Since the subject came up …
There are certain claims (some false) about the correlation (or not) between CO2 in the atmosphere and global temperature. Several folks have pointed out that we shouldn’t really be looking at the correlation between temperature and CO2, but between temperature and CO2 forcing.
This is the climate forcing due to a given concentration of CO2 in the atmosphere, and it turns out to be a logarithmic function of the CO2 concentration. It can be put in many (equivalent) forms, but the one I will choose is
where CO2 is in units of parts per million (ppm) and the climate forcing is in units of doublings of CO2 (that’s why the logarithm is taken to base-2). Note that if the CO2 concentration is 280 (its pre-industrial value) then the climate forcing is zero, so this is the climate forcing due to CO2 concentration relative to pre-industrial.
For CO2 data, I used the yearly averages since 1958 of measurements at the Mauna Loa atmospheric observatory, and from 1880 to 1958 an interpolated dataset from the Law Dome ice core in Antarctica. The CO2 data looks like this:
The climate forcing data look like this:
They certainly look remarkably similar! And so they are, except the numerical values on the y-axis reveal that while CO2 has climbed by over 100 ppm, we are still only a bit above half-way to doubling (on a logarithmic scale). We also see that already in 1880, CO2 climate forcing was a little bit above zero because CO2 was a little bit above pre-industrial.
I started with 1880 because I’m using the global temperature data from NASA:
Now that I’ve selected the data, what do they have to say?
Here’s CO2 climate forcing .vs. global temperature:
The correlation coefficient between the two variables is a whopping 0.9467, but what really counts is its statistical significance (which is not guaranteed by a large coefficient). In this case the significance is undeniable (with a p-value < 10-15).
Perhaps most notable is the slope of the correlation. That’s why I chose units of “doublings of CO2” for the climate forcing: because this slope is an estimate of the climate sensitivity, the amount of global warming (relative to pre-industrial) we expect from a doubling of CO2 (relative to pre-industrial).
That value (2.4 deg.C per doubling) is close to the mean of what the climate models have to say.
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