Which seems to make the whole idea impervious to empirical validation …..
Indeed! No thermal phenomenon changing faster than on a decade time scale can be correlated with global warming. Only the month-to-month changes in the level of CO2 itself can be measured, not its immediate impact of global temperature.
It is however possible to observe the long-term thermal impact of CO2. One way that gives quite a clean picture, in excellent accord with the Arrhenius logarithmic model, is to subtract the expected long-term ocean oscillations of periods 30 years and longer from a temperature record such as HADCRUT3VGL (global land-sea temperature since 1850) then filter out the 11-year sunspot cycle and all faster phenomena such as El Nino. You’ll then see just two things: a 21-year oscillation of amplitude around 0.04 C beautifully correlated with the Sun’s oscillating magnetic field or Hale cycle, superimposed on a smooth rise in temperature that in 1950 was increasing at 0.055 C/decade and by 2000 had reached 0.16 C/decade.
For the purpose of subtracting all the long-term ocean oscillations, it is convenient to model them collectively as a single inverse sawtooth wave of period 151 years stepping straight up by 0.23 C in 1925, with its fundamental or first harmonic (a sine wave of amplitude pi/4*0.23 = 0.18 C and period 151 years) deleted, and the 4th and 5th harmonics both delayed by 3.75 years and attenuated respectively to a tenth and a half of their expected values, and higher harmonics neglected, i.e. set to zero like the fundamental.
There is therefore a total of four sine waves, namely harmonics 2-5. The second harmonic has an amplitude of 0.18/2 = 0.09 C and a period of 151/2 = 75.5 years while the third is 0.18/3 = 0.06 C and a period of 151/3 = 50.3 years, showing none of the delay or attenuation of the higher harmonics.
This model is newer than my December AGU presentation, which was cruder and gave only the second and third harmonics as separate phenomena without noticing that they were harmonically related in the ratio 2:3 in both frequency and amplitude. I’m getting this new model ready for publication.
The ocean oscillations have no generally agreed-on physical basis. My own guess is that at least the ones modeled above are the result of the Earth’s iron core oscillating slightly in place thereby pumping hot magma up and down to vary the temperature below the crust on which the oceans rest, but that’s nothing more than just a guess. No guesses as to where the sawtooth structure comes from.
The ocean oscillations thus modeled should be subtracted before any filtering. If you filter first then subtract, the oscillations as modeled above should be subjected to the same filter before subtraction to avoid ending up with a less accurate picture of what’s going on. Assuming a perfectly linear filter (one satisfying filt(A+B) = filt(A) + filt(B), the usual case for most filters encountered in practice) the results will be completely identical when this precaution is taken as a consequence of this definition of linearity.