Mean Means (part 1)

Reaching for our inner climatological geek

In the field of climate science one thing is more certain than political interference and lapdog journalists and that is climate variability. Things are consistently going up and down in value whether by hour, day, week, month, year, decade or century. Very little stands still regardless of whether we are measuring rainfall, atmospheric pressure, humidity, particulates, cloud cover, cosmic ray flux, ocean pH, hours of sunshine, sea surface temperature, wind speed, sea level or the temperature of airfield tarmac. Jiggling about is what the globe does best.

Humans are not very good at solving problems in n-dimensional covariance space so we try to simplify matters by putting a straight line through data, by adjusting measurements that don’t fit the narrative, by calling black the new orange or by reaching for a measure of central tendency such as the arithmetical mean (a.k.a. average) or median that squashes all that hairy variability into a convenient carrier of information.

We can then make bold statements such as the global mean sea level is rising by 1.7mm per year, or the mean global temperature is rising by 1.5°C per century. Since figures like these are spouted by acknowledged experts and can be found on the lips of all good science journalists we forget to stop and ask what the mean of anything actually means.

Dark Arts

Back when I used to teach young government scientists the dark art of statistics I used to present them with a series of graphs and exercises in linear regression designed to frighten them into thinking instead of just ‘accepting’. This fine morning I am going to adapt some these for subscribers, so get the kettle on and get those biscuits on the platter, for here we go…

Weather Station 1

A straightforward cooling trend is evident at weather station 1, for which the overall series mean is 12.0°C.

Weather Station 2

A straightforward warming trend is evident at weather station 2, for which the overall series mean is 12.0°C.

Weather Station 3

A warming trend followed by a cooling trend is evident at weather station 3, for which the overall series mean is 12.0°C.

Weather Station 4

A cooling trend followed by a warming trend is evident at weather station 4, for which the overall series mean is 12.0°C.

Weather Station 5

A warming trend is evident at weather station 5 that is initially ambiguous in character after an unusually hot early period, for which the overall series mean is 12.0°C.

Weather Station 6

A cooling trend is evident at weather station 6 that is initially ambiguous in character after unusually cool early periods, for which the overall series mean is 12.0°C.

Results Summary

If we ignore the fine detail of temperature variability over time and simply summarised the data using the overall series mean our results table would look like this:

If we were presented with that table and only that table we wouldn’t have a clue as to what was actually going on at each station or whether and why stations markedly differed.

Let us now consider the following pair of tables and imagine we are politicians, policy makers, authorities, regulatory bodies, councils, unions, grant bodies, corporations, institutes, activists, professors, PhDs, science journalists and anybody else with a vested interest. Would we be tempted to take the series means at face value and claim overwhelming evidence for 2°C warming or would we be tempted to delve into the detail of what was actually going on?

Could we construct a series whereby that 2°C mean warming was a bone fide result? You betcha! Could we construct a series whereby that 2°C mean warming was an illusion? You betcha!

Combined stations

Let us now combine the data from each of these 6 stations by calculating the overall mean for each period separately:

Upon combining station data we observe an overall gradual warming trend, and because this has been derived by pooling data from all of our trusty and most reputable weather stations we are going to place great faith in what we see.

Mathematically speaking this is a real result, yet it also generates an illusion in the sense in that 3 of our 6 stations are unequivocally observing cooling! Sure, we can go ahead and claim this is evidence of global warming but in doing so we are sweeping solid evidence under the carpet. Does this numerical trick of the trade happen in real life? You betcha!

In reaching for the arithmetical mean and compressing a complex real-world situation into a brain-sized bite we have traded detailed knowledge for narrow narrative. Please be aware of this next time you turn on the TV, open the newspaper, fire up your smartphone or read a peer-reviewed paper.

Koan For Today

Does a global mean temperature actually mean anything?

Kettle On!