At WUWT, Girma Orssengo, PhD, has a
guest post showing some of the empirical models that he often posts in comments at Climate etc and elsewhere. It shows a parabolic+sinusoid fit to HADCRUT3:
The key plot is the one on the right. It's often been observed that a 60-year (or thereabouts) cycle plus a linear or quadratic does fit in this way. The question is, what does it mean? And in particular, can it be used for prediction?
Girma says that it isn't meant as a basis for
physics interpretation. But when challenged about prediction, he
said:
" Girma says: September 4, 2012 at 12:53 am
Nylo
A model is only useful if it allows predicting future behaviour. I see no predictions by the author that could be later falsified by the real outcome.
The model established a pattern as shown in Graph “f”. From this graph, It is easy to predict the climate if the pattern continues => Little warming in the next 15 years."
So prediction does seem to be an aim.
The problem with curve fitting is that behaviour outside the range is determined by the rather arbitrary selection of basis functions. I tried a regression fit in R using the same basis functions, with similar results: