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.


Sponsored IT training links:

Worried about 642-426 exam results? Join 642-446 training program and get complete set of 350-029 dumps with 100% success guarantee.


Get notified when a new post is published.
Subscribe today!
4.7 19 votes
Article Rating
436 Comments
Inline Feedbacks
View all comments
March 8, 2010 5:17 am

Or alternatively one could look to ‘natural causes’ to account. 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

Baa Humbug
March 8, 2010 5:21 am

Re: David Wells (Mar 8 04:22),

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

My bellyaching changed the opposition leader here in Australia and stopped the proposed ETS in it’s tracks. Why is that important? Well if the likes of Watt McIntyre Monckton et al weren’t bellyaching, you and I and our nations would be that much poorer due to these grab taxes like the ETS. Why is that important? Look at the environments in poor countries compared to well off countries. The people in poor countries don’t give a chit about the environment, they rightfully care about where their next meal will come from.
I’m guessing you made your remarks after being well informed by reading these sorts of blogs for many months now. Why aren’t you outside getting some fresh air? Or were you naughty and just quipped after reading one or two threads?

Bernie
March 8, 2010 5:22 am

Rob:
Somewhat OT but something is odd with the GISS numbers for Mukteshwar http://data.giss.nasa.gov/cgi-bin/gistemp/gistemp_station.py?id=207421470003&data_set=0&num_neighbors=1
I believe Mukteshwar Ku is the location reported in the news story.

Editor
March 8, 2010 5:24 am

More on my note above – my comment about log(exp()) being linear above assumes a graph of the function over time – Archibald’s graphs show temperature wrt to CO2 concentration! I think models and warmists talk about a linear increase over time, this may be a major disconnect between Archibald and them!
Where Archibald has a straight line for modeled warming, it should be a log() curve (or log(baseline + exp()) as I mention before).

March 8, 2010 5:28 am

Here is an interesting explanation and discussion of CO2 saturation in the Physics Forum.
http://www.physicsforums.com/archive/index.php/t-174215.html
Another scientists look at this issue.
http://wrauny.blogspot.com/2009/12/global-warming-leave-co2-alone.html
A graphics from othe studies.
http://www.junkscience.com/Greenhouse/co2greenhouse-X2.png

Boris
March 8, 2010 5:36 am

David,
Your post is interesting, but rests on an arbitrary choice that skews the results.
Your 10% of the greenhouse effect for CO2 is an arbitrary choice, although it is within the range supported by the literature.
Going back to Ramanathan and Coakley 1978, we see that they get a wide range for CO2’s contribution to the greenhouse effect. They get between 9 and 26 percent. The range is calculated by first removing all CO2 from the atmosphere and recording surface temp (9%) then removing EVERYTHING BUT CO2 from the atmosphere (26%) This was done in a basic radiation code and has been repeatedly verified with slight variations of no more than a percent in the 30 years since R&C.
But what exactly does the 9% tell us? Unfortunately, the 9% doesn’t tell us much. Since concentrations of WV are held steady in the radiation code to get the 9% number, there is an assumption of 0 feedback for CO2. (In other words, 9% assumes that none of the WV in the atmosphere is a result of the warming caused by CO2) Since your arbitrary choice is so close to this no-feedback number it is not surprising that you get odd results when compared to climate model predictions.
If we knew the exact contribution of CO2 to the GHE, we would know the strength of feedbacks and have a pretty good estimate of climate sensitivity to CO2 doubling. Unfortunately we do not know this with the certainty you imply in this post.
So essentially your analysis proves that if you select a small effect for CO2, you will get results that support a small effect. An equally arbitrary (and equally supported) choice of 20% for CO2’s contribution would get completely different results.

Mari Warcwm
March 8, 2010 5:41 am

David Wells
‘Get al life, you only have one so make use of it’
I am interested in this subject because it involves such a vast waste of taxpayer money which could be put to much better use. We are in a serious economic recession and out politicians want to handicap us further by imposing taxes on industries that emit CO2. I am horrified by the vast lie that is AGW.
I was brought up on David Archibald’s excellent ‘Solar Cycle 24’, and I am very grateful to have been given a copy of it by an alert friend.
The question of CO2 warming effect being logarithmic seems to me to be a crucial fundamental question. It either is, or it isn’t. Why isn’t this question discussed more often, and more emphasis not put upon the answer? The Earth’s atmosphere has been in equilibrium for the past 500 million years, and life has flourished.
We are bumping along the bottom of the amount of CO2 seen during the past 500 million years. I gather that the average amount of CO2 in the atmosphere during the past 500 million years was 2,500 ppm. Why are we now so paranoid about a mere 388 ppm. And even more paranoid about the mere 15 ppm produced by our burning of fossil fuels?
It seems to me an absurd collective madness has overtaken most of the population. Get a life? Get a grip.
The Earth’s climate has been in equilibrium for millions of years. There must be a robust mechanism that keeps it in equilibrium. CO2 has been as high as 5000ppm during the past 500 million years. There was no runaway warming. Life flourished.
I was brought up on David Archibald’s book ‘Solar Cycle 24’. It was an excellent book

March 8, 2010 5:43 am

David, as a skeptic who is well versed in the logarithmic nature of CO2 forcing, I dont have a clue which message you are trying to give here. The co2 range of interest is 100 to 1500 ppm, and already Arrhenius confirmed in 1906 that this leads to a 1.2 degree temperature rise for every doubling. The only debate is now about feedbacks: Is miskolczi right that tau is a constant (which means co2 is compensated by less water vapour) or is IPCC richt that that the feedback is positive. This posting is really not helping in this debate.
Yes, IPCC knows that carbon dioxide has a logarithmic effect (look for Myhre simplified expression) http://www.grida.no/climate/ipcc_tar/wg1/222.htm

Deanster
March 8, 2010 5:54 am

So … when is this information going to be published in a peer reviewed journal?? .. OR .. has it already been published in a peer review journal?
It would seem to me that in order to make a valid claim that the IPCC scientists are cherry picking their information, alternative information needs to be published in peer reviewed journals. Granted, I’m aware of the conspiracy to block alternative information, and to prevent alternative information from getting to the mainstream. But still, you would run a better chance of making a valid claim if it were published.
I’m a staunch skeptic and find much wrong with Climate Science from a scientific perspective. However, I find myself scratching my head wondering why “science” is not driving ahead according to the accepted protocol. … Publish!
There are so many things. Station drop out, solar forcings, this issue on CO2 forcing, bad models, bad thermometers, etc etc .. but it seem little of it gets published in journals .. just internet.
HECK .. start your own journal if the tainted ones won’t publish it.

Ben W
March 8, 2010 5:57 am

What is the real pre-industrial CO2 level? I am confused. See this webpage:
http://www.biomind.de/realCO2/

MattN
March 8, 2010 6:02 am

I have used this graph and argument in conversations with True Believers(tm) and the reaction is always the same: It doesn’t matter, look at the ice melt.
It is completely useless to continue to engage TBs any longer. There is literally nothing that will convince them. Even a glacier at their front door would be proof positive the “science” is right.
Focus on the the people on the fence….

JonesII
March 8, 2010 6:02 am

Dear Dr.Archibald, stick to your brilliant approach of the Sun cycles. Greenhouse doesn´t exist, it´s dead. The so called “green-house effect” is for closed systems, it really means “trapped heat”. Our earth, HOLY GAIA for the world government conspirers believers, it is not a closed system but an open system…and, as Lord Monckton has shown, based on satellites observed energy balance, energy loss from our planet is greater than energy gain. Temperature is but an almost subjective reference.
The famous physicist Niels Bohr, at the beginning of the 20th.century described this “green-house effect” as non existing:
http://www.scribd.com/doc/28018819/Greenhouse-Niels-Bohr

OceanTwo
March 8, 2010 6:05 am

David Wells (04:22:34) :
Rant much?
1. It isn’t just Americans that post in these threads, or are you truly and specifically targeting Americans for the worlds environmental issues?
2. The ‘environment’ and CO2 (in context) are two different things. Me thinks you have trouble distinguishing the two.
3. It appears you deem the ‘science as settled’: would this be the case?
4. Perhaps it is you who needs to get your ‘face out of the screen’ and go outside to see that the environment *isn’t* crumbling at our hands.
5. Did you forget to mention the evil corporations and big oil?
6. Just because you have no interest in a particular subject [science], and don’t see the relevance, doesn’t mean others don’t.

toyotawhizguy
March 8, 2010 6:07 am

Telford (01:00:29) :
“The final graph is complete junk. Comparing forcing due to CO2 alone with forcing due to CO2 + feedbacks and finding that the latter is larger is pretty trivial.”
————-
Feedbacks are infinitely complex, and the portion that deals with cloud cover, and changes in sea ice and snow cover are poorly understood. Only the water vapor aspect is well understood, and is widely agreed upon as being positive. Accurately assigning a quantity to that positive value for water vapor is another matter. There is wide disagreement (depending on which Climatologist you ask) whether cloud feedbacks due to increased CO2 forcing are positive or negative. What is known is that cloud feedbacks are highly chaotic. Feedbacks due to CO2 forcing don’t just “take off” at some imaginary threshold, but rather logically follows a more smooth curve. The idea that a diminutive increase in forcing due to an increase in atmospheric CO2 could be amplified several times by positive feedbacks (with the assumption that the positive feedbacks overwhelm the negative feedbacks) runs parallel to the concept of an over-unity perpetual motion machine, thus my skepticism. Besides that, the Stefan-Boltzmann law for radiation of a black body predicts that there is always present a strong negative feedback for any type of forcing that changes the temperature of the black body.
It would require a googolplex of data points to actually measure the feedbacks existing on the globe for a single day. Good luck with that. All we have is some limited data, fuzzy theoretical math equations, and GIGO computer models to predict feedbacks.
Here is a statement found at:
http://www.faqs.org/faqs/sci/climate-change/basics/
“These figures are compatible with the IPCC estimate of about 1.5 to 4.5 o C surface
warming for a CO2 doubling.”
The range of that estimate runs the gamut of 300% for the maxima over the minima. Nothing to see here, move along.

John Eggert
March 8, 2010 6:07 am

Someone asked for references. Here are a couple:
Bejan, Adrian; Kraus, Allan D. Heat Transfer Handbook. John Wiley & Sons., 2003 Page 618 (Leckner’s curves, available in electronic form from http://www.knovel.com)
Schumann, Reinhardt, Metallurgical Engineering, Volume 1, Addison-Wesley, 1952 (Hottel’s curves –>> note the year.)
Hottel et. al. developed a method of calculating the impact of CO2 on radiant heat transfer in the atomsphere. Leckner greatly improved on the method. Both take into account all of the “fudge factors” that relate to absorbance. Full spectra, concentration, distance, reradiation within the gas, etc. This work that was ignored by climate scientists is used by everyone else who needs to calculate radiant heat loss in the atmosphere (so many people do this even engineers like me can learn it). Applying this work to the atmosphere shows that the logarithmic relation is an approximation. A log/log relation is more likely. Anyway, the graphs of forcing one gets using these methods is similar to the f=5.35ln([CO2]/{CO2{284}). It just flattens more at higher concentrations (above 100 ppm). It does indeed prove that most radiant heat effects begin at very low levels of gas. Using this method, the maximum absorbance by CO2 would be about 45 W/m³. This is attained at about 200 ppm. (100 ppm is 40) 22.5 W/m³ is attained at about 6 ppm. If Anthony is interested, I can send him a paper I’ve written that clearly shows the method for obtaining these including sample calcs, etc. that make creating the graphs relatively trivial.

Stacey
March 8, 2010 6:08 am

David Wells
I shout
he she or it shouts
we shout
they shout
You make some valid points but start a shouting match with other posters quite un-necessarily so.
The reason this and similar articles on this site have validity is because the foundation of the hypothesis that man made CO2 emissions will cause dangerous global warming is at the heart of the debate.
Finally does anyone know what the CO2 level was during the MWP and earlier warm periods?

Stacey
March 8, 2010 6:09 am

PS Guys
A sponfull of sugar and a pint pot of gall?

AnonyMoose
March 8, 2010 6:09 am

Does anyone remember where that wonderful little article is which shows how much the CO2 levels have increased… by showing a graph of atmospheric gases scaled from 0 to 100%? It really puts 300 PPM in perspective.

March 8, 2010 6:12 am

Dave Wendt (03:19:06) :
I’ve seen elsewhere analysis of the two papers you cite as not only discussing the total intensity/amount of Long Wave Radiation, but also as documenting the lack of a measurable correlative difference in the re-radiated (outgoing) LWR given the increase of CO2 ppm in the atmosphere. In other words, as observational data that directly refutes the claims of CO2 greenhouse effects, as postulated by the AGW theory.
If something can be confirmed, via directly measurable observational data, e.g. Einstein’s prediction of the effects of gravity on light, confirmed by observations during a solar eclipse – then how is a departure from the postulation (absence of predicted behavior) not a credible refutation?
Following on from that, if the main premise is demonstrably inaccurate (in other words, wrong), how is anything based upon the hypothesis anything other than pure malarky?
CO2 – if the numbers don’t fit, you must acquit. And question why so many are so latched on to the one theoretical model that has even the slightest possibility of being influenced by the manipulation of human behavior, becomes extremely relevant, although this thread is not the appropriate venue to explore it.

Don
March 8, 2010 6:16 am

Water vapor is a good greenhouse gas/vapor but water vapor in the form of clouds decreases the solar insolation.

March 8, 2010 6:17 am

AnonyMoose (06:09:31):
Do you mean this one? : click

March 8, 2010 6:22 am

Just to keep it in proportion, this is the average composition of the
atmosphere up to an altitude of 25 km.
Nitrogen N2 78.08%
Oxygen O2 20.95%
Water H2O 0 to 4% (variable, affecting total)
Argon Ar 0.93%
Carbon dioxide CO2 0.0360%

March 8, 2010 6:22 am

I just love someone popping in to discuss “responsible” scientists. Nonsense!
Scientists may be wrong in their theories, or correct, but if they are really scientists, the term responsible doesn’t belong in the discourse.
Referral to socially based grading of behavior is a warning flag that the discussion isn’t about science at all.
Attempts to hide data, algorithms, ad hominem attacks, referrals to discredited papers, and appeals to higher authority are all venal attempts to hide non-science, both from the lay public, and other, competent scientists.
This thread is a poster child for the Warmists method of doing business. It wouldn’t matter if the poster were wrong, it happens frequently that a scientist is wrong. The point is, scientists put everything out on the table to be viewed, right or wrong.
The method of responding is what is telling.

March 8, 2010 6:23 am


It’s the dose the makes the poison, the fact that CO2 is a trace gas is not an issue. CO2 is a very strong IR absorber.
All classic strawmen are passing by.

March 8, 2010 6:25 am

Very informative write up.
The old painting a window glass pane with successive coats of white paint, and hoping to turn the room completely dark trick. After a few coats nothing else much happens. That’s called the logarithmic effect, once you have about three coats of paint, it’s all the paint has got that can be used to block light.
If the positive feedbacks proposed by the IPCC and their merry band of modelers, were true, the earth would be a fireball already. Once the climate ran away, or latched up, it would be stuck hot, or cold, for all time.
Watching a discovery channel presentation last week, they went all over the temperature ups and downs, the sea level ups and downs, and the CO2 levels ups and downs. It’s been far hotter than today, far colder than today, the sea levels have been 300 feet higher and 300 feet lower, the atmospheric CO2 level has been lower and much much higher than today, ice covered the whole planet, and completely melted everywhere, and we are still here. Very enlightening, here is the link … http://dsc.discovery.com/tv/prehistoric/prehistoric.html … watch if you dare.
The effect of plate tectonics was clearly shown in determining earth’s climate.
If only the media would tell the truth … scientists could get back to real science, and stop with the silly stuff. The alarmists have clearly gone past the expiration date on the public’s “Issue Attention Cycle” with their hoaxing. Time to move on.
Suggestion, next a writeup on the absorption of CO2, the lab experiments that prove it, and how it plays into this posting. May not be for the laymen though.