Extreme metrics

There has been a lot of discussion related to the Hansen et al (2012, PNAS) paper and the accompanying op-ed in the Washington Post last week. But in this post, I’ll try and make the case that most of the discussion has not related to the actual analysis described in the paper, but rather to proxy arguments for what people think is ‘important’.

The basic analysis

What Hansen et al have done is actually very simple. If you define a climatology (say 1951-1980, or 1931-1980), calculate the seasonal mean and standard deviation at each grid point for this period, and then normalise the departures from the mean, you will get something that looks very much like a Gaussian ‘bell-shaped’ distribution. If you then plot a histogram of the values from successive decades, you will get a sense for how much the climate of each decade departed from that of the initial baseline period.

Fig 4a, Hansen et al (2012)

The shift in the mean of the histogram is an indication of the global mean shift in temperature, and the change in spread gives an indication of how regional events would rank with respect to the baseline period. (Note that the change in spread shouldn’t be automatically equated with a change in climate variability, since a similar pattern would be seen as a result of regionally specific warming trends with constant local variability). This figure, combined with the change in areal extent of warm temperature extremes:

fig 5, hansen et al (2012)

are the main results that lead to Hansen et al’s conclusion that:

“hot extreme[s], which covered much less than 1% of Earth’s surface during the base period, now typically [cover] about 10% of the land area. It follows that we can state, with a high degree of confidence, that extreme anomalies such as those in Texas and Oklahoma in 2011 and Moscow in 2010 were a consequence of global warming because their likelihood in the absence of global warming was exceedingly small.”

What this shows first of all is that extreme heat waves, like the ones mentioned, are not just “black swans” – i.e. extremely rare events that happened by “bad luck”. They might look like rare unexpected events when you just focus on one location, but looking at the whole globe, as Hansen et al. did, reveals an altogether different truth: such events show a large systematic increase over recent decades and are by no means rare any more. At any given time, they now cover about 10% of the planet. What follows is that the likelihood of 3 sigma+ temperature events (defined using the 1951-1980 baseline mean and sigma) has increased by such a striking amount that attribution to the general warming trend is practically assured. We have neither long enough nor good enough observational data to have a perfect knowledge of the extremes of heat waves given a steady climate, and so no claim along these lines can ever be for 100% causation, but the change is large enough to be classically ‘highly significant’.

The point I want to stress here is that the causation is for the metric “a seasonal monthly anomaly greater than 3 sigma above the mean”.

This metric comes follows on from work that Hansen did a decade ago exploring the question of what it would take for people to notice climate changing, since they only directly experience the weather (Hansen et al, 1998) (pdf), and is similar to metrics used by Pall et al and other recent papers on the attribution of extremes. It is closely connected to metrics related to return times (i.e. if areal extent of extremely hot anomalies in any one summer increases by a factor of 10, then the return time at an average location goes from 1 in 330 years to 1 in 33 years).

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  1. J. Hansen, M. Sato, and R. Ruedy, "Perception of climate change", Proceedings of the National Academy of Sciences, vol. 109, pp. E2415-E2423, 2012. http://dx.doi.org/10.1073/pnas.1205276109
  2. J. Hansen, M. Sato, J. Glascoe, and R. Ruedy, "A common-sense climate index: Is climate changing noticeably?", Proceedings of the National Academy of Sciences, vol. 95, pp. 4113-4120, 1998. http://dx.doi.org/10.1073/pnas.95.8.4113