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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JonesII
March 8, 2010 6:25 am

Wind Rider (06:12:02) :
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
Are you sure?, That was only diffraction.

Pamela Gray
March 8, 2010 6:27 am

The primary global warming potential action of increasing CO2 is said to be an increase in water vapor (not clouds, water vapor) due to the warmer air. Show me one graph that demonstrates a significant and increasing trend in water vapor that lies outside what is expected to occur during natural water vapor increasing events (IE El Nino, warm PDO, etc). Without increasing water vapor, the AGW theory and the models are proven false.

JonesII
March 8, 2010 6:27 am

Just to remember some facts:
Facts about CO2:
CO2 it is not black, but trasparent and invisible
CO2 is the gas you exhale. You exhale about 900 grams a day of CO2
CO2 that you exhale is what plants breath to give you back O2 (oxygen) for you to breath.
CO2 is heavier than air, it doesn´t fly up, up and away CO2 is a trace gas in the atmosphere, it is the 0.038 per cent of it, or 3.8 parts per ten thousand.
The atmosphere, the air you know, does not have the capacity to “hold” enough heat, it only “saves” 0.001297 joules per cubic centimeter, while water , the sea you know, has 3227 times that capacity (4.186 joules).
Would you warm your feet with a bottle filled with air or filled with hot water?

March 8, 2010 6:28 am

Hans Erren (06:23:17) :
“It’s the dose the makes the poison, the fact that CO2 is a trace gas is not an issue.”
That seems to be a contradiction. What am I missing?

Ron E Seal
March 8, 2010 6:28 am

The first sentence starts with a misrepresentation.
It is not “greenhouse gases in the atmosphere” which raise the temperature of the planet above the -15° average calculated for a planet at our distance from the local star, but the ability of the atmosphere to absorb heat by conduction from the surface and distribute it around the globe in an attempt to establish homogeneity.
The presence of any atmosphere, with or without attendant greenhouse gases, would accomplish this to some degree.
It is the lack of a fluid atmosphere with this ability which causes the temperatures on the Moon to range from -233° to +123° over the diurnal cycle.
The greenhouse gases play a minor role in radiative blocking, but not nearly enough to account for the 30° difference between here and the Moon.

Pamela Gray
March 8, 2010 6:31 am

Second potential falsification:
The primary global warming potential action of increasing CO2 is said to be an increase in water vapor (not clouds, water vapor) due to the warmer air. Show me one graph that demonstrates a diminution of OLR (a growing imbalance between incoming shortwave and outgoing long wave infrared radiation) that lies outside what is expected to occur during natural events. Without decreasing LWR, the AGW theory and the models are proven false.
The CO2 AGW theory, as it stands, can be tested with measurements beyond temperature.

1DandyTroll
March 8, 2010 6:42 am

I’m a bit confused with the pre-industrial CO2 levels as well. Actually up to about say 1979.
The measurement done was that for the summer or winter deposits of CO2? What with the winter levels not being so high.
And with what we supposedly know now about CO2, it mostly being concentrated in a couple of streaks around Earth hiking the trade winds and jets streams, isn’t it then kind of looney to rely on measurements from the ever so central place called antarctica, well central for birds that can’t fly anyway?

HelmutU
March 8, 2010 6:44 am

Dear Dr. Archibald,
CO2 in Icecores in no way reliably represents the original atmospheric CO2 level because of fractional processes. The fossil leaf stomata indices for example show CO2 concentrations between 270ppm and 326 ppmv while the Taylor Dome icecore showed only concentrations between 260 and 264 ppmv in the last 6000 years. the chemical measurements of CO2 in the 19th century showed values up 420 ppmv.

Mike M
March 8, 2010 6:46 am

As most plants receive more CO2 than the present day concentration they grow faster and fatter. In order to do that they must be absorbing solar radiation and converting it into potential chemical energy, (fats and sugars, etc.), at a faster rate. Such conversion by photosynthesis could be represented as ‘lost heat’ in the earth radiation budget in that radiation that arrives at the surface then ‘disappears’ from the equation. (Any satellite image you look at shows the vegated / rural areas as much darker than the cities even though they are always cooler than the cities. (Transpiration only can go so far to explain the difference IMO.)
I wonder then, given CO2’s logarithmic, ‘diminishing return’, nature, could the above negative feedback of photosynthetic radiation loss, at some higher PPM concentration, utltimately overtake CO2’s GHG effect on an incremental basis?

March 8, 2010 6:54 am

The problem is, the first sentence is not correct (in my opinion).
1) 33K is not correct, because it is calculated with present albedo. 70% of present albedo is created by clouds, which should not be there since the hypothetical Earth got no “greenhouse gases”. With cloudless Earth, the difference should be some 15K. (I will not go further, considering that such Earth can not have oceans and should be more Moon-like etc.)
2) Presence of greenhouse gases expects existence of oceans and clouds. Clouds cools Earth. Condensed water vapor rains on the surface and cools it by evaporation. Oceans absorb a lot of heat, effectively cooling the surface again. Net effect of “greenhouse gases”, mainly water in various forms, is cooling effect.
3) Earth is warmer, because it has atmosphere consisting of 99% nitrogen and oxygen. Atmosphere absorbs and keeps heat, therefore our night is not as cold as on the Moon. Also, our days is not as hot as on the Moon.
4) Mars has thin atmosphere consisting of 95% CO2, and its temperature is equal to the theoretical value 210K. Its effective CO2 concentration is roughly equal to water vapor + CO2 on Earth, but has no visible effect. Venus has dense atmosphere consisting of 95% CO2, and its temperature is very high. However, Venus is both closer to the Sun and has much higher surface pressure. Its temperature in 1bar altitude, corrected for its Sun proximity, yields average Earth temperature again. –> It does not matter much, from what is the atmosphere composed, but how much of it is present.
5) I believe water vapor has dampening effect, warming nights and cooling days, but thats all. There is no increased “greenhouse effect” observed in polar regions, where is only a little humidity and rising CO2 should increase temperatures by far most. “GH” effect causing +33K is theoretical construction, which wrongly attributes observed reality. How can you recognize IR radiation coming from 300ppm CO2, compared to radiation, emitted by 900,000 ppm warm oxygen and nitrogen?
In case I am wrong, either there are negative effects swallowing all the CO2 addition or per Miskolczi, total “GH” effect is constant, modulated by changes in water vapor.

red432
March 8, 2010 6:56 am

How does an individual assess competing claims on an issue of this complexity? You’ve got to have sympathy with the journalists who basically say “whoa, this biologist from Stanford must know what he’s talking about.” Of course with a little historical perspective we can remember that the entire academic world of Geology was wrong about plate tectonics a few decades ago… In the case of AGW even looking at temperatures doesn’t really help that much because “weather is not climate” and in my opinion even if it started decisively heating up again, that still wouldn’t indicate that greenhouse gases emitted by human activity had anything to do with it, necessarily. It’s a vexing question.

Jim Masterson
March 8, 2010 6:59 am

>>
. . . (the Holocene is an interglacial in the ice age that started three million years ago).
<<
I think it’s more like 12,000 years ago. The current ice age 100,000 year cycle (with 10,000-20,000 year interglacials) started about 2-4 million years ago.
Jim

March 8, 2010 7:00 am

@Smokey,
You are missing that a little bit of CO2 can block a lot of infrared radiation, just like a little bit of arsenic kan kill a lot of rats.
But, But, CO2 behaves logarithmically!
Sure, we knew that.

cba
March 8, 2010 7:01 am

David,
a missed ‘key’ here is the same concept for h2o vapor. Absolute humidity again is a log function. If you assume an increase – say 5K and recompute absolute humidity based upon the standard climate assumption of constant relative humidity, you’ll find there is an increase of 0.3 in absolute humidity. This is far less than a doubling. Note that h2o has much higher concentrations than does co2 and it is much more potent. I haven’t used archer’s modtran calculator to manipulate h2o content but I’ve got my on 1-d model. H2o effects are around 8-10 w/m^2 increase for a doubling versus 3.7 w/m^2 for a co2 doubling.
The net results indicate that a 5 deg C increase in temperature results in less forcing than a co2 doubling. That means we’re missing over 3 deg C of warming to achieve that 5 deg C rise after accounting for h2o vapor and co2 – ignoring additional cloud formation etc. Try it for a 2 deg C rise and you’ve got the same problem, co2 doubling is good for less than 1 deg C on its own and a 2 deg C rise will support much less than a 5 deg C rise – which was roughly comparable to co2 but a little less. For 2 deg C rise, we’re still missing almost half of the necessary forcing as the h2o is going to contribute only about 1/3 what a co2 doubling does.
don’t look now but they’re trying to move the goal posts. the extra will be the methane beast that they didn’t know know about in any quantitative fashion (and still don’t) and didn’t program their models for – the ones that promise 5 deg C rises. LOL

Ken Coffman
March 8, 2010 7:05 am

I would edit this sentence:
“The greenhouse gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere…”
to say:
“Insolating gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere…”
I like the analogy of the earth as hot water bottle over the earth as a greenhouse…I think the hot water bottle is more accurate.

Mike M
March 8, 2010 7:05 am

Mike (04:54:41) “…That the sophisticated mathematical models that run on supercomputers ….”
You mean the ones that run “a href=”http://www.americanthinker.com/2009/11/crus_source_code_climategate_r.html”>code like this? –
yrloc=[1400,findgen(19)*5.+1904]
valadj=[0.,0.,0.,0.,0.,-0.1,-0.25,-0.3,0.,-0.1,0.3,0.8,1.2,1.7,2.5,2.6,2.6,2.6,2.6,2.6]*0.75 ; fudge factor

Ken Coffman
March 8, 2010 7:07 am

Oops, can I retract that? That was dumb, here’s what I meant to say…
I would edit this sentence:
“The greenhouse gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere…”
to say:
“Insolating gasses keep the Earth 30° C warmer than it would otherwise be without an atmosphere…”
I like the analogy of the earth as hot water bottle over the earth as a greenhouse…I think the hot water bottle is more accurate and the CO2 component contributes an interesting added warming effect, but it is small compared to how the sun heats water, and the water then heats the atmosphere.

Anton 1988
March 8, 2010 7:08 am

With that global warming is like religion, except that
forsy church picks from ordinary people, and the spec from GLOBAL WARMING
want to cut the cash already WHOLE COUNTRY, a much higher driving school:)

Gosport Mike.
March 8, 2010 7:16 am

I have a great deal of sympathy with the view taken by Mari Warcwm 05 41 01 .As with so many things, money seems to hold sway over common sense. In the UK we have a government which is practically bankrupt proposing to spend millions we do not have on wind farms which will not work. They also plan to bury CO2 under the North Sea – another Green dream which has already been shown to be impossible.
The AGW pseudo science is so deeply entrenched in money that scientific argument will never shift it.
According to James Delingpole the BBC Pension Fund has £8 Billion invested in the Institutional Investors Group on Climate Change – other people similarly misled include several County Councils and other Pension Funds.
This probably explains the BBC’s reluctance to see the light. To know Just how many more of our sources of information are tainted in this and similar ways would be most interesting.

Gail Combs
March 8, 2010 7:18 am

I find these graphs to be of great use in explaining what David is talking about.
http://www.globalwarmingart.com/wiki/File:Solar_Spectrum_png
http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
and
http://wattsupwiththat.files.wordpress.com/2009/02/eia_co2_contributions_table3.png
First there is very little extra energy available to be absorbed by CO2 as seen in the first two graphs. That is what the logarithmic relationship is all about.
Second H2O is a much bigger player as seen by the total amount of energy absorbed by H2O vs that absorbed by CO2.
Then you must add in the amount of water vapor vs the amount of CO2 in the atmosphere and the tremendous variability in the amount of water in the atmosphere by location and time.
Finally there is the percentage of CO2 generated by mankind (3.1%) compared to the total annual amount of CO2 produced. ( Mankind 23,100 million metric tons/yr vs a total of 793,100 million metric tons/yr.)
Catastrophic Mann-made Global Warming is laughable when you actually look at the facts. I do not care what type of multiplier “forcings” the IPCC and climate scientists try to conjure up to explain how a minuscule amount of man-emitted CO2 is going to make the sky fall.

Archonix
March 8, 2010 7:20 am

Hans Erren (07:00:00) :
Yes, this is true. However once they’re dead, adding more arsenic doesn’t make them more dead.

March 8, 2010 7:22 am

Hans Erren (07:00:00):
“But, But, CO2 behaves logarithmically!
Sure, we knew that.”
Thanks for pointing out that an increase in that minor trace gas can not cause runaway global warming. In fact, we do know that.

Mari Warcwm
March 8, 2010 7:24 am

JonesII
Thank you for the link to hhtp/www.scribd.com/doc/28018819/Greenhouse-Niels-Bohr.
The articel was very illuminating, and I particularly liked the image of ‘Trapping IR with CO2 would be like trapping mice with a chain link fence.’

harrywr2
March 8, 2010 7:30 am

Mike (04:54:41) :
“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.”
The basic physics of the effect of CO2 is well known and well documented.
All other things being equal a doubling of CO2 gives you somewhere in the neighborhood of a 1 degree C rise in temperature. There isn’t any scientific disagreement on this point.
Where the disagreements are is what happens to other things if one raises the tempurature 1 degree C.
Does the amount of the water vapor substantially change? Does the water vapor end up as clouds? Does the water vapor end up as snow? If the earth warms by 1 degree ‘C’ do substantial amounts of methane get released from frozen bogs?
The AGW’ers believe that the earth is very senstive and a minor change in one variable will cause catastrophic changes in other variables.
They also believe that a major change in demand for fossil fuels will not cause a major change in the cost relationships between fossil fuel energy and non-fossil fuel energy.
To get a doubling of Atmospheric CO2 we need to be emitting at the 60 Gigaton a year rate, but we are only emitting at the 30 Gigaton a year rate.
Somehow in the magical world of an AGW’er, humanity doubles its demand for fossil fuels, but the price relationship between coal,natural gas,oil,wind,nuclear and solar stays the same, so government intervention is required.

Doug S
March 8, 2010 7:35 am

David I completely agree with the gist of your post
David Archibald (05:09:20) :
The entire CO2 question is really a political and worldview struggle. The current “Global Warming” group are true religious believers and likely composed of a majority of people who long for a completely different social system. I suspect they desperately hate the petroleum industry and their real goal is to shift financial and political power to a paradigm that fits their definition of acceptability; the financial, economic and human induced harm be damned.
I enjoyed your post, it makes sense to me but even if you are completely wrong it makes little difference to the real struggle at hand. For the sake of real science and openness, the current gate-keepers of the global warming religion must be defeated. Their corruption of the spirit of science must be relegated to the dust bin of history along with the carpetbaggers that ride their coattails.
Keep up the good fight.