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.
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.