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 11:51 am

Gerard Harbison (09:06:07) :
Some parts of the IR spectrum are indeed saturated, and CO2 increase won’t have any effect. But in other regions of the spectrum, and particularly at the poles, the edges of the CO2 bands are anything but saturated.

And the net result of predicted strongest increase of greenhouse effect is..
Antarctic – cooling?
http://climexp.knmi.nl/data/itlt_0-360E_-66–90N_na.png
Arctic – AMO oscillation?
http://climexp.knmi.nl/data/icrutem3_hadsst2_0-360E_66-90N_na.png
Where is the strengthened greenhouse effect fingerprint, when the most sensitive areas on the Earth show nothing or just regular variations, well correlated with oceanic oscillations?

Jimbo
March 8, 2010 11:56 am

Well, how have the IPCC done so far?
http://www.ianschumacher.com/img/TempsvsIPCCModelsWM.jpg
http://deepclimate.files.wordpress.com/2009/05/ar4-a1b-a2.gif
http://joannenova.com.au//globalwarming/graphs/akasofu/akasofu_graph_little_ice-age.gif
And here is Prof Jones admitting the lack of statistically significant warming since 1995.
http://news.bbc.co.uk/2/hi/science/nature/8511670.stm
So rising CO2 since the start of the industrial era means we should be cooking under the positive feedback which we are not. Its
“The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t,”
http://www.eastangliaemails.com/emails.php?eid=1048

Lon Hocker
March 8, 2010 12:29 pm

Help me understand the multiplier.
If adding CO2 means more water vapor and accordingly more greenhouse from the water vapor, then this will, in turn create more heating, water vapor and yet more heating. This appears to be a classic system with positive feedback which would limit at some value unrelated to the initial CO2 increase.
What keeps this from happening in their models?

March 8, 2010 12:31 pm

David,
As this paper is a pretty fundamental & concrete analysis of the potential effects of CO2, could you please provide references for the various facts at the front end of the paper – such as GHG’s providing 30 deg C or warming, CO2 being 10%, etc – It is important to have those for all to see for independent verification – as all analysis flows from those assumptions. Just setting high standards for work presented here to help improve the case being made & show that skeptics are scientists with the highest & most transparent of standards

Jaye
March 8, 2010 12:32 pm

John Finn (10:59:36) :
Jaye (09:10:13) :
John Finn…your application of “appeal to authority” is humorous, entirely fallacious from a logical pov, but definitely humorous.
Whereas you appear prepared to believe any old rubbish as long as it supports your fervent wish that CO2 should have no effect. Well, suit yourself, but when you find that AGWers are able to ridicule sceptic arguments don’t start whining.
I don’t believe I exposed any of my beliefs in pointing your transparent attempt at “appeal to authority”.
The issues are much deeper than a silly jihad between “Warmers” and “Skeptics”. The travails of “Steady State” vs ‘The Big Bang” crowd (fyi, the name Big Bang was an insult just as denier is used today) is an interesting study in scientific jihad. One thing I do know, models and simulation are only tools that can, at best, aid in understanding. The results of M&S are only truly useful if they have gone through IV&V and that they can predict new things. Ultimately, empiricism has to rule the day.

JAE
March 8, 2010 12:41 pm

If the GHG effect of CO2 is logarithmic, then so is it for HOH, yes? If so, then we are so “far-out” on the curve that any type of “water vapor feedback” is not possible. No?

George E. Smith
March 8, 2010 12:42 pm

In ordinary Optical absorption theory, a basic assumption is that an incident photon has a certain probablilty of being captured in passage therough some small thickness of material. To particle physicists, this is a simple concept, where a given potentially absorbing atom/molecule is considered to lie at the center of a target area; its “Capture crossection”, and the assumption is that if the appropriate particle (including a photon) strikes that target area, then the contemplated reaction occurs. Well of course it is a statistical probability so there isn’t really a go/no-go decision made if the target is hit or missed. The Units of “Crossection” are typically “Barns”, yes as in can you hit the broad side of a barn. One barn is 10^-24 square cm, so one might argue that is is one picon square; which makes a pecon pie among the world’s smallest.
In a typical solid, the molecular/atomic density is so high, that a capture crossection would have to be very small to have so many target areas overlapping in a thin section, that a photon was bound to hit something eventually.
In the case of non-fluorescent solids, and say visible light spectrum wavelengths, crossections can be sub-atomic dimensions. For nuclesr reactions they are even smaller, since the incoming particle has to interract with the nucleus, rather than with the surrounding electron cloud, in atomic of molecular capture events.
The result of optical absorption in non-fluorescing materials, is that the captured energy, ultimately appears in the form of heat; thermal agitation of the atom or molecule, that is communicated to surrounding , molecules.
The quantum physicists might refer to such events as “phonon” interractions; a phonon being a quantum of accoustic energy; aka thermal vibration or “heat”.
Solids can have significant “specific heats”, so the temperature rise caused by a photon capture can be extremely small. As a result the increase in BB like thermal radiation from a solid optical medium absorbing photons, might be too small to easily detect.
In any case, the result of the overlapping of crossection targets, is that the transmission, (tau) = exp(-alpha.x) where x is the distance travelled, and alpha is the absorption coefficient.
This is essentially Beers Law, or sometimes referred to as the Beer-Lambert Law.
In a liquid such as say ocean (sea) water , alpha has values as low as 10^-4 cm^-1 at the lowest which is about 470 nm in the blue region. Over the near UV (300 nm) to near IR range (800 nm) , alpha is always less than 0.01, so the light decays to 1/e (37%) in about one metre.
Sea water is most absorptive at 3.0 microns where alpha has a value of about 9,000 cm^-1, so you get 1/3 transmission after only about 1.1 microns of distance. Over most of the IR range longer than 2.5 microns, alpha is about 1000 cm^-1, so you get 37% transmission after about 10 microns for most of that range except the 3 micron abyss.
The temperature rise situation is similar to solids, but you now have the convective effects of heating to siphon off heat to a greater body of water.
So now what about the effects in the atmosphere, where similar molecular absorptions can take place in IR active molecules such as CO2.
Well once again you get the same absorbed photon energy being thermalized by conduction to the ordinary atmospheric gases of N2 and O2; except at bery high altitudes, where the mean free path between collisions is long enough for spontaneous decay of the CO2 excited state to occur.
But now we have a somewhat differnt situation from the soid or liquid case.
The specific heats of gases are orders of magnitude lower than for liquids, and solids; so the result of that CO2 photon capture for an LWIR photon from the surface (or elsewhere) is a MUCH GREATER TEMPERATURE RISE; compared to that seen in solids or liquids.
The result it that the intensity of the increased LWIR continuum thermal radiation from the ordinary atmospheric gases, is much greater than occurs in solids, with there much higher specific heats.
But be careful here; although a given atmospheric region may have a greater temperature increse from LWIR absoirption, that very same low specific heat, means that, the radiation of the thermal emission from that gas region, also results in a greater temperature drop for that pice of gas.
So the atmosphere is a very poor “heat” source, in terms of how much thermal radiation it can emit, for a given resulting drop in gas temperature; compared to what happens when the solid ground, or the ocean surface emits LWIR tot eh atmosphere. The atmosphere is not a very stiff source of thermal radiation, because of the low molecular density. And yes when it does radiate, that emission is pretty much isotropis, so opnly about half of it returns towards the surface.

Michael
March 8, 2010 12:52 pm

David Archibald (05:09:20) : Wrote
“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.”
While I do try to contribute something meaningful to this blog from time to time, I defer for the most part, to the better informed participants on this site for more in depth analysis of the topic.
I do however, understand and appreciate the value of clustersourcing the topic in order to flesh out the fact from the fiction. I know how effective this process is because there is virtually no vested interest on the part of the participants. We have a more altruistic motive for participation here. The betterment of everybody.

dr.bill
March 8, 2010 12:59 pm

 Smokey (07:45:44) :
The average LWR has not been decreasing, and there seems to be little correlation between outgoing LWR and the troposphere temperature: click
It’s clear from your graphs that neither the lower troposphere temperature (LTT) nor the outgoing longwave radiation (OLR) have been doing anything spectacular for the past 30 years. On the other hand, and this is just an observation from my Mark III eyeball, there does seem to be something of an “inverted, lagged, correlation” between them.
If you invert your temperature graph and move it to the left a bit (about 8 months), it tracks fairly well with the radiation graph. Not a perfect match, and there are surely other things happening, but on the whole, (and pardon this phrasing) it’s “consistent with” the following sequence:
(1) Earth dumps more OLR; 8 months later, the LTT drops.
(2) Earth dumps less OLR; 8 months later, the LTT rises.
I have no idea how long it takes for the troposphere to “catch up” to what is (mostly) happening on the ground and oceans, but the response certainly can’t be instantaneous. Nevertheless, the “correlation” might be just an artifact of a short data set, or “whatever it is” that the UAH and RSS people do when processing raw satellite data. (I have some misgivings about that.)
/dr.bill

AC
March 8, 2010 1:00 pm

Larry, Jay, John Finn, RockyRoad, and others who have discussed positive and negative feedback mechanisms:
Is there anything logically wrong with the following AGW position?
1) There are natural negative feedback mechanisms to absorb CO2.
2) These negative feedbacks kept CO2 in check and/or reduced CO2 from previous extremes without causing a runaway hot earth (unchecked positive feedback).
3) The negative feedbacks are now being overwhelmed by man made emissions that are increasing CO2 dramatically faster than in the past.
E.g., something along the lines of what’s being said here:
http://climateprogress.org/2008/04/28/human-driven-co2-rise-14000-times-faster-than-nature-overwhelming-the-slow-negative-feedbacks/

JonesII
March 8, 2010 1:01 pm

son of mulder (10:51:06) :
This relates to the chaotic nature of the climate
God does not play dice. Chaos is a mind disorder.

pat
March 8, 2010 1:12 pm

meanwhile, back at the UEA ranch:
The Carbon Change Agent Programme
SAVE MONEY. MAKE MONEY. BECOME A CARBON CHAMPION. Specialist staff from the UEA’s Low Carbon Innovation Centre (LCIC) will be delivering a training programme to develop Carbon Change Agents in businesses and organisations across Norfolk.
http://www.uea.ac.uk/nbs/evolve/carbon
7 March: UK Tele: Richard Gray: Row over leaked climate emails may undermine reputation of science
The Royal Society of Chemistry (RSC) and the Royal Statistical Society (RSS) have both issued statements declaring that it is essential that scientific data and evidence compiled by researchers be made publicly available for scrutiny.
Their comments come after the Institute of Physics said that emails sent by Professor Phil Jones, head of the CRU, had broken “honourable scientific traditions” about disclosing raw data and methods…
Dr Don Keiller, deputy head of life sciences at Anglia Ruskin University, however, claims that Professor Jones and his colleagues conspired to withhold information in case it was used to criticise them.
He said: “What these emails reveal is a detailed and systematic conspiracy to prevent other scientists gaining access to CRU data sets. Such obstruction strikes at the very heart of the scientific method, that is the scrutiny and verification of data and results by one’s peers.”
Professor Darrel Ince, from the department of computer science at the Open University, added: “A number of climate scientists have refused to publish their computer programs; what I want to suggest is that this is both unscientific behaviour and, equally importantly ignores a major problem: that scientific software has got a poor reputation for error.”
http://www.telegraph.co.uk/earth/environment/climatechange/7385584/Row-over-leaked-climate-emails-may-undermine-reputation-of-science.html
when will ALL the data, raw and adjusted, plus methods, etc be released? surely it’s time to force complete disclosure.

John Galt
March 8, 2010 1:12 pm

Tipping points and how to overcome them:
We get everybody on earth to converge on one spot. The earth gets heavier at that spot and the tilt of the earth’s axis changes (we “tip” it the other way). All we need to do is figure out if we want more tilt or less tilt.
Let the modeling begin!

Bill S
March 8, 2010 1:20 pm

I was reading here ( http://www.aip.org/history/climate/simple.htm ) that viewing the atmosphere as a series of distinct layers as opposed to as a single “slab” increases the likelihood that adding more CO2 will cause more radiative absorption. If CO2 doesn’t “capture” the outgoing radiation in one layer, a higher layer might do so, and still “trap the heat”.
That seems logical on the surface, like having 50 blankets instead of one, but I’m not sure how many layers they would need to propose to make the curve fit the theory. And I can’t imagine a large increase in effect even if it were true. Since greenhouse theory depends on the troposphere being well-mixed, that means the troposphere layer number always has to be 1.
The layer suggestion might hold up better in the stratosphere, but I know next to nothing about the stratosphere. Can anyone enlighten me in this area?

pat
March 8, 2010 1:34 pm

LOL
8 March: USA Today: Al Gore’s climate groups unite as he sees ‘massive’ opposition
“There has been a very large, organized campaign to try to convince people that it (global warming) is not real, to try to convince people that they shouldn’t worry about it,” Gore said during an interview on the Norwegian talk show Skavlan to promote his newest book Our Choice: A Plan to Solve the Climate Crisis. Gore said:
In my country, the oil and coal companies spent $500 million last year just on television advertising just on these questions. There are now five anti-climate lobbyists on Capitol Hill in Washington for every member of the House and Senate. So it’s been a very massive, organized campaign.
To bolster their muscle, two groups that Gore founded in 2006 announced Friday that they are merging.
The union of the Washington-based Alliance for Climate Protection and the Nashville-based Climate Project will create, they said, “one of the largest non-profit educational and advocacy organizations in the world.”
The unified group, which will carry the Alliance’s name, will have branches in eight countries, more than 200 staffers in 30 U.S. offices and 3,000 volunteers in 55 countries.
Some of its funding comes from Gore, who won the 2007 Nobel Peace Prize for his warning about climate change. It gets 100% of the proceeds of both his new book — which uses recycled paper — as well as his 2006 best seller, An Inconvenient Truth.
http://content.usatoday.com/communities/greenhouse/post/2010/03/al-gores-climate-groups-unite-as-he-sees-massive-opposition/1

Mike J
March 8, 2010 1:37 pm

P Gosselin (02:19:05) : “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?”
You ask a good question. A quick search came up with the following, although it is only 3.6% rather than 10…. Hope it helps.
TABLE 3.
Role of Atmospheric Greenhouse Gases
(man-made and natural) as a % of Relative
Contribution to the “Greenhouse Effect”
Based on concentrations (ppb) adjusted for heat retention characteristics
Water vapor 95.000%
Carbon Dioxide (CO2) 3.618%
Methane (CH4) 0.360%
Nitrous oxide (N2O) 0.950%
CFC’s (and other misc. gases) 0.072%
Total 100.000%
http://www.geocraft.com/WVFossils/greenhouse_data.html

Mike Post
March 8, 2010 1:57 pm

Completely O/T but I couldn’t help noticing that the “rogue” Himalayan British weather observatory which has recorded global cooling is in Almora. “Return to Almora” is the name of R K Pachauri’s allegedly smutty first novel!

March 8, 2010 2:01 pm

Alec Rawls (11:26:03) :
An easy source is Wikipedia for “greenhouse effect”.
Mari Warcwm (05:41:01) :
Thankyou very much.
Boris (05:36:48) :
Water is the dominant greenhouse gas so what is allocated to CO2 is the spectrum left over after water.

March 8, 2010 2:22 pm

John Finn (11:36:30):

[Beck’s] measurements are clearly taken at locations which are contaminated by local effects. There are plenty of places where you can measure 500 ppm but they do not provide a global representation of CO2 in the atmosphere, i.e. CO2 is not “well-mixed” in the atmosphere. The Beck numbers make no sense whatsoever.

You are providing incorrect information.
You say that “the Beck numbers make no sense whatsoever.” Beck only collated and reported on the data provided by many internationally esteemed scientists, including Nobel laureates, who performed tens of thousands of CO2 measurements.
There were numerous scientists doing the work that Beck reported [all amateurs in those days, although a few did one-off contract work]. Being a scientist meant that your reputation was everything, unlike today, where corrupt degree holders scheme to finagle the system for grant money. If any scientist in the 1800’s was caught fudging data, he was finished.
The CO2 samples taken, typically between ≈1-3% accuracy, equate to about 4 – 12 ppm when measuring CO2 at 400 ppm. A one percent tolerance is very accurate, even by today’s automated standards, when measuring atmospheric CO2.
Beck reports on six of the locations where CO2 measurements were taken. The only populated location was Leige, a relatively small town in the 1800’s. The other samples were taken in very sparsely populated locations: an island in the Baltic sea, the Geissen weather station, the Baltic sea coast, a high mountain outside of Helsinki, the desolate Ayrshire coast in Scotland, and on fourteen extended ocean crossings on scientific expeditions, from Europe across the Atlantic, to the tropics, Australia, North and South America, the North and South Pacific ocean, Greenland, the Arctic, Spitzbergen, and Antarctica. No samples were taken in large cities or industrial areas.
Thus, the CO2 samples [along with other samples such as ocean pH – which turns out to be the same as today’s ocean pH] were the average readings taken from many unpopulated and very sparsely populated areas in both hemispheres, on mountains, on seashores and on mid-ocean crossings. Contrast those numerous, isolated locations with today’s main CO2 reporting source, located on the Haleakala volcano on Maui.
And the samples taken were not just a handful. Dr Kreutz took 64,000 separate CO2 readings at the Geissen weather station over two years. Wattenburg used 310 separate sampling stations; other scientists provided similar amounts of CO2 data.
Since measurements began in 1812, Nobel laureates such as Krogh and Warburg, and their colleagues Haldane, de Saussure, Bunsen, Callendar [who selected the lowest CO2 values and deleted all data outside a ± 10% bandwidth], and other well known scientists collaborated in the project. All took copious notes and made detailed drawings of their test apparatus – something Phil Jones and the rest of the alarmist scientists either consistently neglected to do, or they lost the original data.
If Mann, Briffa, the CRU crew and the rest of today’s grant seeking scientists had the rigor of the 19th century amateurs, they would not be despised for their self-serving gaming of today’s climate industry, while claiming their findings are “robust.” But neither would there be a runaway global warming scare.
For more information on Dr Beck’s paper: click [the site is very interactive; click around to find information].

Chris Christner
March 8, 2010 2:22 pm

I have a question about the graph showing heating effect per 20 ppm of CO2: a doubling of CO2, by itself with no forcings or feedbacks, is supposed to raise temps by 1°C by the time 550 ppm is reached, yet the graph only shows about 0.4°C of increase over the same period, why the discrepancy?

Fifi
March 8, 2010 2:32 pm

We are all climate scientists now!

March 8, 2010 2:33 pm

Huldén (10:15:33) :
To my knowledge CO2 levels in the Eemian did not exceed current values, which means that 10 ppm/K is a good number for global CO2-outgassing as response to temperature increase. In other words, nothing to worry about.
Corrolary: the dominant cause of CO2 rise is the burning of fossil fuel.

March 8, 2010 2:40 pm

[next time post an excerpt and a link. thanks. ~ ctm

Rhoda R
March 8, 2010 2:41 pm

Toyotawhizguy: “Only the water vapor aspect is well understood, and is widely agreed upon as being positive.”
But is this true? I thought that part of the water vapor aspect was more water vapor available to develop cloud cover which would tend to be negative.

March 8, 2010 2:44 pm

Re: Smokey (Mar 8 14:22),
Dr Kreutz took 64,000 separate CO2 readings at the Geissen weather station over two years.
Yes, he did. And they are extremely erratic (Fig 5). They vary up and down between about 310 ppm and 550 ppm. They don’t correlate with Beck’s global figure at all.
He even (Fig 8) shows one of his sites with a 100 ppm variation overnight.
The chemical analysis may have been accurate. But they are not measuring global CO2.

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