The answer may surprise you
Note: This essay is a result of an email discussion this morning, I asked Dr. Happer to condense and complete that discussion for the benefit of WUWT readers. This is one of the most enlightening calculations I’ve seen in awhile, and it is worth your time to understand it because it speaks clearly to debunk many of the claims of temperature rise in the next 100 years made by activists, such as the 6c by 2050 Joe Romm claims, when parroting Fatih Birol in Reuters:
“When I look at this data, the trend is perfectly in line with a temperature increase of 6 degrees Celsius (by 2050), which would have devastating consequences for the planet,” Fatih Birol, IEA’s chief economist told Reuters.
![dec11-eleven-degrees2[1]](http://wattsupwiththat.files.wordpress.com/2013/04/dec11-eleven-degrees21.jpg?quality=83)
Graph source: IEA.org scenarios and projections
– Anthony
Guest post by Dr. William Happer
For any rational discussion of the effects of CO2 on climate, numbers are important. An average temperature increase of 1 C will be a benefit to the planet, as every past warming has been in human history. And the added CO2 will certainly increase agricultural yields substantially and make crops more resistant to drought. But in articles like “Scant Gains Made on CO2 Emissions, Energy Agency Says” by Sarah Kent in the Wall Street Journal on April 18, 2013, we see a graph with a 6 C temperature rise by 2050 – if we don’t reduce “carbon intensity.” Indeed, a 6 C temperature rise may well be cause for concern. But anyone with a little background in mathematics and physics should be able to understand how ridiculous a number like 6 C is.
The temperature change, ∆T , from the mean temperature of the present (the year 2013), if the concentration N of CO2 is not equal to the present value, N = 400 ppm, is given by the simple equation
(1)
Here ∆T2 is the temperature rise that would be produced by doubling the CO2 concentration from its present value, and ln x denotes the natural logarithm of the number x.
The proportionality of the temperature increment ∆T to ln N is widely accepted. But few know that this is a bit of a “miracle.” The logarithmic law, Eq. (1) comes from the odd fact that the average absorption cross section of infrared light by CO2 molecules decreasesvery nearly exponentially with the detuning of the infrared frequency from the 667 cm−1 center frequency of the absorption band. More details can be found in a nice recent paper by Wilson and Gea-Banacloche, Am. J. Phys. 80 306 (2012). Eq. (1) exaggerates the warming from more CO2 because it does not account of the overlapping absorption bands of water vapor and ozone, but we will use it for a “worst case” analysis.
Recalling the identity for natural logarithms, 
, we write Eq. (1) as
(2)
The only solution of the equation ln x = ln y is x = y, so (2) implies that
(3)
Recent IPCC reports claim that the most probable value of the temperature rise for doubling is ∆T2 = 3 C. Substituting this value and a warming of ∆T = 6 C into Eq. (3) we find
(4)
But the rate of increase of CO2 has been pretty close to 2 ppm/year, which implies that by the year 2050 the CO2 concentration will be larger by about (50−13) years×2 ppm/ year = 74 ppm to give a total concentration of N = 474 ppm, much less than the 1600 ppm needed.
The most obvious explanation for the striking failure of most climate models to account for the pause in warming over the past decade is that the value of ∆T2 is much smaller than the IPCC value. In fact, the basic physics of the CO2 molecule makes it hard to justify a number much larger than ∆T2 = 1 C – with no feedbacks. The number 3 C comes from various positive feedback mechanisms from water vapor and clouds that were invented to make the effects of more CO2 look more frightening. But observations suggest that the feedbacks are small and may even be negative. With a more plausible value, ∆T2 = 1 C , in Eq. (3) we find that the CO2 concentration needed to raise the temperature by ∆T = 6 C is
(5)
This amount of CO2 would be more than a warming hazard. It would be a health hazard. The US upper limit for long term exposure for people in submarines or space craft is about 5000 ppm CO2 (at atmospheric pressure). To order of magnitude, it would take a time
t = 25, 600 ppm/(2 ppm/year) = 12,800 years.
(6)
to get 6 C warming, even if we had enough fossil fuel to release this much CO2.
A 6 C warming from CO2 emissions by 2050 is absurd. It is a religious slogan, a sort of “Deus vult” of the crusade to demonize CO2, but it is not science.
=============================================================
Dr. William Happer is the Cyrus Fogg Brackett Professor of Physics at Princeton University, and a long-term member of the JASON advisory group,where he pioneered the development of adaptive optics. From 1991-93, Happer served as director of the Department of Energy’s Office of Science.
UPDATE: Dr. Happer has contacted the author of the paper cited, and he has graciously setup a free link to it: http://comp.uark.edu/~jgeabana/gw.html
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Tim Folkerts says:
April 22, 2013 at 6:54 pm
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Tim,
you are correct, the experiments mentioned above –
http://wattsupwiththat.com/2013/04/05/a-comparison-of-the-earths-climate-sensitivity-to-changes-in-the-nature-of-the-initial-forcing/#comment-1267231
– have been described in more detail in a number of other threads and on other sites.
I am slowly working toward a full thread to cover these in detail at the Talkshop (the “Reign of Willis” continues at WUWT). Dimensioned diagrams, renderings and materials lists to be included. Building instructions are important as the hope is that others will replicate the work for themselves. There is just too much cut&paste and linking on the web these days. Everyone wants an answer they can get from behind the computer 😉
As to the aluminium water block for Experiment 1, you can use a aluminium electronics “jiffy case” enclosure, however I use a plastic block with a serpentine water channel engraved in the face and then sealed with a thin aluminium plate. The exterior of this black plate should be sprayed with matt black BBQ paint. This design emits a grater amount of IR from the lower face of the block. Silicone model aircraft fuel tube is better than PVC for supply and outlet tubes as it insulates better.
davidmhoffer says:
April 22, 2013 at 8:49 pm
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“ I’ve shown you that areas with high ghg concentrations are warmer than areas with low ghg concentrations despite being at the exact same latitude.”
– David nothing in this contradicts what I have been saying. If look look back over my comments on this thread, you will note that I repeatedly state that radiative gases can slow the cooling of land surface and by intercepting surface IR they can heat gases in the lower troposphere. However strong vertical convective circulation in the Hadley, Ferrel and Polar tropospheric cells is continuing for all regions of the globe you could point to at this time. The issue I am discussing is bigger, more fundamental and more important than radiative exchange between the surface and atmosphere. It is IR radiation to space and it’s role in strong vertical convective circulation. Without this, our atmosphere will heat dramatically.
“That is the end result of the system as a whole, period. More ghg =warmer.”
– No that is only the result for near surface regions, assuming continued strong vertical convective circulation under the tropopause. The result for the system as a whole is atmospheric super heating in the absence of radiative gases.
“Go find your mistake.”
– perhaps the mistake would be being “Not interested” in discussing the critical role of radiative gases in convective circulation in the troposphere? Was that my mistake or yours 😉
Konrad;
It is IR radiation to space and it’s role in strong vertical convective circulation. Without this, our atmosphere will heat dramatically.
>>>>>>>>>>>>>>
If there were no IR active gases in the atmosphere, then the system as a whole would still reach equilibrium with the energy absorbed equal to the energy radiated out. The effective black body temperature of the earth would still be -18 C. The difference would be that the vast majority of the energy flux to space would come directly from the earth surface, resulting in a surface temp close to -18C as well. With the atmosphere now heated exclusively by conduction from surface to atmosphere, the highest temperature that the atmosphere could reach under such conditions would be -18C.
It is clear to me that you have a lot of personal investment in your experiments and their results. I’ve been there, it is tough to “let go”. But one of the fundamental aspects of verifying your results is to determine if the sum total of the individual pieces when combined together gives the same answer as system as a whole. What I have been trying to show you is that the system as a whole behaves differently than the sum total of your experiments. The ERBE data is not about surface temps as you seem to have assumed. It is about net radiation across the atmospheric column. Areas with very high (40,000 ppm) of water vapour can easily be compared to areas at the same latitude with very low (nearly 0 ppm) of water vapour and the net radiation across the atmospheric column is precisely opposite to what you insist your experiments prove.
davidmhoffer says:
April 23, 2013 at 9:25 am
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David, your last post offers some potential for progress.
First up –
“The ERBE data is not about surface temps as you seem to have assumed”
-No, this is not the case. I believe I was quite clear in pointing out that this data did not exist for an atmosphere without radiative gases. Without data of this type for several different moving atmospheres with radically different radiative gas concentrations, it cannot answer the issue I am raising.
“If there were no IR active gases in the atmosphere, then the system as a whole would still reach equilibrium with the energy absorbed equal to the energy radiated out. The effective black body temperature of the earth would still be -18 C. The difference would be that the vast majority of the energy flux to space would come directly from the earth surface, resulting in a surface temp close to -18C as well.”
– This statement is essentially correct, but it contains the basic mistake of almost all early AGW modelling – “Thou shalt not model the earth without a diurnal cycle”. -18C is not surface Tmax under a non radiative atmosphere.
“With the atmosphere now heated exclusively by conduction from surface to atmosphere, the highest temperature that the atmosphere could reach under such conditions would be -18C.”
– This statement is entirely wrong. Here is where the critical flaw in the foundation of all AGW calculations lies. For an atmosphere in a gravity field with a vertical pressure gradient in which the gases are free to move, the gas temperature set by surface conduction will be close to surface Tmax, not Tav. This would be moderated very slightly by gas conduction.
The core problem with the AGW hypotheses is one of fluid dynamics. Experiment 4 & 5 give a clear demonstration of the problem.
In Experiment 4 –
http://i48.tinypic.com/124fry8.jpg http://tinypic.com/r/zmghtu/6
– The gas column in box 1 has a lower average temperature, but the average “surface” temperature at the bottom of the box is high
– The gas column in box 2 has a far higher average temperature, but the average “surface” temperature at the bottom of the box is low.
Experiment 5 gives a clear demonstration of why the surface is far better at conductively heating a column of moving gases above it than it is at conductively cooling it.
Climate scientists have made small mistakes in radiative physics (Experiment 1) however these do not invalidate the AGW hypothesis.
Climate scientists have made critical mistakes regarding fluid dynamics and gas conduction. These mistakes are in the very foundation of the AGW hypothesis. These mistakes totally invalidate the AGW hypothesis. Radiative gases act to cool our atmosphere at all concentrations above 0.0ppm.
Experiments 4 & 5 clearly demonstrate that this statement –
“With the atmosphere now heated exclusively by conduction from surface to atmosphere, the highest temperature that the atmosphere could reach under such conditions would be -18C.”
– is completely wrong.
LOL.
No Konrad, we don’t have ERBE data that compares ghg to no ghg. But we do have ERBE data that compares massive amounts of ghg to near zero amounts of ghg, and we can draw conclusions from that. You’d like to ignore those conclusions because they don’t fit with your belief system.
Second, your argument that the atmosphere would come to a different equilibrium temp than -18 is valid. Temp being linear with the 4th root of the energy flux, a simply average of Tmax and Tmin doesn’t yield the same number as averaging the 4th root. But come up with any means of describing the average temperature that you would like, and the atmosphere in the absence of ghg’s has to vary with that value, and the highest value it can reach is the surface temp, however you calculate it.
Lastly, an atmosphere heated exclusively from the bottom will have higher convection than an atmosphere heated in part from the bottom and in part from the middle. That’s exactly what ghg’s do. They intercept radiance from the surface resulting in heating at altitude via radiative processes as well as at the bottom from conductance and evaporation. A lower temperature gradient must result in lower convection or everything we’ve learned since Archimedes is wrong.
You could argue the last paragraph from a number of perspectives (and probably will) that have some validity. But at day’s end, we do in fact have the data to compare very high levels of ghg to very low levels of ghg, and the conclusions we can draw from that data are opposite to yours. The system is making a statement very different from your experiments. You can argue that almost zero isn’t the same as zero, but seriously, almost zero makes a pretty bold statement.
davidmhoffer says:
April 23, 2013 at 8:17 pm
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LOL, David?
“With the atmosphere now heated exclusively by conduction from surface to atmosphere, the highest temperature that the atmosphere could reach under such conditions would be -18C.”
– Now that comment was amusing, especially as it cannot be erased from the Internet.
“No Konrad, we don’t have ERBE data that compares ghg to no ghg. But we do have ERBE data that compares massive amounts of ghg to near zero amounts of ghg, and we can draw conclusions from that.”
– The ERBE data says exactly what it should say and in no way contradicts my conclusions.
“You’d like to ignore those conclusions because they don’t fit with your belief system.”
– My conclusions are based on empirical experiments you do not understand and have not bothered to replicate. My belief system is based on the traditional scientific method. You seem to have a problem with this.
“Second, your argument that the atmosphere would come to a different equilibrium temp than -18 is valid. Temp being linear with the 4th root of the energy flux, a simply average of Tmax and Tmin doesn’t yield the same number as averaging the 4th root. But come up with any means of describing the average temperature that you would like, and the atmosphere in the absence of ghg’s has to vary with that value, and the highest value it can reach is the surface temp, however you calculate it.”
– Wrong again. As experiment 4 clearly shows surface Tmax is the driving factor in a deep atmosphere with a pressure gradient in a gravity field. A “ different equilibrium temp than -18” does not cut it. Try a dramatically different equilibrium temperature. Better still try building and replicating empirical Experiment 4. You know, Science.
“You can argue that almost zero isn’t the same as zero, but seriously, almost zero makes a pretty bold statement.”
– No David, I was intentionally being conservative when I suggested that tropospheric temperatures would rise to surface Tmax and the troposphere would go isothermal. MiCro raised the issue of super heating of N2 and O2 due to their small response to IR and UV. The issue is not how many angles can dance on the head of a pin. The issue is not a few degrees here or there. The real issue is that without radiative gases, most of our atmosphere would boil off into space. Yes, you and the AGW believers have gotten the role of radiative gases in our atmosphere that badly wrong.
Try naming one planet or moon in our solar system that has managed to retain an atmosphere without strongly radiative gases.
I have a good understanding of radiative physics. You do not appear to understand fluid dynamics. I suspect you are going to very, very annoyed when you work out what Experiment 6 was 😉
The real issue is that without radiative gases, most of our atmosphere would boil off into space.
>>>>>>>>>>>>>
ROFLMAO
davidmhoffer says:
April 24, 2013 at 8:27 am
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“ROFLMAO”
Your understanding of radiative physics and fluid dynamics is that bad?
When you finally realise what the core problem with with the AGW hypothesis is, you will be wincing so hard while biting your fist you will find that you have swallowed your eyes and are missing fingers.
Sleeper! Ex 6…..Gotcha!
solar radiance = 1340 w/m2
less 30% for albedo = 938 w/m2
Via SB Law, max surface temperature at the equator at high noon assuming zero heat loss from conduction/convection/evaporation and zero heat capacity:
358.8 degrees K
85.8 degrees C
Not enough to boil water!
And that’s at the equator, assuming ZERO cooling processes from conduction, convection, and evaporation. That’s assuming a heat capacity of zero meaning the the earth at that point would have to heat up to that temperature instantly.
If you think that 85.8 degrees at the equator as an absolute Tmax could boil away the atmosphere, you have descended from physics that is just wrong to completely absurd. Throwing in the fact that heat capacity isn’t zero alone would reduce that number by several tens of degrees. Throw in evaporative processes, conduction/convection and circulation via hadley cells and other process from higher latitudes (which will be even a lower temperature) and the number drops further still.
In other words, your statement is preposterous, just like those of Al Gore, Bill Nye, Michael Mann and James Hansen. You’re presenting evidence that supports your belief and you simply ignore any facts that get in the way. Give your head a shake. You’re no better than they are at this point, and you will simply be used by warmists as evidence that skeptics don’t know what they are talking about.
davidmhoffer says:
April 24, 2013 at 12:54 pm
“Via SB Law, max surface temperature at the equator at high noon assuming zero heat loss from conduction/convection/evaporation and zero heat capacity:”
– Was there anywhere I suggested surface conduction would be the factor that would cause atmospheric super heating in the absence of radiative gases? No. I quite clearly indicated that surface conduction would drive a non-radiative atmosphere isothermal and close to surface Tmax. It will of course be obvious to those reading previous comments that heating above the boiling point of water would occur due to IR and UV heating of N2 and O2 at the top of the former troposphere in the absence of strong vertical convective circulation.
Maybe I should add another “do not”. Thou shalt not apply the SB equations to a moving atmosphere.
“You’re no better than they are at this point, and you will simply be used by warmists as evidence that skeptics don’t know what they are talking about.”
– Not concerned David. Previous attempts to link me with warmist assault clowns or get me to engage with them have failed. However the point you raise, “evidence that sceptics don’t know what they are talking about”, is worthy of mention. Unable to find sufficiently crazy sceptics, warmists had to make them up. Hence the assault clowns M and G.H. Assault clowns, popcorn warriors, snowstormers, proxies and sleepers. Have sceptics ever engaged in that on warmist blogs? Does this speak to the character of character of warmists? Why do they feel it is ok to cheat and lie? No one with the truth on their side needs those tactics.* No one believes they are saving the planet any more. Warmists are now just fighting to save their skins.
In fact if you, as a sleeper, needed to try that argument, it is simply adding weight to my science. The more workable tactic would have been to concede that initially radiative gases cause cooling, but after a certain point they cause warming and argue that we are well beyond this point. That would have brought the ERBE data back into play.
*interesting tactics in the short term, poor strategy long term. Sceptics will never forgive and the Internet will never forget.
Konrad, I’ve had 4 shots of bourbon this evening and you are starting to make sense to me. I suspect however that in the morning I shall once again be sober and you will still be wrong.