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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MC
March 8, 2010 12:50 am

Monckton:

Steveta_uk
March 8, 2010 12:57 am

This seems a perfectly clear exposition of what’s wrong with AGW theory.
So what in the above it beyond the capabilities of main-stream journalists? If I was a Harabin or Black, I would want to know from the Met Office experts exactly where the errors are in this, because clearly there MUST be some serious mistake, as we know from the Met Office just last week that AGW is real, and MUST be due to man-made interference with nature.
So seriously, if any main-stream journalists get to read this, why are you not doing your jobs and investigating? Surely it is the low-level arguments such as this that need to disproved by the AGW supporters who constantly tell us that the science has been clear for 150 years.
If they cannot disprove this, why do the MSM listen to them?

Richard Telford
March 8, 2010 1:00 am

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.
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.

sHx
March 8, 2010 1:06 am

Excellent post for the layman. But it would be nice to have a few citations. What is the source of the claim that “the first 20 ppm accounts for over half of the heating effect ?”
But the following is the true statement that is gives some perspective (and puts a smile on my face): If plants were doing climate science instead of us humans, they would have a different opinion about what is a dangerous carbon dioxide level.

Lawrie Ayres
March 8, 2010 1:08 am

The IPCC projection looks decidedly odd even for a layman. Unbelievable in fact. Since the amount of warming is also in doubt due to poorly sited and deleted thermometers I’m beginning to wonder what the AGW hypothesis has left to support it. Manic rants from those about to lose their cash cow appears to be the last resort. Even chairman Rudd has gone quiet and Penny Wrong has gone off to buy some floodwater.

toyotawhizguy
March 8, 2010 1:15 am

“To paraphrase George Orwell, anthropogenic carbon dioxide molecules are more equal than the naturally occurring ones. Much, much more equal.”
————–
Borrowing another idea from Orwell’s “Animal Farm”:
– Four legged CO2 is a friend.
– Two legged CO2 is an enemy.

JohnH
March 8, 2010 1:26 am

They have a nice theory, they have models that use the theory but these models future predictions all end up being wrong so end of theory in my mind.

Vincent
March 8, 2010 1:27 am

The temperature sensitivity of CO2 is clearly not logarithmic over the entire range. The logarithmic relationship appears to range from about 40ppm to about 200ppm. After that it looks more like a 1/x type relationship. Maybe the whole curve is closer to 1/x. Has anyone tried doing such a plot?

Sunk
March 8, 2010 1:53 am

I’ve read Davids papers on this before (I’m a layman I hasten to say). Apart from a derivative graph on the Junk Science site and a quote from Fred Hoyle I’ve not been able to dig out any further papers that support this idea. I’m told the science is settled, but something as basic as this seems to cut right to the heart of the whole argument…how could something as simple as this have been overlooked?

Mooloo
March 8, 2010 1:56 am

forcing due to CO2 + feedbacks
You mean like the melting ice-caps decreasing albedo. How’s that particular forcing working out for you?
The idea that water vapour suddenly kicks in at a particular CO2 concentration is extremely odd. Water vapour levels doesn’t depend on CO2 levels, just temperature and wind. We already have parts of the world which remain at high temperatures year round — the tropics. They would already be exhibiting the vapour feedback, and have done so for centuries. We have parts of the world which are always cold — the poles. No substantial mechanism effect there because they don’t get hot enough. So any water vapour effects will have to come at the margins, and they won’t generate the accelerating effect you need.
The idea that water vapour will cause accelerated warming seems to rest on the idea that the earth is a consistent temperature. Since it isn’t, there can be no magic kick-in point.
So what forcing are you actually relying on?

Trevor
March 8, 2010 1:56 am

Nice one David,
I can’t stand it when an alarmist states (unchallenged) that the sceptics have not come up with one argument to upset the settled science. Well how about we get this into the head of the next talking head (to challenge) – hey dude CO2’s contribution is logartithmic not linear – heck that scientific enuff for ya. Plimer touches on it in his book – but well explained here, good job. I like the line about the point of view of the plants. You know, I reckon corals and foraminifera might like it for their skeletons too.

March 8, 2010 2:05 am

Excellent!
Mr Archibald:
May I translate this article into Spanish and publish it in my blog, with due recognition and links to the original, of course?

Antonia
March 8, 2010 2:14 am

David Archibald’s conclusions are either true or not. Or am I being simple-minded? If he’s wrong why don’t climate scientists stop holding their noses and say why. Wouldn’t that be science?
This we’re-not-talking-to-each-other mentality is what is so frustrating to non-scientists like me.
I’d like Richard Telford to comment in greater detail. Then I’d like to see David Archibald respond.
And yes, I know we’ve all got day jobs … but hang on! Aren’t we sceptics all funded by Big Oil?

Ronaldo
March 8, 2010 2:17 am

Richard Telford (01:00:29) :
May I respectfully suggest that you re-read the penultimate para. of the post, think, engage brain, think again, then make a considered response.

P Gosselin
March 8, 2010 2:19 am

I’ve read in literature somewhere that CO2 contributes to about 25% of the greenhouse effect, i.e. 7-8°C. Can you cite where the 10% value comes from?
And there are other logarithmic curves, e.g. Lindzen, that are less flat after the first 300 ppm than the ones presented above. I’m wondering which are correct. Has Willis’s graphs been peer-reviewed? (Not that it makes a difference).

Peter Taylor
March 8, 2010 2:21 am

Its a curious thing that this point – well made by David here, still gets re-iterated and as far as I am aware, without response from the modellers. In the middle of last year I wrote a book aimed at my fellow environmentalists where I outline this issue – especially the 300% ‘gain factor’ in the equations – which is not so easy to derive from IPCC documents and for which I must thank Christopher Monckton in his article for the American Physical Society, where he tracks it down to James Hansen way back at the very beginning. It is a theoretical feedback, as Richard Lindzen pointed out at IPCC-1 in 1990! The modellers have taken the ‘warming’ (partly it now appears to have conjured and manipulated in the ‘gridded data set’ process) as evidence of the theoretical projection – and small wonder that when, after 2002, the warming ceased (no appreciable rise in upper oceanic heat content which is where 80% of the ‘warmth’ is held) that Kevin Trenberth at NCAR states in exasperation that it is a ‘travesty’ that they can’t account for the ‘lack of warming’.
You would think that at least one environmentalist from the long list of IPCC supporters would have either written to me, or pointed out in numerous public talks and discussions, where the refutation can be found – or that the MetOffice would have issues some guidance. Not one word!
So – given that this blogsite is visited by the orthodox – he is a challenge – please explain in simple terms, what is wrong with David Archibald’s presentation. I, for one, am open to listening and being re-educated – I care about the future of humanity, biodiversity…..the planet, but right now much of what I and others greatly value is threatened not by the projected consequences of carbon dioxide, but by the supposed remedy for climate change which will seriously and immediately damage landscape, biodiversity and community throughout the world, not to mention draining the pockets of taxpayers in a feeding frenzy of ‘jobs-for-the boys’ (Friends of Rajendra Pachauri rather than Friends of the Earth) – the technologies of turbines, barrages and biofuels.
So lets have an intelligent dialogue around this central issue – please!

Alleagra
March 8, 2010 2:27 am

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.
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.”
Looks like you have an excellent opportunity to demolish the sceptics with at most one follow-up submission which I hope you’ll make. Please avoid abuse such as ‘complete junk’ (makes you feel better but does not enlighten us) and tell us exactly where the author has gone wrong and mislead us

Mari Warcwm
March 8, 2010 2:29 am

Richard Telford
Why is the last paragraph complete junk? Forcing is logarithmic. Surprisingly, climate scientists were aware of that….. were they? So why do you get such alarming amounts of warming out of a trace gas?
Either you know a lot that needs to be explained to the rest of us, or you don’t now nuffin.

March 8, 2010 2:43 am

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 result?
Reply: Do you mean arithmetic? ~ ctm

David Wells
March 8, 2010 2:43 am

If these graphs display the reality then why does the IPCC and the MET office want – seriously want – to continue propating the myth of AGW what is the purpose? If someone could describe to me in simple detail the reason behind the corruption of data and evidence that at the end becomes simple propaganda then whilst not being happy with the current situation I could at least understand why it exists.
You see it is a really big issue because if the BBC is correct according to their documentary serious about the solar system (last night) we only have 5 billion years left to sort the problem out.
Within that time frame the sun will implode and turn planet Earth into Walkers crisps hopefully if Al Gore is still around then he will get fried first so I am not going down to the gym and then restrict my diet to the minimum amount of calories so I live long enough to watch the episode on reality TV, I cant wait!
David Wells

MostlyHarmless
March 8, 2010 2:49 am

I’m a little confused on this. The logarithmic nature of the Beer-Lambert law is well established but my understanding is that it applies even with an abundance of IR radiation that CO2 can absorb and dissipate as kinetic energy. Now, I’m under the impression that there exists a scarcity of IR radiation in the wavelengths which CO2 absorbs and the only effect of increasing the amount of CO2 in the atmosphere is that this finite amount of available energy gets absorbed closer to the ground.
So, is it correct that there are, in fact, two influences here, i.e. (a) the logarithmic impact on temperature according to the Beer-Lambert law and (b) the finite amount of reflected IR energy already being absorbed to extinction by the CO2 already in the atmosphere. Can someone please clarify this for me?

Mike J
March 8, 2010 2:57 am

MC – thanks for the link : brilliant debating, just superb. Monckton, with wit and humour aplenty, describes the reduced greenhouse effect of each additional atmospheric CO2 molecule over its predecessor, so this debate is not entirely off topic. It is well worth a watch if you have a spare 80 minutes or so.

March 8, 2010 3:07 am

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.

I’m not sure what claim the first sentence is based on. Can the writer elaborate?
My initial thoughts when I look at the post. The current radiative forcing at top of atmosphere from 380ppm of CO2 is around 1.7W/m^2 and from all increases in “greenhouse” gases = 2.4W/m^2. What I would call “non-controversial physics”, because it nicely ignores the rest of climate effects – the radiative-convective effect in isolation.
When you calculate the “rule of thumb” surface temperature increase from these 2 numbers above from the Stefan-Boltzmann equation you get 0.5’C and 0.7’C increase in surface temperature respectively. This is without feedbacks. You can see this all laid out in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers
But these are just rules of thumb – a “ready reckoner” approach to save standing in the long queue for the GCM each time you want to know something..
As far as I understand the point of this post, the climate modeling community is wrong because the current temperature increase isn’t 0.5’C x 2 or 0.7’C x 2 ?
I have my skepticisms about the climate models, but is this critique based on what climate modelers say? Is there a paper to reference?
The water vapor feedback is perhaps one critical aspect of climate models.
Do climate modelers presume it linear from pre-industrial times?
Do they calculate it to be linear from pre-industrial times?
I don’t know the answer. There seems a presumption in the article but no reference. It would be nice to check.
A few extra notes on the boring detail..
2. Where did “Carbon dioxide contributes 10% of the effect” come from? Kiehl and Trenberth (1997) calculate CO2 as about 26% of the “greenhouse” effect (see CO2- An Insignificant Trace Gas? – Part Five
3. Where does the forcing calculation in the 2nd graph come from and what is it saying?
The IPCC, effectively quoting Myhre (1998), says radiative forcing at top of atmosphere = 5.35x ln(C/Co), where Co is industrial levels of CO2, 278ppm. It is specified in boring detail (see it at the http://scienceofdoom.com reference above) and tells us the expected addition to radiative surface forcing.
This 2nd graph says “Net downwards forcing” – at surface? at TOA? And is this after feedback, before feedback?

Steveta_uk
March 8, 2010 3:07 am

Please can we all play nicely!
Contrast the comment by Antonia (02:14:59), which attempts to get more information from Richard Telford, with the following one from Ronaldo (02:17:36) which is guaranteed to kill any serious discussion.
What’s the point of the nastiness? It doesn’t help anyone.

Nick Stokes
March 8, 2010 3:08 am

“The whole AGW belief system is based upon positive water vapour feedback starting from the pre-industrial level of 280 ppm and not before.”
This is just assertion. No reference, no cite. It’s a fabrication.

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