RealClimate logo

Extremely hot

Filed under: — stefan @ 26 March 2012

By Stefan Rahmstorf and Dim Coumou

One claim frequently heard regarding extreme heat waves goes something like this: ”Since this heat wave broke the previous record by 5 °C, global warming can’t have much to do with it since that has been only 1 °C over the 20th century”. Here we explain why we find this logic doubly flawed.

One can ask two different questions about the influence of global warming on heat waves (Otto et al. 2012), and we take them in turn.

1. How much hotter did global warming make this heat wave?

We have some trouble with framing the question like this, because it tacitly assumes that the same weather situation would have also arisen without global warming, only at a (say) 1 °C lower temperature level. That need not be the case, of course, since weather is highly stochastic and global warming can also affect the circulation patterns of the atmosphere.

But even if we accept the basic premise (and it could be meant in a purely statistical sense, although that is not usually how it is expressed), would an average anthropogenic warming by 1 °C in the relevant location mean that 1 °C is also the amount added to an extreme event? Only in a linear climate system. Imagine a heat wave that pushes temperatures up to 30 °C in a world without global warming. In the same weather situation with global warming, you might expect that this weather then results in a 31 °C heat wave. But that could well be wrong. Possibly in the situation with warming, the soil has dried out over the previous months because of that extra 1 °C. So now you lost evaporative cooling, the incoming sunlight turns into sensible heat rather than a large fraction going into latent heat. That is a non-linear feedback, and not an imagined one. Detailed studies have shown that this may have played an important role during the European heat wave of 2003 (Schär et al. 2004).

The basic phenomenon is familiar to oceanographers: if the mean sea level in one location rises by 30 cm, this does not mean that the high-tide level also rises by 30 cm. In some cases it will be more, due to nonlinear feedback. I.e., a higher water level increases the flow cross-section (think of a tidal inlet) and reduces bottom friction so the tide rolls in faster, reaching a higher peak. The tidal range increases as well as the mean sea level.

Numerous other non-linear mechanisms are possible, which we are only beginning to understand – think of the recent studies that show how changes in snow cover or sea ice cover as a result of global warming affect weather systems. Or think of factors that could affect the stability of particularly strong blocking events. Thus, we’d be very cautious about making an essentially linear, deterministic argument about heat extremes to the public.

In the scientific literature, the influence of global warming on extreme events is therefore usually discussed in terms of probabilities, which is more fitted to stochastic events. The typical question asked is:

2. How much more likely did global warming make this heat wave?

For this question, it is easily shown that the logic “the greater the extreme, the less global warming has to do with it” is seriously flawed. The change in probability of certain temperature values being reached can be visualised with a probability density function (see Figure). The probability distribution could be shifted unchanged towards warmer values, or it could be widened, or a combination of both (or some other deformation).

IPCC (2001) graph illustrating how a shift and/or widening of a probability distribution of temperatures affects the probability of extremes.

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).

210 Responses to “Extremely hot”

  1. 201
    SecularAnimist says:

    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. 202

    #198 Dan H.

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

  3. 203
    Norman says:

    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. 204
    Ray Ladbury says:

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

  5. 205

    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. 206
    Tokodave says:

    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…

  7. 207
    Hank Roberts says:

    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. 208
    grypo says:

    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. 209
    Norman says:

    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. 210
    Dan H. says:

    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.