Selectively chosing the period over which a “linear trend” is fitted leads to largely varying results.
Here data is taken from Kaplan’s North Atlantic SST and the author’s trend added back in to recover the actual SST.
Various periods are fitted including a linear plus cosine model to represent a purely cyclic AMO.
It can be seen that the choice of “last 50 years” apart from being a innocent sounding convenient round number also produces the steepest slope. This is often used to suggest a rapidly accelerating warming attributable to human induced climate change ( AGW ).
However, a simple linear plus cosine model fits the data well and does not show a deviation in either direction at the end of the data.
ie there is no ‘acceleration’ other than that of the harmonic variability. There is no need to invoke AGW to explain the record.
The illusion of accelerated warming is totally a result of the periods chosen. There is more slope in half a cycle of a cosine than there is two and a half cycles. Neither is real since a purely harmonic function like a cosine has long term mean of zero and a long term rate of change of zero.
The same illusory effect can be produced with a pure cosine function: