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
Gail Combs says:
January 4, 2013 at 5:54 pm
Gail, how many times one need to point to the obvious: the residence time of any CO2 molecule (whatever its source) has nothing to do with the decay time of an excess amount of CO2 (whatever its source) in the atmosphere. Thus Segalstad and Essenhigh and you and so many others are comparing two completely different, independent of each other half life times.
If you have made an investment in a factory, you may be interested in the turnover and the gain of that factory: the turnover is how fast your investment (in the form of raw materials) is going through the factory and recycled. But more interesting is the gain (or loss) of your investment: that is what is left over after all costs are substracted from the sales price. Two total different things. You can double the turnover speed, but still you can have a loss or a gain or a break-even at the end of the year…
Thus the ~5 years residence time of any CO2 molecule in the atmosphere says next to nothing about what happens at the end of the year (after a full seasonal cycle). What is measured is a net loss of ~4 GtC/year for the natural cycle. That gives a e-fold decay time of ~210/4 or ~52.5 years or a half life time of ~40 years.
The human contribution nowadays is ~9 GtC/year, one-way addition. Thus if that CO2 is not disappearing in space, it is the sole contributor to the increase.
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.
The increase is not completely linear, but slightly exponential. It follows the human emissions, which are slightly exponential too, with an incredible fixed ratio over the period since the start of the industrial revolution. See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_emiss_increase.jpg
Temperature on the other hand has periods with negative correlation (1945-1975 and 2000-current) and positive correlation (1910-1945 and 1975-2000).
Willis Eschenbach says*:
January 4, 2013 at 12:54 am
“You’re busting me because my graph doesn’t look like your graph? It doesn’t show the details you say that you are interested in?
Well, since in this topic I could care less about the details, and I’m just interested in the overall view, I use an overview graph. So sue me.”
I was just pointing out something helpful, which would aid the article’s presentation. The overall theme of the article’s text is that CO2 variation is not the main driver of the temperature variation. That overall theme is not a mere detail, and posting zoomed-in data as well would aid that presentation, since the zoomed in version drastically highlights how the temperature curve is not the same as the CO2 curve. For instance, in the article, you state: “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.” What would particularly fit the latter text would be visual display of http://www.climate4you.com/images/GISP2%20TemperatureSince10700%20BP%20with%20CO2%20from%20EPICA%20DomeC.gif highlighting divergence in CO2 and temperature trends.
* regarding when I wrote on January 3, 2013 at 8:53 pm:
“Some good points.
But a graph so zoomed out as figure 1 should be posted with a more zoomed-in version too. For instance, the following, while somewhat like the GISP 2 plot I often post, is for Vostok data specifically to match the Vostok subject of this article:
http://c3headlines.typepad.com/.a/6a010536b58035970c01348128c941970c-pi
Without [solely] a graph so zoomed out as to make a millenium be close to a pixel, without century-scale info in the data being hidden, CO2 being the prime driver of temperature becomes blatantly absurd, as opposed to the oceans slowly warming or cooler (slower than the surface), with the temperature affecting CO2 release or absorption as this article notes.“
S. Meyer says:
January 4, 2013 at 7:18 pm
If Professor Hayden were correct though, we would be looking at a doubling of CO2 for each 2 degrees of temperature increase.
I have followed the lecture of Professor Hayden at the ICCC7 (I was at the ICCC8 in Munchen BTW) conference. What he doesn’t show is the correlation between human emissions and the CO2 increase and he doesn’t show the (lack of) correlation between temperature and CO2 levels outside the most recent period (negative during 1945-1975). Further, he shows the solubility curve of CO2 in water (seawater is different, but that doesn’t matter here), but doesn’t apply that to his CO2/temperature estimate…
Further, if we may assume that the oceans are the main driver, that would mean that the maximum release is 12.5 ppmv/°C (16 ppmv/°C according to other sources). Thus not more than 10 ppmv since the depth of the LIA. The rest of the 100+ ppmv (80 ppmv since the measurements at the South Pole started) is NOT from the seawater temperature increase.
Then from a process viewpoint:
– the CO2/temperature dependency over the seasons globally is about 5 ppmv/°C
– the year to multi-year temperature induced variability around the trend is 4-5 ppmv/°C
– the multi-decade to multi-millennia temperature dependency is ~8 ppmv/°C
But according to Professor Hayden, and many others here, the temperature dependency of CO2 on the scale of 5 decades is over 100 ppmv/°C.
Any bet what kind of natural process(es) should perform the above behaviour of modest – hughe – modest response? Including a match with other observations like the mass balance, the 13C/12C and 14C/12C trends, the oxygen balance, the increase of carbon species in the ocean surface and vegetation, etc…
FerdiEgb , Thanks for the link to the paper you referenced indicating the biosphere has recently been a net producer of 02 while CO2 levels are simultaneously increasing. This conclusion was based on precise measurements of the atmosphere’s O2/N2 ratio and indicates that the biosphere’s response to increasing temperatures is to increase plant growth rates faster than decomposition rates. I would not have expected this to be the case as the decomposition process involves oxidation reactions that are exponential functions of temperature while the alarmists have been been arguing for years that the plant growth process is limited by, and dependent on, factors other than just temperature.
One problem I have with their paper, is that the authors never seem to consider nitrogen fixing properties of the biosphere which convert atmospheric N2 to NH3. They seem to assume any change on the O2/N2 ratio is due solely to changes in O2. The lack of any accounting for natural nitrogen fixing processes is a loose end that doesn’t seem to be addressed, but then, my quick scan of the paper may have missed something somewhere. It may very well be too small to effect their conclusion but should be addressed in their paper.
The carbon flux from the biosphere is very large compared to the flux from anthropogenic sources and small errors in the determination of natural processes can be meaningful. Particularly when the conclusions are based on very small measurement differences to begin with, as is the case here.
dan houck:
I hesitate to enter your discussion because it is off-topic from the fine article by Willis. Indeed, I attempted to deter this inevitable side-track in my post at January 4, 2013 at 3:21 am and explained why I think the side-track needs to be avoided in my posts at January 4, 2013 at 5:15 am and at January 4, 2013 at 6:46 am.
I am providing this brief answer to your question in hope that the side-track can be halted.
At January 3, 2013 at 8:15 pm you ask
As Ferdinand Engelbeen says at January 5, 2013 at 12:11 am, it is not linear. The apparent linearity results from the short time (i.e. 55 years since 1958) over which the increase has been monitored.
Ferdinand and I strongly dispute what can be deduced about the cause of the rise (he is convinced the cause is anthropogenic while I don’t know if it is anthropogenic or natural). My view is outlined in my post at January 4, 2013 at 3:21 am and slightly clarified in my post at January 4, 2013 at 5:15 am.
You ask for references. I commend that you refer to Ferdinand’s excellent blog where I suspect you will find all you want and I know you will find his explanation of the cause of the rise.
Richard
Lester Via says:
January 5, 2013 at 5:51 am
They seem to assume any change on the O2/N2 ratio is due solely to changes in O2.
Indeed there is no account for N2 fixation. This indeed may influence the oxygen balance and explain a part of the unexplained variabilty between the different stations. But the main problem is the necessary accuracy of the method, including sampling and handling: less than 1 ppmv oxygen on 200,000 ppmv… A strong example of modern analytical possibilities…
richardscourtney says:
January 5, 2013 at 5:52 am
I commend that you refer to Ferdinand’s excellent blog where I suspect you will find all you want and I know you will find his explanation of the cause of the rise.
Wow! Thanks a lot, Richard, for your kind words…
Here is the URL for those who are interested:
http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html
FerdiEgb,
I have not yet found a treatment of the effect of carbonic anhydrase on the biological carbon-isotope ratios. This seems surprising to me since this ubiquitous enzyme accelerates the
CO2 + H2O=H2CO3 exchange reaction by about 7 (seven) powers of ten above it’s, rather slow, uncatalyzed rate. I would have thought this would be more significant than the much less frequent reactions occuring during photosynthesis, especially in oceanic environments.
Do you know of such treatments in the literature?
Ferdinand Engelbeen says:
January 5, 2013 at 12:01 am
Gail Combs says:
January 4, 2013 at 5:54 pm
Gail, how many times one need to point to the obvious: the residence time of any CO2 molecule (whatever its source) has nothing to do with the decay time of an excess amount of CO2 (whatever its source) in the atmosphere. Thus Segalstad and Essenhigh and you and so many others are comparing two completely different, independent of each other half life times….
The human contribution nowadays is ~9 GtC/year, one-way addition. Thus if that CO2 is not disappearing in space, it is the sole contributor to the increase.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
The key points that you believe:
1. CO2 is a ‘well mixed’ gas in the atmosphere despite all the sources and sinks, despite the 180 ppm reading in the ice cores being too low to support C3 plants, despite the daily and seasonal sawtooth Also see former EPA scientist – slide 24: “Most of the atmospheric carbon dioxide is being transported by water droplets.”
2. That the historical data in Beck ‘s compendium and the Ice Core data published before 1985 pointed out by Jaworowski and Segalstad are all too high and should be tossed out.
3. There is no other explanation for the 2% change in the C13/C14 ratio except Mankind’s use of fossil fuel.
………
I do not agree with any of these ASSUMPTIONS as you well know. If there has been no actual increase in the CO2 as the historical data shows but that you and the climastologists ignore, then ” the decay time of an excess amount of CO2 (whatever its source) in the atmosphere” has no meaning because there IS NO ‘EXCESS’
For those wanting to see the other POV. Historic variations in CO2 measurements.
For the last assumption here is the data that blows it out of the water.
C13 percentage:
C3 plants = 28%
C4 Plants = 14%
Air = 8%
Slide 21 from Biology course
To change the atmospheric ratio of C12/C13 all you have to do is change the ratio of C3 to C4 plants. AS E. M Smith said Over the last 100 years we’ve planted one heck of a lot more grasses world wide than ever before. Grasses are often C4 metabolism… Corn and sugar cane are also C4 while trees are C3.
It is also worth looking at F. H. Haynie’s presentation since he is an Environmental Scientist retired from the EPA.
Does carbon cycle round and round in the Carbon Cycle? Yes thank goodness, and some of it has been recycled for millions of years. All humans are doing is seeing the carbon continues to cycle.
Warmth (not warming) causes the atmospheric CO2 rise. When the cooling really kicks in, the change in CO2 will decrease. The annual CO2 cycle (caused itself by the annual temperature cycle) causes the annual change – it’s like a CO2 ‘pump’. At higher temperature levels it pumps the CO2 out of the water and at lower temperatures vice versa.
michael hart says:
January 5, 2013 at 10:55 am
I have not yet found a treatment of the effect of carbonic anhydrase on the biological carbon-isotope ratios.
From a quick search, it seems that carbonic anhydrase doesn’t discriminate against carbon isotopes at all. See:
http://www.chem.tamu.edu/rgroup/marcetta/chem636/Presentations/Carbonic%20Anhydrase-Randara.pdf sheet 20.
That plays a role in land plants: C4 plants use CA, which facilitates the uptake of CO2, while that isn’t used in C3 plants. See:
http://www.woodrow.org/teachers/esi/1999/princeton/projects/c3_c4/Group3web.html
As far as I remember from past discussions, part of the discrimination is at the air-water border in the stomata, similar for C3 and C4 plants. That gives an overall discrimination of -4 per mil for C4 plants and -16 to -18 per mil for C3 plants against the d13C level in the atmosphere.
That plays no/less role in marine plants, as most of CO2 (over 90%) is already present as bicarbonate (less than 10% as carbonate) and CO2/H2CO3 is less than 1% of the equilibrium between CO2/H2CO3 HCO3- CO3–
Hope this helped…
I thought I saw on this site some time back a home experiment you can do to show that temperature causes an increase in atmospheric CO2 levels.
Gail Combs says:
January 5, 2013 at 11:25 am
Dear Gail, you have done a lot of research. Unfortunately not at the right places…
1. The difference between “background” and other CO2 levels:
CO2 is not well mixed in 5% of the atmosphere: that is in the first few hundred meters over land. In all the rest of the atmosphere the levels are within +/- 2% of the full scale, including the seasonal variability and the NH-SH lag. See the difference between the raw data for “baseline” stations from near the North Pole (Barrow), Mauna Loa and the South Pole and those of Linden/Giessen over a few days. Linden/Giessen is where one of the main series of the late Ernst Beck’s 1942 “peak” in CO2 was based on:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.jpg
Further, land plants as usual grow on land, where CO2 levels are average 40 ppmv higher than background and even higher during inversion, giving at least a few hours of sufficient CO2 during ice ages.
“Most of the atmospheric carbon dioxide is being transported by water droplets.”
Did you make any calculation? I didn’t, but if that were true, there should be large differences between CO2 levels on rainy and clear days and between altitudes: less CO2 where the drops are formed and more CO2 at sealevel… As far as I know, no such huge differences exist…
2. Ice core and historical data.
The late Ernst Beck’s historical data compilation suffers from site bias: including series like the Giessen data makes his compilation as good as worthless, as there is no connection with the “background” CO2 levels of that period. That is confirmed by all other observations: nothing unusual around 1942 in high resolution (less than a decade) ice cores, not in coralline sponges and not in stomata data.
The late Jaworowski objected to the deleting of outliers in the oldest ice cores, where drilling fluid was detected in some of the samples, leading to a large variability of CO2 levels. These were rightfully discarded, as the cause was known and repeating of the drilling didn’t show high values.
3. ” the decay time of an excess amount of CO2 (whatever its source) in the atmosphere” has no meaning because there IS NO ‘EXCESS’
If there was no excess, why should nature be a net sink for CO2, if there is no driving force at all to absorb more CO2 than it releases?
4. The C3 and C4 plants.
Please, if you copy something, look at what is really written: the 13C/12C ratio is expressed as per mil d13C, not percent, and is negative for many species (except carbonate deposits and the oceans):
C3 plants: -28 per mil
C4 plants: -14 per mil
air: -8 per mil and falling.
One can imagine that more plant decay, as good as fossil fuel burning (at -24 per mil for coal and oil to -40 per mil for natural gas) will lower the d13C level in the atmosphere. But the oxygen balance shows that the biosphere is a net source of O2, thus a net sink for CO2 and preferably of 12CO2. Thus leaving more 13CO2 in the atmosphere. Thus NOT the cause of the d13C decline in the atmosphere, no matter if C3 or C4 plants are involved. The only difference between these two is that the rate of change to the wrong side is different…
5. The work of Fred Haynie.
My impression is that Fred gives too much weight at curve fitting, without any plausible explanation of the cause-effect relationship. Take e.g. his slide 32: there is a nice relationship between d13C change and temperature change over the period 1950-present. But there is hardly any cause-effect relationship: even over the huge temperature changes between glacials and interglacials, including the current Holocene, with the corresponding ice sheet cover changes, the change in d13C was only a few tenths of a per mil. Meanwhile we see a drop of 1.6 per mil since about 1850, completely in ratio with the use of fossil fuels. So how can slide 32 rule out the use of fossil fuels as cause, while that gives a perfect fit of the decline? See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
And again, I haven’t seen any calculation of quantities of CO2 released and absorbed by raindrops and their effect on local/global CO2 levels…
Hello Mr. Eschenbach,
I did not understand this Argument:
Quote:
“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”
Why is it the “wrong direction”? both 15ppmv and 17ppmv are larger than 12.5ppmv.
I calculated using a simple converging series, that a feedback of 1.92° per doubling of CO2 would increase the effective rate of thermal outgassing from 12.5ppmv/° to your observed 15ppmv/° on a basis of 200ppmv.
MB
Thanks for the reply, Ferdinand.
I think the isotope mentioned in the first ref was deuterium only, not carbon, and, as the article points out, the breaking of H-bonds is thought not to be part of the rate-determining step(s). So I think my question remains unanswered.
(There is in fact more literature I have found with a cursory look, but if I was missing something really obvious I thought you might be a person aware of it before I spend more time.)
michael
Hi Willis,
The circumstance whereby X is said to be Granger-caused by Y is said to occur when the function X contains information found in historical part of function Y that is not contained in the historical part of function X.
An essential requirement is that some information originates in Y before it is found in X.
In the case where Y is purely an element of a feedback loop around X, the function Y derives all its information from X so it cannot Granger-cause X.
More generally, when X and Y are in a feedback loop where only one element is driven, whichever is that driven element will Granger-cause the feedback element but not vice versa.
In your case, unless Y could be shown to have some significant driver independent of X, you should not expect evidence for X being Granger-caused by Y.
Alex