The Logarithmic Effect of Carbon Dioxide

Guest post by David Archibald

The greenhouse gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere, so instead of the average surface temperature being -15° C, it is 15° C. Carbon dioxide contributes 10% of the effect so that is 3° C. The pre-industrial level of carbon dioxide in the atmosphere was 280 ppm. So roughly, if the heating effect was a linear relationship, each 100 ppm contributes 1° C. With the atmospheric concentration rising by 2 ppm annually, it would go up by 100 ppm every 50 years and we would all fry as per the IPCC predictions.

But the relationship isn’t linear, it is logarithmic. In 2006, Willis Eschenbach posted this graph on Climate Audit showing the logarithmic heating effect of carbon dioxide relative to atmospheric concentration:

And this graphic of his shows carbon dioxide’s contribution to the whole greenhouse effect:

I recast Willis’ first graph as a bar chart to make the concept easier to understand to the layman:

Lo and behold, the first 20 ppm accounts for over half of the heating effect to the pre-industrial level of 280 ppm, by which time carbon dioxide is tuckered out as a greenhouse gas. One thing to bear in mind is that the atmospheric concentration of CO2 got down to 180 ppm during the glacial periods of the ice age the Earth is currently in (the Holocene is an interglacial in the ice age that started three million years ago).

Plant growth shuts down at 150 ppm, so the Earth was within 30 ppm of disaster. Terrestrial life came close to being wiped out by a lack of CO2 in the atmosphere. If plants were doing climate science instead of us humans, they would have a different opinion about what is a dangerous carbon dioxide level.

Some of the IPCC climate models predict that temperature will rise up to 6° C as a consequence of the doubling of the pre-industrial level of 280 ppm. So let’s add that to the graph above and see what it looks like:

The IPCC models water vapour-driven positive feedback as starting from the pre-industrial level. Somehow the carbon dioxide below the pre-industrial level does not cause this water vapour-driven positive feedback. If their water vapour feedback is a linear relationship with carbon dioxide, then we should have seen over 2° C of warming by now. We are told that the Earth warmed by 0.7° C over the 20th Century. Where I live – Perth, Western Australia – missed out on a lot of that warming.

Nothing happened up to the Great Pacific Climate Shift of 1976, which gave us a 0.4° warming, and it has been flat for the last four decades.

Let’s see what the IPCC model warming looks like when it is plotted as a cumulative bar graph:

The natural heating effect of carbon dioxide is the blue bars and the IPCC projected anthropogenic effect is the red bars. Each 20 ppm increment above 280 ppm provides about 0.03° C of naturally occurring warming and 0.43° C of anthropogenic warming. That is a multiplier effect of over thirteen times. This is the leap of faith required to believe in global warming.

The whole AGW belief system is based upon positive water vapour feedback starting from the pre-industrial level of 280 ppm and not before. To paraphrase George Orwell, anthropogenic carbon dioxide molecules are more equal than the naturally occurring ones. Much, much more equal.


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March 8, 2010 3:08 am

Positive feedback, assumed by the AGW hypothesis, can’t just kick in today or at 280ppm: it would have to apply at all CO2 concentrations if such feedback exists. If every 20ppm CO2 causes 0.46 degC warming, then this would hold for concentrations below the level of today, and because of the logarithmic effect, each 20ppm reduction in CO2 concentration would give a monotonically increasing effect on cooling (lack of heating). So going down to the so-called pre-industrial level of 280ppm would appear to knock out about 2.5 degC of heating, if this positive feedback be true.
The fourth graph says it all, if your calculations are correct: the cumulative effect declines to zero at around 280ppm. No – that can’t be right: any cumulative effect must go through the origin: there can be no good reason why positive feedback would kick in at 280ppm. I would expect to see the cumulative effect starting at the X-Y axes origin and monotonically increasing with CO2 concentration, BUT with the increase in the cumulative temperature per 20ppm CO2 decreasing with increasing CO2 concentration.

Bill Tuttle
March 8, 2010 3:16 am

Bill Tuttle (02:43:21) :
Then why do their models produce an algebraic result?
Reply: Do you mean arithmetic? ~ ctm

Yup — thanks, Charles.
Too little sleep from enjoying the celebratory tracer fire over here last night…

KimW
March 8, 2010 3:17 am

There does appear to be some question as to the actual, say 1880, level of atmospheric CO2. At the Air vent blog http://noconsensus.wordpress.com/2010/03/06/historic-variations-in-co2-measurements/ points out that perhaps that generally accepted figure of 280ppm, may be too low a figure. If we are questioning assumptions, then this seems to be one that needs rechecking.

Dave Wendt
March 8, 2010 3:19 am

Where do the numbers in the second graph, indicating CO2 contributing over 250W/m2 to the downward forcing, come from. These two papers
http://www.webpages.uidaho.edu/~vonw/pubs/TownEtAl_2005.pdf
http://ams.confex.com/ams/Annual2006/techprogram/paper_100737.htm
which describe experiments which used spectral analysis of downward longwave radiation to determine the contribution of the various GHGs to the total signal, show that CO2 doesn’t contribute more than 35W/m2 at its most active range and would likely be below 10W/m2 throughout most of the Tropics and Subtropics.

cohenite
March 8, 2010 3:34 am

A great post by David; of course the effect of increasing CO2 on temperature has been known to be miniscule by the IPCC because that is why they have invented the enhanced Greenhouse effect which depends on the slight warming from increased CO2 releasing water into the atmosphere with its much greater greenhouse effect.
This is wrong on many levels despite Mr Telford’s typical warmist snark. First there has not been increased levels of water going into the atmosphere; Paltridge’s excellent paper establishes that with the ghost in the machine of Miskolczi present in the stability of optical depth over the enhanced greenhouse period.
Secondly, the role of clouds has been profoundly misunderstood by AGW proponents; the recent Pinker et al dispute between Monckton and Lambert in their Sydney debate shows this; the SW flux findings of Pinker, most likely caused by cloud variation, are sufficient to explain recent warming. In this respect Monckton, despite misunderstanding cloud forcing, was correct about climate sensitivity to increases of CO2; this tiny CS from ^CO2 must be based on the log effect described by Archibald and this fact coupled with the moderating role water plays against temperature movement in any direction fundamentally contradicts AGW.

Dave N
March 8, 2010 3:49 am

sHx (01:06:52) :
Refer the MODTRANS facility, University Of Chicago.
Alarmists will tell you that the climate is far more sensitive than Archibad suggests, however I’ve never seen a convincing argument for *why*

David Archibald
March 8, 2010 3:51 am

Heber Rizzo (02:05:53) :
Please do. If you email me at david.archibald westnet.com.au ,
I can send you the original.

Sera
March 8, 2010 3:59 am

“Plant growth shuts down at 150 ppm”
Try telling that to Mr 350.

rob
March 8, 2010 4:00 am

Great News: Over the past 140 years the British weather observatory situated in the Himalayas revealed a temperature drop of .4 degrees
http://www.hindustantimes.com/india-news/northindia/Global-Warming-has-no-impact-on-Himalayas-claims-Wadia-Director/Article1-515763.aspx
Senior scientists at the Wadia Institute of Himalayan Geology (WITG) has rejected the Global Warming Theory and told that the Himalayas are quite safer zone on earth, where Global Warming has no role in controlling the conditions. They also said that the conditions of Himalayas are controlled by the winter snowfall rather than external factors like much hyped Global Warming.

ginckgo
March 8, 2010 4:03 am

So a doubling of CO2 relative to pre-industrial times leads to an increase of 2W/m2. The difference between the solar minima and solar maxima IIRC is about that much.

March 8, 2010 4:12 am

Just in case you missed it, more over enthusiasm from the IPCC on CO2.
http://www.fysast.uu.se/ges/en/headline-news/new-research-questions-the-ipcc

David Wells
March 8, 2010 4:22 am

God save me from scientists and pseudo scientists, you are all as bad, if you are so concerned about the environment then for goodness sake do something practical eg dont buy biscuits or anything else that uses palm oil.
50,000 Orang Utans have already been sacrificed for your own personal health and wellbeing before you even consider the average Americans concern about the cash in his pocket, palm oil being the cheapest vegetable oil available, then if you moan about water shortage then consider that it takes 14000 litres of fresh water to make one litre of biofuel.
Who for goodness sake cares whether or not Co2 is logarithmic or suffers from attention deficit disorder and maybe subject to rabies, what we do know is that none one single prediction made by the IPCC, Gore or Hansen has come true therefore commonsense would clearly indicate that its all hot air and that only someone severely retarded would want to continue this idiotic debate rather than actually do someone about the absolute destruction of our environment.
Americans should eat less hamburgers not because cows belch but because more rainforest is destroyed each year just to fuel the average Americans desire to cheap subsidised food.
Get your face out of the screen, go out and let some daylight into your challenged brains and recognise that none of you bellacheing about pointless statistics well change anything or is your chosen sense of status more important that the biodiversity that you think will be saved by your craven indulgence?
Get a life, you only have one so make use of it.
David Wells

John Finn
March 8, 2010 4:31 am

I would urge WUWT readers to take anything written by David Archibald with a large pinch of salt.
The main (only) point of debate between responsible sceptics and AGWers concerns feeback. Sceptics think it’s likely to be small or even negative – AGWers think it will be large and positive.
David A says “ Carbon dioxide contributes 10% of the effect so that is 3° C . This is rubbish. Jack Barrrett, a leading expert in spectroscopy – and a sceptic (see http://www.barrettbellamyclimate.com/page3.htm ) reckons the effect of CO2 is more like 9 deg (see the link to his paper on Warwick Hughes site). In fact David Archibald’s own graphs suggest his numbers are wrong. The Modtran plots show the net downward forcing increasing by ~25 w/m2 (~235 w/m2 -> ~260 w/m2) due to the current concentration of CO2.
Is David saying that 25 w/m2 only equates to a 3 deg rise?
How does that square with his claims that weaker solar output will result in a temperature decline of ~2 deg over the next “few years”. TSI measurements show that the sun’s output varies by ~0.1% or ~0.24 w/m2 at the earth’s surface.
In this WUWT post, Richard Lindzen estimates 1 deg increase from a doubling of CO2
http://wattsupwiththat.com/2009/03/30/lindzen-on-negative-climate-feedback/
Here, Jack Barrett calculates an increase of ~1.3 deg
http://www.barrettbellamyclimate.com/page45.htm
There are many other reputable (not AGW) scientists who say much the same. If the feedback effect is small (or negative) then we don’t have a problem and it’s quite possible that natural variation will ‘hide’ most of the effect. CO2 will, though, have an effect. There are also very good reasons that continuing to add CO2 will not, as David says result in the effect being ‘tuckered out’, but result rather in indefinite warming. I’m not prepared to go into that now, though.

Steve Goddard
March 8, 2010 4:37 am

This effect is the opposite of a “tipping point.” More like a “disappearing effect.”

Richard Telford
March 8, 2010 4:39 am

That CO2 forcing increases logarithmically with concentration has been known for over a century. Arrhenius (1896) did the necessary calculations:
“if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression”
The IPCC are well aware of this
“Note that for CO2, RF increases logarithmically with mixing ratio” (AR4 WG1 chapter 2.3.1)
and this knowledge is implicit in all the model projections. To imply otherwise is disingenuous.
Graph 4 is simply wrong. The bar chart is warming per 20ppm increase in CO2 concentration, the line is the cumulative effect. The units of these two parts are different – the first is deg C/ppm, the second is deg C. They are incomparable.
That problem is fixed in the last plot: at least the units are the same in this figure. But there is a second problem. The natural CO2 forcing is shown without any feedbacks, whereas the anthropogenic forcing is shown with feedbacks. This is misleading. Nobody would argue that the natural changes in CO2 are not magnified by feedbacks (try to explain the glaciations without feedbacks) One can argue about the magnitude of the feedbacks. Perhaps the IPCC has them too high. Perhaps too low.

Steve Goddard
March 8, 2010 4:41 am

Richard Telford,
Are cloud feedbacks positive or negative?
How is it that earth’s temperature has remained in a narrow range for 600 million years, despite 2000% changes in CO2 concentration?

Richard111
March 8, 2010 4:42 am

As a non-scientist, can anyone please explain why there is no convective heating
of the atmosphere? Are thermals due entirely to CO2 in the deserts?

wes george
March 8, 2010 4:43 am

Thank you, David. This one simple fact has not been repeated often enough. Dare I say it has been suppressed in the mainstream debate.
I know that most disinterested people I talk to are under the impression driven by media alarmists that as atmospheric CO2 levels increase the temperature follows in a linear, if stochastic, fashion. That is the single greatest myth behind AGW demagoguery.
Watts and others should repeat some version of this post once a month for the next decade. It can not be stated often enough!

John Finn
March 8, 2010 4:44 am

ginckgo (04:03:44) :
So a doubling of CO2 relative to pre-industrial times leads to an increase of 2W/m2. The difference between the solar minima and solar maxima IIRC is about that much.

The doubling of CO2 relative to pre-industrial times leads to an increase od ~3.7 w/m2. When looking at the difference between soalr minima and maxima you need to look at insolation, i.e. what the earth receives, not TSI. If TSI increases by 2w/m2, the earth’s surface, on average, only receives 25% of this (think day, night, winter, summer). Of that ~30% gets reflected back to space due to the earth’s albedo. A 2 w/m2 increase in TSI equates to an increase of ~0.35 w/m2 averaged over the earth’s surface. You should take a bit more notice of Dr. Leif Svalgaard’s posts and it a little less of Dr. David Archibald’s.

March 8, 2010 4:50 am

Or alternatively one could be to look to ‘natural causes’. One of the better proxies is GMF (geomagnetic field)
http://www.vukcevic.talktalk.net/LFC8.htm
which not necessarily mean that GMF is either the cause or a consequence, but possibly two offsprings of the same parentage.
http://www.vukcevic.co.uk/GandF.htm

Mike
March 8, 2010 4:54 am

Let’s see, usually we are told by AGW skeptics that the atmosphere is too complex to understand. That the sophisticated mathematical models that run on supercomputers cannot possibly come close to the real climate. But, now we are to believe that some guy with a graphing calculator has got it all figured out! He didn’t even need calculus, just an ln x button. Think of all the tax dollars that could have been saved!
http://www.aip.org/history/climate/GCM.htm
http://www.giss.nasa.gov/research/briefs/schmidt_04/
http://www.logicalscience.com/skeptic_arguments/models-dont-work.html
http://www.grist.org/article/climate-models-are-unproven/

Jordan
March 8, 2010 5:08 am

I have been on the receiving end of proponents’ reply to the temperature changes mentioned in the above post.
The counter argument is that we need to make a distinction between the “equilibrium” climate sensitivity, and “transient phase”. We are suppiosed to be in the transient phase at the moment, and it is argued that the climate will take centuries to settle to equilibrium. According to this argument, we would not expect to see the equilibrium conditions for a long time to come.
I have not found this to be convincing.
Even if we were to accept that the present condition is the transient en route to a much higher equilibrium, the transient should still be evident in measurement. IPCC AR3 Chapter 9 has a beautiful chart of the “big red spot”, which show how atmospheric heating above the surface is necessary to observe heating at the surface (if heating is due to radiative physics). We should be able to see the red spot forming by now (transient or not) – especially if some past warming has been attributed to CO2.
I know of no confirming measurements which do so. Some people claim that cooling in the ionosphere is evidence – but cooling in the ionosphere without warming further down does nothing to explain recent warming. In the absence of such evidence, I’d look upon the hypothesis as falsified.
Secondly, what I consider to be the unphysical argument of amplification of temperature change by positive feedback. The term “amplification” means a dimensionless constant, where a change of an input variable results in a greater change of an output variable with the same dimensions. In the case of climate sensitivity, we’re talking about units of temperature or units of radiative flux at the surface (take your pick), where a change of input results in some multiplied change, when the system eventually settles to equilibrium.
Given that amplification is dimensionless, it’s clear that there is an increase of energy from the input to the output. We need to identify and account for this energy to make a convincing case for amplification in climate sensitivy.
And this applies equally to feedback systems – without an “auxiliary” source of energy, feedback cannot amplify a signal. Trying to say it does would be like arguing that I could jump into a basket and lift myself off the ground using the handle. You might get that to work in the cyberworld of computer models, but it doesn’t work in the real world.
I’m not trying to say that amplification is wrong. I just haven’t seen the full explanation of energy flows, so references would be welcomed. And until I see this, I would tend to view amplification of the climate sensitivity as another falsified hypothesis.

David Archibald
March 8, 2010 5:09 am

There is no need to rehash the science. Real Climate attacked my graph back in October 2007 in a piece entitled “My model, used for deception”. http://www.realclimate.org/index.php/archives/2007/10/my-model-used-for-deception/
That was the seal of approval. Real Climate felt they could no longer ignore it, they had to try to counter it. Thanks guys. Without that sort of feedback, you don’t know how effective you are.
There are two sorts of IPCC scientists – the ones that fake the historical record and the modellers who generate warmings for a doubling of CO2. We hear a lot about the former but the latter are required to give credence to the alarmist projections. Looking at a graphic that Roy Spencer produced in early 2008, there are 21 model results contributing to the IPCC concensus, with the lowest warming 2.5 degrees and the median 3.5 degrees.
But it had been bugging me for a while that global warming belief system has their heating from the pre-industrial level, and not some other point. Never mind that Spencer has shown that the feedback is negative, not positive. What the AGW belief system requires is that the system is quiescent up to the pre-industrial level and then it just explodes. It requires everybody to believe in fairies at the bottom of the garden. It defies the laws of physics and nature. It is the big lie upon which the whole AGW edifice is founded.

Editor
March 8, 2010 5:09 am

Bill Tuttle (02:43:21) :

Richard Telford (01:00:29) :
I don’t know if this post was supposed to be misleading and confusing but is certainly is.
Forcing is logarithmic! Surprisingly, climate scientists were aware of that.
Then why do their models produce an algebraic [arithmetic] result?

I think some of the answer is that if CO2 are climbing exponentially, then the log() of that is a straight line. The catch is that current CO2 levels can better be modeled, I believe (i.e. no references and I wouldn’t believe this if I were you), as a baseline plus an exponential. The log() that is quite a bit
flatter until the exponential overwhelms the baseline.

March 8, 2010 5:17 am

OT, but being the science blog, some of you may find these interesting, I think they are fascinating (to see next position cursor over the photo).
http://www.telegraph.co.uk/science/picture-galleries/7397841/Creepy-crawlies-Amazing-Scanning-Electron-Microscope-pictures-of-insects-and-spiders.html