# 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”.

P.s.

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

References:

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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