What’s in a Standard Deviation?

“By 2100, global average temperatures will probably be 5 to 12 standard deviations above the Holocene temperature mean for the A1B scenario” Marcott et al.

WHO: Shaun A. Marcott, Peter U. Clark, Alan C. Mix, College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, Oregon, USA
 Jeremy D. Shakun, Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA.

WHAT: A historical reconstruction of average temperature for the past 11,300 years

WHEN: March 2013

WHERE: Science, Vol. 339 no. 6124, 8 March 2013 pp. 1198-1201

TITLE: A Reconstruction of Regional and Global Temperature for the Past 11,300 Years (subs req.)

We all remember the standard deviation bell curve from high school statistics; where in a population (like your class at school) there will be a distribution of something with most people falling around the mean. The usual one you start off with is looking at the height of everyone in your classroom – most people will be around the same height, some will be taller, some shorter.

The more you vary from the mean, the less likely it is that will happen again because around 68% of the population will fit into the first standard deviation either side of the mean. However, the important bit you need to keep in mind when reading about this paper is that standard deviation curves have three standard deviations on either side of the mean, which covers 99.7% of all the data. The odds that a data point will be outside three standard deviations from the mean is 0.1% either side.

The standard deviation bell curve (Wikimedia commons)

The standard deviation bell curve (Wikimedia commons)

What does high school statistics have to do with global temperature reconstructions? Well, it’s always good to see what’s happening in the world within context. Unless we can see comparisons to what has come before, it can be really hard to see what is and isn’t weird when we’re living in the middle of it.

The famous ‘Hockey Stick’ graph that was constructed for the past 1,500 years by eminent climate scientist Michael Mann showed us how weird the current warming trend is compared to recent geologic history. But how does that compare to all of the Holocene period?

Well, we live in unusual times. But first, the details. These researchers used 73 globally distributed temperature records with various different proxies for their data. A proxy is looking at the chemical composition of something that has been around for more than our thermometers to work out what the temperature would have been. This can be done with ice cores, slow growing trees and marine species like coral. According to the NOAA website, fossil pollen can also be used, which I think is awesome (because it’s kind of like Jurassic Park!).

They used more marine proxies than most other reconstructions (80% of their proxies were marine) because they’re better suited for longer reconstructions. The resolutions for the proxies ranged from 20 years to 500 years and the median resolution was 120 years.

They then ran the data through a Monte Carlo randomisation scheme (which is less exotic than it sounds) to try and find any errors. Specifically, they ran a ‘white noise’ data set with a mean of zero to double check for any errors. Then the chemical data was converted into temperature data before it all got stacked together into a weighted mean with a confidence interval. It’s like building a layer cake, but with math!

Interestingly, with their white noise data, they found the model was more accurate with longer time periods. Variability was preserved best with 2,000 years or more, but only half was left on a 1,000 year scale and the variability was gone shorter than 300 years.

They also found that their reconstruction lined up over the final 1,500 years to present with the Mann et al. 2008 reconstruction and was also consistent with Milankovitch cycles (which ironically indicate that without human interference, we’d be heading into the next glacial period right now).

Temperature reconstructions Marcott et al. in purple (with blue confidence interval) Mann et al. in grey (from paper)

Temperature reconstructions
Marcott et al. in purple (with blue confidence interval) Mann et al. in grey (from paper)

They found that the global mean temperature for 2000-2009 has not yet exceeded the warmest temperatures in the Holocene, which occurred 5,000 – 10,000 years ago (or BP – before present). However, we are currently warmer than 82% of the Holocene distribution.

But the disturbing thing in this graph that made me feel really horrified (and I don’t get horrified by climate change much anymore because I read so much on it that I’m somewhat de-sensitised to the ‘end of the world’ scenarios) is the rate of change. The paper found that global temperatures have increased from the coldest during the Holocene (the bottom of the purple bit before it spikes up suddenly) to the warmest in the past century.

We are causing changes to happen so quickly in the earth’s atmosphere that something that would have taken over 11,000 years has just happened in the last 100. We’ve taken a 5,000 year trend of cooling and spiked up to super-heated in record time.

This would be bad enough on its own, but it’s not even the most horrifying thing in this paper. It’s this:

‘by 2100, global average temperatures will probably be 5 to 12 standard deviations above the Holocene temperature mean for the A1B scenario.’ (my emphasis)

Remember how I said keep in mind that 99.7% of all data points in a population are within three standard deviations on a bell curve? That’s because we are currently heading off the edge of the chart for weird and unprecedented climate, beyond even the 0.1% chance of occurring without human carbon pollution.

The A1B scenario by the IPCC is the ‘medium worst case scenario’ which we are currently outstripping through our continuously growing carbon emissions, which actually need to be shrinking. We are so far out into the tail of weird occurrences that it’s off the charts of a bell curve.

NOAA Mauna Loa CO2 data (396.80ppm at Feb. 2013)

NOAA Mauna Loa CO2 data (396.80ppm at Feb. 2013)

As we continue to fail to reduce our carbon emissions in any meaningful way, we will reach 400ppm (parts per million) of carbon dioxide in the atmosphere in the next few years. At that point we will truly be in uncharted territory for any time in human history, on a trajectory that is so rapidly changing as to be off the charts beyond 99.7% of the data for the last 11,300 years. The question for humanity is; are we willing to play roulette with our ability to adapt to this kind of rapidly changing climate?

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One thought on “What’s in a Standard Deviation?

  1. Pingback: What’s in a Standard Deviation? | Amy Huva

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