YUIKHt1 | test …

BTW if I am not mistaken the presumed trend component in EMD is actually a long period sinusoidal. This differs from SSH which is a moving average I believe. And of course, the objections you raise have not prevented these methods from being used in climate science (had to get that one in).

One issue that concerns me about the issue of how much warming since 1950 is from AGW is that it is mostly of rhetorical value. Despite the huge prominance given it in the SPM as so on, its probably of little research interest. What does it matter of the figure is 49% or 51% depending on your assumptions. What does the word “most” mean? Is it falsified by less than 50%, less than 80%, less than 90% or what. Does anybody care?

“In the range up to the present, this actually better represents the usual understanding of AGW.”

and

“But of course, the future is quite different, with the black curve heading for infinity in 2040.”

Couldn't agree with you more!!!

Now the AGW effect claimed is not a uniform rise, but rather the prominent rise over the last few decades. The straight line just can't fit that – if it did, there would be big errors further back. So it has to be fitted by the periodic functions. That sort of works, but leads to the false claim that the AGW effect is periodic and about to dive downwards. This comes because of an arbitrary function chosen to represent it.

So again I did a test. I did your fit with an added term, but where you added a quadratic, I added the function 1/(2040-t), t time in years AD. In the range up to the present, this actually better represents the usual understanding of AGW. This is reflected in generally better fit statistics, although the residual SS was just slightly more than for the quadratic. My figures weren't exactly the same as yours – I think you must have smoothed the raw monthly data.

Anyway, here's the result, shown in black with your fit (quadratic) shown in red. Up to now, the curves are very similar, and track the green Hadcrut3. But of course, the future is quite different, with the black curve heading for infinity in 2040.

Now you may say, that's what happens when you fit a silly curve. But it agrees with the data better than the quadratic, which also has no justification as truly representing AGW. The fact is that none of this means anything. That is why the IPCC goes to a lot of trouble to develop scenarios for future GHG, rather than relying on arbitrary fitting function choices.