Extremely hot

For illustration, let’s take the most simple case of a normal distribution that is shifted towards the warm end by a given amount – say one standard deviation. Then, a moderately extreme temperature that is 2 standard deviations above the mean becomes 4.5 times more likely (see graph below). But a seriously extreme temperature, that is 5 standard deviations above the mean, becomes 90 times more likely! Thus: the same amount of global warming boosts the probability of really extreme events, like the recent US heat wave, far more than it boosts more moderate events. This is exactly the opposite of the claim that “the greater the extreme, the less global warming has to do with it.” The same is also true if the probability distribution is not shifted but widened by a constant factor. This is easy to show analytically for our math-minded readers.

Graph illustrating how the ratio of the probability of extremes (warmed climate divided by unchanged climate – this increased likelihood factor is shown as a dashed line, scale on right) depends on the value of the extreme.

So in summary: even in the most simple, linear case of a shift in the normal distribution, the probability for “outlandish” heat records increases greatly due to global warming. But the more outlandish a record is, the more would we suspect that non-linear feedbacks are at play – which could increase their likelihood even more.

Update 29 March: New Scientist magazine cites this RC post in an article about the “summer in March”.


Our Perspective article on the unprecedented extremes of the last decade was just published by Nature Climate Change: Coumou & Rahmstorf (2012) A decade of weather extremes


Otto et al., Reconciling two approaches to attribution of the 2010 Russian heat wave, Geophysical Research Letters 2012, VOL. 39, L04702, doi:10.1029/2011GL050422

Schär, C. et al. The role of increasing temperature variability in European summer heat waves. Nature 427, 332–336 (2004).

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210 comments on this post.
  1. SecularAnimist:

    Dan H wrote: “So far, no one has shown a clear connection between global warming an increased ‘blocking,’ …”


    Evidence linking Arctic amplification to extreme weather in mid-latitudes

    Jennifer A. Francis, Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, New Jersey, USA
    Stephen J. Vavrus, Center for Climatic Research, University of Wisconsin-Madison, Madison, Wisconsin, USA

    GEOPHYSICAL RESEARCH LETTERS, VOL. 39, L06801, 6 PP., 2012 doi:10.1029/2012GL051000

    Discussion at ClimateCentral:

  2. John P. Reisman (OSS Foundation):

    #198 Dan H.

    Why do you make claims that are popular on denialist blogs without checking up on the scientific literature first?

  3. Norman:

    March 2012 is out on the NOAA web page and it is really exceptional for area that was warm in US and how warm. There are very few like it but in searching I did find a year that did look somewhat similar. October 1963.

    Here are the links for your own viewing.
    October 1963


    March 2012


  4. Ray Ladbury:

    Google Extreme Value Theory, and then perhaps you can talk out of the proper orifice.

  5. Daniel Bailey:

    Umm, Norman, aside from the issue of your links not working, you must really compare like-to-like. As in March-to-March, or October-to-October, with the year being the variable.

    Same apples=oranges improper analytical thinking and cognitive bias cherry-picking as in his SkS iterations.

  6. Tokodave:

    Put another way; if it’s 30 or 40 degrees warmer than normal in March that’s pretty damn warm for that time of year….were it 30 or 40 degrees warmer than normal in August….that’s hell or high water country… http://tamino.wordpress.com/2011/05/07/hell-and-high-water/

  7. Hank Roberts:

    That illustration is of a pick mattock and scythe, just to be, er, picky. Restoration tools.

    Every time I see an eagle on a stick, I think of Julius Caesar, oh, wait, I mean George Washington. And you know the rule about mentioning the fyflot.

    Ok, that ends _this_ exchange, I trust.

  8. grypo:


    Hoerling’s take on Stefan Rahmstorf and Dim Coumou

    — Not a scientific paper, but more Op-Ed

    — Exaggerated language, and many unsubstantiated assertions.

    — Overly simplistic view of the relation between damage, human suffering, and the extremes. Much more balanced arguments can be found in R. Pielke Jr.’s work

    — Very few of the [cases of extreme weather listed in the paper] have undergone a scientific investigation of contributing factors, let alone human impacts.

    — The piece lacks all perspective on the human and technological elements contributing to greater observational capacity to sense extremes

    — The matter of attribution, as raised in the second to last paragraph, is a much broader science that merely determining the change in probability due to greenhouse-gas forcing

    — Consistent with the policy-direct tone of this piece, hyperbole is used throughout.

    [Response: He doesn’t appear to be reading the same paper that I saw – or perhaps he wanted them to write about something else entirely. Either way, this is not a constructive addition to the general discussion. – gavin]

  9. Norman:

    Dan H. @198

    I was able to find this thesis from a student to obtain a Master’s Degree. He does show a sharp increase in the number of blocking events and the duration, but the intensity drops off. He adds global and Northern Hemisphere temperature anomalies to the blocking pattern graphs.

    I thought you may find this thesis of interest.


  10. Dan H.:

    Very nice.
    The paper found an increase in the duration of blocking events, but a decrease in intensity with increasing temperatures. The major impact of blocking events appears to be the PDO; increased blocking in the northern hemisphere during the negative phase of the PDO, and an increase in the southern hemisphere during the positive phase.