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

A point that I’ve have also questioned. Nature, in all its glory, is build of many interlocking cycles, with myriads of feedbacks some closely coupled, many loosely coupled.

The analysis of climate appears very simplistic when realizing that biological life has a major influence on how the entire system reacts to small parametric variations.

Well as a simple low pas filter (near Gaussian) of the data matches your cosine one….

http://www.woodfortrees.org/plot/hadcrut4gl/plot/hadcrut4gl/mean:220/mean:174/mean:144

Thanks for the comment Richard.

What do you think this means for climate change? Presumably there is no point fitting a straight line to the temperature data?

I am not sure that two cycles of anything can be considered definitive :-). I certainly think that natural cycles have been underestimated in most considerations of climate to date.

The number of times that 60 years comes up in anecdotal and temperature series is surprising.

To get a sine wave out of the data by simple low pass filtering makes it very difficult to deny that it exists at least 🙂