Correlation between temperature and CO2: A statistical view of drivers

June 14, 2010 by jason

Taking a step back from global warming politics and debate, I'm going to provide a simple, unbiased look at the relationship between CO2 and Temperature. Skeptics and believers alike will agree that CO2 and temperature have been strongly linked for the past half a million years. What they do not agree on, is whether CO2 has been the cause of those changes. This article will shed light on the relationships between CO2 and temperature, drawing on both recorded CO2 levels, and projections based on the EPICA ice coring effort.

Temperature and CO2, an Overview

A simple place to start to get a good idea of what temperature against CO2 levels look like, is this very famous plot, reproduced here in Matlab. A more comprehensive explanation of these temperature/CO2 relationships can be found in my previous articles.

From this, one can interpret a clear relationship between CO2 and Temperature.

Statistical relationships between CO2 and Temperature

By removing the time element from the graph, and reproducing the data as a scatterplot, we can obtain a more direct indication of this phenomenon:

The correlation of this relationship is 89%, illustrating the obvious fact that a relationship does exist between temperature and CO2. It should be noted though that this says nothing which factor was a driver for the other, just that they are related. To further visualize the relationship between CO2 and temperature, I analyzed the correlation between temperature and CO2 for 5000 year sub-periods throughout the past 450,000 years, and mapped the resulting correlation coefficients for each of the resulting scatter plots against time. This is the result:

This graph shows 2 things: Firstly, the relationship between CO2 and temperature is extremely complex. Secondly, it shows that there is in fact a relationship between the two, and despite the fact that other forces are obviously driving at least one of the two elements, there is a strong relationship throughout history.

The temperature data for the above plots was obtained from Jouzel, J., et al. 2007, and CO2 data was obtained from the Nature Supplementary Materials for Lüthi et al. (2008).

Correlation in Recent History?

This is where the science gets a bit sketchy, but as a points of interest I also wanted to map what this relationship looks like in more recent times. Lets take the data used in my previous article on global warming trends, namely from the National Oceanic & Atmospheric Administration and the GISS Surface Temperature Analysis. We can now perform the same analysis with data from the past 50 years, and time steps of 2 years:

The overall correlation between CO2 and temperature data is 76%, indicating a similar, although slightly lower, correlation compared with the past half a million years. The interesting thing about this result though, is that it shows a persevering relationship between CO2 and temperature, even though CO2 is now known to increase independently of temperature and ahead of temperature. The existence of this phenomenon prior to anthropogenic CO2 emissions is the source of much dispute, although scientific consensus generally agrees that CO2 has had a significant effect on temperature (and vice versa). Another thing which should be noted is that there is an inherent delay between CO2 and a subsequent increase in temperature, so the analysis used in this article could be drastically improved by accommodating for this lag. An optimization with respect to lag would also be interesting, as it would provide a statistical method for analyzing what the lag between CO2 and temperature is, both in the far past and recorded history.

Comments are, as always, welcome :)