You see, it's very easy to associate CO2 with temperatures in a "naive" way. It's also very easy to associate the number of pirates with temperatures this way. In fact, you can associate any two trends in this manner.
I suggested removing the trends from the data, and then comparing the resulting detrended series. I explained it a little differently back then, but that's what it amounts to. Since that time I have learned this is called detrended cross-correlation analysis.
There were a number of criticisms of my analysis posted in comments. I didn't find any of them very convincing, to be honest, but they can be addressed as follows.
- Instead of using northern-hemisphere land temperatures, I will use global sea-surface temperatures (HadSST2 data set.) The criticism was that fluctuations of CO2 emissions could be associated with (i.e. confounded by) fluctuations of the urban heat island effect. I think that's a bit of a stretch, and this sort of objection has been addressed elsewhere, but I thought I would simply use sea-surface temperatures to eliminate the potential confound altogether.
- Instead of using cumulative CO2 emissions, I will use an ice core-based CO2 reconstruction from Etheridge et al. (1998), combined with Mauna Loa CO2 data. I will use Mauna Loa data only for 1979 onwards, and I will adjust it by subtracting 0.996 ppmv from each data point. There's an excellent match between the Etheridge et al. data and Mauna Loa data for the years 1958 to 1978, but there's a tiny offset of 0.996 ppmv between the two.
- I will use the logarithm of the CO2 concentration. This is theoretically more accurate. The equilibrium temperature of the planet depends on the concentration of green house gases, logarithmically. That's why climate scientists talk about sensitivity to CO2 doubling.
I will start by posting a graph of the original sea surface temperature (SST) and (logarithm of) CO2 series. This is Figure 1.
I said we would remove the trend from the series. What exactly is the trend, you might ask. There are many ways to model a trend. We could use a straight line, but then you could say that the series are not linear. The wobbles around each of the linear trends might also coincide. A polynomial trendline can model trends that are not linear. A 2nd-order polynomial trendline might be enough. I went straight for the cubic or 3rd-order polynomial trendline, which gives a slightly better fit. Those are the yellow lines that you see in Figure 1.
To detrend a series, you simply subtract the trendline from the series. The result of the operation can be seen in Figure 2 below.
The scales are a little different, but you should be able to tell, visually, how Figure 2 is obtained from Figure 1.
I added a vertical dashed brown line around the year 1890. I suspect data is simply wrong prior to 1890, for no other reason than the fact that it doesn't look good visually. I will analyze both the entire range (1850-2008) and the shorter one (1890-2008). Curiously, I had previously found something similar in a comparison of SSTs and named storms, but I assumed the storm data was the one in error.
Obviously, changes in CO2 won't be reflected in temperature fluctuations instantaneously. It takes time for heat to be trapped. Or to put in more technical terms, CO2 is logarithmically proportional to the equilibrium temperature. So there should be a lag.
Looking at the whole series, a statistically significant association between the detrended series starts to become significant with a lag of 6 years. The best lag (based on correlation coefficient) is 15 years. At a lag of 15 years, the association is significant with 99.997% confidence.
In my previous analysis I had found a lag of 10 years was the best lag, not 15. Interestingly, a lag of 10 years is exactly the best lag in the current analysis if I only consider data starting at 1890. In my estimation, 10 years is the true best lag, and this is completely justifiable theoretically by other means.
When you look at data from 1890 onwards, even a lag of zero will result in a statistically significant association. With a lag of 10 years, the association is significant with 99.99996% confidence. I think it's worth looking at a graphical representation of this association: the following scatter chart (Figure 3.)
In Figure 3, each dot represents a year. The graph tells us that the higher the detrended CO2 concentration in a given year, the higher the detrended sea-surface temperature, 10 years later. We can also calculate the 95% confidence interval of the slope of the trend, which is 13.7 to 29.7 in this case.
Given the methodology used, and the direction of the lag, this result can't be anything but indicative of a causal association between CO2 and sea-surface temperatures.
The association can't be explained by:
- Coincidence.- Because we removed series trends, and because the associations are highly significant, mere-chance coincidences are exceedingly improbable.
- Correlation is not causation.- For the same reasons, because of the lag, and because there appear to be no confounds, the only plausible explanation for the correlation is causation in this case.
- Urban heat island.- The urban heat island effect should not be relevant to sea-surface temperatures.
- Error and bias.- Errors would tend to hinder the analysis rather than help, just like we see with the data prior to 1890. Any systematic bias should be taken care of by the detrending step.
- Conspiracy.- It would be preposterous to suppose that someone doctored the data sets (in just the right manner) anticipating this type of analysis several years in advance.
- Assorted Non-sequiturs.- Arguments such as "Al Gore sucks" can be dismissed off-hand.