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
Mosh you are better than this, c’mon.
Caveat emptor. You might want to be careful relying too much on the timing and amplitude of ice signals. Siegenthaler and others covered this ground pretty well already, but I like the 5 points.
Mosher: Do you think that video is more than propaganda? Again letting someone else influence you rather than you explain why you think CO2 was anything more than a short lived correlation? Hansen et all say that the recent warming was 90% certainly caused by CO2. Yes – CO2 went up and temperatures went up. But what does Hansen say now that CO2 continues to go up and correlation stoppedis this period not important, but the last 30 year period was important?
Jeeze, Steve–Did you study the graph D. Boehm posted for your benefit? Do you know how to tell which came first–temperature increase or CO2 increase? Or the converse–temperature decline or CO2 decline?
Is your “belief system” so inculcated in your soul that logical thought and rational deduction are impossible? If so, you are no scientist, but simply a cult follower.
Perhaps Ayn Rand said it best in Atlas Shurgged when she had John Galt say (p. 1059):
“Learn to distinguish the difference between errors of knowledge and breaches of morality. An error of knowledge is not a moral flaw, provided you are willing to correct it; only a mystic would judge human beings by the standard of an impossible, automatic omniscience. But a breach of morality is the conscious choice of an action you know to be evil, or a willful evasion of knowledge, a suspension of sight and of thought. That which you do not know, is not a moral charge against you; but that which you refuse to know, is an account of infamy growing in your soul. Make every allowance for errors of knowledge; do not forgive or accept any breach of morality. Give the benefit of the doubt to those who seek to know but treat as potential killers those specimens of insolent depravity who make demands upon you, announcing that they have and seek no reasons, proclaiming, as a license, that they ‘just feel it’–or those who reject an irrefutable argument by saying ‘It’s only logic’ which means: ‘It’s only reality.’ The only realm opposed to reality is the realm and premise of death.
@ur momisugly Steven Mosher
Projection much? That was propaganda.
Note the one blurb about the Sun with no supporting evidence?
Note the “denier” label in like every other sentence?
Note the “Professional Climate Deniers” idiocy?
Note the Hansen hero worship?
Note the “amplification” meme that you and Lief are critical of wrt solar?
Come on man, snap out of it! Is there no cure for SkS Syndrome?
You’re listening to activists like they’re scientists:
http://climatecrocks.com/about/
“Peter Sinclair is a long time advocate of environmental awareness and energy alternatives. An award winning graphic artist, illustrator, and animator”
I wonder if asked to sign a petition to ban dihydrogen monoxide what he’d do.
More to the point if he promoted signing it would you?
Professor Hayden at the ICCC7 reported a very striking 99% correlation between sea surface temperature anomalies and atmospheric log(CO2 ratio). He stressed that this was a correlation, not a time series, and came to the conclusion that temperature is likely to be the main driver of CO2 and not the other way around. I have a hard time reconciling this 99% correlation with the fact that human emissions must have added some amount of CO2 to the atmosphere. The only way the correlation could remain 99% (that I can think of) is, if human contribution were a constant, which is plainly not the case. Can anybody shed some light on this for me?
http://climateconferences.heartland.org/howard-hayden-iccc7/
And similarly this one:
http://icecap.us/images/uploads/Globalclimatechangehasnaturalcauses.pdf
So are you saying that you don’t believe that an increase in co2 in the atmosphere will increase the earths temperature?
The video that Steven Mosher links to, mentions the movie The Great Global Warming Swindle, which was debunking the alarmist claim that CO2 was a climate DRIVER. The video explains that the argument is that CO2 is, rather, an “amplifier”. That’s not the argument. Sceptics appreciate the amplifier claim and the issue is whether the amplifier is a significant player in climate or not. So why link to an argument that assumes sceptics are (a) stupid and (b) knocks down a strawman?
CAGW is Granger-dead.
Henry Clark says:
January 3, 2013 at 8:53 pm
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.
Certainly, when you write a post, you are free to use the specific graphs that you judge will best elucidate the points you wish to make.
As am I …
Best regards,
w.
Possibly the strongest indication of whether A drives B or B drives A; is that the lag is much greater during the cooling periods than it is during the warming periods. During warming periods CO2 will be outgassed from whatever part of the ocean profile that exceeds the temperature at which the existing CO2 concentration can stay in solution. However during the cooling periods, CO2 can only go into solution at the atmosphere, ocean surface interface, irrespective of the ocean temperature.profile. This would lead to a much greater lag during cooling should temperature be the driver; and this is the observed evidence. If Co2 drives temperature than this would not be the case.
In Wills article he says:-
“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, ”
Temperature certainly changes the rate of respiration – photosynthesis – not so much – otherwise the Yamal trees and the hockey stick would not be controversial.
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.
——–
Ignoring that the equilibrium relationship between CO2 partitioned between atmosphere and ocean is not linear, but logarithmic.
Most physical and chemical processes that depend on temperature are logarithmic with temperature. Not good if temps are going up.
John F. Hultquist says:
. . . but to the logarithm of CO2 to the base 2.
Is it not the natural logarithm (ln; base e) and not the binary logarithm (log2 n)?
It’s the same thing. I was going to point out that Willis was making an unnecessary detail in specifying log2. A log relationship is a log relationship , whatever the base. The only difference is a scaling factor: the logA(B) eg log(2.0) or log2(10.0) or ln(10.0) etc .
It would have been sufficient (and perhaps clearer) if Willis had just said ‘logrithmic’.
Thanks to Willis for yet another informative article. Especially in covering the question of outgassing.
Steven Mosher says:
January 3, 2013 at 9:26 pm
Or they might not want to watch it. Let me give people the digested version of the video you link to. First, it is viscerally unpleasant, with lots of “deniers” and well funded skeptics and the like. Next, it contains lots of cutesie tricks, cartoons and bits from movies, that mark it for the meretricious trash that it is, and aren’t funny in the bargain.
More to the point, his argument is that CO2 is necessary to explain the ice ages. He doesn’t establish that, he asserts it. In support of his assertion, he cites only one paper, called “Timing of Atmospheric CO2 and Antarctic Temperature Changes Across Termination III“.
He refers triumphantly to the following section in the paper, which says:
Note that this statement does nothing to support the assertion that CO2 is necessary to explain the ice ages. It does nothing to support the idea that CO2 plays a “key role”.
All it says is that the new finding, that changes in temperature lead changes in CO2 by 800 ± 200 years, is not inconsistent with the assertions. It provides no supportive evidence for the assertions. It just says, we can’t rule them out.
But the guy in the video thinks he’s found the Holy Grail. He thinks he has the scientific proof that CO2 is required to explain the ice ages. Unfortunately, you can read it for yourself—the paper said nothing of the sort. All he has is a statement that the new findings don’t rule out the hypothesis. It does nothing to support it.
Man, what a waste of time. One saving grace, though. The inclusion of the cartoons wasn’t as inappropriate as I thought at first, given the childish nature of the scientific claims. After hearing the claims, the cartoons fit right in. That whole extravapalooza was a waste of electrons.
w.
PS—In the paragraph above, there is a cryptic reference to how the “CO2 increase clearly precedes the Northern Hemisphere deglaciation (Fig. 3)”. However, I see no such thing in Fig. 3, which shows the rise in CO2 and CH4 (as a proxy for NH deglaciation) occurring pretty much simultaneously. Next, remember that the temperature rise would of necessity precede and be the cause of the deglaciation, since the ice sheets would respond only slowly to increased summer insolation. They would not melt instantaneously, so deglaciation would necessarily lag temperature rise by some years. Since the deglaciation and CO2 rise are contemporaneous, we can conclude that the NH temperature rise must have preceded the CO2 rise, and not the other way around as they claim.
“CO2 only goes up by ten or fifteen ppmv for a one-degree temperature rise” that might apply if ocean and air temperature was constant around the globe. Various areas of the ocean at different times of the year absorb, as other areas desorb, to a total of almost 20 times man’s CO2 output. A slight imbalance might be sufficient to account for recent increases.
I also find the claims that ice cores trap an exact representation of the air at the time the core is dated, extremely dubious. Beck and Jaworowski have been dismissed too easily.
Steven Mosher says:
“since hansen predicted the lag of versus temperature in 1990, folks might want to watch this”
I clicked because I was interested in what Hansen may have “predicited”. I got about 10s into it and binned it when it became clear it was smart-arsed propaganda not information.
If you have a link that tells us something about Hansen’s lag (I presume this is his “pipeline” hypothesis) in a factual way that may be of interest.
Willis
Nice article.
I think that co2 outgasses at the rate of 6ppm per 1 degree C temperature rise of the ocean. So is it the oceanic temperature we need to be most concerned about? That will vary according to the ocean temperature gradient in as much water is not at all well mixed and so some strata will be warm whilst other parts will be cool. Equally temperatures vary according to the geographic area.
I was most struck by the scientific reports from the arctic in the 1940’s that SST’s in many parts of the Arctic were up to 10C warmer than measured by Nansen fifty years earlier. There were also some very high readings taken of co2 in the greenland area by various scientists at that time that showed that CO2 concentration was very similar to today.
I make no conclusions about any of this as co2 readings made in the relatively recent-pre mauna loa era-are regularly discounted.
tonyb
I am inclined to think that this is another article somewhat poverty stricken in understanding feedback, when the climate system can be subject to different driving forces at different times.
Consider for example a feedback stabilized dc power supply. When the input supply changes negative feedback keeps the output constant. When the output load changes the negative feedback keeps the output constant. So the power supply can be subject to multiple forcings either singly or together with varying amounts.
The same applies to the climate with multiple positive and negative feedbacks operating on different timescales.
Both external changes to CO2 and solar insolation can affect temperature and these both can affect the amount of CO2. To varying degrees at different times and simultaneously.
Willis: “PS—In the paragraph above, there is a cryptic reference to how the “CO2 increase clearly precedes the Northern Hemisphere deglaciation (Fig. 3)”. However, I see no such thing in Fig. 3, which shows the rise in CO2 and CH4 (as a proxy for NH deglaciation) occurring pretty much simultaneously. Next, remember that the temperature rise would of necessity precede and be the cause of the deglaciation, since the ice sheets would respond only slowly to increased summer insolation. They would not melt instantaneously, so deglaciation would necessarily lag temperature rise by some years. Since the deglaciation and CO2 rise are contemporaneous, we can conclude that the NH temperature rise must have preceded the CO2 rise, and not the other way around as they claim.”
Thanks for parsing that for me Willis, Probably saved me half an hour pouring over details to find out what dubious Fig3 claim was all about.
Having debated this issue with British Antarctic Survey scientists and found astonishingly that they had no evidence for the hypothesis that CO2 amplifies the orbital-induced warming once it has begun — they were left lamely saying that the data “is entirely consistent with” that hypothesis — I have to agree with Willis’s characterisation of the very weak video above: it amplified rather than damped my doubts about that hypothesis. Ever Since Gore’s film, the attempt to link ice ages to CO2 has been one of the most egregious examples of confusing cause with effect. It is time that polar scientists were brave enough to admit it.
Thanks, Willis, for a superb essay.
If the CO2 is driving the temperature, what is then increasing and decreasing the level of CO2?
Assuming (knowing) that more CO2 improves the plant grows and the plants would use more CO2, then I think we have a Predator-Prey Relationships.
Assuming that the CO2 drives the temperature, then the plants would grow even better and this would then remove even more CO2 from the air.
The argument for me is that I haven’t seen any credible explanation for CO2 to go up for a time frame of estimated 10% and then go down to a low level for a time frame of estimated 90%.
What’s about the Daisyworld simulation, which is a self regulating system? The white Daisies have a negative feedback and the black Daisies have a positive feedback. This means they will balance the temperature in the end.
As long as we can’t explain both direction, increase and decrease, of CO2 on its own we have no explanation at all for the past. How could we than predict the future?
My conclusion is that there must be an external source. Someone is playing with something like a dimmer. Who could that be. Don’t tell me it is the sun. 😉
Professor. Dr. Mojib Latif, German meteorologist and oceanographer, had said on German TV “This is obviously a lie, if it is claimed that we do not consider the sun. There is no climate model that the sun is not taken into account. I mean we’re not idiots. This will somehow give the impression as if we are the biggest idiot ever.”. I would never say that they are the BIGGEST idiots ever. You can top anything that was before.
/joke on/ Some comedian said that we have not investigated the moon energy. How much energy is used by the moon to make it dark? ;-))
Willis says: “Certainly, when you write a post, you are free to use the specific graphs that you judge will best elucidate the points you wish to make.
“As am I …”
Well said. In fact, many times, if not presented as the author wishes, a graph will lead to off-topic discussions, which always detract from a thread.
Willis, nice summary. Indeed the change of CO2 after temperature changes is near-linear, where CO2 lags some 800 years. That ratio doesn’t change over the past 800 kyears (including Epica Dome C, which shows the same CO2 and temperature changes), which shows that there is little CO2 migration in the ice cores over that time span, or the ratio should fade away each interglacial back in time.
A few additions:
– While coastal ice cores reflect the temperatures of the nearby Southern Ocean (via dD and d18O proxies), the deep inland, high altitude, ice cores of Vostok and Epica Dome C reflect the ocean temperatures for near the whole SH. These are less variable than Southern Ocean alone or the whole NH, where ice sheets did cover large parts of land during most of the time. But the Greenland ice sheet temperature record shows a similar trend over the glacial-interglacial transition, be it with much larger swings, as that mainly reflects the North Atlantic seawater temperature:
http://www.climatedata.info/Proxy/Proxy/icecores.html
That means that the CO2-temperature ratio is probably less than 15 ppmv/°C. Vostok shows 8 ppmv/°C and is taken as rather globally representative.
– 12.5 ppmv/°C is the solubility curve of CO2 in seawater (other sources give 16 ppmv/°C), but at higher temperatures, land plants in general sequester more CO2 in more permanent way and more land area is occupied by plants, reducing the CO2 levels with increased temperatures. That too reduces the ratio of CO2 to temperature.
– An interesting part of the Vostok record is the end of the previous interglacial, the Eemian: while CO2 and temperature go up in parallel, temperatures go down while CO2 levels remain high. At the moment that the temperature is again at a new minimum (and ice sheet growth at a maximum). CO2 starts to go down. The 40 ppmv drop in CO2 level has no observable effect on the temperature record… See:
http://www.ferdinand-engelbeen.be/klimaat/eemian.html
Dr Burns says:
“CO2 only goes up by ten or fifteen ppmv for a one-degree temperature rise” that might apply if ocean and air temperature was constant around the globe. Various areas of the ocean at different times of the year absorb, as other areas desorb, to a total of almost 20 times man’s CO2 output. A slight imbalance might be sufficient to account for recent increases.
Very good point. Too much global averaging going on. This is particularly important when dealing with what is apparently a T^5 relationship. Average global temp may be a fair indication in the presence of a linear relationship. If it’s T^5 it mostly likely needs to be broken down to at least regional average temp.
While Willis’ linear approx may be good enough for rough estimate with small variations, with ampified warming/cooling at the poles where cold waters will be providing a CO2 sink the effect could be much greater.
I have not thought through how this would affect his arguments or conclusions, maybe Willis can comment on that.