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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David says:
April 19, 2013 at 4:04 am
Thanks Richard, and “we do not know” is actually an excellent answer. Without humility we have very poor science.
=============
Take the total sum of what all human beings on earth know to be true. This is a finite value. Now take the total sum of all that is yet to be discovered. It is fairly simple to show that this value must be infinity, because if it isn’t then what outside of the set of things known and yet to be discovered? This must also be part of the set of the unknown ad infinitum.
So, when one decides how much we really know, we get finite/infinite = 0.0% of the true total. And no human being knows more than this, no matter how many fancy letters after their names.
-ddavidmhoffer says:
April 18, 2013 at 8:24 pm
The greenhouse effect is a function of SW from the sun (which isn’t absorbed by CO2) being absorbed by the earth and radiated back out as LW (which is absorbed by CO2). In answer your question, I posted the link to atmospheric transmission, you can see for yourself. I also suggested reading more detailed explanations by Ira Glickstein. If you think you’ve scored some points by mocking me, you done nothing of the sort. I attempted to help you out with an error that you made, nothing more.
>>>>>>>>
Sir, I see you finally responded last night after I had left. Your response helps me to understand your confusion now, so let me see if I can help:
Your link has a presentation of “transmission”. I think you are confusing transmission with total solar energy the atmosphere receives, ie, the atmosphere receives more energy from the Sun than does the Earth, due to the losses/heating/reflections of the atmospheric layer. Your link presents what “gets through” the atmosphere. Here is a link to total solar output:
http://en.wikipedia.org/wiki/Solar_radiation
And a relevant pasting from the iink:
“Sunlight in space at the top of Earth’s atmosphere at a power of 1366 watts/m2 is composed (by total energy) of about 50% infrared light, 40% visible light, and 10% ultraviolet light.[3] At ground level this decreases to about 1120–1000 watts/m2, and by energy fractions to 44% visible light, 3% ultraviolet (with the Sun at the zenith, but less at other angles), and the remainder infrared. Thus, sunlight’s composition at ground level, per square meter, with the sun at the zenith, is about 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation.”
Hope that helps.
Oh, and as to “mocking” you–you blindsided me with a non-constructive comment trying to start an argument. When I asked one question that you realized lost your case for you, you then did not respond for hours. When you finally responded, you tried to fake victory, while at the same time claiming “victimhood”. Hint: The perp is the victim only in unside-down justice systems.
joeldshore says:
April 19, 2013 at 6:02 am
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.
I know of that assumption of a few years ago. Meanwhile there were studies showing that the “airborne fraction” from the extra induced CO2 still is the same over the years.
The main point is that saturation does occur in the oceans surface at 10% of the atmospheric changes, but that is far less the case for the deep oceans, simply because the ocean waters are far undersaturated at the sink places. Even if all CO2 emissions since 1850 mixes into the deep oceans, that would give an increase of 1% (3 ppmv) in the atmosphere at equilibrium (with a half life time of ~40 years). For semi- to permanent storage in plant debris (peat/brown/coal) there is no limit at all and only depends of CO2 levels in the atmosphere (for equal other necessities like water, temperature, fertilizers, minerals,…).
The “Bern” model and similar models used by the IPCC may be right if we burn 10-20 times the total amount of carbon as used until now, but that is not the case for the next 50-100 years…
geran says:
April 19, 2013 at 7:46 am
sunlight’s composition at ground level, per square meter, with the sun at the zenith, is about 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation.
Be careful, the incoming infrared radiation of the sun and the outgoing IR radiation of the earth are quite different in wavelengths. CO2 has only a small absorption band in solar IR, water has a lot more. Most IR captured by CO2 is in the earth radiation band, not in the solar one.
See page 4 of 7 in:
http://www.nat.vu.nl/CondMat/rw/DuEnSBI/DuurzEn4HeatBalanceOfEarth.pdf
Thanks, Dr. Happer. Very good article.
geran says:
April 19, 2013 at 7:46 am
…
http://en.wikipedia.org/wiki/Solar_radiation
And a relevant pasting from the iink:
“Sunlight in space at the top of Earth’s atmosphere at a power of 1366 watts/m2 is composed (by total energy) of about 50% infrared light, 40% visible light, and 10% ultraviolet light.[3] At ground level this decreases to about 1120–1000 watts/m2, …
——
That’s odd. No problem with TOA 1366 W/m^2, but then I’ve always read that you have to adjust for surface area of a sphere as opposed to a disk (disk RPI, sphere 4RPI, so divide by 4), and then adjust again for albedo (1-0.3), which gives about 240 W/m^2 at the surface. Is this wrong?
This said, I’ve always thought this adjustment a bit odd as well. It’s only half a sphere during the day when solar radiation is coming in after all. Also, obviously solar power varies substantially with the cos of the zenith angle; I.E., time of day and date. And the prevailing weather. etc.
One of these days I’m going to spend the time and effort to actually measure the solar radiation in my backyard….
Mark Bofill says:
April 19, 2013 at 9:05 am
One of these days I’m going to spend the time and effort to actually measure the solar radiation in my backyard….
>>>>>>>>>
You are correct about the sinusoidal relations, but generally between 40 degrees and the equator, 1000 Watts/meter squared is accepted as a close average/approximation, especially in solar panel work.
Can someone go through CO2’s logarithmic absorption of long-wave in the atmosphere again. As I understand it, the CO2 ‘greenhouse effect’ reduces anyway, with less and less response as CO2 levels increase.
.
Ferdinand Engelbeen says:
April 19, 2013 at 2:07 am
Thank you for the link. Lot of useful information there. I have posted the link on another forum.
Sadly I failed to find any information on the ‘heat trapping’ capability of CO2 and why this is a problem if the current levels of CO2 double.
Also puzzled as to why atom bomb generated C-14 has a half life of 5 years but natural C-14 has a half life of 6,000 years which is useful for carbon dating.
Richard M postulates: “The change from having added CO2 to the atmosphere must lead to extra energy transfers to space. “
Sort of ….
The extra CO2 radiates to space in the 15 um band from somewhere near the top of the troposphere where it is quite cool (220-240 K). Any radiation from warmer CO2 below this layer is absorbed by the CO2 above it. And any 15 um radiation from the even warmer ground is ALSO absorbed by the intermediate layers.
But remember that the IR radiation is a function of temperature. The cool CO2 radiates poorly; the warm ground radiates well. So there is indeed an extra energy transfer to space from the atmosphere due to the presence of CO2, as you realize. But there is a REDUCED transfer to space from the ground. The net result is that the “bright” 15 um radiation from the ground is absorbed and the “dim” radiation from the atmosphere escapes –> LESS total radiation escapes.
Lots of things happen between the surface and the top of the troposphere, but the net result is that the CO2 cools the top of the atmosphere, but warms the bottom.
(There is a program called MODTRAN that models the spectra quite well: http://forecast.uchicago.edu/Projects/modtran.html . You can play around with CO2, viewer location, clouds, etc and see the effects. For this case, the most instructive might be to start with the default settings (looking down from 70 km) and then remove all the CO2. The IR emitted to space INCREASES, which would cause the earth to cool until balance is restored.)
joeldshore says:
April 18, 2013 at 7:57 pm
However, historically, the rate of increase of CO2 has been accelerating over time: 40 years ago
That is true, however in the last 16 or 17 years when temperatures have flattened on several data sets, the rise in CO2 is no longer accelerating. See the slopes below. They are virtually identical over the last 17 years as over the last 9 years.
http://www.woodfortrees.org/plot/esrl-co2/from:1996/plot/esrl-co2/from:1996/trend/plot/esrl-co2/from:2004/trend
Geran;
Oh, and as to “mocking” you–you blindsided me with a non-constructive comment trying to start an argument. When I asked one question that you realized lost your case for you, you then did not respond for hours. When you finally responded, you tried to fake victory, while at the same time claiming “victimhood”. Hint: The perp is the victim only in unside-down justice systems.
>>>>>>>>>>>>>>>>>>>>
I did not realize that you are such an important person that I must sit attentively at my desk, doing nothing else for an entire day, waiting in breathless anticipation of a comment from you to respond to.
Your initial response to how CO2 traps energy was wrong. The GHG effect has nothing to do with CO2 absorbing LW from the sun. Get over it. Check out the links I provided to you and follow closely the responses of this thread by rgbatduke, richardscourtney, Ferdinand Englebeen, Joel Shore and others. Perhaps you’ll figure out your mistake or perhaps you’ll continue you’ll continue to spout drivel while insulting and mocking those who make an honest effort to help you understand.
Geran;
I suggest also that your read Tim Folkert’s last comment as well:
Tim Folkerts says:
April 19, 2013 at 9:36 am
Tim, I agree with everything you said … almost. Keep in mind that even the radiation at the low levels of that atmosphere will move higher due to more CO2 before it is absorbed. From there that energy has a higher probability of radiating to space in the future.
I’ve always said the warming effect of CO2 (the GHE) should be stronger at low concentrations of CO2. However, as CO2 increases the GHE is a log function while the cooling effect should be linear. Where these might balance out is a good question that I don’t believe anyone has answered.
Also keep in mind that he GHE is the strongest closest to the surface which should promote more convection. The cooling effect is strongest in the upper atmosphere where there is less water vapor. This also promotes more convection. So, the feedback is basically enhanced at both ends.
What is the net? Can modtran really answer that question? I doubt it.
Richard111 says:
April 19, 2013 at 9:34 am
Ferdinand Engelbeen says:
April 19, 2013 at 2:07 am
Thank you for the link. Lot of useful information there. I have posted the link on another forum.
Sadly I failed to find any information on the ‘heat trapping’ capability of CO2 and why this is a problem if the current levels of CO2 double.
Also puzzled as to why atom bomb generated C-14 has a half life of 5 years but natural C-14 has a half life of 6,000 years which is useful for carbon dating.
That means that the atom bomb generated C14O2 has a lifetime in the atmosphere of ~5years, because it exchanges with the oceans (predominantly), in equilibrium for every molecule of CO2 that enters the ocean another one leaves the ocean. So inject a spike of C14O2 into the atmosphere and watch its decay in concentration and you can determine the rate of exchange between the two reservoirs. It’s not the radioactive halflife.
Richard M;
Also keep in mind that he GHE is the strongest closest to the surface which should promote more convection. The cooling effect is strongest in the upper atmosphere where there is less water vapor.
>>>>>>>>>>>>>>>>>>>
Agreed with all your comments save this last one. With water vapour hitting 40,000 ppm over ocean in the tropics, CO2’s effects are pretty much lost in the noise. As you rise in altitude, temps drop and water vapour precipitates out while co2 concentrations stay the same, and so become more significant in terms of their ratio to water vapour. Hence I think your statement is correct, but that point much occur at an altitude above the water vapour layer rather than close to earth surface. Then it gets more complicated when we consider that the water vapour layer gets thinner by latitude, and also by season (winter vs summer) and also over deserts.
so my expectation is that where CO2 becomes significant enough to promote a measurable amount of convection varies by altitude, latitude, season, and geography. I expect also that this is almost impossible to measure.
First time for ages I have ticked the ‘Notify me of follow-up comments via email’ box – the exchange between geran and davidmhoffer looks like it may be a doozy 😉
Richard M says:
April 19, 2013 at 6:43 am
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?
You’re laboring under a misunderstanding, this has indeed been quantified, notably by Clough and Iacona, published inter alia in J Geophysical Research, vol 100.
Suppose you are a ‘chief ecoomist’ like Fatih Birol; suppose you are also ignorant of statistical regression analysis – but I repeat myself…
Ferdinand Engelbeen:
My post at April 19, 2013 at 6:16 am only consisted of accurate statements.
The first sentence in your reply (at April 19, 2013 at 5:05 am) says
Bollocks! The rise of any year is the residual of the seasonal variation in that year.
Again, this is a graph of the data
http://cdiac.ornl.gov/trends/co2/graphics/SIOMLOINSITUTHRU2008.JPG
If the seasonal rise equalled the seasonal fall then there would be no annual rise.
In other words, your statement is the opposite of the truth. In reality
Imbalance in the seasonal variation CREATES the year by year variability in rise of CO2 levels AND the trend itself.
You continue saying
I used the Mauna Loa data because it is the longest time series. Using the measurements from any other site does not reduce the clear and absolute truth and validity of my statements.
Your statement that “The seasonal cycle simply is a false argument” is pure arm-waving intended to ignore the fact that rise of any year is the residual of the seasonal variation in that year. You are metaphorically putting your fingers in your ears and shouting, “La, la, la..” when you say the seasonal variation “that doesn’t influence the trend (neither do the tides for sea levels…). Only the change over a full seasonal cycle is of interest.”
The imbalance in the seasonal variation CAUSES the trend. In fact, it IS the trend.
You go on saying
Perhaps Joel was doing that. Indeed, it is reasonable to suppose he was ignoring the seasonal variation because he has a ‘track record’ of ignoring information which refutes his assertions.
I provided the graph which shows ALL “the important details” but you are arguing for use of graphs which do not include the important seasonal variation which YOU – not me – “try to hide”. It is hiding that variation which enables you to choose a curve which suites your assertions.
But I did not ignore anything. I merely stated the truth and I wrote
And when you questioned the matter I made the true and accurate reply
And your reply to that is ridiculous. It says
Yes, I repeatedly said “the choice of Happer for a constant increase rate is his assumption”. But, unlike you, I did not ascribe any motive for that assumption except scientific propriety; i.e.
Your choice of curve is based on your prejudices which cause you to expect emissions to increase and to induce additional atmospheric CO2 increase. In reality, nobody does know or can know how atmospheric CO2 concentration rise will vary in future, so Happer’s extrapolation is the ONLY correct assumption.
Richard
davidmhoffer says:
April 19, 2013 at 10:00 am
At first, I recognized your confusion. Often, confusion can make folks angry. I tried to help your confusion, but it appears you are just getting angrier.
I will leave it at that, and have a great day!
“joeldshore says:
April 19, 2013 at 6:02 am
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.”
Give me a break Joel. As a physiologist I’ve seen no data that plants will not increase sequestration of soil CO2. Unless of course, you confound the data with assumptions of increasing temperature and/or less rainfall. Those scientists you allude must be climate scientists…………….
Increased production of stover in response to co2 enrichment:
http://www.ars.usda.gov/research/publications/publications.htm?SEQ_NO_115=245953
http://www.nature.com/scitable/knowledge/library/effects-of-rising-atmospheric-concentrations-of-carbon-13254108
Leads to increased sequestration of carbon in the soil:
http://www.jstor.org/discover/10.2307/2845980?uid=3739672&uid=2&uid=4&uid=3739256&sid=21102066143131
http://www.bio.anl.gov/environmental_biology/terrestrial_ecology/CO2.html
The results indicated that CO2 enrichment increased soil carbon by an average of 5.6% over 2-9 years, at a median rate of 0.19 Mg C ha‑1 y‑1. We also observed increases in soil carbon, at rates exceeding 0.4 Mg C ha‑1 y‑1 for 5-8 years, in Tennessee sweetgum forest and Kansas prairie exposed to elevated CO2. Carbon accrual in both systems was measurable because the vegetation responded to CO2 enrichment with large increases in the production of root litter.
geran;
At first, I recognized your confusion. Often, confusion can make folks angry. I tried to help your confusion, but it appears you are just getting angrier.
>>>>>>>>>>>>>>>>>>>>>
You think I am angry? You must be confused.
I mean about my anger, not about your physics. On your physics you’re just wrong, no confusion about it.
Henry Galt says:
April 19, 2013 at 10:28 am
First time for ages I have ticked the ‘Notify me of follow-up comments via email’ box – the exchange between geran and davidmhoffer looks like it may be a doozy 😉
>>>>>>>>>>
Nah. Courtney, Englebeen and Shore. That’s turning into a doozy.
ferd berple says:
April 18, 2013 at 8:34 pm
Konrad says:
April 18, 2013 at 8:04 pm
Radiative cooling at altitude is critical for continued convective circulation… Energy loss at altitude is just as important for convective circulation as energy input near the surface.
=========
correct. without ghg the atmosphere would be isothermal and there would be no vertical circulation.
Not true, the surface on the night side would cool and cause convection currents.