An exercise about meaningful numbers: examples from celestial “attribution studies”

Reproduction of L&S2001 Fig. 2A

It’s typical, however, that geophysical time series, such as the global mean temperature, are not characterised by one or two frequencies. In fact, if we try to fit sinusoids with other frequencies (here only one was used rather than two), we get the following picture (source code):

The blue curves represent a set of different best-fits for sinusoids with different frequencies.

In fact, we can compare the amplitudes of these different fits, and we see that the frequencies of 20 and 60 years are not the most dominant ones (source code):

Amplitudes of the sinusoids, based on the regression coefficients.

Fitting sinusoids with long time scales compared to the time series is dangerous, which can be illustrated through constructing a synthetic time series that is much longer than the one we just looked at. This time series is shown below (source code):

A synthetic series mimicking random 10.000-yr variations

We can divide the above time series into sequences with the same length as that L&S2001 used to fit their model, and we can then do a similar fit to these sequences (source code):

The synthetic time series split into 100-yr segments (grey), mimicking the sampling of L&S2011. The red curves show the best-fit of their model to these random series.

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