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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Can I please wake you gentleman up here? Hello……?
There is no increase in warming……there is no increase in warming
Can you hear me?………helllllloooooooooooo?
Go outside look around, listen and feel and stop writing things to try and
impress……………………………..its cooling!!
There is no global warming…helllllooooooooo….nerds!!
Tim Folkerts says:
April 19, 2013 at 9:36 am
“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.”
———————————————————————————————-
Yes, Tim. Absolutely correct. And then?
What happens to a free moving body of gas in a gravity field when you heat at the bottom and cool at the top?
Could it be strong vertical convective circulation?
Does all the strong vertical convective circulation in our atmosphere occur below the tropopause? Where are 99.99% of all radiative gases?
Is our lower atmosphere cooler or hotter due to radiative gases and their critical role in tropospheric convective circulation?
Radiative gases are critical to tropospheric convective circulation and atmospheric cooling. There is no escape. You got the “basic physics”of the “settled science” totally and utterly wrong.
Dry air DLR as measured by IR thermometer pointed at the sky (-40F) iirc is about 180w/sq m, the rest is from water vapor, which easily varies to regulate DLR.
MiCro says:
April 20, 2013 at 12:15 am
So, if air temperature at 1 meter height is 10 C, and the ocean’s water temperature is 4 degrees C, what temperature (degrees K of course) should be used to calculate the energy lost by radiation into the air? The (clear sky) temperature of -40 C ?
RACookPE1978 says:
April 20, 2013 at 1:18 am
Yes, this is why clear sky night time temp drops like a rock once the Sun goes down. But note, I haven’t measured clear sky temp on a warm day, it is suppose to be much closer to surface temp, but at warmer temps there’s much more water vapor in the air.
@JohnMarshall
Last I looked the sun was definitely outside the earth and its energy is most definitely entering from outside the system because there is an almost perfect vacuum isolating earth. So I am sorry the situation in every reguard is identical to a CO2 laser tube the fact you can’t even realize that says a lot about your science understanding.
@kretchetov
I guess you at least worked out that one side of the earth would be several hundred degrees and the side away from the sun would be several hundred below zero .. the situation that exists on the moon and the international space station. So you are at least one step up from the lunatics who think there isn’t any such thing as a greenhouse effect. Ok so you have at least worked out the atmosphere does something a fact some of the other pseudoscience lunatics haven’t so now follow the science properly you cant say it just cools because that is true only of the side facing the sun it is heating the reverse side to stop it going massively negative so your logic breaks down. What you have correctly worked out is it moderates the temperature somewhere between the two possible extremes NOW GO AND FIND OUT HOW IT DOES IT.
Jeff L says:
FYI of those that didn’t get what Terry was alluding to , 270 ppm is the pre-industrial CO2 level & 400 is the current CO2 level. Reference :
http://wattsupwiththat.com/2010/12/26/co2-ice-cores-vs-plant-stomata/
And over that time, the rise in temps is about 0.85 C :
http://ete.cet.edu/gcc/?/resourcecenter/slideshow/3/1
Note that this calculation assumes that all observed warming is due to carbon dioxide. Effectivly it’s a “worst case senario”.
There could be other causes for the observed warming, including “heat island” effects. Even if the warming is “real” assuming that the only possible cause can be the concentration of a trace gas in the atmosphere is a mighty big assumption.
Tsk Tsk:
Re your post at April 19, 2013 at 10:17 pm. I completely agree.
I draw your attention to the post of Ferdinand Engelbeen at April 19, 2013 at 1:42 pm which makes your point very clear.
Ferdinand there says to me
I cannot get Ferdinand’s link to work and I do not accept his assertions concerning anthropogenic cause of the variations (why not temperature, or etc.), but he accurately states the nature of the curve.
As he says;
“an increasing slope in trend, except for 1990-2000 and as Werner Brozek showed not increasing over the past years.”
So, he agrees the data indicates there is NOT an accelerating increase to atmospheric CO2 concentration: recent decades show a DEcelerating increase. Indeed, Ferdinand uses different words but they agree with my comment (at April 19, 2013 at 2:18 am) to joeldshore and tjfolkerts. I said there of the data since 1958
The data says that, and I accept the data.
Richard
Tsk Tsk::
In addition to my recent post addressed to you, another way to see the truth of the matter is to observe the graph of Annual Mean Growth Rate (it is the third graph down) at
http://www.esrl.noaa.gov/gmd/ccgg/trends/
The growth rate is NOT following a consistent curve of “doubling each 40 years”. Joel D Shore is plain wrong.
Richard
richardscourtney says:
April 20, 2013 at 3:13 am
Dear Richard,
The NOAA graph you linked to clearly shows that the CO2 increase 2000-2010 more than doubled compared to the 1960-1970 average, that is over a 40 years span.
That is what Joel and I said, nothing else. That some periods show a temporary sink doesn’t make that untrue. Where we differ in opinion is that I expect a flattening of the increase rate in the future and Joel doesn’t. But there is no more scientific reason to expect that there will be no increase in increase rate in the near future than that the increase in increase rate will linearly go up unabated…
Ferdinand Engelbeen:
Thankyou for your post at April 20, 2013 at 4:31 am.
Sorry but you are displaying a distorted and blinkered view of the data.
I have repeatedly said in this thread
.
Your post I am answering says
.
In other words, I describe the data but you put an interpretation on the data.
The “wiggle” at the start of the short (available) sample period does provide a low rate.
But to say that this fluctuation from the trend indicates an accelerating rise is extremely misleading.
The last decade was the warmest on record but that does NOT mean we now have global warming.
The implication does not follow from the stated fact
The rate of rise of atmospheric CO2 concentration was lower in 1960-1970 than in 1990-2000 but that does NOT mean the rate of rise is accelerating.
The implication does not follow from the stated fact.
And the use of that implication by Joel Shore was barmy.
The best that can be said of the rise in atmospheric CO2 is – as I have repeatedly said –
Richard
@ur momisugly LdB says:
April 20, 2013 at 1:44 am
LdB – Your 1:44 post beautifully highlights the danger of lazily and wrongly sprinkling the term “greenhouse effect” in exchanges such as these. By your own words, you acknowledge that the atmosphere cools the surface. Bizarrely, you seem to think this only happens during daylight. Let me know what the mechanism is that makes this behaviour flip twice per day, from acting as a fridge, to acting as a blanket, rinse and repeat.
Your temperature predictions by lunar comparison are useful, in principle. Sadly, they are fatally flawed in your claim that diurnal temperatures would vary by 2 x ‘several hundreds of degrees’. This can’t happen on Earth, as there simply isn’t time, given that the Earth rotates 29.5 times faster than the Moon. This same error generates the specious need for a ‘greenhouse effect’, to explain why the dark side stays so ‘surprisingly’ warm overnight. Hence, a multi-trillion $$$ scam is born and gets sustained by people like you, for now.
[snip – see point #17 here http://wattsupwiththat.com/about-wuwt/policy/ ~mod]
@ur momisuglyKONRAD April 19, 2013 at 10:58 pm
You rather confused me with your post. Other than asking questions, you only stated three things:
1) “Yes, Tim. Absolutely correct.” I’m glad that we are on the same page so far.
2) “Radiative gases are critical to tropospheric convective circulation and atmospheric cooling.” — which I agree with.
3) “You got the “basic physics”of the “settled science” totally and utterly wrong.”. hmmm .. somewhere between you agreeing with me, and me agreeing with you, you have concluded that I am not just slightly wrong, but utterly and completely wrong!
Since the rest of your post is questions, we are all left to “read between the lines” to figure out your intent. Rhetorical questions can be quite powerful in political speeches or philosophical debates, but don’t work so well in scientific discussions.
KONRAD: “Where are 99.99% of all radiative gases?”
My reading-between-the-lines answer would be “in the troposphere”. But my understanding is that only ~80% of all gases and ~99% of water vapor is in the troposphere (and that most of he ozone is in the stratosphere). If these numbers are even close to correct, there would be no way that 99.98-100% of radiative gases are actually in the troposphere.
Thus there is no “correct” answer to this rhetorical question.
KONRAD: “Is our lower atmosphere cooler or hotter due to radiative gases and their critical role in tropospheric convective circulation?”
Now I suspect there are TWO “correct” answers! The answer hinges on asking “hotter or cooler than what?”
Convection cools gases as they rise. So the air 1 km up typically will be ~ 6.5 K cooler than the air at the surface. So the first correct answer is “the lower atmosphere is COOLER than the SURFACE due to convection.”
But (in very broad strokes), the surface is ~ 288 K, so the lapse will reduce that temperature to ~ 281 K @ur momisugly 1 km altitude. Without radiative gases, the surface would be ~ 255 K — which is much cooler than the surface or lower atmosphere with radiative gases. Thus the 2nd correct answer is “the lower atmosphere is WARMER than A SIMILAR ALTITUDE on a planet without radiative gases.”
Or put another way, the “effective radiating temperature” of the earth as a whole is ~ 255 K. The upper troposphere is cooled BELOW 255 K by radiative gases. By conservation of energy, somewhere else (ie the lower troposphere & surface) must be warmed ABOVE 255 K. Radiative gases will tend to increase this temperature gradient; convection will try to limit this
temperature gradient.
Galileo: ““Mathematics is the language with which God has written the universe.”
Cart, Horse? Funny how a warming ocean releases CO2 and more ends up in the atmosphere.
http://i38.tinypic.com/2em288z.jpg
richardscourtney says:
April 20, 2013 at 5:27 am
Richard,
The NOAA graph clearly shows a near linear increase in year by year CO2 increase rate from 0.85 ppmv/year in 1960-1970 to 2.0 ppmv/year in 2000-2100.
To help you out, here the 10-year moving average 1969-2012 where the average is taken from the preceding 9 years and the year where the data are plotted (data taken from T.J. Folkerts April 19, 2013 at 1:26 pm):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_increase_rate_1960_2012.jpg
It doesn’t make anyimportant difference if you plot the linear trend, the logarithmic trend or a polynomial trend. All trends look near identical and don’t flatten at the end.
Dr. Happer used the last increase rate as a constant for estimating the future increases in the atmosphere.
Joel Shore used the slope in increase rate for estimating the future increases in the atmosphere.
Both are arbitrary and both have good arguments pro and con.
But if you think that a more than doubling in the increase rate over 40 years is a “constant” increase rate, then sorry, there is no real discussion possible.
Steve Keohane says:
April 20, 2013 at 8:42 am
Cart, Horse? Funny how a warming ocean releases CO2 and more ends up in the atmosphere.
Yes, but that doesn’t say anything about the cause of the trend, only that temperature has a direct influence on the sink rate (NOT the source rate!). Human emissions are twice the average increase in the atmosphere, only about halve of that remains (as quantity, not as original molecules) in the atmosphere. Thus nature is a net sink for CO2, not a source. If one plots emissions and increase in the atmosphere together, one can see how the (mainly temperature dependent) natural sink capacity changes over time:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em.jpg
Ferdinand Engelbeen:
The Mauna Loa atmospheric CO2 data runs from 1958 to 2012. The rate of increase is not constant over the period (it is up and down like a yoyo). And the period is only 54 years during which time temperature has risen and other changes have occurred.
The rate of increase has recently slowed to nothing as temperature rise has stalled, the rise in anthropogenic emissions has stalled (as a result of economic recession), and many other changes may have happened..
At April 20, 2013 at 9:11 am you provide a graph showing a 9-year running mean of the data with a linear trend through it and no significance limits; i.e.
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_increase_rate_1960_2012.jpg
Even that smoothed graph shows the increase rate was negative from 1974 to 1976, from 1985 to 1987, from 1990 to 1997, and since 2010 (although you don’t say how you obtained a 9-year mean for data before 1967 and after 1999). Ignoring end effects, your data runs for 34 years from 1967 to 1999 and is negative for 11 of those years.
So, having processed the data to smooth it, you still have not obtain a consistently increasing rate of rise over the short (available) sample period.
THERE IS NO CLEAR CURVE WHICH CAN BE FITTED TO THE DATA AND/OR HAS THEORETICAL JUSTIFICATION.
In this circumstance, the ONLY reasonable extrapolation of the data is linear.
But you conclude your post saying to me
No!
I say only a linear fit to the data can be accepted as being justifiable for extrapolation of the data because any other curve is an expression of prejudice. And if your prejudices about the causation of the rise in atmospheric CO2 prevent you accepting that, then sorry, there can be no discussion.
I yet again repeat
Richard
Ooops! Sorry, Ferdinand, I now see I typed “34 years” but intended “43 years”.
Richard
@Andrew
Seriously think about things before you respond … it doesn’t matter how fast the earth rotates 50% of the atmosphere will be exposed to the sunlight you know the half the world that currently has daylight .. pretty basic.
Now go and look at the amount of energy coming from the sun to earth per second the answer is 120000000000000000 joules per second or 120,000 TW.
Doesn’t matter how fast you turn a pig on a spit the pig still cooks doesn’t it.
So you have a basic problem you have energy coming in and the earth isn’t heating up like the moon and the ISS to several hundred degrees so how is it balancing the temperature and no amount of earth spin speed is going to solve that problem because half the earth is always facing the sun.
Somehow the earth by magic is managing to do something that a planet without an atmosphere can’t and you may want to look at how they cool the ISS here is a start point.
http://science.nasa.gov/science-news/science-at-nasa/2001/ast21mar_1/
At the moment you have a big problem energy coming into earth and none going back out.
@Andrew
I forgot to say that the International Space Station travels in orbit around Earth at a speed of 17,500 miles per hour much faster than the earth and they see a sunrise every 92 min.
So based on your great logic they shouldn’t need to cool the ISS at all because it’s spinning around in orbit much faster than the earth.
But yeah they do have to cool it because it like earth is a closed system in space and you have to balance incoming and outgoing energy.
See that’s my problem with you anti greenhouse effect types you think that any of this level of science is somehow in dispute. I have no problem if you want to attack some of the stretches of science in AGW but please stop trying to tackle hard normal physics that is well known and understood.
richardscourtney says:
April 20, 2013 at 9:53 am
The rate of increase has recently slowed to nothing as temperature rise has stalled
The rate of increase of the increase (that is not the same as the rate of increase itself, which is about constant over the past decade) did stall in the past decade, as good as in a few other periods, but in adjacent periods, the rate of increase of the increase doubled. That is what the trend does: showing the slope of the rate of increase in increase over the full period. If you prefer to look at only the past years, that is your good right, but that is as discutable as simply using the trend over the full period.
I say only a linear fit to the data can be accepted as being justifiable for extrapolation of the data because any other curve is an expression of prejudice.
The linear fit of the increase data shows a slope with a doubling per 40 years. What do you mean with your “linear fit”? A linear fit only over the past 10 years? Why not the past 3 years, which show a decellerating? Who’s prejudice is that?
The important point is that Happer has adopted the assumption of extrapolating the linear trend which has existed since 1958
Richard, for the last time, the trend in atmospheric CO2 levels since 1958 is not linear, it is slightly exponential with a lot of ups and downs, but no matter what curve you may use to fit the real trend, the increase rate per year doubled over the past 40 years. See how badly your linear fit follows the data:
http://www.woodfortrees.org/plot/esrl-co2/from:1960/plot/esrl-co2/from:1960/trend
The linear trend is even outside the seasonal variability…
Ferdinand Engelbeen:
At April 20, 2013 at 11:12 am you say to me
Ferdinand, for the last time, almost any curve can be to the data over the period,
and
Richard
richardscourtney says:
April 20, 2013 at 11:39 am
Richard,
If you don’t want to see that the increase of CO2 in the atmosphere is NOT linear, that is up to you. I am still waiting to see your linear fit which is within the seasonal band at Mauna Loa over the full period. Until then, here it stops for me.
@ur momisugly LdB
Here’s your problem LdB, taken from your attempted patronization of ‘kretchetov’ on April 20, 1:44 am (my bold):
“you cant say it just cools because that is true only of the side facing the sun it [presumably you mean the GHE] is heating the reverse side to stop it going massively negative”
Whether a hemisphere is in sunlight or shade, both hemispheres are always cooled 24/7. Are you seriously stating that the hemisphere in shade ceases to shed energy, not least by radiation? Why would the hemisphere in shade suddenly stop radiating? Hence, there is no basis for your assertion that I “have a big problem energy coming into earth and none going back out”. You are aware that ice cubes radiate, as does anything with temperature >0K, aren’t you?
I’m still awaiting your explanation of how the atmosphere knows how to flip from fridge mode to blanket mode and back again (reaching for popcorn). Try to patronise a little less and punctuate a little more.
Thanks.
Ferdinand Engelbeen:
At April 20, 2013 at 1:05 pm you say to me
1.
I do not need to provide a linear fit. Throughout I have been saying that Happer was right to use a linear extrapolation because that is the ONLY extrapolation which is not a reflection of prejudice. THAT IS TRUE. You have not addressed it in any way.
2.
You claim it is “not linear”. OK. Demonstrate that with a fitted curve which is supported by theoretical understanding and is not merely an expression of your prejudice.
3.
It stopped for me when I gave you the ‘last word’ but you re-started it.
Richard