Not surprisingly, some global warming "skeptics" showed up in the comments and argued some points that are, frankly, not relevant to the analysis. But they were mostly civil. More recently, however, a commenter shows up, saying things like...
There is too much wrong with this analysis to do a thorough critique...
There is nothing at all impressive about your statistics...
Personally, I find these types of comments fairly rude, but that wouldn't matter so much if the commenter had actually advanced some challenges of note. Have you ever encountered guys like this? While this is the first time I've come across global warming denialists, I do have considerable experience with their anti-science counterparts in the autism community. We call them "anti-vaxers" and "the mercury militia." I doubt global warming denialists are nearly as nasty, though. But I digress.
Additionally, it's a little funny that the guy hadn't apparently read the post at all, judging by the following comment.
Also, there's not a thinking person on the planet who disagrees that from 1850 to present both carbon dioxide and temperature have increased. That alone will cause a positively-sloped line.
In the first paragraph of my post I had made it perfectly clear that my intention was to test a methodology that controls for potentially coincidental trends. In the first paragraph! I don't think I would've bothered to do a global warming analysis otherwise. You have to keep in mind that I have no dog in this fight (except perhaps for the fact that I live in this warmed up planet). My interest in the topic is scientific and not political.
This is a good opportunity to repost more clear versions of the figures from the analysis, nevertheless. Figure 1 shows the two time series without any adjustments. Figure 2 shows the residuals of the time series relative to the modeled trend lines. I've come to realize that a more intuitive way to think of Figure 2 is as a detrending of the time series from Figure 1. Note that in Figure 2 the residuals of temperature are calculated from a temperature time series that is 10 years ahead of observed values. I've also widened the CO2 Y scale a bit for clarity.
I encourage the reader to click on the figures to get familiar with their nuances. Print them if you prefer. I hereby also grant permission to use these images in any way the reader sees fit.
Note that Figure 2 includes linear fits of both detrended time series. The fits are completely flat. This means that the temperature residuals are not associated with the year, and neither are the cumulative CO2 residuals. Any independent property of the year should not associate with either. If the residuals cross-associate, at 99.99999999% confidence, then it's very difficult to argue that we're not looking at an actual effect.
Let me get back to some of the points the commenter raised.
If you wish to prove Anthropogenic Global Warming, you'll need to use temperatures from the whole globe. You cannot simply ignore the entire Southern Hemisphere. And you really should test other temperature data sets using your methodology...
Here the commenter seems to be suggesting that finding an effect of CO2 on Northern Hemisphere (NH) temperatures is not convincing enough. Unless we can show the whole planet is affected, it doesn't really matter if CO2 is warming the NH. Plus we have to show this using all data sets. Amazing.
When I first did the analysis, I didn't know much about all the data sets available. I just wanted to find one that contains as many data points as possible. When it came time to pick a data set, I chose a NH one simply because most CO2 is generated in the NH, and so by choosing this data set theoretically less noise would be introduced in the analysis.
The general temperature trend behavior is similar when you compare the globe with the NH and SH, even though the size of the effect of greenhouse gases varies. This is true of all data sets. If the commenter hopes the analysis won't hold if we look at different temperature data sets, frankly, he's engaging in self-deception.
When you're trying to validate a theory, you have to use measurements of what's ACTUALLY IN THE THEORY. For AGW, this means you have to model the CO2 concentrations in the atmosphere.
Here the commenter is suggesting that cumulative human CO2 emissions are not a good proxy of the CO2 concentrations in the atmosphere. This is not true, as I will elaborate on, but in any case, how does this explain the association found?
As far as I know, data on CO2 atmospheric concentration is only available for the range 1958 to 2004. I don't believe this is enough for this type of analysis considering how noisy the data in question is. Would you find Figure 2 convincing if you could only see a third of the graph? But more importantly, early on I realized that if I wanted to make an argument about anthropogenic global warming, it was key to look at the human contribution of CO2.
I have modeled cumulative CO2 emissions vs. atmospheric concentrations at Mauna Loa, Hawaii. The fit is excellent. For those who are versed in statistics, if I put both data sets in a scatter and do a linear fit, the R2 of the fit is 0.9981.
I can get slightly better fits by assuming there's a constant half-life of CO2. To do this I use a simple model where our total atmospheric contribution at any point in time is calculated as follows.
total(year) = (total(year - 1) + emissions(year)) * constant
The constant is what tells us how much of the extra CO2 we've put into the atmosphere is lost after 1 year. Of course, we're assuming that naturally produced CO2 is in equilibrium with the environment; which was roughly the case before the industrial revolution.
I've tested different values of constant and compared the resulting R2 fit measures of the linear association between total emissions and atmospheric concentrations. The results can be seen in the following graph.
What this tells us is that the best values of constant are somewhere between 0.99 and 0.9908. These translate to an atmospheric half-life between 69 and 75 years.
None of this detracts from the fact that cumulative emissions are an excellent proxy of our contribution to atmospheric concentrations. But in case readers have any doubts, the following is a graph of anthropogenic CO2 contribution where we assume a half-life of 69 years. Please compare and contrast with Figure 1.
Evidently, this is all just a distraction from the facts in evidence: An association was found, and data imprecisions cannot explain it away.