In reality, the very concept of a "scientific consensus" is a negation of the scientific process. You never hear anyone talking about "scientific consensus" when they discuss things like General Field Theory, SETI, or even such locally-contentious issues as evolution.

Indeed, even if there were a "scientific consensus" about something, any advances in that field would more likely result from challenging the consensus as vindicating it. As the late Isaac Asimov once observed, most scientific breakthroughs start not with "Eureka!", but with "Hm, that's funny..."

First of all, it has to be understood that a scientific consensus is not the same sort of animal as a consensus in a normal group.

For example, in a standards committee, consensus means that enough people agree that a compromise among conflicting views (really, we're usually talking about commercial interests here) can be brokered. Whatever unhappy people there are, they are not numerous enough or vehement enough to make a difference. The operational definition I have heard an experienced committee chair give: "A consensus is when the shouting has stopped."

But in scientific discussion, there is no compromise. Among scientists of a given discipline, there are two things going on: On the one hand, no one believes anything based just on authority. That's not the way it works. On the other hand, everybody knows that there are some people who actually are smarter than other people, and it makes a lot of sense to listen to them.

Because of that, the folks who are considered really smart have a large degree of influence in swaying opinion and, more important, determining the direction of analysis. These are people who've proven to be good at figuring out ways of thinking about things that have been useful in the past, so people have a greater degree of trust that their way of thinking is informed with insight.

So what really happens in the formation of a scientific consensus is that the smart guys come to a common understanding about which experimental results are significant and need to be taken into account, which discrepancies are really a problem and which ones are probably not too important (No, Virginia, all discrepancies are NOT equal), and therefore, in which direction the truth probably lies.

That direction, and the detailed logic that supports it, creates the nucleus around which the consensus of the group forms. There is no compromise and no negotiation. If you, as an individual, still don't agree, no one will try to coerce you, although some people may try to explain it to you. But if you persist in your own point of view, no one will stop you.

What will happen? Most likely, as Richard Feynman once said, the conventional view (the consensus) is right, and you will be wrong. In that situation, as Max Planck once said, the scientific revolution (if the term "revolution" applies to this particular difference of opinion) will be complete, not when every objector has been convinced - but when every objector has retired, and his/her students have failed to take up the cause. End of story.

Occasionally, very occasionally, the rebel will prove to be right. Eventually that shows up when experimental results fail to support the theory, and more experiments are done but the problems don't go away. The smart guys come back to see if they can figure it out, in terms of the conventional view. If they don't manage to find the explanation, a new theory has a chance of birth.

But this is a rare event.

I can give a modest example of a scientific consensus forming:

I was taking a 3rd-year undergraduate class in Analytical Mechanics. I'd finished the week's problem set, and went to the student lounge in the Physics department to hang out.

I saw 5 fellow students, trying to figure out a particular problem of the set. Listening to them, I could tell that they were clueless: Not a single one of them knew what was going on, or even knew which of the different aspects were important.

However, as I listened to one student after another explain his/her understanding of the problem (and as I noticed his/her misunderstanding of essential aspects), I noticed how the other students reacted. When the presenter was actually on solid ground, the other students would resonate to what s/he was saying; when s/he was confused or bullshitting, the others were also confused and couldn't follow it. The result was that, on the average, the "correct" part of the argument seemed to earn approbation, and the "flakier" part didn't.

After about 3 rounds, over about 40 minutes, they actually converged on the correct answer to the problem - something that I would never have expected from what they were saying at the beginning of the discussion.

My conclusion is that science does, in fact, move forward by consensus. It works pretty well - better than one would expect - most of the time, and is self-correcting the rest of the time. And it works best when the folks involved are focused not on the end results, but on doing the problem as correctly and honestly as possible.

They're right. A scientist comes up with an idea regarding a phenomenon. He does tests, makes observations, and compiles evidence and arguments he'll use to try and convince other scientists. His work does a good job of explaining what's going on his ideas get adopted as the best explanation.

Something like climate change is horribly complicated. Lots of feedback, lots of variables, tons of chaos. Even the best models are hopelessly inadequate to give more than a vague suggestion of a hint of a notion of a possibility we might have some half-assed idea as to what's going on.

But there's one thing there should be no doubt about. That is, thanks to our actions greenhouse gases are piling up in the atmosphere faster than they otherwise would. Yes, the amount of CO2 we produce is but a fraction of what volcanoes porduce. However, the amount of CO2 that gets added to the atmosphere every year is the sum of what we produce and what volcanoes produce. In short, the natural CO2 sequestering mechanism is being overwhelmed.

Locally the nights tend to be warmer when they're overcast. When they're clear the night will be colder. I expect it's the same way in your part of the world. That's because water vapor is a greenhouse gas. It's really effective when it's condensed into little water droplets. During the day sunlight warms up the ground. At night that energy is re-radiated back out into space, but at a longer wavelengths. Now clouds and water vapor are pretty good at stopping light regardless of wavelength, but CO2 and methane (another greenhouse gas) are better at stopping longer wavelengths than they are shorter ones. So the more CO2 and methane you've got in the atmosphere, the more long wave light gets trapped in the atmosphere. The more energy you have in an inherently chaotic system, the more chaotic that system gets. The extremes get more extreme, and anomalous events happen more often.

In short, it's never a simple, straightforward rise in temperature. On the average the temperature does go up, but overall you see an increase in variation and variability, and these short term events can obscure long term trends. And we tend to engage in short term thinking. We see the storm over the distant mountains and think ourselves safe, ignoring the high, scudding clouds coming towards us from the mountains.

No, scientific consensus is nothing at all like academic consensus. It's not perfect, but it does a far better job of coming to a real agreement about how the world works.

Neal King's lengthy post obscures the ideologically driven premise of the environmentalists, trained at liberal universities, many the children of earlier breeds of radicals and hanger-ons, who jumped on this issue for a perfect attack on capitalism (or what's left of it) and on the base of our economy - fossil energy.

Of course they will reach a consensus at finding the truth. Their politics will drive them to only follow certain paths of inquiry, all leading to their pre-conceived premise, and to work very hard at disproving or ignoring evidence to the contrary - even down to using ad hominem attacks, firings, and ridicule.

To the extent that scientists like this make up the bulk, or at least most vocal group of those studying weather and climate change, we no longer have scientific method.

In a local environmentalist rag pretending to be a newspaper in Astoria, Oregon, there was an article about severe flooding in the Columbia River estuary a winter back. Animals
drowned, flood tides unseen in hundreds of years flowed up a tributary of the Columbia washing away structures built a century or more ago.
Reason? Global warming and higher sea level, according to a number of noted climatologists. As usual they hedged their opinions with such phrases as "general consensus" and "generally accepted" and interspersed the usual disqualifiers that indicates to any rational mind quesswork - and hope.

Since I own property in the affected area I have intimate knowledge of what really happened. Over the past few years a non-profit collective (see:http://www.fws.gov/news/newsreleases/showNews.cfm?newsId=769E6B3C-A2D9-F6C9-1D01150181B866DA
has been giving out very large sums of money to conservancy groups to buy old unprofitable dairy farms at the mouth of the Columbia.
When purchased they promptly blow up the levies that have protected the farms.
Combine this with the fact that an entire island has been created at the mouth of the above mentioned tributary by goverment paid channel dredging, which blocks a good part of flood tides, directing them up the side channel, and you know what happened.
Water washed onto old farms recreating the re-claimed wetlands, & flooding neighbors yet to be convinced to sell out.
Since I rarely visit the area, and my property is unaffected, I don't know how many civil lawsuits have been filed, or most likely settled by "above market value" purchases.

The environmental movement in general, and the as yet unproved Global Warming Hypothesis, would be a joke in scientific circles had they not been infected by this joke of a religion, or intimidated into silence.

Allan Kellog:

One point of yours I would take issue with: The amount of C-O2 produced per year by volcanoes, worldwide, is about 1/134 of what humans produce through burning of fossil fuels.

Check out the USGS site.

Frank,

The fact that some environmental groups may use, or abuse, the issue to their advantage does not mean that the issue does not exist.

The scientific case for GW is, in the broadest of broad outlines:
- There is a straightforward (indeed, textbook) analysis of how C-O2 acts in the atmosphere that shows how more C-O2 should increase the greenhouse effect.
- Based upon the measured increase in C-O2, the calculated increase in global average temperature is in-line with the observed increase, over the last 100 years (the relevant period for industrialization). This takes into account other drivers of warming, such as known variation in solar luminosity (minor), volcanic activity, and sulfate aerosols from the unscrubbed burning of coal.
- All other proposed mechanisms, aside from the emissions of greenhouse gases, fail to to explain the extremely rapid rise in temperature: 0.5 degrees in 100 years may not sound like much, but it's at least 6 times faster anything observed before, and much higher than "customary". These failures include: variation in solar luminosity (at 0.1%, too small), cosmic-ray flux (no trend, so no change that can effect a change), urban heat island (proven not to have an effect on measured GW trends). None of them have panned out.
- Based on carbon-14/carbon-13 isotope ratios, it is clear that this increase in C-O2 is due to fossil-fuels: It cannot be from out-gassing from the ocean or land, and, as noted above, the volcanic addition is a tiny fraction. It has to be from fossil fuels.

As Sherlock Holmes said, "Once you have eliminated the impossible, whatever remains, however improbable, must be the truth."

In this case, we're not even talking about "improbable" explanations - we're talking about textbook atmospheric physics.

Lets see if I can explain the "rapid" rise in the surface temperature record over the last thirty years.
Look here. Notice the air conditioner. Have you ever spent some time underneath an a/c heat exchanger on a summer day? I have. It gets really hot in a short time.
Now check here. That big black thing is a trash incinerator. Notice the little thing that looks like a bird house right next to it, it's not a bird house.
Now check here. And here. Notice the box wedged in between high voltage power transformers and a sidewalk. And here. Notice the pole marked "MMTS shelter"
mounted in the middle of a parking lot, surrounded by a/c units.
What are those things?
Those are the thermometers that Hansen and Jones et el used to measure the global surface temperature.
I prefer to use this temperature gauge. It's more honest.
Less fudge factor.

Neal, my profession is not in any way related to scientific inquiry in which facts are determined by probability. That's quessing. You may or may not be proved correct. I've spent 40 adult years dealing with the real world of business. And in those years I've witnessed numerous strangleholds placed on my profession by quack science of the type that is now infecting almost every field.

Most of those regulations to "save the environment" and now the world, they grandly proclaim, have achieved the very opposite effect of their alledged intentions. The controls on manufacture of the base chemicals and finished product that regulators have placed on some of my necessities has made them simply move off-shore, where they are produced without ANY safequards.

The immediate effect on Western manufacturing economies will be to furthur hobble them. In the long run the effect would be decimate them. With a population in this country alone approaching 400,000,000 how long do you think until food shortages start? Already goverment mandated diversion of corn to fuel production has caused feed grains to almost double.

But what is most troubling about all this is assumption of a command economy, where decisions about what light bulb to use, what kind of car to drive, how much fucking toilet paper to use, are dictated by those simply out to destroy any vestiges of advanced civilization.

"CO2 and methane (another greenhouse gas) are better at stopping longer wavelengths than they are shorter ones."

Actually, if you look up the absorption spectrum of carbon dioxide (by, say, Googling that very phrase) it turns out that CO2 is really good at stopping three narrow bands of wavelengths centered near 2.7, 4.3, and 15 microns. It doesn't do much of anything to wavelengths outside those bands. Water's absorption spectrum, by the way, is at 100% at 2.7 microns and more than 50% at 15 microns; the 4.3 micron band is the only one at which CO2 absorbs energy and H2O doesn't.

Frank,

Maybe things seem very definite in your day-to-day world. But I can tell you it would be a very different world indeed if in the 1930s, people hadn't been thinking about bizarre concepts of reality that most people still can't deal with or accept, the apparent paradoxes of which make anything that might trouble you wrt GW childishly straightforward.

I am talking, of course, about quantum mechanics - which deals very largely in terms of probability. Without the study of quantum mechanics, we wouldn't have made any significant progress with transistors, lasers, the understanding of the star...

Nor is its influence over. If they ever get quantum computing to work, watch out! They will be able to crack any code. No password and no security system will be secure. For financial institutions, it will be ... a problem.

And unlike the case of the Y2k bug, I don't think there is any easy answer.

So the facts, and even the plausible speculations, of science have the potential to rock your world. Not everything and everybody is motivated by political or control fantasies.

Michael Brazier,

The best picture I've seen comparing the absorption spectra of C-O2 and H2-O vapor is at (http://brneurosci.org/co2.html). (Even though I disagree profoundly with the point of view of that site!)

The spectra indicate that C-O2 absorbs significantly where H2-O does not, around 4 and 15 microns. (Even though H2-O does absorb around the 15, you can see it is ramping up over a section when the C-O2 is already high.) But there is another aspect that I hadn't thought about which also plays a role.

The way the enhanced greenhouse effect works is that the radiation at a particular wavelength is the blackbody radiation at that frequency for the temperature at the distance where the Optical Depth = 1, coming in from space.

Another way of putting it: the gas radiates in all available frequencies and at every altitude. But the intensity of that radiation reflects the local temperature of the gas molecule. At Optical Depth = 1, that means that a photon leaving the atom in an upward direction will have a "clear shot" at escaping to space; whereas at Optical Depth = 2, it is very likely to hit another molecule and be absorbed and eventually re-radiated. So the radiative transfer physics works out that the radiation that ultimately escapes from the atmosphere has the intensity that reflects the temperature at OD = 1 (equivalently, one mean-free-path for a photon at that frequency).

For different frequencies, because of the different spectral lines of the molecules constituting the atmosphere, the point of OD = 1 will differ. In particular, if both C-O2 and H2-O absorb that frequency, both absorptions have to be taken into account to determine the OD = 1 point.

Ordinarily, I would expect that, since there is so much more H2-O than C-O2, that whatever effect the C-O2 would have on the optical depth would be negligible. But there is another factor: the limitation of humidity.

Usually we assume that gas species are well-mixed in the troposphere: that is to say, that if C-O2 is x% in the atmosphere overall, then it is x% at every altitude in the troposphere. But this is NOT true of water vapor, because the maximum concentration of water vapor at a given temperature is limited by the saturation vapor pressure, which declines with temperature. That means that, as you proceed up the atmosphere, the water vapor becomes a less and less significant fraction of the atmosphere. This is actually shown at Figure 1 at
(http://www.agu.org/sci_soc/mockler.html), where you can see the decline in the water-vapor mixing ratio with height. It looks like the drop should be about a factor of 20 or so, corresponding to the temperature of the original greenhouse effect.

The point I'm getting at is that, if it comes out that the OD = 1 point is at an altitude where there is lots of C-O2 but not much water vapor, then the C-O2 can be significant even if there's tons of water vapor at levels below. Because the way that the enhanced greenhouse effect works is by changing the altitude of the OD = 1 point: when you add C-O2, the OD = 1 point moves upwards, and therefore since air temperature is largely controlled by altitude, the effective temperature of radiation (at that frequency) becomes lower, so the radiated power declines. And then we have radiative forcing, because not enough long-wave power is leaving to balance the incoming visible radiation; what has to happen is that the ground-level temperature rises from the extra heat, and then the whole atmospheric temperature profile rises, until the temperature at the OD = 1 point becomes the same as it was before all this began. And then it will be in radiative equilibrium again.

So I expect that the explanation is that, between the issue of absolute humidity on the one hand, and the profiles of the absorption lines for C-O2 and H2-O on the other hand, that there is a substantial range of frequencies (around 15 micron) where the OD = 1 point is controlled by the concentration of C-O2, and not just buried in the H2-O. Because if it's buried in the H2-O, it would really be true that even large changes in C-O2 would not affect the effective temperature of radiation.

Anyway: the generally accepted solution to all this is that the radiative forcing is, when all is added up, 3.8 Watts/m^2 per doubling of C-O2, when all spectral lines are taken into account. I have never heard anyone challenge it, not even Lindzen or Singer: they just stay away from it. I guess, to preserve my soul, I shall have to find the original articles in which these hairy details were worked out, and see if all proper respect has been paid to the caveats.

A technical point: saturation vapor pressure is a physical limit on the concentration of all gases, not just water. The difference between water and CO2 is simply that water's triple point is quite close to the temperatures and pressures found in Earth's atmosphere, so that this physical limit is reached in practice; while CO2's triple point is far away, and its saturation pressure is larger than the real pressure at all altitudes.

By the way, at what point do you think Nelson's article goes wrong? The two key facts in the argument are that temperature rises logarithmically with CO2 concentration, which you yourself have stated as a fact; and that CO2's present contribution to the greenhouse effect is not more than 2K out of a total of 33K. Grant both those facts and it follows that several doublings of CO2 concentration would be necessary to raise the Earth's temperature by 5K; and since we have yet to reach even one doubling from the preindustrial baseline, global warming from burning fossil fuels looks much less urgent than the environmentalists are claiming it to be.

MB,

Who is Nelson? What article?

MB,

- Another way of saying that is that water is the only naturally occurring liquid on this planet.

- I still have no idea of whom you mean by Nelson, or what his article says. However, it is interesting to think about how two separate gases contribute to the greenhouse effect. It is not too complicated in the case that the two absorption spectra have no overlap, because then you can consider them separately (although even then, spectral lines at greatly different frequencies will contribute differently to the heating, even though they are due to the same molecules).

When the two kinds of molecules have spectral lines in common, I think the total contribution cannot quite so easily be broken down into the sum of two separate contributions: the two absorptions add up, but what matters is how that moves the altitude at which the optical depth at that frequency = 1.

A small twist in the picture: at least some of the lines of interest in C-O2 have enough pressure-broadening that it changes the way the optical depth depends on concentration. I think it goes like 1/sqrt(concentration) instead of 1/concentration, as one would normally expect.

And, as mentioned above, the decrease of absolute humidity with temperature (and thus with height) gives the C-O2 a second chance to be important: if it manages to push the point at which optical depth = 1 above the level that there is significant amount of water vapor, then it will be acting essentially alone. From my quick look at graphs of water vapor as a function of height, it looks as though that won't be quite the case: There should be a reduction of water vapor at that level, but not an elimination. So that means there will still be a "drag" on how much radiative forcing the C-O2 will produce.

- With regards to the degree of threat posed by the C-O2 doublings, keep in mind that global emissions of C-O2 have been growing exponentially in the last few decades. (By the way, this is a relatively recent trend, and that fact explains why, earlier in the 20th century, atmospheric scientists did not expect C-O2 to be such a big deal: they did not anticipate that kind of growth.) People have argued that there may not be enough petroleum left to double the amount of C-O2; but the last time I heard, there's about 500 years or more of coal, even at exponential growth of power usage, so I think we have plenty enough to cause ourselves trouble. (There is also another limit: At a rather high level of concentration, C-O2 is toxic. But I think this is well beyond the range of our worries wrt C-O2 concentration and GW.)

Neal King:

T. J. Nelson is the author of the article containing the graphs of absorption spectra you referred to, Cold Facts on Global Warming. I'm asking why you disagreed with the thesis of that article.

"Another way of saying that is that water is the only naturally occurring liquid on this planet."

Not quite right; what it really means is that water is the only substance that naturally occurs in solid, liquid, and gaseous phases on this planet.

Michael Brazier:

- H2-O: The only example of a gas, that is actually present, that is also a liquid here.

- Thanks, I eventually figured it out, too. (I had glanced at the article, but didn't remember the author's name.)

There are various problems I have with this article. He half understands the issue: He talks about how the IR is absorbed and re-emitted, not just absorbed. But his way of dealing with it does not allow him to calculate what the effect will be. And he never really shakes the misconception that the emission is being blocked.

If you look at the end of his section, "Absorption of Infrared Radiation", you can see the confusion: "The net effect of all these processes is that doubling carbon dioxide would not double the amount of global warming. In fact, the effect of carbon dioxide is roughly logarithmic. Each time carbon dioxide (or some other greenhouse gas) is doubled, the increase in temperature is less than the previous increase. The reason for this is that, eventually, all the longwave radiation that can be absorbed has already been absorbed. It would be analogous to closing more and more shades over the windows of your house on a sunny day -- it soon reaches the point where doubling the number of shades can't make it any darker."

What he says (I have put it in boldface) is exactly right. And then what he says right after it (which I have put in italics) contradicts it! If the dependence is logarithmic, you can keep on increasing the temperature; but if it's like doubling the number of shades on a window, you can't. He can't have it both ways.

Then, in the next section, "Linear Climate Predictions": He creates a linear model, which is simpler. It's nice that it's simpler, but why does he believe that it's therefore better? Normally, when we compare a model in which the attempt is made to take all effects into account, and compare it with a model that blithely assumes everything is linear, we give more credence to the folk who have worked harder on the physics.

Another point of confusion: at the beginning of that section, he says: "From the above numbers, it is easy to calculate, assuming a linear dependence of temperature on greenhouse gas concentrations, that a doubling of atmospheric carbon dioxide would produce an additional warming of (0.042 to 0.084) x 33 = 1.38 to 2.77 degrees centigrade."

a) Why would you assume a linear dependence of temperature increase on concentration? The natural assumption would be to assume a linear dependence of temperature increase on the radiative forcing: the additional radiative power.
b) He says it's easy to calculate the increase in temperature. I wish he would give a little more detail. Where do the 0.042 and 0.084 come from?

The worse thing is his section on "Comparison with the IPCC projections". First, I don't know where he is getting the 9-degree increase, or what specific assumptions it is based upon. There must be some, because in fact he himself says that the range given by the IPCC is 3 to 9, for a doubling of C-O2. But the main problem is that he takes this 9-degree number, which is (according to him) based on a logarithmic model, and then projects backward using his linear model. And then he complains about getting ridiculous results. Well, why would you expect to get anything sensible from using two models, which contradict each other, within one calculation?

Going back to the conventional calculation, by the way, I see from Houghton's book, Global Warming: The Complete Briefing, that the general result of the simulations is that temperature increment is proportional to the radiative forcing. When C-O2 is doubled, radiative forcing is increased by 3.8 W/m^2 and the temperature increase is 2.8 degrees-C. Not 9 degrees-C.

My conclusion:
- Nelson's understanding of the calculation for the GW effect from the enhanced greenhouse effect is incomplete and inconsistent.
- He describes the effect as being logarithmic at one moment, and then as linear in the next breath. This is simply not possible.
- Ultimately, his concept of an upper bound for the temperature increase is a modified version of the misunderstanding that "once all the IR photons have been blocked, you can't do any more cooling". Maybe he doesn't think of it this way (at least not part of the time; but part of the time he does), however, mathematically, his linearization amounts to the same misconception. It's just wrong.

[Note: It is a fair question to ask, "What happens if I do try to reduce C-O2 concentration? The formula says that if I reduce the C-O2 to zero, I get log(0) = - infinity decrease in temperature. That's impossible." That is correct, it is impossible. And it shows the limitation of the formula. What actually happens is the following: The effect of adding C-O2 to the naked Earth is to elevate the effective point of radiation (at the frequency of interest) several kilometers above the surface. This point is determined by the point at which the optical density, measured coming down from space towards the Earth, at the frequency of interest, = 1. At some concentration Xo, not as small as zero, the OD = 1 point will be ground level: That means the optical depth will be 1 just passing through the entire atmosphere. At that point, further reductions in C-O2 will not have any effect on the temperature. So at that point, the logarithmic dependence drops out.

In other words: The best simple representation of the enhanced greenhouse effect should be:
Forcing = 3.8 W/m^2 log(C-O2_concentration/Xo), for C-O2 concentration above Xo

Forcing = 0, for C-O2 concentration

Typographic correction to above:

The best simple representation for the enhanced greenhouse effect, as a function of C-O2 concentration, is:

Forcing = (3.8 W/m^2)* ln(C-O2/(2*Xo)) for C-O2 above Xo

Forcing = 0 for C-O2 less than 2*Xo

where Xo is the concentration such that the optical depth of the important C-O2 spectral line = 1 at ground level.

Neal King:
"Where do the 0.042 and 0.084 come from?"

Carbon dioxide ... contributes about 84% of the total non-water greenhouse gas equivalents [4], or about 4.2-8.4% of the total greenhouse gas effect. Reference [4]: U.S. Climate Action Report 2000, US Environmental Protection Agency, page 38.

"Well, why would you expect to get anything sensible from using two models, which contradict each other, within one calculation?"

But that's not what he did. He is running two calculations in parallel, one for each model. The point of that is, if a linear and a logarithmic model give the same temperature rise y0 at a given level of CO2 concentration x0, then at any x > x0, the y predicted by the logarithmic model must be less than the y predicted by the linear model. Since the current level of CO2 concentration raises the temperature by 2.77K, adding as much again cannot raise the temperature by more than 2.77K.

"Forcing = (3.8 W/m^2)* ln(C-O2/(2*Xo)) for C-O2 above Xo"

So where does that coefficient of 3.8 W/m^2 come from? If the answer is "computer simulations" I don't trust it; this is a number that should be calculable from first principles.

MB:

4.2-8.4%
Quoting the EPA on this matter doesn't explain anything, because they are operating on the "standard model" for doing GW calculations, and he is trying to contradict that. His claim is that "From the above numbers, it is easy to calculate, assuming a linear dependence of temperature on greenhouse gas concentrations, that a doubling of atmospheric carbon dioxide would produce an additional warming of (0.042 to 0.084) x 33 = 1.38 to 2.77 degrees centigrade." Can you show me how this is done?

Two models
I'm still failing to get your point: The 2.77 degree number is only from his linear model; I don't see how it is supposed to come out of the logarithmic model. Maybe you can explain what you believe he's thinking about in terms of his Fig.3: I understand him to be setting the (0,0) point there to be a "naked Earth", and the (100%, 33) point as being today's situation. Can you re-express what you think his reasoning is?

3.8
Quite right, this cannot come out of simulations. It comes out of calculations of what happens at different frequencies, summed up.

I gave some background to this calculation in the posting above at:
Neal J. King·June 6, 2007 01:51 PM
but to save hunting around, I will quote myself:

"However, it is interesting to think about how two separate gases contribute to the greenhouse effect. It is not too complicated in the case that the two absorption spectra have no overlap, because then you can consider them separately (although even then, spectral lines at greatly different frequencies will contribute differently to the heating, even though they are due to the same molecules).

When the two kinds of molecules have spectral lines in common, I think the total contribution cannot quite so easily be broken down into the sum of two separate contributions: the two absorptions add up, but what matters is how that moves the altitude at which the optical depth at that frequency = 1.

A small twist in the picture: at least some of the lines of interest in C-O2 have enough pressure-broadening that it changes the way the optical depth depends on concentration. I think it goes like 1/sqrt(concentration) instead of 1/concentration, as one would normally expect.

And, as mentioned above, the decrease of absolute humidity with temperature (and thus with height) gives the C-O2 a second chance to be important: if it manages to push the point at which optical depth = 1 above the level that there is significant amount of water vapor, then it will be acting essentially alone. From my quick look at graphs of water vapor as a function of height, it looks as though that won't be quite the case: There should be a reduction of water vapor at that level, but not an elimination. So that means there will still be a "drag" on how much radiative forcing the C-O2 will produce."

(The reason why I was talking about 2 gases is that we must consider the role of water vapor. As spelled out, their contributions to the GHE are not independent, but affect each other.)

Doing the calculation myself, I have looked at the simplest case:
- One gas (say C-O2)
- One frequency of interest (say 15 microns)
- No condensation effects
Then I get:

dT-eff = -(gamma-1)/(2*gamma) T-eff (dln(x))

where:
T-eff = the temperature at the OD = 1 point
x = relative concentration of C-O2
gamma = 7/5 (the adiabatic gas expansion exponent)

This tells how much the temperature would change if that frequency band were the ONLY band for the GHE. But since there are lots of bands, this has to be summed up for all of them (and they will generally have different values of T-eff). And in real life, the effect of water vapor has to be taken into account, as I mentioned above. So there is a lot of work between this calculation and the 3.8. (Just because I said the calculation was straight-forward does not mean that it's easy!)

However, what should "survive" all this massive integration is the "dln(x)" factor. And that is where the logarithmic dependence comes from.

Um Neal.

Where is the fact that CO2 is heavier then air, and would naturally settle, especially in zones of high pressure (usually accompanied by clear bright sunshiny skys), addressed in your theory of atmospheric stratification?

Oh and one other thing.
Isn't, "where Xo is the concentration such that the optical depth of the important C-O2 spectral line = 1 at ground level.",
AGW speak for, "No measurable effect at all"?

Well that's what my eye's read when it passed through my Rube Goldberg, crazy straw mind. Maybe I wasn't listening close enough. It is a tedious, mindknumbing piece, even by Neal standards.

Papertiger:

"C-O2 is heavier than air"
This is actually a good point. However, in the troposphere, it seems to be the case that the atmosphere is well-mixed with respect to most gases (exception: water vapor) so that difference doesn't matter. In the stratosphere, the atmosphere is no longer well-mixed, and I guess that C-O2 will be dropping out of the picture.

Water vapor starts to drop out even in the troposphere because of the reduction in absolute humidity allowable by temperature, which keeps dropping as you ascend.

Xo
Ding! Correct, Papertiger: When the C-O2 concentration is only Xo, there would be no greenhouse effect at all.

Unfortunately, the actual x is well above Xo. So there is plenty of greenhouse effect to measure.

By the way, I notice I got the equation wrong. Here's the correct one:
Forcing = (3.8 W/m^2)* ln(C-O2/Xo)/ln(2)) for C-O2 above Xo
That's the equation that adds 3.8 W/m^2 to every factor of 2.

Watch out, Papertiger! It looks like I'm having an effect on you. Your mind is becoming "comfortably numb".

Watch out, Papertiger! It looks like I'm having an effect on you. Your mind is becoming "comfortably numb".
Nope. That would be the booze.

Water vapor is broken down directly by ultraviolets in the ionosphere, so you are going to have to rethink your atmospheric mixing model.
Those con trails are all in the stratosphere, troposphere boundary area (where the air is coolest).

On the otherhand if your theory were correct we wouldn't have to worry about CLF's destroying the ozone layer. So, by all mean, make it work. I would prefer your version of reality.

Papertiger,

Water vapor
If you look at a really neat atmospheric calculator here at:
(http://www.spectralcalc.com/spectralcalc.php),
you can look at the relative % (volume mixing ratio) of H2-O as a function of altitude. It drops from about 1% at ground level to less than 0.001% at 20 km up.

Whereas C-O2 is steady at 0.03 % up to 90 km up.

So, as I said, C-O2 is well-mixed, but H2-O is pretty well confined to lower levels. That doesn't mean there's nothing at stratospheric levels - but nothing like what appears down at our level.

CLFs vs. CFCs
I guess you're talking about chlorofluorocarbons. But I don't see how anything I'm suggesting implies anything wrt their role in catalyzing the breakup of ozone in the stratosphere. Perhaps you could be more explicit.

aw crap

You want me to think about it again.

Alright. As I pointed out, in a more general manner, water vapor is broken up in the ionosphere. The hydrogen escapes into space, the O2 combines with free oxygen to become ozone.

I deduce from your statement regarding a lack of co2 mixing beyond the troposphere that there must be a reason that co2 can't get up that high. Must be too heavy.
If co2 is too heavy to get out of the troposphere then CFC's would be much too heavy.
Of course you changed your position in the last post. Throwing some mind judo at me.

So how did "In the stratosphere, the atmosphere is no longer well-mixed, and I guess that C-O2 will be dropping out of the picture" become "Whereas C-O2 is steady at 0.03 % up to 90 km"?

Papertiger,

Thinking again? I like that.

- No, I am not saying that C-O2 is too heavy to get there: I am saying that the relative concentration of C-O2 is pretty constant up to 90 km, and after that it starts to decline. It's more or less constant in the troposphere because the turbulence there keeps it well-mixed, and because C-O2 is not involved in any chemistry that would tear it apart. C-Cl2-F2 is pretty steady (at 10^(-9))up to about 30 km, and then declines quite a bit: seems to get to about 10^(-15) at 70 km and stays there.

But the stratosphere seems to be between 10 and 50 km. So, if I look at the plots:
- Water vapor: 10^(-2) at sea level, 10^(-4) at 10 km.
- C-O2: 0.03% at both sea level and 10 km
- C-Cl2-F2: 5*10^(-10) at both sea level and 10 km. Unlike C-O2, it drops a factor of 2 from 10 to 20 km, and keeps dropping.

So: Both C-O2 and C-Cl2-F2 are well represented in the stratosphere. Water vapor "barely" gets into the stratosphere.

I don't know, off-hand, why the C-O2 is so stable up to 90 km: if the mixing were going on, I would expect the temperature to continue to decline with height. But there is another effect: the ozone also absorbs UV and heats the atmosphere. So I don't know exactly what is going on; but I see that N2 and O2 behave the same way as C-O2, whereas the highly reactive gases (O3, OH, etc.) jump around a lot.

So I conclude that there must be continuing turbulence of some form to keep the stable gases well-mixed, up to about 80 km or so; even though the stratosphere starts at about 10 km.

Live & learn.