without the radiation, therefore it by-passes the CO2 blocking of radiation completely.

As for what happens to the water vapor up there, how it releases it's heat to the space, whether CO2 plays a role or not, that is not a concern to us on the ground. All we know is the water vapor did upload its heat in the upper atmosphere, and it comes down as rain or snow to cool the ground further.

This part of cooling is HUGE. We can estimate by the average rain fall snow fall per year. A rough estimate is about one meter of rain fall per year, if you average the land as well as the ocean. Each gram of water, when evaporated, absorbs at least 539 cal. of heat. That's a huge effect. If you conver the solar radiation 100% to evaporate water, it counts to just 4 meter per year. So at least 1/4 of the ground heat is dissipated through water evaporation, by-passing the green house effect. The ground only needs to radiate 75% of heat through the atmosphere, which is easy, since without green house effect it could have radiated 100%.

Quantoken

21. Lumo - in Arctic you would need something closer than a year than a month to melt 2 meters, using all sunshine that you actually receive.

You really should learn the elementary facts before you pronounce so rashly. As I point out on my blog, the net radiative flux is always negative in the Antarctic and only microscopically positive in the middle of the Arctic summer. Polar sunlight doesn't melt any ice - the melting that occurs in the Summer is mainly due to heat transfer from air warmed somewhere else.

22. quantoken said - It is a fact that air molecules of different mass DO get segregated under gravity field, so heavier molecules tends to take up a larger percentage at lower altitude than high altitude.

A little knowledge is a dangerous thing. I'm not sure where or if you took Ph 101 (or Ph 1), but your "law of atmospheric distribution" only works in an essentially collisionless atmosphere - above, say, 100 km. (Like in the exosphere of your link). In the troposphere and stratosphere, gases are well mixed by collisions. Consult any Atmospheric Physics 101 book.

The physical reason is easy to see - gravity keeps trying to sort out the moleculesm but it is incredibly weak compared to the intermolecular forces which scatter randomly, quadrillions of times per second.

23. Hi QT. Congratulations: you have surprised me: I expected you to persist in your error.

OK, your main point: that latent heat carries energy up from the ground. This is true, but not as true as you say. The latent heat doesn't get to the top of the atmosphere; radiative transfer is still important above; and it varies spatially.

Most simplified presentations of the GHE omit the latent heat point. Don't be mislead by that into thinking that the process is omitted from climate models, or that the people in the field don't realise it.

Also be aware that the convective mixing is limited to the troposphere, and that for much of the earth it doesn't get very high into the troposphere (with the important exception of some of the tropics).

So when you say "by-passes the CO2 blocking of radiation completely" you have pushed your argument too far. It by-passes it partially, but enough remains.

24. KO. Not quite sure what you are doubting. The FAQ says very clearly:

In reality, however, molecules do not segregate by weight in the troposphere or stratosphere. The relative proportions of Helium, Nitrogen, and Krypton are unchanged up to about 100 km.

and

Why is this? Vertical transport in the troposphere takes place by convection and turbulent mixing. In the stratosphere and in the mesosphere, it takes place by "eddy diffusion" - the gradual mechanical mixing of gas by motions on small scales. These mechanisms do not distinguish molecular masses. Only at much higher altitudes do mean free paths become so large that _molecular_ diffusion dominates and gravity is able to separate the different species, bringing hydrogen and helium atoms to the top. The lower and middle atmosphere are thus said to be "well mixed." [Chamberlain and Hunten] [Wayne] [Wallace and Hobbs]

and

Experimental measurements of the fluorocarbon CF4 demonstrate this homogeneous mixing. CF4 has an extremely long lifetime in the stratosphere - probably many thousands of years. The mixing ratio of CF4 in the stratosphere was found to be 0.056-0.060 ppbv from 10-50 km, with no overall trend. [Zander et al. 1992]

Those seem to be clear statements, with explanations, and backed up by observational evidence and references. What more do you want?

25. Belette, as you say, gases in general are well mixed in the troposphere. However, the most important greenhouse gas, water vapour, is not well mixed at all.

In the tropics, where most of the heat enters the earth, a huge amount of the heat is removed quite quickly. The sun hits the ocean, evaporating water. Thunderstorms form, and the water vapour moves way high into the troposphere. Vertical rates for the movement of this water vapour are on the order of 300-500 metres per minute or more, so it arrives at the top of the cloud very quickly.

At this point, it is free to radiate into space. (Before reaching the top, the majority of the radiation is merely re-absorbed in the upward-moving column due to the presence of lots of water in liquid, vapour, and/or solid form.) This intense long-wave radiation can be seen very clearly in infrared pictures, which show the very tops of the tropical clouds radiating strongly to space. The strength of this radiation, as seen from space, shows that a large amount of this radiation is not being absorbed in the atmosphere. Why not?

As another poster pointed out, at that point the radiation is emanating from well above the majority of the CO2 in the troposphere. For this reason, a large (but unknown) amount of the radiation cooling the earth will not be affected much by any changes in CO2.

Since thunderstorms are way below the cell size of the GCMs, it is very hard to see how this effect might be taken into account. Do you, or anyone, know if/how this physical phenomenon is modeled in the GCMs?