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Extreme events as evidence for differences in distributions

I think Lawrence Summers would like this paper by James Hansen, Makiko Sato, and Reto Ruedy (link from Krugman via Palko). Hansen et al. write:

The distribution of seasonal mean temperature anomalies has shifted toward higher temperatures and the range of anomalies has increased. An important change is the emergence of a category of summertime extremely hot outliers, more than three standard deviations (σ) warmer than climatology. This hot extreme, which covered much less than 1% of Earth’s surface in the period of climatology, now typically covers about 10% of the land area.

The point is that it makes sense to look at the whole distribution, but extreme events provide information also.

P.S. Here are some papers by my Columbia colleague Wolfram Schenkler on potential impacts of global warming on agriculture.


  1. numeric says:

    An important change is the emergence of a category of summertime extremely hot outliers, more than three standard deviations (σ) warmer than climatology.

    Lets see. Climatology is the study of climate, so these hot outliers are three standard deviations greater than the science of climate (which, I would have thought, was a constant). This is either a completely inchorent sentence, or climatology has its own peculiar statistical lingo.

    • PI says:

      In this case, “climatology” refers to the climate of the period 1951-1980, chosen “because that is a time of little global temperature trend just prior to the rapid global warming in recent decades. It is a period that older people today, particularly those of the ‘baby boom’ generation, can remember. Global temperature in 1951-1980 is also within the Holocene temperature range, and thus it is a climate that the natural world and civilization is adapted to. In contrast, global temperature in the first decade of the 21st century is probably already outside the Holocene range […]”.

  2. Andrew says:


    Unfortunately (or maybe fortunately), statistical terminology is not well standardized across fields of application.

  3. Jonathan (a different one) says:

    Does the global warning science (or simulations therefrom) support the notion of increased variance? Or is the presence of outlying events supposed to indicate a righteard shift the distribution? And is this variance increase in both tails? Does the science support an increase in one tail only?

    • PI says:

      I don’t think there is consensus about predictions of increased variance. One well-cited paper discussing simulated future extremes is Kharin et al. (2007), although they don’t really phrase their results in terms of changes in variance.

  4. John Mashey says:

    Increased variance, increased high-end tail:
    I think the jury is still out.

    See tamino on Increased variability.
    He may or may not be right, but he is generally quite credible and the discussion is relevant.

  5. […] nickgb posted on the extreme data of late verifying that climate change is real. Via Andrew Gelman, a chart from a new article on the same […]

  6. John Mashey says:

    See also Temperature Variability part 2, especially comments. Real statisticians welcome.