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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. 1
    Salamano says:

    I have a question.

    If your specific methodology in regards to the “Moscow Warming Hole” research was applied directly to the extreme cold event in Europe that has been discussed continuously this winter (ie, )

    …How would the loaded climate dice exercise conducted then show the likelihood of this event occurring?

    [Response:Our approach in that paper assumes a probability distribution that shifts towards warmer temperatures, but is otherwise unchanged – just like the simple example given in the second graph above. Something like an extreme cold event related to sea ice loss obviously can not described in this way – it is a great example of a highly non-linear mechanism. stefan]

  2. 2
    Kasuha says:

    I believe there’s no dispute the increase in mean has occurred (if not later then sure between 1950 and 2000), all main temperature records agree on that. But I know record lows are still being reported – they just don’t get as much publicity as highs. For example this year’s Europe/Asia cold wave in February was a particularly nasty one, many stations recorded more than one record low over the ~month it lasted. I happen to live in that area so I had that experience directly delivered to me.
    Another thing is I don’t know how record low statistics compare with record highs. I know here are record highs recorded, there are record lows recorded but I don’t know how many and how extreme. Plus, as there was that above mentioned mean shift, one would expect the record low statistic to be affected by it regardless on current trend.
    Could I ask for your guess/results on how much the variance has changed and how big the variance is compared to the recorded mean change?

    [Response:I’m looking after my sick little daughter today so won’t be able to be involved further in the discussion. But I’m sure some of our readers can answer your questions. -stefan]

  3. 3
    Lab Lemming says:

    Re #2:
    Some of those numbers are here:
    Ask Dan (that blogger) if his sources are US or worldwide.

  4. 4
    Salamano says:


    I believe ‘everyone’ does agree that record lows exist and will continue to exist, but just in fewer numbers. I think the current data has the establishment of record highs far outpacing record lows, which would be expected in a warming world.

    I asked Dr. Mann about the European cold spell as well at a different venue, and his initial thinking was that the event was not “global warming induced” (instead brought on by natural variability), but then left open the idea that it would be, because of what Rahmstorf was saying regarding the loss of sea ice. However, it led me to wonder what goes into the selection process to identify ‘event candidates’ for the application of the methodology that gets published.

    Also, considering the anticipated greater loss of sea ice in future years, I suspect we’ll have to have more of the extreme cold events of the kind that affected Europe. Perhaps this is a non-linear ‘feedback’ that non-zero-ly affects the forward progression of global warmth?

    I was analysing those three graphs put out by the IPCC and trying to resolve in my head a scenario that would accomodate both the Moscow warming event and the record Europe cold of this year. It would seem that graph #2 is best, but then that would imply no net warm progression of temperature. If one of the ‘warming’ graphs are chosen, than the “climate dice” idea becomes unworkable for any extreme event involving cold. I would hope that such methodology doesn’t just become only applicable for warming events– it then becomes technically unfalsifiable. Perhaps there will be a 4th graph developed that demonstrates a warmer progression while also maintaining a higher variance that makes both cold events and warm events more likely. At this point, perhaps the thinking is “less cold events, but more ‘extreme’ cold events”(?) Makes for an interesting distribution.

    …I wonder if we all are home with sick daughters today (mine just finished with “spring break” and today was to be their first day back, go figure).

  5. 5
    J Bowers says:

    Re. 2 Kasusha

    For the US: Heat Wave Sends Temps Soaring into Uncharted Territory

    The volume of records being set during this long-duration heat wave is staggering. On March 18 alone there were 1,597 warm temperature records set or tied in the U.S., compared to just 58 cold temperature records. For the year-to-date, there have been 14,737 warm temperature records set or tied, compared to 1,296 cold records — a ratio of about 11-to-1.

  6. 6
    Pekka Kostamo says:

    Jeff Masters has discussed recently the mechanisms on his blog.

    In a warming world hot and cold waves are both generated by changes in the polar jet stream. Slower rotation of the meandering jet ring and and its bigger fluctuations give more time for the cold and hot flows to do their work. In general, the “prevailing weather types” are becoming slower changing, which incidentally makes the weather forecaster’s work a little bit easier. “Tomorrow the same weather as today” holds good a bit more. Periods of fair weather become longer and the successions of depressions bringing rain likewise.

    Another aspect of warming impact is that the timing and geographic patterns of what is called “weather” changes completely, as explained also by Masters. Probabilities shift a little bit as described here, but the everyday readings have no relation between the “warmed up” and “unwarmed” weather situation.

    On this single day, the thermometer at my window reads +1,0 degC. In an “unwarmed” world the reading could be anything between -25 degC and +10 degC, that being the observed previous range for this particular day of the year.

    This applies also the the low probabily tails. To the consternation of most, the “Katrina” would almost certainly not have happened on that particular day in an “unwarmed” world. Nor necessarily on any other day either, as it was a very low probablity event, the like of which the Gulf coast has seen only 3 in a hundred years.

    Yet, it is not right to say the particular storm was caused by climate warming. It was just a random fluctuation generated within a given climate framework and could have occurred with the same very low probability also in an unwarmed world, on that day or on any other day of the active seasons.

  7. 7
    wili says:

    JBowers, you beat me to it. And that 11-1 ratio for heat records over cold so far this year comes after years of steady increase–2-1 over the last couple decades, 3 to 1 in the summer of 2010, and 8 to 1 last year.

    But these are still just US ratios. I, too, would like to know what the ratios are and have been on the global level.

    In general, it strikes me that, useful as these abstract probabilistic models can be, they can’t really capture the complexity of a the system and the wide range of possibilities, especially over the relatively short term.

    Just for one example, if it turns out that, between melt of sea ice and Greenland ice, the North Atlantic Current slows or stops, we would expect to see fairly dramatically colder weather in Europe for a while, even thought this condition could be directly linked to results produced by GW (though in the long term, the warming would, presumably eventually overtake the cooling from change in ocean currents).

    The main point is that the disruption provided by greater overall warming of the global atmosphere is leading to all sorts of extremes, mostly, but not all necessarily, on the hot side. Gaussian distribution may not be fully adequate to describe the complexity of the system.

  8. 8
    James Staples says:

    Yes, and then, whenever it ISN’T ‘Hot enough to convince them that Global Warming is “real”‘, that, too, it “proof” that it’s all BS, Blargl, Yargl, Blaaarh!!!
    Don’t you wish Everyone had taken Statistics? (Note: I didn’t, but I ‘get it’, any-old-way); that they understood ‘The Law of Averages’?
    Probably out buying Lotto Tickets, in the full assurance that ‘After they’d lost X number of times’ then the odds MUST have Improved…….
    Keep Up the Good Work!!!

  9. 9
    LarryL says:

    Durng the recent, and on-going, heat wave impacting most of the central and northern US and southern Canada, temperatures in many areas were well over 30 degrees above average.
    Is that same type of heat anomaly possible with summer time temperatures? Or does the outside range of the anomaly get smaller as the average temperatues get warmer?

    Here in St. Louis, the average Aug temp is 88F. What types of temperatures could we hit if the March heat wave occured in August?

    [Response:Good and extremely important questions, and I do mean extremely. You apply the same magnitude of relative heat anomaly (i.e. relative to the seasonal mean) at the hottest time of the year and you are looking at serious trouble, highly dependent on precipitation and general soil moisture levels, but potentially extremely serious in effects. This is why the example in the post about the amplifying effects of previous, cumulative heating due to a gradual shift in the T distribution, on a subsequent heat wave event, is a very good and important one–Jim]

  10. 10
    Chris Dudley says:

    This is a good point and it counters my recent criticism of Jeff Masters’ statement to some extent:

    “Of course, using 30 years of data to estimate extreme events with a return period of centuries is a sketchy proposition. However, keep in mind that had we used a century-long climatology instead of using the past 30 years, yesterday’s warmth would have been classified as much more extreme, since the climate has warmed considerably in the past 30 years. It is highly unlikely the warmth of the current “Summer in March” heat wave could have occurred unless the climate was warming.” –Masters

    Probability-wise shifting the mean back O.3 C or so, to match the situation in the Midwest, you might go from 4.5 sigma to 4.6 sigma making the extreme 1.6 times less likely for a 100 year timescale climate estimate than for a 30 year timescale climate estimate.

    But, I think that problems arising from including the trend within the variance estimate still make the statement problematic.

    And, the warming is global and may not be local, or at least not perceptibly so. There are regions of cooling in the 100 year gistemp trend map for March in northern Canada and in central Australia but is seems doubtful that these local cooling trends make a warming attributable heat wave less likely in those areas. Have those regions had less cooling than they would have without global warming? Or, rather, would a different realization of warming have shifted the cooling spots to different places? April looks different from March in this measure.

    Surly, also, most scientists realize that scrabbling around at the 0.1 sigma level is methodologically very dangerous ground. Telling the difference between 4.5 and 4.6 sigma implies a precision in the determination of sigma that is rarely justified given the influences of non-Gaussian effects that may interfere. The point made here by Stefan and Dim seems valid but faces difficulties in its practical application.

    As a practical matter, I think that Hansen’s recent approach of looking at the fraction of the Earth’s surface which is experiencing extreme warmth does a good job of making a global measure to compare with global warming.

    This avoids the problem that any particular 4.5 sigma event might be expected simply because we expect a 4.5 sigma event somewhere some time. I think what is presented here by Stefan and Dim could be very profitably applied to a discussion of that work.

  11. 11
    jgnfld says:

    I think one problem with the “it’s really hot therefore global warming” argument is that people do not see it in the (quite correct) terms you are presenting it. Many, I think, tend to think the whole globe has been experiencing a heat wave this March–something that is patently not the case–and then feel cheated when the aggregated number come out so minimal in any short period as they must over any sufficiently short period given the first law.

    For example, I doubt that worldwide, the monthly GISTemp, HadCRUT or other series will be wildly anomalous as the great heat in the US/Central Canada is well balanced by cool areas elsewhere–Newfoundland where I live being one of them :-( .

    Basically, I think that the inability of untrained people to see that the statistical argument you’re making is correct is a real problem. I’m not sure I have any ideas for countering this problem, but it sure makes explanation hard.

  12. 12

    Again nice work which demonstrates and compresses a 4 dimensional event into a 2 dimensional graph.
    It explains the possibility of such an occurrence, but I rather have pictures and maps, it also may be a 5 dimensional phenomena including chemistry (CO2 for instance). The greatest cause of this heat wave is the shrinkage of winter around the North Pole, which took decades before happening this way, one side of the world is bound to be hotter while the other normal, its been going this way for more than a decade, and its getting hotter during winters; no ice in High Arctic Mid-November (1998), bees in N.Y. January, tulips in the UK February, summer heat in North American March, the spinning of the heat zone during winter will continue and expand . Again one must look at mirror causations, the biggest one is the shrinking Cryosphere, This heat wave is the reflection of sea ice volume disappearance.

  13. 13
    Susan Anderson says:

    Wonderful, I will look forward to reading some real science on this issue and studying the article in depth as far as I am able to.

    GSW, here’s some fodder for your question to the scientists that I unfairly fielded with my amateur comments (elsewhere).

    nice taste (niciest gutta captcha!)

  14. 14
    Ray Ladbury says:

    It seems to me that the basic problem with this type of analysis is that the question one is trying to answer is whether the distribution is changing by looking at the extremes of the distribution. This is bound to be problematic since the extremes of the distribution are always poorly known do to the rarity of events from this poriton of the pdf.

    The one thing you can probably say with relative certainty is that by the time you get out to 5 sigma, the pdf probably ain’t normal.

    [Response:But you’re not restricted to looking at the extremes Ray. You can look at the rest of the distribution as well. EDIT: Meaning, to get an idea of whether the overall distribution is changing, and how–Jim]

  15. 15
    Edward Greisch says:

    ”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” LOL [laughing out loud] Any excuse, no matter how contorted the logic.

    And I sure do wish statistics was a required course in K-12 and for all majors in college. Most people who know nothing about it think they know all about it.

  16. 16
    Mike Roddy says:

    Chris Dudley, a Dot Earth commenter, linked this RC article, and pointed out that Andy Revkin has long denied links between extreme weather and global warming. Andy responded by linking to an article behind a paywall written by a “leading climate scientist” I have never heard of, named John Wallace, I believe. Andy implied in his comment that RC, a careful and rigorous group, is in some sort of alarmist camp, and that his guy is the one sticking to the evidence.

    I know that RC people are serious, and don’t want to get dragged into yet another “debate” by people like Revkin and the Breakthrough Institute, who love to wag their fingers at anyone who proposes a link between extreme weather events and global warming. The science here is rather obvious if one has a mathematical mind, which BTI and Andy do not. I don’t know about the study he quoted, but can assume it’s more soft denier material.

    Not sure if there’s any remedy for this, but wanted RC readers to know what’s going on. Quality climate science is now being routinely targeted by news organizations and previously credible reporters and politicians. The time is long past for scientists and their professional organizations to go beyond general statements, and begin to aggressively counter the flood of the discredited science that continues to worm its way into our media outlets. Nobod else is going to do it for you, since almost all MSM reporters are either bought or terrified.

  17. 17
    GSW says:


    Thanks for remembering me!

    I think on the other thread the question was couched in a slightly different manner to how it has been outlined here.

    Specificaly, we were talking about a regional warming event in the context of an otherwise unremarkable month for “Global” temperatures. So should we look for, and attribute, “significance” in short term, regional, anomalously Hot and Cold events? is it correct to do so?

    Posing the problem in a contrary manner; if the yearly Global Temperature anomaly was above average, but the year was marked by a number of very anomalous “Cold events” in say Russia, what weight would we attribute to these events relative to the Global signal?

    I’d argue that short term regional events are not a good metric either way. They are more a consequence of an unusual weather pattern than a background “Global” trend.

  18. 18
    Steven Franzen says:

    @2, Kasuha,

    For Europe a nice and accessible data source is the ECA&D (European Climate Assessment & Dataset) project. For example, one can easily plot individual time series as narrow as a single station or compiled maps showing anomalies/trends for the whole continent.

    As measures for extreme values, the indices TX90p (incidence of daily max. temperatures above 90th percentile) and TN10p (min. night temps below 10th percentile) could be informative. Even though 10th/90th percentile conditions are not particularly extreme deviations, a discrepancy in the trends of both numbers is quite apparent, with daytime maxima increasing quicker than nighttime minima are decreasing.

    That said, not only the eastern USA, but also the northwestern Europe has been shielded by a surprisingly stable area of high pressure for the past week or so. In my area (Netherlands) it has produced daytime maxima of 18-20 degrees (Celsius), very unusual compared to the 1981-2010 average of 10.6. The current month is certainly going to end up in the top 5 warmest March months on record, possibly in the top 3.

  19. 19
    Brian Brademeyer says:

    I have recently been looking at weather effects on bark beetles with a century of weather data (1910-2009) for the Black Hills, and the standard deviation of average monthly temperature does indeed show an annual cycle, with minimum in August (1.521 F) and maximum in January (3.514 F).

    March is nearly double the August standard deviation (2.866 F), so a “similar” August heat wave would involve a smaller absolute temperature deviation (about half) than the current March heat wave.

    [Response:Your argument misses the point in three different and important ways, not even considering whether or not the Black Hills data have any general applicability elsewhere, which they may or may not: (1) It ignores the point made in the post about the potential effect of previous, seasonal warming on the magnitude of an extreme event in mid summer to early fall, due to things like (especially) a depletion in soil moisture and consequent accumulation of degree days, (2) it ignores that biological sensitivity is far FAR greater during the warm season than the cold season for a whole number of crucial variables ranging from respiration and photosynthesis to transpiration rates, and (3) it ignores the potential for derivative effects, particularly fire and smoke, in radically increasing the local temperature effects of the heat wave. So there is no comparison whatsoever.–Jim]

  20. 20
    Paul S says:

    GSW – ‘So should we look for, and attribute, “significance” in short term, regional, anomalously Hot and Cold events? is it correct to do so?’

    I think the point is to determine how often extremes might happen, statistically speaking, in order to inform planning decisions. Think of the 100-year flood concept as an analogue.

    ‘They are more a consequence of an unusual weather pattern than a background “Global” trend.’

    I think you should read Stefan and Dim’s post. Global warming does not manifest only as a linear trend on a graph, averaging at the global level. The changes brought about through human activity will influence and are influencing regional weather patterns. The question is ‘in what way?’ Some extremes may become more likely, some less likely.

  21. 21
    Ray Ladbury says:

    Yes, certainly, you have to look at the events from the central portion of the pdf. However, they don’t provide much constraint on the extremes. How do you know that you haven’t affected the skew, for example, as well as the mean and standard deviation? How do you know your distribution is still unimodal, or indeed was unimodal in the first place?

    Attribution is always a fraught proposition when it comes to extreme value stats.

    [Response:I agree Ray, that the central portion provides little information, if any, on the probabilities represented by the tail ends. As for the distribution shape, it’s always going to be unimodal, that’s for sure. And the changes in the higher moments was exactly my point in saying you need to look at the rest of the distribution–that will indicate whether the skew, kurtosis etc are changing–or rather the other way around: changes in those computed moments will tell you if the shape of the distribution is changing, which is what you want to know.–Jim]

  22. 22
    Tokodave says:

    I can’t help but be reminded of a post over at Tamino’s Open Mind Site that concluded with:I’ll continue to do what I can, come hell or high water. Expect both.

  23. 23
    Ray Ladbury says:

    Sorry if I am being a bore, but skew and kurtosis require quite large datasets to estimate–and the thicker the tails the more data they need.

    And just to play devil’s advocate, given the importance of the jet stream, would if always be unimodal?

    [Response:Not being a bore Ray. But if I follow your line of reasoning, how are you ever going to detect any type of climatic change of any magnitude at all? Your reasoning seems to preclude it, because it doesn’t allow you to estimate the shape of the distribution, either before or after the change. And I can’t imagine any situation in which the distribution of a T variable is other than unimodal–other than perhaps a uniform distribution, which itself would be highly unusual.–Jim]

  24. 24
    Poul-Henning Kamp says:

    What surprises me is that people still hang so much onto standard deviations, when extreme events are much more powerful witnesses to change in the underlying probability density function, be it gaussian or not.

    Given that JASON nailed this in 1992, albeit not in peer-reviewed literature, I’m amazed that nobody has taken up where they left.



  25. 25
    Hank Roberts says:

    Jim’s inline response to LarryL above talks about the various factors that make a difference

    The farmers watch this.
    Planting a bit early, if the fields are dry enough to support farm machinery, can improve results — but that outcome depends on having enough soil moisture, and having no peak temperature during the summer high enough to stop seed from forming.


    If a smaller than normal portion of the 2012 corn crop is planted late, expectations should be for an average U.S. yield as much as two bushels above trend unless there are offsetting factors. One of the potentially offsetting factors is the dry soil conditions at planting time in portions of the western Corn Belt. Actual yields in 2012, like all years, will be most heavily influenced by summer weather conditions.

    Issued by Scott Irwin and Darrel Good
    Department of Agricultural and Consumer Economics, University of Illinois”

  26. 26
    jgnfld says:

    @16 You make my point quite clearly: It takes education to see things quantitatively. Making the point for those lacking these two makes for a hard argument

  27. 27
    Andy Revkin says:

    Mike Roddy, above, would do well to review John Michael Wallace’s publication record before casting stones. )Click here: )

    Here’s a section from his EOS piece:

    Arguing about whether or not today’s extreme events are early indicators of climate change does nothing to advance the priority of global warming and other pressing environmental issues on our national policy agenda. The real significance of extreme events is as harbingers, not just of a changing climate but also of a changing world in which human society and the infrastructure that supports it are becoming increasingly vulnerable to natural disasters. The mounting disruptions in their wake reveal the progressive deterioration of our planetary life-support systems. Extreme events are, indeed, teachable moments: “wake-up calls” that an environmental crisis of global proportions is imminent—much more so than the subtle and sometimes ambiguous early warning signs of global warming might lead us to believe.

  28. 28
    Brian Morsony says:

    @9 I think LarryL had a good question, that never really was addressed – Would a similarly extreme heat wave in summer produce a similar increase in temperature relative to the (monthly) average?

    To use a local example, on March 20th in Madison, WI it was 83F, about 40F above the March average (42.8F). This was also a record high for March, breaking the previous record of 82F set on March 29, 1986 and March 31, 1981. For the sake of argument, let’s call this a 5-sigma event.

    Would a similarly extreme 5-sigma event in July (average temp. 82.1F) produce a day with a high of 122F? A 122F day in July seems (to me) much more unlikely than an 83F day in March, even though they are the same number of degrees above average. Maybe a more reasonable expectation for a similar event in July would be 108F, 1 degree above the all-time high of 107F? Would it take a much more extreme event, say 8-sigma, for Madison to have a 122F day in July?

    [Response:Right. You use the standard deviation of the relevant season, not one from a different season. This is actually another point that I meant to raise in response to the comment about the Black Hills data. You don’t compare the absolute numbers to evaluate equivalency of (or lack of) extreme events across seasons, you compare the deviations from the relevant seasonal means.–Jim]

  29. 29
    Hank Roberts says:

    PS — if you follow the link in the quote above, and look at the range of outcomes — the worst case is quite bad. That’s for one species (corn) in quadrants of one state (Iowa), based on the historical climate.

    I haven’t found whether they’ve worked out worst cases for the new climate that we’re heading toward.

  30. 30
    kramer says:

    For the year-to-date, there have been 14,737 warm temperature records set or tied, compared to 1,296 cold records — a ratio of about 11-to-1.

    What was the global ratio for the year to date?

  31. 31
    Paul S says:

    Andy Revkin – I agree with your thoughts about Mike Roddy’s prejudice regarding John Wallace.

    I don’t understand your characterisation that this post was ‘well countered’ by Wallace’s piece. They seem to be about different things: Wallace’s article is about communication strategies; Stefan and Dim’s post is about concepts used to understand extreme weather events within climate regimes.

  32. 32
    tpinlb says:

    What do you think of the new paper by Solheim, Stordahl and Humlum, “The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24,” in Journal of Atmospheric and Solar-Terrestrial Physics?

  33. 33
    Hank Roberts says:

    for tpinlb:

    type “humlum” in the box in the upper right corner labeled “Search”
    to find the answer:

  34. 34
    Dan says:

    re: 32. Here is the abstract from

    “Relations between the length of a sunspot cycle and the average temperature in the same and the next cycle are calculated for a number of meteorological stations in Norway and in the North Atlantic region. No significant trend is found between the length of a cycle and the average temperature in the same cycle, but a significant negative trend is found between the length of a cycle and the temperature in the next cycle. This provides a tool to predict an average temperature decrease of at least 1.0 ◦C from solar cycle 23 to 24 for the stations and areas analyzed. We find for the Norwegian local stations investigated that 25–56% of the temperature increase the last 150 years may be attributed to the Sun. For 3 North Atlantic stations we get 63–72% solar contribution. This points to the Atlantic currents as reinforcing a solar signal.”

    1. This was not a study of *global* temperatures but of just Northern Europe and Scandinavia. In other words, a small areal sample set.
    2. “…the last 150 years…” The global warming that we are concerned with is the warming that has occurred since the 1970s, not over 150 years. Back then, natural causes were the dominant forcings on global temperature trends. But recent warming trends can not be explained by natural causes/forcings alone. The warming since the 70s can only be explained when the additional forcings from man-made greenhouses are considered. Furthermore, the current global temperature anomalies when compared to the climatic normals are well within the projected model ranges.
    3. You can be certain that various anti-science, anthropogenic global warming denialist web blogs and op ed writers (with no scientific background) will take this study and trumpet it from the hills, completely out of context in order to continue to be disingenuous and to purposely mislead people.

  35. 35
    Clark Lampson says:

    Those commenting on LarryL’s question regarding extreme heat in Summer are missing a very fundamental thermodynamic issue: In the winter for a given area, significant heat can be transported into the region, because much warmer temps exist elsewhere on the globe. That is not the case for many regions in their local summer.

    The symmetrical question would be what sort of extreme cold spells could one see in the summer.

    [Response:Yes, but the point I’ve been trying to make is that it’s not the absolute magnitude of the anomaly that’s important, it’s the relative anomaly, as measured in standard deviations from the seasonal (or weekly or monthly or whatever) mean. That’s what organisms are adapted to tolerate. You shouldn’t use the absolute magnitude to evaluate similarity of “extreme-ness” between different seasons–it just doesn’t make any sense. This seems pretty basic to me–Jim]

  36. 36
    Susan Anderson says:

    “one of the country’s most eminent climatologists, John M. Wallace” (publications date from 1964):

    Wikipedia John Michael Wallace is a professor of Atmospheric Sciences at the University of Washington, as well as the former director of the Joint Institute for the Study of the Atmosphere and Ocean (JISAO)–a joint research venture between the University of Washington and the National Oceanic and Atmospheric Administration (NOAA). His research concerns understanding global climate and its variations using observations and covers the quasi biennial oscillation, Pacific decadal oscillation and the annular modes of the Arctic oscillation and the Antarctic oscillation, and the dominant spatial patterns in month-to-month and year-to-year climate variability, including the one through which El Niño phenomenon in the tropical Pacific influences climate over North America. He is also the coauthor with Peter V. Hobbs of what is generally considered the standard introductory textbook in the field: Atmospheric Science: An Introductory Survey. He was the third most cited geoscientist during the period 1973-2007.

    A further look via Google finds Dr. Wallace promoting positions similar to Andy Revkin’s, inclusive of energy exploration including extreme fossil fuels, and he is cited as being not entirely unsympathetic with Dr. Lindzen, not enough to condemn but there it is.

    His textbook, written in 1977 and revised in 2006 (Amazon) is said to be one of the best on meteorology around. He appears to encourage an energy quest. I am not qualified to guess at the quality of his current research on cycles and so on.

  37. 37
    Thomas says:

    To jump in on LarryL’s quetion. I can make a simplistic argument in favor of lower warm season variance than cold season variance. (1) Postulate that on any given day a locale experiences the expected seasonal temperature of some point at the same longitude, but which is displaced north or south depending upon anomalous circulation effects. Then if we assume the distribution of this north south variance is the same, the expected variance should be proportional to the north south climatogical temperature gradient.

    Of course Jims observations about the potential buildup of nonlinear effects from the state of the ground (soil moisture, vegetaion, snow/ice cover etc.), is still valid. We can’t rule out that these effects could throw a monket wrench into my simplistic explanation of seasonal variance.

    I’m not convinced that the T distribution has to be unimodal. There certainly exist nonlinear phsyical which exhibit quasi bistable behavior; the earths magnetic field is one such system. Is there a good argument for why weather is different in this respect?

  38. 38
    Susan Anderson says:

    In considering the potential for increased temperatures in summer, don’t forget the acceleration of the increase in ocean temperature.

  39. 39
    sidd says:

    Mr. Hank Roberts wrote on the 26th of March, 2010 at 2:03 pm:

    “The farmers watch this.
    Planting a bit early, if the fields are dry enough to support farm machinery, can improve results — but that outcome depends on having enough soil moisture, and having no peak temperature during the summer high enough to stop seed from forming.”

    There also is sumpn about crop insurance not kicking in unless you plant after the last frost date…

    And speaking of distributions, i notice that the TRMM global precip data are much narrower than gaussian, with long tails, and the mode is moving toward lower precip, while both extremes are increasing…


  40. 40
    Edward Greisch says:

    Note that the last graph has its own RealClimate post at:

    Question: How far away from the poles can Rossby waves have an effect?

  41. 41
    Chris Dudley says:

    Larry (#9),

    Northern Hemisphere winter has a broader range of variability than Northern Hemisphere summer. Fig. 2 here: shows this. So, the variability depends on season. In the same paper, it is shown that 3 sigma summer seasons are covering a larger fraction of the surface of the earth than they used to. The next step would be 4 sigma perhaps. Let’s place that where sigma is 1 C. And lets have a three week heatwave be what makes the summer so warm. Then the heatwave will be about 16 C above normal. If normal is about 23 C then we’d be at about 39 C or 102 F, quite a lot for the Midwest. 115 F is the hottest ever recorded for St. Louis. If you pack the offending heatwave into 2 weeks, you can hit that record for the duration.

  42. 42
    MIke Cope says:

    I stumbled upon the following, from a primer on entropy by Rishidev Chaudhuri and Jason Merrill

    “Adding more energy to a system usually increases the number of states available to it. This is both because with more packets of energy there are more ways to distribute them between the members of a system, and because more energy makes high energy states accessible in addition to lower energy ones.”

  43. 43
    GSW says:

    It’s a mammoth task I know, but has anyone ever published a study on the spectrum of record Hot and Cold events, either for the US or Globally, say over the last 100yrs?

    It would be satisfying to get some confirmation of the theory vs real world data.

    At the moment these records are very anecdotal and the significance attributed to them is very short lived. Over the last few years there have been regionally significant 100yr Cold events (as well as Hot) recorded in both Russia and China for example. Each event stands on it’s own however, without context, has anyone ever tried to the analysis?

  44. 44
    Dan H. says:

    The variability in the Hansen paper has not change; it is simply that the mean has moved. Scrolling down each column of graphs in Fig. 1, the average JJA temperature has increased by ~0.65C (more than one sigma higher according to Hansen). Therefore, sigma events should be calculated for the new mean, not the old (using a similar mean, 3-sigma events such be occurring at the same rate as 2-sigma events did 50 years ago). The standard deviations have not changed shape over the past three decades, only shifted higher by one sigma (Fig. 9).

    Hansen does show support for our statements that the recent warming experienced in the Midwest is much more likely to occur in winter than summer due to “the huge difference of temperature between low latitudes and high latitudes in winter. This allows the temperature at a given place to vary by tens of degrees depending on whether the wind is from the south or north.” Similar to Jim’s statement about lower standard deviation in the summer.

  45. 45

    #42–That seems quite insightful–a really good summary comment.

    Warning: random, uninformed musings ahead!

    The counterargument in terms of climate would seem to be the notion that the temperature gradient between poles and tropics is supposed to lessen, due to ‘polar amplification.’ Intuitively, you’d think that that would mean fewer energetic ‘states.’ But maybe not?

    It also occurs to me that these blocking events–and even more so the phenomenon of the WACCy winters, seen in 2009 and 2010, with “Warm Arctic, Cold Continents”–represent atmospheric mixing in action, essentially. So, maybe part of the process leading toward those lessened temperature gradients?

  46. 46
    Ray Ladbury says:

    It is not that I despair of identifying “change,” but rather of identifying it in precisely the portion of the pdf we know least well. A one in 10 billion year event has finite probability of being realized for both the original and the changed pdf. How would we tell the difference between them? How would we know that a one in 10 billion year event for the original distribution corresponds to a one in a billion year event for the changed pdf? This is why good actuaries are so well paid–it’s more an art than a science.

    [Response:Ray, I agree that distinguishing those two states would be essentially impossible with any real world climate data of any relevance. It’s always going to be more difficult to identify changes in the tails compared to some measure of central tendency, I get that. And in a system where you have ~continuous change, rather than a definite step from one stable equil. state to another, you have complications in determining what the two relevant distributions to compare are exactly (though I think that’s a relatively minor issue). But you do need some decent idea of the shape of the original state’s distribution, including the tails. If you then have evidence that includes (1) a shift in the central tendency and (2) increasingly frequent observations of events going over x sigma, over some decent sample of space or time or both and based on the best estimated shape of the original distribution, then it is at the very least, reasonable to assume that the former tails have shifted +/- in concert with the rest of the distribution; that is to say, the entire original distribution has shifted. If the central tendency does not appear to have shifted, but some other higher moment has changed, say an increase in the variance, then you’re into deeper water I imagine, but still approachable given a decent sample size I would argue. So yes, you don’t know the changes in the tails with the same confidence as the middles, and you never will, but you can have some pretty strong and defensible clues based on the totality of the evidence coming from the estimated changes in various parameters of the distribution. And also, we are dealing with events that are much more probable than your example–1 in 200 years say or similar orders of magnitude. That’s how I look at this issue.–Jim]

  47. 47
    Paul S says:

    Northern Hemisphere winter has a broader range of variability than Northern Hemisphere summer.

    One good way to see this is in the HadCET (Central England) annual cycle. Note the percentile ranges are considerably broader in Winter compared to Summer.

    One further point of interest here is the min and max annual cycles. There is sharp drop in maximum temperature after Summer but the the change in minimum temperatures is on average pretty slow and highly asymmetric.

  48. 48
    grypo says:

    Andy Revkin referring to this as a “viewpoint” piece that has been “countered” by Wallace is just wrong. What Wallace is saying is that discussing extremes and man-influenced climate is fear-mongering and therefore we should stress something else. He’s also saying that “opponents” can exploit the inability of exact attribution statistically.

    In other words, shut up scientists, you’re messing up Revkin’s environmental narrative.

  49. 49
  50. 50
    Chris Dudley says:


    Thanks for that link.

    This bit seems out of date with regard to heatwaves:

    “Even in the presence of climate change,
    extreme events do not occur often
    enough to enable scientists to track
    decade-to-decade changes in their sta-
    tistics in real time, as they successfully
    do with more aggregated quantities
    such as global mean temperature and
    sea level [Palmer and Räisänen, 2002]

    “Realtime” treatment given recently by Hansen et al. seems to answer, and also for the prior bullet’s mention of Russia’s heatwave.

    It seems to me that it is a mistake when writers bundle together events with varying levels of attributional certainty. Heatwaves are more certain than deluges which may be more certain than droughts. But too often tornadoes or hurricanes are included, called uncertain and that uncertainty applied backwards to the whole list. Grammatically it may be correct, but procedurally it isn’t. Not saying there is that much bundling going on here, but there is some.

    I also seem to spy a strawman. Discussing attribution, is not the same as taking extreme events as indicators that warming is occurring. We start with the problem of attribution, these events are not signs as in a Shakespeare tragedy. The warming is already measured, these extreme events are expected consequences.