Fourier Series simulation of temp record
Here's a thing I've been toying with for a few days. You take the temperature record - hadcrut3v global. Use narrow band bandpass filters on it to find peak frequencies/phase/amplitude. Add the output of the filters ansd see what you get.
By taking mid band frequency amplitude and phase one should then be able to reconstruct the temperature record from a series of sine (cosine) waves - this is shown in the second plot.
1/Frequency bands from .5 years to 1000 years were searched but the longest period that produced output was 150years.
The green line in these plots is the output of the 36 bands/cosines and as can be seen there is no trend. There is something else pushing the trend upwards.
One bodge has been to increase the amplitude of all bands by 2.3 to give the same sort of variability in the temp record.
A second bodge is to add a trend line that forces the synthesised temperature to conform to the hadcrut3v. As can be seen both the cosine and filter outputs follow the curve "rather well". Of particular note is the lack of temperature increase followed by fall over the last few years and 2 peaks at 1877 and 1998 being modelled with a "good" correlation.
There is a rapid warming between 1930 and 1945 which is not followed by the synthesised data.
This plot shows the relative amplitudes and periods of the synthesised waves
The synthesis of course means that individual periods can be removed to see the effect of tsi etc.
This is a work in progress but unless someone shows it to be a pile of poo I think it is interesting!