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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Schitzree says:
April 18, 2013 at 5:20 pm
you can also reverse this.
to get 6C by 2050 with a CO2 raise by then of 74ppm from 400ppm would require a Climate Sensitivity per doubling of what?
I don’t have the math to figure it myself but I think it would be between 12C and 18C.
Anyone up to figuring this precisely?
————————————————–
Schitzree actually under-estimates this :
Use equation (3)
N= 400 x 2^(∆T/∆T2).
N is your target concentration in 2050 (474 PPM, from the post); ∆T is our target warming (6 deg C) and we solve for ∆T2, our sensitivity.
When I solve for ∆T2, I come up with 25.7 °C/ doubling to get 6 deg C warming with the current rate of increase of CO2 increase by 2050.
25.7 °C / doubling …… Completely Absurd , even by alarmist standards
@ur momisugly Reed Coray
To “Trap Heat” is nonsensical because heat is energy being transferred, therefore if you trapped heat it wouldn’t be heat anymore.
What they’re actually referring to is the ability of certain gas molecules (GHG’s) to absorb IR (infrared radiation) into vibration.
Energy of vibration could be gained by absorbing IR or by collision and then could be released through either collisions or IR emission; thus a GHG can act as a cooling or warming agent with respect to the surrounding mass of gas.
Note that temperature of a gas is a measure of translational motion ONLY. The energy of vibration in a gas (unlike in a solid) does not contribute to the temperature of the gas.
Personally, I tend to tune out anyone who uses the term without quotation marks, but this might not be entirely fair as the term “Heat Transfer” is often used in science and engineering (& me too) even though this is literally say “Energy Transfer Transfer”.
Yet another great example of logic, scientific analysis and ultimate truth to combat propaganda in a post on WUWT. Thank you!
One can only stifle the truth for so long through disinformation.
Just like the information Dr. Darko Butina, Dr. Spencer, and dozens of others bring to the forefront on this site.
I have a proposal for all who view this site. A proposal that will mimic that of other groups who cannot see things aside from their finely tailored vision.
You see, the climate alarmists are well organized, government funded, and sponsored by the media in all forms. The skeptics are not as well organized, not government funded and have limited funding from sponsors, and virtually no media exposure.
What if we could form an unified front and fight for truth in science as a group?
A union if you will.
Perhaps we could call it the “Union of Concerned Skeptical Scientists and Citizens” ?
Now, we would have to develop some standards around membership, but would certainly allow Kenji to join too ( on purpose )!
Perhaps it would be a good excuse for a formal meeting that could also be a fund drive to help improve what, how, and the way things are communicated on the “known science” of climate science.
I certainly realize that there are other organizations out there trying to do the same thing, but not many. The visibility and detail of this site provide a unique opportunity to take advantage of assets that may normally not be available to other groups.
It is obvious to me that many knowledgeable persons who are truly “in the know” are finally (with confidence) stepping up and out to expose the myths and untruths that are being purveyed as facts on climate, in an unchallenged manner, in too many instances.
If people can’t see or hear your reply, they simply don’t. That is why it is called mass media, no?
I can only hope to see on my cable guide one day the “WUWT-TV special with the Union of Concerned Skeptical Scientists and Citizens”
Hey,,,,, remember that you miss 100% of the shots that you do not take !
This world grows from opportunity, innovation, and most importantly, initiative! 🙂
Regards, and thanks again for the opportunity to be part of this revolution.
davdmhoffer: “The vast bulk of light from the sun is short wave”
“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.”
davidmhoffer says:
April 18, 2013 at 6:00 pm
‘Not quite. The vast bulk of light from the sun is short wave which goes right through CO2. It gets absorbed by the earth which then radiates toward space in the infrared range.’
>>>>>>>>
“Not quite”! LOL, you just love to be argumentative. Okay, let’s have at it.
During daylight, does an atmospheric molecule of CO2 receive more IR from the Sun or from the Earth?
It best to remember that with CAGW you need to use post-normal math:
2+2=8 (+/- 6)
This provides me with an opportunity to present my thoughts on averting future calamity.
[Rant mode on]
Oh No! scream the Warmistas, if we continue our behavior as is, we will all die; in fact, everything will die. Well, I got news you Warmistas: Whatever we do, we, and all current living things, will die in the future.
If there is any way of avoiding this calamity, then please let me know. Until then, let me alone in comfort and allow the birds sing and not be chopped up by your bird mincing propellors.
I predict that 6 billion people, or more, will die by the end of the 21st. century.
[Rant mode off]
I can not seriously believe that rational people can not understand how the greenhouse effect works any basic science readings will fix that issue up and you can avoid the whole climate change science go to a hard physics site.
For absolute proof read up on CO2 lasers there you deliberately pump CO2 with energy to get a specific wavelength of light emitted at 10,600 nm which is mid-IR.
CO2 is a quantum active gas that is a fact that can be readily shown and it may be hard to explain using classic physics and people with only that level of science may struggle understanding but the ridiculous comments that people “want to be shown how CO2 traps in heat” should be attacked for the science ignorance they show.
Water is by far the most potent greenhouse gas which is also a fact for the people who don’t understand what the termed trapped heat means. You can even read up on the physics of water as a greenhouse gas that also isn’t difficult to show with simple science,
I agree with Anthony that 6 degrees by 2050 is impossible and Joe Romm or anyone else who says that it is needs to be taken to task for there science understanding. However we need to also take to task those commenting who also fail basic science.
Bad science from either side of the stupidity that is climate science debate is still bad science.
Yes, and how long will it take to melt the glaciers. I believe that Greenland and Antartica is well bellow -6 Centigrade.
Except that completely ignores ANY OTHER CAUSE OF TEMPERATURE CHANGES. That is why this belief is in error. Your belief relies on CO2 being the ONLY cause of any change.
Could that be more simple?
Has Tamino “debunked” this yet?
“Except that completely ignores ANY OTHER CAUSE OF TEMPERATURE CHANGES. That is why this belief is in error. Your belief relies on CO2 being the ONLY cause of any change.”
That’s exactly my view. How can the Warmists be so sure the 0.7C warming of the 20th century was caused by increases in man-made CO2? Forget the juiced climate models. Where’s the empirical evidence? For all we know, an active sun was the main contributor to the temperature increase. Or perhaps some of the increase was simply the artifact of poorly sighted thermometers.
There is plenty of research challenging the man-made-CO2-is-warming-the-earth theory. And that’s all it is: a theory.
As far as I can see the only way “heat” or energy is trapped on Earth is through :-
1. “Conversion” to mass by plants, algae etc. Mass obviously contains vast quantities of energy as burning wood for example amply demonstrates.
2. Melting ice into liquid water. The latent heat of fusion is thus “trapped” as long as the water remains liquid. Any latent heat of vapourisation is merely a temporary “trap” as it is released and radiated to space during condensation – ie rain or snow. Any increase in the temperature of liquid water is also likely to be transitory but may involve long timespans – besides it is likely to result in increased evaporation which is a very effective cooling mechanism as we animals demonstrate by our cooling mechanism – sweat.
The latest catchphrase is that GHGs “slow down” the radiative heat loss by “scattering” a portion – some say half – and therefore the Earth’s surfaces do not cool down as much as they would during the night as they would with less GHGs.
The problem with this argument is twofold :-
1. It requires the energy from the Sun to cause the extra heating as the Earth is starting from a warmer initial value next morning – and this contradicts the whole insolation is a quarter of the solar constant argument.
2. It requires consideration of the period of rotation of the Earth as cooling occurs when the Sun has set – ie at night. Unfortunately this brings up the comparison with the Moon which has a 14.75 Earth day long night. During the 531 Earth hours from lunar noon to the next dawn the Moon goes from ~390 K to ~100 K. This results in a cooling rate of 290/531 K per hour – about 0.55 K per hour.
There is little reason to suspect that the Earth’s gaseous radiative layer at close to 255 K would lose energy at anywhere near that rate.
In a 12 hour night the Earth would never cool to anything like the Moon – NEVER.
Both the Moon and Mercury – planetary surfaces subject to significant radiation both have extremely long nights.
The only other places we know about that get extremely cold – the poles – have long “nights” of some months and receive low levels of incident radiation.
Yet the period of rotation – obviously a major factor in explaining the loss of energy by a surface radiating to space – the Moon and Mercury for example have similar minimum temperatures – does not seem to have any place in this discussion yet it is one of the few real facts about planetary surface temperatures and heating and cooling we have.
The theoretical blackbody temperature is meaningless when the temperature varies from 390 K to 100 K for the Moon or from 700 K to 100 K for Mercury.
Mercury has a night time of 115.8 Earth days or 2779.2 Earth hours – even at the fastest rate of cooling observed for the Moon Mercury would only require 600 Earth hours to reach 100 K – less than one quarter of the night or about 1/7 of the time from noon to the next dawn.
Dr. Happer writes:
“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. Happer is far too kind. It is a slogan used by people who are playing the citizenry for suckers. And there are some very big names who have recently endorsed this slogan once again. Trenberth is the biggest name that comes to mind.
“..with no feedbacks.”
Then Dr. Happer has absolutely no one to argue with. No one. JP
It has always made me wonder how people make such claims when a pencil and a piece of paper would show them how stupid their claims are. Oh I forgot the computer replaced pencil and paper with the ability for people to think.
John West says: April 18, 2013 at 6:17 pm
@ur momisugly Reed Coray
To “Trap Heat” is nonsensical because heat is energy being transferred, therefore if you trapped heat it wouldn’t be heat anymore.
What they’re actually referring to is the ability of certain gas molecules (GHG’s) to absorb IR (infrared radiation) into vibration.
Energy of vibration could be gained by absorbing IR or by collision and then could be released through either collisions or IR emission; thus a GHG can act as a cooling or warming agent with respect to the surrounding mass of gas.
I agree–especially do I agree that under certain circumstances a GHG can act as a cooling or warming agent with respect to the surrounding mass of gas. I believe that many AGW proponents (a) use the term “heat-trapping gas” to connote the IR absorption/IR emission properties of some gases, and (b) then argue that everything else being equal the heat-trapping nature of a gas is by itself sufficient to conclude that material possessing an internal source of thermal energy will when surrounded by a heat-trapping gas be warmer that it would be in the absence of the heat-trapping gas. There may be cases where this is true, but I believe there are cases where the opposite is true–i.e., surrounding material possessing an internal source of thermal energy will result in a lower material temperature.
CodeTech says:
April 18, 2013 at 6:40 pm
Except that completely ignores ANY OTHER CAUSE OF TEMPERATURE CHANGES. That is why this belief is in error. Your belief relies on CO2 being the ONLY cause of any change.
Could that be more simple?
——————————————————
Fair enough , but I think you missed the point of my comment.
I agree that there are certainly other forcing mechanisms out there, BUT CAGW alarmist do not think this way. It’s all about CO2 to them. So what’s the easiest way to dismantle this argument – do the math as presented. The conclusion you have to come to is it is not all about CO2.
I should have been more specific that the set of calculations presented can be used to completely dismantle the CAGW hypothesis. It does nothing to address other forcing – which I agree with you certainly exist.
There are a couple interesting side thoughts to this as well. If there are other positive forcings in the system, to get a net forcing of 1.5, it by definition implies that the forcing of CO2 is even smaller than this and even further de bunks the CAGW hypothesis.
Alternatively, if there are negative forcings at work, which would then imply that CO2 sensitivity is greater than 1.5 to get a net “observed” 1.5, then CO2 is actually preventing us from cooling, maybe even from harmful cooling (ie an ice age ??) in which case we should continue to push as much CO2 in the air as we can. No matter how you slice it, there is no valid argument in this framework as to why we should cut CO2 emissions.
We have a public meeting tomorrow night in our local market town where Tim Yeo – my MP – who is Chairman of the Parliamentary Committee responsible for climate and energy matters, is going to speak about the necessity to continue with aggressive pursuit of green policies.
Can anyone suggest some pertinent questions I can ask, without getting too technical so that other attendees can’t follow the import of them?
The man is a fanatic, and has invested heavily in green technology – a clear conflict of interests as many have remarked on WUWT before
http://www.guardian.co.uk/environment/2013/feb/08/tory-mp-amendment-energy-bill
Indeed, a 6 C temperature rise may well be cause for concern.
==========
since most of the rise is calculated to be at the poles, even 6 C is not going to be an issue. There is a reason there are very few people in the high latitudes. it is bloody cold.
Does anyone truly believe that emperor penguins are going to be unhappy if temperatures are only -50C instead of -60C?
Sam the First says:
April 18, 2013 at 7:30 pm
1) How much money will you make from your “green” investments?
2) Why haven’t the last 15-16 years shown any “global warming”?
3) Why are polar bear populations increasing?
4) What “green” policy has been financially successful AND reduced CO2 emissions?
5) Do scientists and engineers, non-salaried by green or gov, agree with AGW?
There you go….
Let us enumerate a few of the errors and logical fallacies in Will Happer’s argument:
(1) The entire argument being attacked is essentially a “strawman” since in the very article of Joe Romm’s that Anthony linked to, Romm says he was talking about a 6C rise by 2100, not 2050.
(2) He assumes that CO2 levels will continue rising at their current rate of 2 ppm per year. However, historically, the rate of increase of CO2 has been accelerating over time: 40 years ago, it was rising at only about 1 ppm per year ( http://wonkroom.thinkprogress.org/wp-content/uploads/2009/03/co2_growth_rate.PNG ). Hence, it is unlikely that 40 years from now it will still be rising at 2 ppm per year, especially under assumptions of no constraints on CO2 emissions. And, if the rate of rise keeps doubling every 40 years, it will be going up ~8 ppm per year by the end of the 21st century.
(3) He computes the necessary CO2 level for a 6 C rise from current temperatures (i.e., that with a 3 C sensitivity, one has to quadruple CO2 from 400 ppm to 1600 ppm). If we talk about from pre-industrial levels, a quadrupling of CO2 only means going up to ~1100 ppm.
LdB says:
April 18, 2013 at 6:32 pm
“I can not seriously believe that rational people can not understand how the greenhouse effect works”
—————————————————————————————————————–
LdB,
There is nothing wrong with radiative physics, it has just been incorrectly applied to atmospheric physics. This has lead to radiative gases being wrongly called “greenhouse”gasses.
Can radiative gases intercept surface IR and heat the atmosphere? Yes.
Can radiative gases emit IR to the surface (land only) and slow it’s cooling rate? Yes.
Will adding radiative gases to the atmosphere cause global warming? No.
The radiative green house hypothesis has a fundamental flaw. The basic calculations that predict warming are based on modelling the atmosphere as a static body or mathematical layer. However the gases in our atmosphere are free to move and this invalidates all AGW calculations. At first glance, failing to model a moving atmosphere does not look like a huge error. Radiative flux to and from the earth and space is the big concern right? Why would the movement of gases in the atmosphere need to be modelled? The answer is atmospheric temperature.
Failing to model a moving atmosphere leads to two fundamental errors in AGW calculations.
1. Conductive flux between the atmosphere and the surface.
In an atmosphere with moving gases, gravity keeps cooler gas near the surface during the day maximising conductive flux. At night gravity keeps cooler gas near the surface, minimising conductive flux. Basically for a moving atmosphere the surface is better at conductively heating the atmosphere than it is at conductively cooling it. Static atmosphere calculations give entirely the wrong answer for surface to atmosphere conductive flux. While land surface Tmin may be lower under a non-radiative atmosphere, this does not translate to a significantly cooler atmosphere.
2. Convective circulation.
Radiative gases play a critical role in convective circulation below the tropopause. Rising warm air masses lose energy at altitude by IR radiation to space from radiative gases. If the only way atmospheric gases could lose energy is by conductive contact with the night surface, tropospheric convective circulation would stall and our atmosphere would heat dramatically. Radiative cooling at altitude is critical for continued convective circulation. It is a common mistake to believe that adiabatic cooling will allow continued convective circulation, but this is matched by adiabatic heating on decent and plays no role in convective circulation. Energy loss at altitude is just as important for convective circulation as energy input near the surface.
When you take a moving atmosphere into consideration, radiative gases cool at all concentrations above 0.0ppm. Adding radiative gases to the atmosphere will only speed up convective circulation and tropospheric cooling. At 0.04% there is no hope of measuring any such effect from CO2. This is why the models keep failing.
davidmhoffer says:
April 18, 2013 at 6:00 pm
‘Not quite. The vast bulk of light from the sun is short wave which goes right through CO2. It gets absorbed by the earth which then radiates toward space in the infrared range.’
>>>>>>>>
“Not quite”! LOL, you just love to be argumentative. Okay, let’s have at it.
During daylight, does an atmospheric molecule of CO2 receive more IR from the Sun or from the Earth?
>>>>>>>>>>>>
>>>>>>>>>>>>
David will not be re-appearing tonight. He is quietly “not quite” available. He is “not quite” quiet. Quietly, he is “not quite” amongst us. Quietly, he is “not quite” certain why he is “not quite” right.
Sadly, it’s “not quite” not my bedtime….
geran says:
April 18, 2013 at 6:26 pm
davidmhoffer says:
April 18, 2013 at 6:00 pm
‘Not quite. The vast bulk of light from the sun is short wave which goes right through CO2. It gets absorbed by the earth which then radiates toward space in the infrared range.’
>>>>>>>>
“Not quite”! LOL, you just love to be argumentative. Okay, let’s have at it.
During daylight, does an atmospheric molecule of CO2 receive more IR from the Sun or from the Earth?
>>>>>>>>>>>>>>>>>
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.