Guest essay by Robert Balic

A summary of a problem with estimates of the average concentration of carbon dioxide in the atmosphere and questioning of how it is possible that the rate of increase correlates well with global temperature anomalies.

I saw an interesting plot in the comments of of WUWT a while ago. It was based on the work of Murray Salby who pointed out the strong correlation between the concentration of carbon dioxide in the atmosphere (NOAA ESRL CO2 at Mauna Loa) and the integral of mean global temperature anomalies. How well the CO2 levels correlate with various temperature anomalies can be seen in this plot of the derivative of CO2 levels with respect to time (rate of CO2 level increase) alongside some estimates of global temperature anomalies – HadSSTv3 SH (southern hemisphere sea-surface temperatures) and RSS (lower troposphere temperatures from satellite observations).

http://woodfortrees.org/graph/esrl-co2/mean:12/derivative/scale:3/plot/hadsst3sh/from:1958/offset:0.3/plot/rss/offset:0.2/from:1990

The first time that I saw this, I thought that what was meant by “derivative” was an estimate from differences between consecutive months but in ppm per year (as time is in years) so I was twelve times as confident that something was amiss as I should have been. Even after realizing that the results were in ppm per month, I thought that the results were still implausible. That changes in sea surface temperature would have an effect on CO2 levels is plausible but to correlate so well and then to be measured so precisely in order to be able to see the correlation did not seem possible.

In the above plot, the CO2 levels in ppm per month were scaled by 3 to compare with temperature anomalies. If I were to use ppm per year, then I would divide by 4 to do the same comparison iehey are not the same dimensions so the scaling is irrelevant. The data clearly needs to be scaled and also offset to fit each other well so by good correlation I am referring to the way they differ from a line of best fit after scaling to have the same slope.

I have put this out there in comments on blogs and received few replies. One that I need to mention is the claim that the derivative values are some sort of concoction and are so small that they are negligible, about 0.03% of CO2 levels. I don’t know why I need to point this out but an average of 0.125 ppm per month is the rate of change of CO2 estimated using the same method since even Newton was a boy and is equal to 90 ppm per 60 years. Its not negligible but there is the question of whether the uncertainty in measurements are too large to see fine trends over a period of a few years (and you should never multiply the quotient of two values of different dimensions by 100 and call it a percent).

Eyeballing the graph, it appears that the data needs to be very precise in order to see a correlation and a little bit of math makes things clearer. Rather than using the above derivative of smoothed data (12 month moving mean), I took the CO2 levels from woodfortrees.org and the difference between values 13 months apart. Essentially the same with the results being in ppm per year.

There is a good fit to the global temperature anomalies, especially RSS lower troposphere after 1990 (and to HadSSTv3SH before 1990) when the rate of change of CO2 levels is scaled by 0.26 and offset by -0.30. The mean absolute differences between the two is 0.13 and the standard deviation (SD) is 0.17 but varies from 0.08 to 0.2 for blocks of 1 year .

Using the lower value, this is consistent with an uncertainty in GTA of 0.1 K and in monthly CO2 levels as low as 0.34 ppm as calculated using

0.26^2 x 2ΔCO2^2 + ΔT^2 = (2 x 0.08)^2 where ΔCO2^2 and ΔT is the random error of CO2 levels and GTA which would be 2SD of repeat measurements.

This assumes that when differences are at a minimum that it is solely due to random error in the two measurements but its worth remembering that HadSSTv3NH differs much more than this from the rate of CO2 change so there are obviously other errors. Its also a stretch to assume perfect correlation of the real values, especially since its claimed that CO2 levels have increased due to human emissions and the latter have been at a steady rate for the last three years. There is also the question of why such a good correlation with SH sea-surface temperatures and not NH, and why should the correlation be so perfect when things like changes in ocean currents should have a large effect on how much is sequestered into the depths of the oceans.

So unlike I first thought, the precision didn’t need to be ridiculously good to see the correlation but this is still to good to be true.

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