LINEARITY.
The F3 filter is well designed in terms of the form of the frequency response but is only applied correctly in the central 110y of data. The 25y on each end are not filtered as intended. This is almost 1/3 of data.
The last 25y period is of particular interest since this is where the CO2 model diverges from reality so the incorrect implementation of the filter matters.
As Pekka has explained, in this period the ‘fitler’ is not longer a convolution filter since no longer has a fixed kernel. Neither is it a uniform transform, however it is still algebraically linear. This is also confirmed by the check column CK1.
This means that the numerical error introduced into F3(AGW) is equal to the error in F3(DATA-SAW)
Now since SAW was calculated to remove the deviation of the data from the model the latter term will have exactly the same long term rise as the exponential. This can also be seen in Pekka’s graphs where he corrected most of the error in the F3 filter. http://pirila.fi/energy/kuvat/VPmodif_2_3.jpg
So having distorted the data to rise at the same rate as the exponential AGW, both quantities have the same slope and are effected in the same way by the botched filter implementation.
However, since the real, unmodified data is much flatter, it will NOT be affected in the same.
This was my initial concern is seeing the AGW model being bent down to resemble the data. Similarly the distortion of the data by subtracting SAW bends the flat portion of the data up towards the exponential.
I initially, incorrectly attributed that to the filter being non-linear when I should have said non-uniform. The result is the same: the distortion to DATA is not the same as the distortion to AGW since they do not have the same rate of change in the last 25y.
