Graphing Out Loud: curves and lines

I love graphs – my eyes quickly glaze over at a table of numeric data, but a graph, used correctly, can quickly and easily tell the whole story.

‘Used correctly’ is the key phrase – for all their power, graphs are infamously easy to bungle, and when used incorrectly they can misinform – or lie outright.

I’m going to look at an example that touches on a few graphical and statistical concepts near and dear to my heart, as well as carbon geochemistry.

Fig. 1: An image from C3Headlines; the 3 C's are "Climate, Conservative, Consumer". Oh, and the article is titled "The Left/Liberal Bizarro, Anti-Science Hyperbole Continues". It sure would be tragic if they made obvious n00b mistakes after using such language. Click for link!

Coming from an article on the website C3Headlines, this image claims that carbon dioxide concentrations have ‘Linear, Not Exponential Growth’. thereby ‘expos[ing] the lunacy of typical left/liberal/progressive/Democrat anti-science’, The author has reached this conclusion by graphing January CO2 levels* and fitting a linear trendline to them.

Already this is a warning sign – the comparisons the author makes are entirely qualitative, apparently  based up on eyeballing the graph. However, trend lines are created by a statistical process called a linear regression, which comes with a caveat: it will fit a trend line to ANY data given to it, linear or nonlinear. Fortunately, there are also ways of evaluating how good a trend line is.

temperature aNOMalies

If you are new to climate science, you might be wondering what, exactly, this ‘temperature anomaly’ thing is that you keep hearing about. I know I was a bit confused at first! This post explains the concept, using a real-world example.

Absolute temperatures (yearly averaged) from two sites in the UK: one urban (St. James Park, green) and one rural (Rothamsted, red). Although the urban site is consistently warmer, the two sites show the same warming trend. But is there a way to compare them directly? Data from Jones et al. 2008, kindly provided by Dr. Jones.

Cities tend to be warmer than their surrounding countrysides, a fact known as the urban heat island effect (UHI). This occasionally is offered as an alternative explanation for greenhouse warming, but it fails on closer inspection. We can use data from Jones et al. (2008) [PDF] to see one reason UHI can’t explain observed warming. One time series is from St. James Park, in the city of London; the other is from nearby Rothamsted, a rural site some tens of miles away. As you can see, the urban location is consistently about 2 C warmer; however, the warming is nearly identical at both sites (a strongly significant 0.03 deg C/year). Jones et al. note:

“… the evolution of the time series is almost identical. As for trends since 1961 all sites give similar values …  in terms of anomalies from a common base period, all sites would give similar values.”

This gives us a hint about what a temperature anomaly is: