Below are my replications of Figure 4 and Figure 5 of the controversial paper “Influence of the Southern Oscillation on tropospheric temperature” by J. D. McLean, C. R. de Freitas, and R. M. Carter.
Above is the comparison of global atmospheric temperature (RATPAC-A) with the SOI, smoothed with a flat 12 month filter.
Above is the comparison of the 12 month differences (not derivative) of global atmospheric temperature (RATPAC-A) (lagged) with the SOI, smoothed with a flat 12 month filter.
I found a 2 month lag gave an optimal alignment. The regression output below shows an R2 of 0.52. I don’t know if that is what they got for this particular data combination, but it is in the same ballpark.
lm(formula = d$ddGTTA ~ d$dSOI)
Min 1Q Median 3Q Max
-0.55874 -0.08093 0.01564 0.09929 0.40064
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0085806 0.0060261 1.424 0.155
d$dSOI 0.0158019 0.0006306 25.059 <2e-16 ***
Signif. codes: 0 â€˜***â€™ 0.001 â€˜**â€™ 0.01 â€˜*â€™ 0.05 â€˜.â€™ 0.1 â€˜ â€™ 1
Residual standard error: 0.1447 on 575 degrees of freedom
Multiple R-squared: 0.522, Adjusted R-squared: 0.5212
F-statistic: 628 on 1 and 575 DF, p-value: < 2.2e-16
At this point I am satisfied that they did what they said they did, that I know what they have done, and that the correlations they report are actually there.