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By using just a few climate factors, one can reproduce the global temperature series with incredibly fine detail. The green curve is the NASA GISS temperature data and the dark blue is the model.
The overall trend is scaled log(CO2). The mutidecadal wobble is deviations of the Length-of-Day (-dLOD).
The fine structure is made up of the ENSO Southern Oscillation Index (-SOI) which is the atmospheric pressure at Tahiti minus the pressure at Darwin.
Any place the fine structure is not represented well by SOI, cooling spikes caused by significant volcanic eruptions are more than likely too blame. Thus, the model includes volcanic eruptions of those with at least a volcanic explosivity index (VEI) of 5.
Those are the main ingredients so far. Because the model works so well, I have a few more factors that I experiment with. One is a correction that I apply for the WWII years where the temperature calibration appears to be very poor.
I have shown this around to various blogs and the most common accusation I get concerns over-fitting. Fitting curves and manifolds to data is what science is all about when it comes down to it, so I guess that criticism comes with the territory.