Global Temperature Rise Do Cycles Or Straight Lines Fit Best – May 2013

Which line best fits this graph of global temperature rise  ( HADCRUT4 global mean via woodfortrees.org )

Ok they’re not graphs of temperature but temperature anomaly, which is the difference between temperature at average over some period.

A combination of 2 cosines

A straight line resulting from linear trend best fit

A straight line along average temperature

The amplitude, period and phase of 2 cosines were free parameters.

Initial values for the periods were 50 and 500 years, final values were about 64 and 305.

The two cosines were constrained to have a common peak at some point, with the initial value set at 1992, but this ended up at 2097!  I had expected 1998.  The extended curve looks like.

Of course you need to bear in mind the saying of John von Neumann

With four parameters I can fit an elephant, with five I can make him wiggle his trunk

[Digression John D Cook shows  how to draw an elephant with 4 parameters in python]

Trying to predict how a curve will develop outside the range show on a graph can give results which are completely wrong.  You should only attempt this if you know (or at least a strong reason for believing) what the equation which describes the curve is.

What do think the curve on this graph does?

Trick question – the graph actually had 6 different curves on which develop like this

And here are the curves over a wider range

The data and python script used to produce the temperature graphs are here