This is the application of the work-in-progress Fast Fourier Transform algorithm by Bart coded in R on the total solar irradiance (TSI via Lean 2000) and global temperature (HadCRU). The results show (PDF) that the atmosphere is sufficiently sensitive to variations in solar insolation for these to cause recent (post 1950) warming and paleowarming.
The mechanism, suggested by the basic energy balance model, but confirmed by the plots below, is accumulation. That is, global temperature is not only a function of the magnitude of solar anomaly, but also its duration. Small but persistent insolation above the solar constant can change global temperature over extended periods. Changes in temperature are proportional to the integral of insolation anomaly, not to insolation itself.
The figure below is the smoothed impulse response resulting from the Fourier analysis using TSI and GT. This is the simulated result of a single spike increase in insolation. The result is a constant change, or step in the GT. This is indicative of a system that ‘remembers shocks’, such as a ‘random walk’. Because of this memory, changes in TSI are accumulated. (Not sure why its negative.)
Below is the Bode plot of the TSP and GT data (still working on this). The magnitude response shows a negative, straight trend, indicative of an accumulation amplifier. This is also consistent with the spectral plots of temperature that cover paleo timescales in Figure 3 here.
Bart’s analysis is going to be very useful doing this sort of dynamic systems analysis in a very general way. Up to now I have been using spectral plots and ARMA models.
This analysis above is an indication of the robustness of the method, as it gives a different but appropriate result on a different data set. Its going to be a very useful tool in arguing that the climate system is not at all like its made out to be.
I will post the code when its further along.