Guest Post by Willis Eschenbach
There’s been a recent paper claiming a long-term correlation between CO2 and sea level, discussed here at WUWT. The paper implies that CO2 controls temperature and thus indirectly sea level. I thought I might follow up the comments on that thread by looking at what the ice core records actually tell us about variations in CO2. There is plenty of dispute about the ice core records, but I don’t want to touch on that here, that’s a separate discussion. Instead, let me take the ice core records as given and see where that leads us. Figure 1 shows the Vostok ice core CO2 and temperature variations.
Figure 1. Temperature and CO2 variations as per the cited data sources. Temperature variations have been divided by 2, as discussed in the text. Graph ends at 1950, most recent CO2 data is from about 2,300 years ago. Maximum temperature during the previous interglacial was about a degree and a half warmer than 1950. Photograph shows that Photo Source http://dxing.at-communication.com/en/ri1anc_vostok-base_antarctica/
These two data traces, unfortunately, are from two different records. The temperature record contains almost ten times the number of data points as the CO2 record (~ 3,100 vs ~360). Accordingly, I have smoothed the temperature data (17-point Gaussian) and then interpolated it to match the dates of the CO2 data points.
In addition, the temperature record is (presumably) a proxy for the temperature of Southern Ocean and environs. This, like all areas near the Poles, tends to experience larger temperature swings than the world as a whole. As a result, I’ve followed the common practice of making a rough estimate of global average temperature changes by dividing the Vostok changes in half.
So what can we learn from these graphs? Well, first off, we can see that this is the coldest interglacial we’ve enjoyed in the last hundreds of thousands of years. I note that humans, and indeed the majority of all species, survived the previous warmer interglacials without thermal meltdown. Next, we can tell from this data whether CO2 is causing the temperature variations, or vice versa.
Let me introduce and discuss five pieces of evidence that all show that the likely direction of the causation is that the temperature is causing the CO2 change, and not the other way around. These are 1) the linearity of the relationship, 2) the agreement with known physics, 3) the lag in the CO2 with respect to temperature, 4) the Granger causality of the relationship, and 5) the disagreement with the IPCC values for climate sensitivity.
The weakest piece of evidence is the linearity of the relationship. The outgassing of the ocean is a linear function of temperature. Looked at the other way, the temperature of the world is said to relate, not linearly to CO2, but to the logarithm of CO2 to the base 2. In the data above, the R^2 (a measure of correlation) between the temperature and the CO2 is 0.68 … but the R^2 between the temperature and the logarithm of CO2, rather than being better as we’d expect if CO2 were actually driving temperature, is marginally worse for the logarithmic relationship (0.67) than the linear. Weak evidence, as noted, but you’d expect the correlation with log CO2 to be better than linear, if not a lot better, if the relationship were actually logarithmic.
Second, the agreement with known physics. Given the data above, I calculate that for every 1°C of temperature increase, CO2 goes up by about 15 ppmv. According to this source, for every 1°C of temperature increase, CO2 goes up by about 12.5 ppmv … so the number I calculate from the data is in rough agreement with known physics.
Third, the lag. Direct correlation of the two datasets is 0.83 (with 1.0 indicating total agreement). The correlation between the two datasets is better (0.86) with a one-point lag, with the change in CO2 lagging the change in temperature. That is to say, first the temperature changes, and then the CO2 changes at some later date. Additionally, correlation is worse (0.79) with the opposite lag (CO2 leading temperature). Again, this is in general agreement with other findings that the changes in CO2 lag the changes in temperature.
Fourth, the Granger causality. You can’t establish a cause statistically, but you can say whether something “Granger-causes” something else. A Granger test establishes whether you have a better chance of predicting variable A if you know variable B. If you do, if knowing B gives you a better handle on A (beyond random chance), we say that B “Granger-causes” A.
Now, there’s an oddity about Granger causation. There are four possibilities for Granger causation with two variables, viz:
1) Variable A doesn’t Granger-cause variable B, and B doesn’t Granger-cause A
2) Variable A Granger-causes variable B, and B doesn’t Granger-cause A
3) Variable A doesn’t Granger-cause variable B, and B Granger-causes A
4) Variable A Granger-causes variable B, and B also Granger-causes A
It is this last one that is an oddity … for example, this last one is true about the CO2 variation versus temperature on a monthly basis. This makes sense, because of the seasonally varying drawdown of CO2 by plant life and the seasonal temperature variations. CO2 levels affect plant life, and plant life also affects CO2 levels, and all of that is in a complex dance with the seasonal temperature changes. So the dual causality is not surprising.
In the current example, however, the results of the Granger test in the case of the Vostok data is that temperature variations Granger-cause changes in CO2, but not the other way around—CO2 doesn’t Granger-cause the temperature.
Finally, the disagreement with the IPCC values for “climate sensitivity”. If we use the data above, and we assume that the temperature actually is a function of the CO2 level, we can calculate the climate sensitivity. This is a notional value for the change in temperature due to a doubling of CO2. When we calculate this from the Vostok data given above, we find that to work, the climate sensitivity would have to be 23°C 7°C per doubling of CO2 (corrected, thanks to commenters) … and not even the most rabid alarmist would believe that.
So those are my five reasons. The correspondence with log(CO2) is slightly worse than that with CO2. The CO2 change is about what we’d expect from oceanic degassing. CO2 lags temperature in the record. Temperature Granger-causes CO2, not the other way round. And (proof by contradiction) IF the CO2 were controlling temperature the climate sensitivity would be seven degrees per doubling, for which there is no evidence.
Now, the standard response from AGW supporters is that the CO2, when it comes along, is some kind of positive feedback that makes the temperature rise more than it would be otherwise. Is this possible? I would say sure, it’s possible … but that we have no evidence that that is the case. In fact, the changes in CO2 at the end of the last ice age argue that there is no such feedback. You can see in Figure 1 that the temperatures rise and then stabilize, while the CO2 keeps on rising. The same is shown in more detail in the Greenland ice core data, where it is clear that the temperature fell slightly while the CO2 continued to rise.
As I said, this does not negate the possibility that CO2 played a small part. Further inquiry into that angle is not encouraging, however. If we assume that the CO2 is giving 3° per doubling of warming per the IPCC hypothesis, then the problem is that raises the rate of thermal outgassing up to 17 ppmv per degree of warming instead of 15 ppmv. This is in the wrong direction, given that the cited value in the literature is lower at 12.5 ppmv
Finally, this is all somewhat sensitive to the assumption that I made early on, which is that the global temperature variation is about half of the variation shown in the Vostok data. However, this is only a question of degree. It does not negate any of the five points listed above.
w.
PS—One final thought. IF we assume that the change in CO2 is due to the temperature change, as my five arguments support, this would indicate that the degassing from temperature changes is far from sufficient to cause the recent rise in CO2. I hold that the recent rise in CO2 is anthropogenic, but others have claimed that it is not from the burning of fossil fuels, that it is (at least in significant part) due to the temperature change.
But my calculations, as well as those in the reference I cited, show that CO2 only goes up by ten or fifteen ppmv for a one-degree temperature rise. As such, this is way too small to explain the rise in atmospheric CO2, which has been on the order of 75 ppmv since 1959.
SOURCES
Matt Skaggs says:
January 4, 2013 at 8:26 am
Powerful argument. I am new to Granger causality. Is there a fifth outcome in which the Granger test would suggest that both temperature and CO2 respond to an entirely different driver? In comparing the two curves, that seems to be a legitimate third possibility beyond one driving the other.
You are correct.
Granger causation isn’t a form or type of causation. It is a test for the existence of causation by testing for correlation. Granger causation can result from a third common cause of a correlation between A and B (temperature and CO2).
Great article Willis. However, I think your last comment concluding that the rise in atmospheric CO2 not explained by increased ocean temperatures, must therefore be anthropogenic, is unjustified, as it doesn’t consider the effect of increased temperature on the land based sources and sinks. Even the IPCC report, AR4, indicate that land based sources and sinks of atmospheric CO2 are greater than the all the oceans combined and are therefore worthy of consideration.
Forested areas alone both absorb and release great quantities of CO2. Trees grow until eventually dying, then decomposing and returning the absorbed CO2 to the atmosphere. Given sufficient time, the absorption due to growth must eventually balance the release by decomposition, else the amount of dead wood will continually build up on the forest floor producing a mountain of wood on a geologic time scale.
The source and sink processes are not likely to respond identically to changes in climate, thus climate changes will upset this balance and cause forested areas to become net sources or sinks until an equilibrium is established again. The growth rate change in response to a climate change is immediate, while any change in the quantity of dead material rotting on the forest floor needed to reestablish a balance, depending on the tree species, could take tens or even hundreds of years to achieve. I suspect the decomposition/oxidation process may be more sensitive to temperature than the growth process, thus causing a forested area to become, for a limited time, a net source of CO2 with an increase in average annual temperature.
I have never seen this addressed when discussing recent atmospheric CO2 increases, but then, I am not a climate scientist that would be familiar with papers on such things, particularly since most are paywalled
I also find it useful, at times, to express atmospheric CO2 in terms that give a better perspective to most people – such as 27 tons per acre (at sea level) rather than 390 ppm by volume. Or, for carbon alone, 18 tons per acre. Most people have some feel for the area of an acre and how heavy a ton is and consequently, can put such relationships in perspective when told trees easily absorb atmospheric carbon at an annual rate of a ton an acre or more.
dan houck says:
January 3, 2013 at 8:15 pm
….I am new to this, and I was wondering why the recent (100 year) increase in CO2 ppm has been so linear. Can you point me to any references? Thanks.
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You can try :
EASIER:
#1. http://www.greenworldtrust.org.uk/Science/Scientific/CO2-flux.htm
#2. http://www.greenworldtrust.org.uk/Science/Scientific/CO2-ice-HS.htm
Scientific
http://www.co2web.info/stoten92.pdf
http://www.rocketscientistsjournal.com/2006/10/co2_acquittal.html
http://www.rocketscientistsjournal.com/2007/06/on_why_co2_is_known_not_to_hav.html#more
Willis –
I track the monthly NOAA CO2 data, monthly Hadcrut3 temperature, Global Emissions (estimated from the BP statistical review), and monthly MEI, among other things.
There is a very clear relationship between the 12 month change in atmospheric carbon (GigatTonnes C ~=2.3*ppmv) , 12 month change in temperature, and carbon emissions, especially apparent on the 12 month averages of these things. Termperature leads carbon by 7 months, on an OLS best fit basis, when incremental carbon is linear fitted to incremental temperature and carbon emissions. Most interestingly, not only is the fit extremely close, but the residual has a striking relationship to the MEI index. I calculate Delta GT carbon = 6.5*Delta T+ 0.48*emitted carbon, which I make to convert to 2.8 ppmv per degree C. That’s much less than your figure, but given the timescales one would expect much more outgassing over a longer period because a greater quantity of water will warm.
Let me know if you want to see the fits, I can’t work this interweb-thingy to post it somewhere.
Hope this makes sense and is of interest.
crosspatch says:
January 3, 2013 at 9:58 pm
….All we need now is a cooling trend and it blows the entire thing right out of the water.
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With Hansen et al in charge of the records we can have snow in July in Alabama and he will still be declaring it is the 5th warmest year Ev’ah! /snark
Willis Eschenbach says:
January 4, 2013 at 9:20 am
However, the answer is still absurd, at 7°/doubling.
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Ask an absurd question, get an absurd answer.
Make straw men, expect them to burn.
Firstly, no-one thinks that the glacial-interglacial difference in climate was entirely due to CO2 and CO2 driven feedbacks. Insolation changed, albedo changed, other greenhouse gasses increased – all these contribute to the glacial interglacial difference.
Second, you cannot directly compare the IPCC estimates of Charney sensitivity (which excludes slow feedbacks like ice sheets and vegetation) and earth system sensitivity (which includes slow feedbacks).
Steven Mosher, further to the video alleging that CO2 is necessary to explain the ice ages, let me recommend to you and other readers “In Defense of Milankovich“. Inter much interesting alia he says:
This size disparity between Milankovich NH summer forcing and CO2 forcing implies that IF CO2 is acting as a positive feedback, it will be very hard to find that signal in the data.
This reinforces the point that the presenter in your video was just blowing smoke when he claimed that CO2 was necessary to explain the ice ages, or that it acted as a feedback to those ice age changes. Maybe, but we have no evidence that it is so. As a result, for your video to claim it is established scientific fact is entirely incorrect.
w.
Lester Via says:
January 4, 2013 at 2:33 pm
Great article Willis. However, I think your last comment concluding that the rise in atmospheric CO2 not explained by increased ocean temperatures, must therefore be anthropogenic, is unjustified, as it doesn’t consider the effect of increased temperature on the land based sources and sinks.
Increased temperatures means more vegetation growth, both on land as in the seas and over glacial – interglacial transitions also less ice sheets and more land occupied by plants. Thus higher temperatures means more CO2 uptake out of the atmosphere by the biosphere…
That is confirmed by satellites (the “greening earth”) and by the oxygen balance: there is less oxygen use measured than should be from fossil fuel use. That means that the biosphere as a whole is a net producer of oxygen, thus a net user of CO2 by more growth than decay and a buildup of organic material in roots, humus, peat,.. until browncoal and coal. See:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
In short: the oceans can’t be the cause of the increase, by Henry’s Law and because the 13C/12C ratio is higher than in the atmosphere while we see a continuous drop in ratio both in the ocean surface layer and the atmosphere in ratio with human emissions.
The biosphere is not the cause, as is proven in the oxygen balance. All other sources are either too small or too slow.
Lester Via says:
January 4, 2013 at 2:33 pm
Curious. I get a different value.
About 730 Gtonnes C in the atmosphere
World surface is 1.26e+11 acres
That gives me 5.8, call it 6 tonnes of carbon per acre, not 18, which is equivalent to 22 tonnes of CO2, not 27 … what am I missing?
w.
PS—if CO2 is 27 tonnes per acre as you say, then carbon alone would not be 18 tonnes per acre as you suggest. Instead, it would be 27 * 12/44 = 7.4 tonnes per acre. Don’t feel alone, the dang math, it bites me all the time too …
Move North America 250 kms farther north. Is there a permanent ice age? Yup. Until the glaciers depress the northern-most Land enough to make it Ocean once again (which does happen). Then, the ice age is up for grabs as Milankovitch changes will govern whether there is an ice age or not.
But, move North America 500 kms farther north and the Earth is back into Snowball conditions again until North America is moved off of this location by continental drift.
No change in CO2 levelsl are required at all to explain these two scenarios. Only Land near or on the poles is required because ice-sheets build up on Land and not on the Ocean.
Peak Warming Man says:
January 4, 2013 at 12:26 am
So are you saying that you don’t believe that an increase in co2 in the atmosphere will increase the earths temperature?
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The amount is minuscule. The IPCC Climate types had to combine the effect of CO2 AND H2O (calling it a feed back) to get the sensitivity they wanted. Unfortunately for them while CO2 has increased atmospheric water graph and temperature graph have not.
MIT Professor Richard Lindzen said in a WUWT guest post:
Given we are at the chaotic end time of a interglacial it is time to cut the bovine feces and actually do some science before we are blindsided by a drop in temperature that is much more likely and much much more devastating.
The idiots in Washington D.C. listened to the Committee on Economic Development , the financial traders and the grain traders and got rid of the US food reserves. (Think 2008 Food riots) The French Revolution tells us what happens when people get really hungry because of the idiocy of their political leaders. Despite Homeland Security Secretary Janet Napolitano pointing fingers at American red necks it is the inner city drug runners and street gangs that are going to be really dangerous and gun laws will have zero effect on them.
The ABA Band of Bakers has already marched on Washington, D.C due to the ‘record high wheat prices and tight supplies.’
“Increased temperatures means more vegetation growth, both on land as in the seas and over glacial – interglacial transitions also less ice sheets and more land occupied by plants”
This is not true.
The bioproductivity of the oceans is not temperature dependent, but nutrient dependent.
The bioproductivity of land mostly depends on rainfall patterns. Although you lose a lot of land under the ice, you get a lot back by the greening of the deserts and the drop in sea level.
This is what the land area was when the sea level was 110 meters lower than today:-
http://www.ngdc.noaa.gov/mgg/topo/pictures/GLOBALsealeveldrop110m.jpg
The great deserts we have today were not there during the last ice-age.
LearDog says:
January 4, 2013 at 4:57 am
…. Besides human input of CO2 (easy to default to this, confirmation bias, can’t think of anything else so this is the answer) – what other factors could explain? Changing CCD depth? What if the ‘ocean’ isn’t a single, well-mixed tank?
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The other possibility is the effect of humans/animals on vegetation. There was the 1930’s Dust Bowl
“In 1935, one of FDR’s advisors, Hugh Hammond Bennett, was in Washington D.C. on his way to testify before Congress… A dust storm arrived in Washington all the way from the Great Plains. As a dusty gloom spread over the nation’s capital and blotted out the sun, Bennett explained, “This, gentlemen, is what I have been talking about.” link
That is perhaps the most dramatic effect but certainly not the only one.
36 million acres of natural forest are lost each year (Forests cover 31% of total land area )
Land degradation is a more subtle form of loss of plant life vigor.
DocMartyn says:
January 4, 2013 at 4:07 pm
The great deserts we have today were not there during the last ice-age.
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Sorry, but that just isn’t true. There is a large amount of data from pollen and palaeolake level to show that, at least the Sahara, was at least as dry in the LGM as it is now. Not only was the climate cool and dry, but the low CO2 concentrations cause physiological drought. See e.g. http://www.sciencedirect.com/science/article/pii/S0277379198000158 for a summary of the data.
Alfred Alexander says:
January 4, 2013 at 8:35 am
Now my question,when guys are looking 1000ky,what does the earth look like in your mind…
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I think this site might answer your question
http://www.esd.ornl.gov/projects/qen/nercNORTHAMERICA.html
A paper of interest dealing with CO2 redience time and C12/C13 and C14 is over at CO2science.org
But, of course, the idea that high CO2 correlates with high temp is completely consistent with AGW.
Just saying.
“The radiative forcing due to CO2 may serve as an amplifier of initial orbital forcings”
Test this hypothesis by examining how CO2 lacks serving as an amplifier when temps are dropping after an interglacial.It would be impossible for temps to drop at all if CO2 were the amplifier.
How can the same levels of CO2 cause rising amplification,yet the exact same levels fail to amplify with temps dropping into ice age?
If CO2 were the main amplifier ,CO2 LEVELS WOULD NEED TO DROP PRIOR TO ANY TEMP DROP.
But we know that temp drop precedes CO2 level drop by 800 years.
CO2 cannot be the amplifier nor the driver.
I suspect that the orbital initiator is the amplifier as well as the driver.
trafamadore:
Please explain what – if any – relevance your comment at January 4, 2013 at 6:50 pm has to the subject of this thread.
Richard
Willis,
You appear to have confused the Charney sensitivity with the Earth System sensitivity. The Charney sensitivity is estimated to be about 3C per doubling. This is the rapid response to increase in carbon dioxide. It is the widely discussed number in the IPCC reports. The Earth System sensitivity includes slow albiedo effects (for example from ice sheet melting) and vegetation changes that are longer term than the Charney sensitivity. You have calculated the Earth System sensitivity. Your result of 7C agrees well with Hansen’s estimate of 6-8C here . It is good to see that you agree with Hansen on the calculated value of the Earth System sensitivity from the ice core data.
trafamadore says:
“But, of course, the idea that high CO2 correlates with high temp is completely consistent with AGW. Just saying.”
High CO2 also correlates with Ice Ages, and low CO2 correlates with high temperatures.
Just saying.
Willis, this post is priceless. A treasure trove of useful information. I cant wait for your next post.
Thank you, Dan Houck, for your question, which I am wondering about, too. The question was: why is the rise of CO2 in the atmosphere so linear? Linearity usually (but not always) indicates that we are dealing with a simple relationship between just two variables, such as y=ax+b…. Unless the linearity is an illusion and we are looking at a segment of a sinusoid or logarithmic curve or something similar. But, for the sake of the argument, let’s assume that the straight line is just that. BY the way, Professor Hayden’s 99 % correlation which I mentioned earlier is a similarly vexing straight line.
Gail, I followed you links, but I am as dumb as before. CO2 in the atmosphere is influenced by temperature, acidity of the oceans, ocean water turn-over, human emissions, plant growth, volcanic activity….. How, on earth, do all these activities add up to a simple straight line?
I have been thinking that maybe it is all ocean temperatures, but if Willis is correct, and the increase of CO2 per degree of temperature increase is only a few ppm, that idea does not hold water either.
If Professor Hayden were correct though, we would be looking at a doubling of CO2 for each 2 degrees of temperature increase. In that case, I’d come up with the following back of envelope estimation:
Lets suppose that the mixed layer of ocean currently contains 1000 GT of carbon, the atmosphere contains 836 GT, human contribution per year are about 10 GT.
Preindustrial carbon in the atmosphere was 450 GT or 209 ppm.
Not sure what preindustrial carbon in the ocean was, but let’s assume about 1000 GT.
Now, for no temperature change, one would have a preindustrial equilibrium of 450/1450 (atmospheric carbon over total carbon). If humans add 1000 GT to the system (over 100 years), a new equilibrium would develop:
450/1450 = x/2000; X= 621 GT of carbon in the atmosphere, corresponding to 289 ppm. Without any warming, even a huge emission of 1000 GT would not raise atmospheric carbon all that much.
Now, if we assume that two degrees of temperature increase moves the equilibrium from 450/1450 to say 900/1450 (in the absence of any human influence), we would expect 419 ppm in the atmosphere just from 2 degree warming.
Now, if we add human emissions to the 2 degree warmer world, we would get 900/1450 = x/2000; x = 1241 GT of carbon in the atmosphere, or 578 ppm in the atmosphere from a combination of 2 degree warming plus 1000 GT of human emission.
Note that the above is very flawed, as it assumes that all the human emissions are added all at once, and it does not take into account deep ocean sinks, vegetation sinks and, and, and.
If on the other hand, one uses an estimate of only 12 ppm per degree of temperature change, the whole thing does not work.
But then… Explain the straight line?
Oops, typo, put in the wrong number for human emission… Should have been 550 GT.
Willis, you are correct of course, 12/44 is the correct ratio to use which gives a little over 7 tons per acre of CO2. For some unexplained mental lapse (not double checking a quick series of computations) I had used 29/44 which is the ratio of average air molecular weight to the CO2 molecular weight rather the using 12, the atomic weight of carbon.
I obtained the 27 tons per acre by multiplying 390 ppm by 44/29 to get 592ppm of CO2 by weight and then, at sea level, the atmospheric pressure being 14.7 psi, which is the weight of the atmosphere above one square inch of which .0592% or 0.0087 psi is due to CO2. This corresponds to a CO2 partial pressure of 1.25 lbs per square foot or 54,574 lbs per acre (the 27 tons per acre) unless I made another dumb mistake.
Anyway, I hope I made the point I was trying to make about using units that can be useful when making mental comparisons to certain sinks and source data. Pointing out my error at least let me know that someone actually paid attention to what I said.
Willis, I believe the difference between your 22 tons/acre and my 27 is your method gives a value based on distributing the CO2 equally above the Earth’s surface. Since land masses rise above sea level, thus displacing some of the atmosphere, its distribution isn’t uniform . At higher elevations you have less atmosphere and, consequently, less CO2 above you. The local atmospheric pressure can tell you how much CO2 you are looking through when gazing at the sky (after correcting for humidity)
On Earth, sea level is a convenient reference point. Lack of a sea level makes it difficult when making similar comparisons on the planet Mars. I suppose one must use the average elevation. At the average elevation of Mars I once calculated that you are looking through 27 times the amount of CO2 that you do on the Earth at sea level. (but I could easily have made more dumb errors).