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
“Michael D Smith says:
April 19, 2013 at 12:13 am”
You might find this helpful.
http://www.ilovemycarbondioxide.com/pdf/Understanding_the_Atmosphere_Effect.pdf
tokyoboy says:
April 19, 2013 at 12:42 am
For the past 20 years the Mauna Loa CO2 concentration trend is almost perfectly linear.
It is slightly exponential, but you better look over the full period:
http://www.woodfortrees.org/plot/esrl-co2/from:1960/to:2013/plot/esrl-co2/trend
The increase in the atmosphere near perfectly follows the increase in CO2 emissions with a fixed ratio between 50-55%. That means that the sinks follow the increase in the atmosphere at a near fixed ratio to total CO2 in the atmosphere.
Ferdinand Engelbeen says:
April 19, 2013 at 1:55 am
Sorry,
That means that the sinks follow the increase in the atmosphere at a near fixed ratio to total CO2 in the atmosphere.
must be:
That means that the sinks follow the increase in the atmosphere at a near fixed ratio to total CO2 in the atmosphere in excess above the (temperature controlled) equilibrium.
Richard111 says:
April 19, 2013 at 12:28 am
I read that “man made” CO2 in the atmosphere is calculated on the basis of the absence of C-14.
The absence of 14C in fossil fuels is one of the ways to calculate the contribution of anthro CO2 to the increase in the atmosphere. There are many others, like the 13C/12C change in ratio, the oxygen balance and last but not least the mass balance. See:
http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html#The_mass_balance
joeldshore and tjfolkerts:
I am responding to your comments at April 18, 2013 at 7:57 pm and April 18, 2013 at 10:57 pm, respectively.
With one exception, your complaints at the above article are the same. The exception is that tjfolkerts claims the considered temperature projection should be 4 deg.C and not 6 deg.C. Perhaps so, but it is a trivial point because it would make no real difference to the result of Happer’s calculation; i.e. millennia are required to achieve 4 deg.C or 6 deg.C.
joeldshore provided the first of your two posts so I will quote each statement in his post and address it in turn.
The irony of joeldshore mentioning “logical fallacies” is enhanced by the fact that he states none made by Happer. The “errors” are knit-picking trivia which do not alter Happer’s conclusions.
I am addressing in turn each and all of the points made by joeldshore.
This entire statement by joeldshore – and later repeated by tjfolkerts – is a “strawman” and is ‘knit-picking’.
Whether Romm claims “6C rise” by 2050 or by 2100 is of no importance when the calculation shows 6C rise cannot occur for several millennia.
This is so wrong it is risible.
Happer accepts the assumption – and it is only an assumption – that the rise in atmospheric CO2 is induced by the trivial anthropogenic emission of CO2. And he does not “assume” the present rate of CO2 rise in the atmosphere will continue: he extrapolates the ~2ppm p.a. rate of that rise which has existed since 1958 when measurements began at Mauna Loa.
Over that period the trend is near to linear but has a few wiggles. Within the variation of seasonal oscillation, the annual rise is linear. This is a graph of the data
http://cdiac.ornl.gov/trends/co2/graphics/SIOMLOINSITUTHRU2008.JPG
joeldshore makes a ridiculous assertion when he claims the rate of rise in atmospheric CO2 has doubled from 1 to 2 ppm “over the last 40 years”.
And his assertion that the rate of rise will quadruple over the next 90 years is fantasy beyond belief. It is based on his falsehood that the rate of rise is doubling each 40 years. It is NOT: it is approximately constant.
This is more irrelevant knit-picking by joeldshore.
The calculation explained by Happer indicates that it would take millennia to reach4 deg.C, 5 deg. C or 6 deg. C rise in global temperature whether one calculates atmospheric CO2 rising to ~1100 ppm or 1600 ppm.
In conclusion, joeldshore and tjfolkerts, your attempts at damage limitation are pathetic.
Richard
Those calculations are only important if you are a true believer in the GHE. I believe in the laws of thermodynamics which do not seem to be within Dr Happer’s sphere of thought.
Increased atmospheric CO2 will increase the atmospheric density this increasing temperature by a miniscule amount. BUT that increased CO2 will increase the heat loss from the atmosphere thus cancelling the adiabatic increase. NO OVERALL EFFECT.
@Konrad says:
April 18, 2013 at 8:04 pm
This is a great explanation of why “greenhouse effect” does not work.
Consider this – surface of the Moon in sunlight is over 100deg Celsius. Surface of Earth in sunlight is not 100deg C anywhere on the planet, therefore, whatever atmosphere we have, has cooling effect.
Greenhouses on Earth work only by stopping heated gases rising, i.e. by literally trapping heated gas, and not by trapping radiation. Your “greenhouse” can be a shipping container made of steel, and it still will be warmer inside even on a dull day than outside. CO2 is not a rigid structure with a roof.
If our atmosphere was “trapping heat” then the Sun will have even easier job of heating the surface in the morning, (i.e not starting with minus 150, or whatever, as it is on the Moon), then you would expect Earth surface temperatures to be significantly higher than on the Moon.
LdB CO2 lazers are pumped with external energy to get the lazing. They do NOT generate that energy within the lazer from nothing which is what the GHE tries to get. Greenhouses work by cutting convection not any self induced energy input. Any greenhouse will only get to the radiative equilibrium temperature which with surface insolation at ~1000W/m2 gives a temperature of 88C and that is it regardless of how long in the sun. Conductive and external radiative losses will reduce the above temperature considerably.
If you doubt my words DO THE EXPERIMENT. Get a greenhouse, close it up and measure the temperature rise and its plateauing.
Most surface heat is lost by convection not radiation. Atmospheres do not prevent convection in fact convection is a major part of heat loss and weather.
richardscourtney says:
April 19, 2013 at 2:18 am
joeldshore makes a ridiculous assertion when he claims the rate of rise in atmospheric CO2 has doubled from 1 to 2 ppm “over the last 40 years”.
Dear Richard,
The increase of CO2 in the atmosphere indeed was rising near linear from slightly less than 1 ppmv/year to near 2 ppmv over the past 40+ years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em.jpg
The question is if this linear increase will be maintained over the next 50-100 years or will flatten when industrialisation reaches maturity in developing countries and/or new types of non-fossil production of cheap energy will emerge.
Ferdinand Engelbeen:
I am replying to your post at April 19, 2013 at 2:58 am.
At April 19, 2013 at 2:18 I made the true and accurate statements
Those two paragraphs are true and indisputable except by – as you provide – arm waving assertion. The truth of my statements is apparent to anybody who clicks the link and looks at the graph.
However, the ‘wiggles’ and the range provided by the seasonal variation enable almost any curve to be fitted to the data because the data only exists for the short time since 1958. This enables anybody to choose a curve which fits their prejudice and to apply it to the data: this is what you and joeldshore have done.
The important point is that Happer has adopted the assumption of extrapolating the linear trend which has existed since 1958, and for his calculation that is the ONLY reasonable assumption because is not an expression of any prejudice.
Richard
Konrad says:
April 18, 2013 at 8:04 pm
I agree with RGBs call for the numbers, and I do understand that a GHG both warms and cools. I like to charterize it as a function of time; ie, “the only way to change the energy content of any system (in this case the atmospher, the earth, and the oceans) in a radiative blance is to change the residence time of some aspect of those energy, or to change the input.”
So the only way to quantify all this is to produce the engineering quality paper Steve McIntyre has called for, but never recieved. How much of the energy within the atmosphere is other then radiative, conducted from the surface to convection currents, and or latent heat moved via evaporation? I have never seen the numbers.
Furthermore, what are the relative percentages of energy to and from CO2, conducted, vs radiative? How often does the CO2 molecule recieve energy through collision via the establishment of a LTE? (Local thermodynamic equalibrium) If a GHG recieves energy via conduction, then radiates to space, its net effect is cooling. If it recieves same energy from surface emitted LWIR, and redirects said energy downwards, then it is warming. If it recieves energy via conduction, from the latent heat of evaporation released via condensation, then it is cooling. If it recdieves said energy via conduction, and releases via conduction, then it acts just as any othe non radiative gas. I imagine that the chances of a GHG both recieving and releasing energy via conduction accelerates relative to the density of the molecules it is encountering, but think it likely more complicated then that.
I imagine that the physical location, both latitude, longitude, and altitude of any GHG affects the warming cooling properties of said gas. In a non GHG world, where would all the conducting energy go. Would it not have to conduct back to the surface, in order to radiate to space? However, would not it first continuesly conduct to cooler molecules above it, untis the majority of said molecules reached an equalbrium, establihing a fairly even enrgy vibrational rate, only registering a different T due to the relative, per SQm density of molecules? (Lapse rate based primarily on atmospheric density) Yes, of couse convection, evaporation, and relative conduction spreads would continuesly conduct said atmosphere.
I have been asking the above questions for a long time, so would appreciate any thoughtful answers.
Wilson and Gea-Banacloche, Am. J. Phys. 80 306 (2012).
The paper is paywalled. Is it available anywhere for those without library facilities nor budget to access paywalled info?
David:
At April 19, 2013 at 3:31 am you refer to your good post at April 19, 2013 at 3:30 am and say
The reason you have not been obtaining answers is because nobody really knows the answers.
As you say, the effects vary temporally and spatially. (What is happening in two places is not the same at any time, and it varies throughout the year at each of them). And these differences interact. This complexity is why climate models have been constructed.
However, real data for input to the models is sparce and incomplete, so the models are not much use. For example, how and why clouds form, behave and disperse is poorly understood. Furthermore, clouds are too small to be modeled in climate models so effects of clouds are ‘parametrised’ (i.e. guessed). But clouds affect incoming and outgoing radiation, precipitation, and convection.
Hence, anybody who claims to have specific answers to your questions is misleading you.
Sorry, to be so negative. But ‘them’s the facts’.
Richard
Thanks Richard, and “we do not know” is actually an excellent answer. Without humility we have very poor science.
So I see we have at least 2,000 years before we ‘panic’ about co2 in the air. Such levels have been exceeded greatly in the past and Latam neotropical vegetation thrived in high co2 and warmer world during the PETM.
I doubt we will still be burning fossil fuels in 2,000 years let alone 1,000 years. I wish these pant wetters would stop panicking over the trace rise of the trace gas co2.
http://youtu.be/P2qVNK6zFgE
@David
If you build and run the experiments linked above, you should find the results so robust (tm climate science) that you will not require precise numbers. They have gotten the “basic physics” of the “settled science” so wrong it beggers the imagination.
Experiment 3 shows the importance of energy loss at altitude to convective circulation. Experiment 4 shows what happens when radiative cooling at altitude is not occurring. Build the columns tall enough and use 1C cooling water and 80C heating water and you should achive a 30C+ differential between gas columns. AGW? Game over man! Game over!
I think we should dust off and nuke “climate science” from orbit. It’s the only way to be sure 😉
richardscourtney says:
April 19, 2013 at 3:26 am
Those two paragraphs are true and indisputable except by – as you provide – arm waving assertion.
Dear Richard,
I don’t agree with many points that Joel Shore does say, but one need to be honest for what is true, no matter who says it. When Joel says that the increase of CO2 in the atmosphere increased from about 1 ppmv/year to 2 ppmv/year in 40 years time, he is correct and you are not (pointing to a graph which doesn’t show the details of interest is not the right answer). That is what is measured as average increase of the increase. Even significant if you include the year by year variability in increase rate (of +/- 0.5 ppmv) around the trend. The seasonal variability is here of no interest at all.
But as said before, it is questionable if the linear increase in increase rate will remain the same in the future. That will make a huge difference in CO2 levels over the next 50-100 years.
AGW is based on, as was eugenics, bigotry, ignorance and a thin veneer of science. All combined with rent seeking and self promotion.
That 6.0o is both ridiculous and embraced by the loudest of the AGW hypesters is not surprising.
Ferdinand Engelbeen:
re your post addressed to me at April 19, 2013 at 4:56 am.
I consider information on its worth and not who presents it.
You say
Que sera sera, whatever will be will be.
There are only three pertinent points and I stated them, viz.
and
and
Richard
TerryS says:
The history of such growth processes has generally been that they are roughly exponential. Doubling every 40 years assumes a modest growth rate of about 1.8% per year in CO2 emissions. At the rate China and India are currently industrializing, that may well be an underestimate.
Again, that depends on the acceleration. You are assuming a low acceleration. That also assumes that no saturation occurs in the sinks that are currently sequestering about half of our emissions. Many scientists find that assumption to be implausible.
In general, CO2 emissions have continued to grow in industrialized countries over the last several decades, although not as rapidly as in the industrializing ones.
I will leave it to Ferdinand Engelsteen to correct the blatant falsehoods that Richard S Courtney is spewing (and, unfortunately, continuing to spew) in this thread.
David Cage says:
April 18, 2013 at 11:48 pm
No pay walled document should be allowed to be cited in any action involving public policy.
Especially the IPCC assessments
richardscourtney says:
April 19, 2013 at 5:05 am
Come on Richard,
The seasonal variation has nothing to do with the year by year variability in rise of CO2 levels nor with the trend itself. For the same year by year variability and trend one can use the South Pole data or one of the other SH stations, where hardly any seasonal variability is visible. The seasonal cycle simply is a false argument, as that doesn’t influence the trend (neither do the tides for sea levels…). Only the change over a full seasonal cycle is of interest. See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/month_2002_2004_4s.jpg
and
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_trends.jpg
Joel was discussing the year by year rise in CO2 over the past 40 years. That significantly doubled over that period, even taking into account the year by year variability in increase rate. That is undoubtedly true, no matter how you try to hide that by choosing a graph that doesn’t show the important details. If you can provide another curve of the year by year CO2 increase rate that doesn’t show a linear increase over time, I am very interested to see that.
Thus the choice of Happer for a constant increase rate is his assumption, probably based on the expectation (as is mine) that CO2 emissions in the future will flatten with maturing industrialisation and/or newer energy production techniques. But it is an assumption, not more reasonable than expecting an ongoing increase in CO2 emissions / increase in the atmosphere for the next 50-100 years.
Re: Mark Besse 6:29pm: 8 (+/- 6)
Does that mean the result is statistically significant???
Dr. Brown asks: So, any papers, computations, models, actual evidence to support your assertion
I have been mentioning the cooling effect of CO2 for years now. One of things I often ask is why I’ve never seen a paper attempting to determine this value. To me, that says a lot about climate science. Something so obvious and so basic to the net impact of increased CO2 has NEVER, I repeat NEVER been quantified? Just how strange is that?
I love the fact that Konrad has gone beyond my base assertions to try and put a little meat on the bone. This is not the first time he has provided a description of his experiments and yet still not a single climate scientist has attempted to repeat them.
For me it gets very basic. At one time we had a perfectly happy O2 molecule buzzing around the atmosphere. Whenever it collides with a N2 molecule an energy transfer might occur but no radiation would result. Hence, all the energy stayed in the atmosphere.
Now, we turn that O2 molecule into a CO2 molecule by burning some fossil fuel. The brand new CO2 molecule now collides with one of those N2 molecules and not only does an energy transfer occur, but some energy gets radiated away on occasion. At least 50% of that energy heads towards space. Statistically, we should see a net increase in the flow of energy to space.
The change from having added CO2 to the atmosphere must lead to extra energy transfers to space. This is evident by simply looking at the molecular interactions. So, the only question is how much? Without knowing the answer to that question there is no way for climate scientists to understand the impact of adding CO2 to the atmosphere. The fact they have ignored this issue says they really aren’t interested. They have an agenda and it is not science.