Correlation and Causation


Estimate of the annual and decadal land surface temperature from the Berkeley Earth average (black line) , compared to a linear combination of volcanic sulfate emissions and the natural logarithm of CO2 (red line). It is observed that the large negative excursions in the early temperature records are likely to be explained by exceptional volcanic activity at this time. Similarly, the upward trend is likely to be an indication of anthropogenic changes. The grey area is the 95% confidence interval.

‘Your Majesty, during the course of a long academic career, I have observed that I can become inebriated by imbibing scotch & soda, brandy & soda, and gin & soda, but I have not concluded that soda is intoxicating.’

Thus Sir Edward Appleton explained to the King of Norway that correlation did not prove causation. It is a fair point, and is the main cause of criticism amongst Climate Sceptics of a recent paper from the Berkeley Earth Surface Temperature team.

Their novel analysis of the surface temperature records basically agrees with the other three estimates and confirms that the Earth appears to be warming by around 2.5 °C per century. In their latest paper, they go further, and assert that this warming can be explained as the sum of just two effects:

  • a warming effect associated with anthropogenic emissions of carbon dioxide, and
  • a periodic cooling caused by volcanic emissions.

Their analysis is admirably simple, but is not based on a physical model: they just tried different mathematical functions and found that these ones matched the data. In other words they are a reporting a correlation and using this as evidence for causation. This was too much for Berkeley team member Judith Curry, who refused to have her name on this paper:

If determining attribution is as simple as comparing a couple of curves, why is everybody else wasting their time with sophisticated modelling and analyses?

In this case I am with Judith Curry and Sir Edward Appleton. Despite the neatness of the fit, without a physical model to explain why the fit works, this is nothing more than an interesting coincidence.

However, if the Berkeley team had bothered to try, they could have run numerical models and compared their record with the predictions of models based on real physics. They just chose not to do that. This kind of weakness may be one of the reasons that none of the groups five papers have yet passed through the peer review process.


The same data as shown at the head of the article, but now showing data averaged over one year rather than over a decade. This shows the way in which the effect of named volcanoes has been modelled.

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