To continue our excursion into natural variation models of global temperature: What do they predict?
Here are a couple of different models fit with data up to the year 1990. This was in order to compare their projections with out-of-sample reality after 1990. The year 1990 is also the start of the major IPCC projections from the TAR WG1 available here.
The upper panel shows the entire HadCRUT global temperature in black up to 1990, the linear models are in red, while the IPCC projections are the grey triangle fanning out from 1990. Shown are two linear combinations, in red. The first is a regression containing linear and sinusoidal 21 and 63 year terms. The next higher red line contains a quadratic ‘acceleration’ term as well. The temperatures excluded from the model are in blue.
The bottom panel is a closeup of the period from 1980 to 2020. Which model predicted the temperatures the best? I would say that the middle one, containing quadratic and sinusoidal terms was a ‘remarkably’ good predictor of global temperatures. It remains to be seen if it stays that way, and the confidence intervals just have to be too narrow, although the dashed lines already represent a 99.9% level. (Yes I know, autocorrelation, I have yet to work that out). The region is so narrow because the significance of the terms is so high.
lm(formula = y~sin(2*pi*x/P)+cos(2* pi*x/P)+sin(2*pi*x/P)+cos(2*pi*x/P)+x+I(x^2))
Min 1Q Median 3Q Max
-0.581099 -0.083164 0.003191 0.091657 0.514905
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.544e+02 9.292e+00 16.619 < 2e-16 ***
sin(2*pi*x/P) -1.011e-01 5.074e-03 -19.921 < 2e-16 ***
cos(2*pi*x/P) 3.839e-02 5.059e-03 7.588 5.35e-14 ***
sin(2 *pi*x/P) 2.522e-02 4.727e-03 5.334 1.09e-07 ***
cos(2*pi*x/P) -4.283e-02 4.802e-03 -8.920 < 2e-16 ***
x -1.647e-01 9.682e-03 -17.015 < 2e-16 ***
I(x^2) 4.383e-05 2.521e-06 17.383 < 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: 0.1371 on 1674 degrees of freedom
Multiple R-squared: 0.5752, Adjusted R-squared: 0.5736
F-statistic: 377.7 on 6 and 1674 DF, p-value: < 2.2e-16
What is remarkable to me is how well the decadal features were projected, including the shape of the last 10 years or so.
The model with the acceleration term, potentially attributable to AGW, arrives at 2100 right outside the low end of the IPCC projection.