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Extreme metrics

Filed under: — gavin @ 18 August 2012

There has been a lot of discussion related to the Hansen et al (2012, PNAS) paper and the accompanying op-ed in the Washington Post last week. But in this post, I’ll try and make the case that most of the discussion has not related to the actual analysis described in the paper, but rather to proxy arguments for what people think is ‘important’.

The basic analysis

What Hansen et al have done is actually very simple. If you define a climatology (say 1951-1980, or 1931-1980), calculate the seasonal mean and standard deviation at each grid point for this period, and then normalise the departures from the mean, you will get something that looks very much like a Gaussian ‘bell-shaped’ distribution. If you then plot a histogram of the values from successive decades, you will get a sense for how much the climate of each decade departed from that of the initial baseline period.

Fig 4a, Hansen et al (2012)

The shift in the mean of the histogram is an indication of the global mean shift in temperature, and the change in spread gives an indication of how regional events would rank with respect to the baseline period. (Note that the change in spread shouldn’t be automatically equated with a change in climate variability, since a similar pattern would be seen as a result of regionally specific warming trends with constant local variability). This figure, combined with the change in areal extent of warm temperature extremes:

fig 5, hansen et al (2012)
are the main results that lead to Hansen et al’s conclusion that:

“hot extreme[s], which covered much less than 1% of Earth’s surface during the base period, now typically [cover] about 10% of the land area. It follows that we can state, with a high degree of confidence, that extreme anomalies such as those in Texas and Oklahoma in 2011 and Moscow in 2010 were a consequence of global warming because their likelihood in the absence of global warming was exceedingly small.”

What this shows first of all is that extreme heat waves, like the ones mentioned, are not just “black swans” – i.e. extremely rare events that happened by “bad luck”. They might look like rare unexpected events when you just focus on one location, but looking at the whole globe, as Hansen et al. did, reveals an altogether different truth: such events show a large systematic increase over recent decades and are by no means rare any more. At any given time, they now cover about 10% of the planet. What follows is that the likelihood of 3 sigma+ temperature events (defined using the 1951-1980 baseline mean and sigma) has increased by such a striking amount that attribution to the general warming trend is practically assured. We have neither long enough nor good enough observational data to have a perfect knowledge of the extremes of heat waves given a steady climate, and so no claim along these lines can ever be for 100% causation, but the change is large enough to be classically ‘highly significant’.

The point I want to stress here is that the causation is for the metric “a seasonal monthly anomaly greater than 3 sigma above the mean”.

This metric comes follows on from work that Hansen did a decade ago exploring the question of what it would take for people to notice climate changing, since they only directly experience the weather (Hansen et al, 1998) (pdf), and is similar to metrics used by Pall et al and other recent papers on the attribution of extremes. It is closely connected to metrics related to return times (i.e. if areal extent of extremely hot anomalies in any one summer increases by a factor of 10, then the return time at an average location goes from 1 in 330 years to 1 in 33 years).

A similar conclusion to Hansen was reached by Rahmstorf and Coumou (2011) (pdf)) but for a related but different metric: the probability of record-breaking events rather than 3-sigma events. For the Moscow heat record of July 2010, they found that the probability of a record had increased five-fold due to the local climatic warming trend, as compared to a stationary climate (see our previous articles The Moscow warming hole and On record-breaking extremes for further discussion). An similarly concluded extension of this analysis to the whole globe is currently in review.

There have been been some critiques of Hansen et al. worth addressing – Marty Hoerling’s statements in the NY Times story referring to his work (Dole et al, 2010) and Hoerling et al, (submitted) on attribution of the Moscow and Texas heat-waves, and a blog post by Cliff Mass of the U. of Washington. *

*We can just skip right past the irrelevant critique from Pat Michaels – someone well-versed in misrepresenting Hansen’s work – since it consists of proving wrong a claim (that US drought is correlated to global mean temperature) that appears nowhere in the paper – even implicitly. This is like criticising a diagnosis of measles by showing that your fever is not correlated to the number of broken limbs.

The metrics that Hoerling and Mass use for their attribution calculations are the absolute anomaly above climatology. So if a heat wave is 7ºC above the average summer, and since global warming could have contributed 1 or 2ºC (depending on location, season etc.), the claim is that only 1/7th or 2/7th’s of the anomaly is associated with climate change, and that the bulk of the heat wave is driven by whatever natural variability has always been important (say, La Niña or a blocking high).

But this Hoerling-Mass ratio is a very different metric than the one used by Hansen, Pall, Rahmstorf & Coumou, Allen and others, so it isn’t fair for Hoerling and Mass to claim that the previous attributions are wrong – they are simply attributing a different thing. This only rarely seems to be acknowledged. We discussed the difference between those two types of metrics previously in Extremely hot. There we showed that the more extreme an event is, the more does the relative likelihood increase as a result of a warming trend.

So which metric ‘matters’ more? and are there other metrics that would be better or more useful?

A question of values

What people think is important varies enormously, and as the French say ‘Les goûts et les couleurs ne se discutent pas’ (Neither tastes nor colours are worth arguing about). But is the choice of metric really just a matter of opinion? I think not.

Why do people care about extreme weather events? Why for instance is a week of 1ºC above climatology uneventful, yet a day with a 7ºC anomaly is something to be discussed on the evening news? It is because the impacts of a heat wave are very non-linear. The marginal effect of an additional 1ºC on top of 6ºC on many aspects of a heat wave (on health, crops, power consumption etc.) is much more than the effect of the first 1ºC anomaly. There are also thresholds – temperatures above which systems will cease to work at all. One would think this would be uncontroversial. Of course, for some systems not near any thresholds and over a small enough range, effects can be approximated as linear, but at some point that will obviously break down – and the points at which it does are clearly associated with extremes that with the most important impacts.

Only if we assume that the all responses are linear, can there be a clear separation between the temperature increases caused by global warming and the internal variability over any season or period, and the attribution of effects scales like the Hoerling-Mass ratio. But even then the “fraction of the anomaly due to global warming” is somewhat arbitrary because it depends on the chosen baseline for defining the anomaly – is it the average July temperature, or typical previous summer heat waves (however defined), or the average summer temperature, or the average annual temperature? In the latter (admittedly somewhat unusual) choice of baseline, the fraction of last July’s temperature anomaly that is attributable to global warming is tiny, since most of the anomaly is perfectly natural and due to the seasonal cycle! So the fraction of an event that is due to global warming depends on what you compare it to. One could just as well choose a baseline of climatology, conditioned e.g. on the phase of ENSO, the PDO and the NAO, in which case the global warming signal would be much larger.

If however, the effects are significantly non-linear then this separation can’t be done so simply. If the effects are quadratic in the anomaly, a 1ºC extra on top of 6ºC, is responsible for 26% of the effect, not 14%. For cubic effects, it would be 37% etc. And if there was a threshold at 6.5ºC, it would be 100%.

Since we don’t however know exactly what the effect/temperature curve looks like in any specific situation, let alone globally (and in any case this would be very subjective), any kind of assumed effect function needs to be justified. However, we do know that in general that effects will be non-linear, and that there are thresholds. Given that, looking at changes in frequency of events (or return times, as is sometimes done), is more general and allows different sectors/people to assess the effects based on their prior experience. And choosing highly exceptional events to calculate return times – like 3-sigma+ events, or the record-breaking events – is sensible for focusing on the events that cause the most damage because society and ecosystems are least adapted to them.

Using the metric that Hoerling and Mass are proposing is equivalent to assuming that all effects of extremes are linear, which is very unlikely to be true. The ‘loaded dice’/’return time’/’frequency of extremes’ metrics being used by Hansen, Pall, Rahmstorf & Coumou, Allen etc. are going to be much more useful for anyone who cares about what effects these extremes are having.


  1. J. Hansen, M. Sato, and R. Ruedy, "Perception of climate change", Proceedings of the National Academy of Sciences, vol. 109, pp. E2415-E2423, 2012.
  2. J. Hansen, M. Sato, J. Glascoe, and R. Ruedy, "A common-sense climate index: Is climate changing noticeably?", Proceedings of the National Academy of Sciences, vol. 95, pp. 4113-4120, 1998.
  3. S. Rahmstorf, and D. Coumou, "Increase of extreme events in a warming world", Proceedings of the National Academy of Sciences, vol. 108, pp. 17905-17909, 2011.
  4. R. Dole, M. Hoerling, J. Perlwitz, J. Eischeid, P. Pegion, T. Zhang, X. Quan, T. Xu, and D. Murray, "Was there a basis for anticipating the 2010 Russian heat wave?", Geophysical Research Letters, vol. 38, pp. n/a-n/a, 2011.

158 Responses to “Extreme metrics”

  1. 51
    Mike Roddy says:

    Cliff, #44:

    You are not entering the lions’ den, but are rather participating in a world of very bright scientists. Your claim that Hansen failed to establish a link between hot summers and global warming- something he established through temperature readings and detailed statistical variance analysis- is false.

    Sorry, Cliff, we don’t have time for chumps here, especially the verbose kind, who have just enough knowledge to get in a lot of trouble.

  2. 52
    John E. Pearson says:

    48 John Pollack: I always believed it was an actual occurrence. It was an incredible story. Her story didn’t take place in the 30’s though. She wrote the books long after the events.

  3. 53
    Rick Brown says:

    Cliff Mass at 44: “the definition of deceptive is:
    ‘Giving an appearance or impression different from the true one'”

    That’s it? Apparently you didn’t look very hard, but I guess that’s not too surprising.

    Here’s what I find, with the briefest of looks:

    concealment or distortion of the truth for the purpose of misleading; duplicity; fraud; cheating

    Deliberately misleading; deceptive. See Synonyms at dishonest

    intended to deceive; misleading; fraudulent

  4. 54
    Edward Greisch says:

    Sigmas: Most people THINK they understand statistics. But Prob& Stat class was a real shock. I came out a different person.

  5. 55

    #44 cliff mass

    I will agree with you that most don’t really understand ‘3 sigma’. I know I’m not a math or statistics expert.

    But is a science paper the best place to ‘not’ use scientific language, or maybe it’s okay in science papers to be scientific and then to have folks such as yourself, talking to a non scientific audience, explain what it means using relatable percentages, such as the ‘roll of the dice’ analogy (which really isn’t that bad because it is relatable).

    re. “Hansen had no basis to say confidently that last summer’s heat wave was caused by global warming”

    This is where I get confused.

    Are you saying that loading the climate system with 29 ZJ (increased RF) of energy every year or that the cumulative effects of increasing the loading over time, say more than a century, would not increase the odds of having heat waves?

    Are you saying that all heat waves that are occurring right now are not occurring in a system loaded with said extra energy?

    If so, upon what scientific basis? And if per chance your going to bring up the ‘Iris Hypothesis’ I would remind you that it has not been indicated as having significance in the available data and there are many reasons to doubt the strength of said self regulating mechanism such as: data indicates it ‘has’ been warmer in the past.

    So upon what confidence do you base such a ‘claim’ that the enhanced greenhouse effect is not influencing heat waves right now?

    Let me put it this way. Let’s say you are in a car, in the back seat, and the driver is heading south down highway 5. Are you saying it’s okay for you to claim without evidence that since you are not in agreement that the car is heading south on highway 5, such a fact/observation is specious? You might think the car is headed east, but thinking such does not make it so.

    It’s true you are entitled to your own opinion, but you are not entitled to your own facts no matter how many times you tap your heals and wish the increased radiative forcing is not influencing heat waves.

    The null hypothesis has been reversed. Can you prove that current extremes in heat waves are not human influenced?

    That is something I would like to see. There’s a reasonably old saying don’t try to remove the splinter from your brothers eye until you remove the log from your own.

    The gauntlet has been laid at your feet and you asked for it. Prove your point. It’s the ‘Chicago Way’. If Hansen makes a claim and you can show it is wrong, do it. But do it though scientific comment and the relevant peer review, not an email to Anthony Watts. It doesn’t make you look as good as you might think, even though you do get a lot of folks over there fawning over you. Whether you realize it or not, over there, you are fanning the flames of ignorance.

  6. 56
    Craig Nazor says:

    The concept of sigma as it relates to a bell curve is not a difficult concept. The name assigned (“sigma”) may be outside of normal everyday conversation, but the concept is not. If we hold our discourse to only what others can already understand, how will anyone learn anything? Humans can only make intelligent decisions about new phenomena by learning more about them.

    You state: “Hansen had no basis to say confidently that last summer’s heat wave was caused by global warming…” Well, Hansen didn’t actually say that – he was much more specific about to what heat wave he was referring. And he put forward a very good argument for his statement, supported by some relatively simple, understandable math. Your statement above, on the other hand, has no such support. That type of logic is the kind of support that is required if you wish to be taken seriously in the lion’s den.

    I live in central Texas. Last year’s heat wave was exceptional – and the drought associated with it is really not over. The entire state is having to reassess its water resources, and those numbers are all down. In some areas of the Texas Hill Country that I drove through yesterday, over 50% of the trees are dead. It is very real to us, and, believe me, people are paying very close attention.

  7. 57
    michael sweet says:

    You need to keep in mind that Hansen’s paper was published in PNAS. He used sigmas for a scientific audience. Hansen has publicly used the dice analogy to assist people to understand the concept. Here is a non-technical discussion of what sigmas mean.

    You have not provided any data to support your wild claim that the annual average temperature change has a relationship to the temperature change in extreme events.

    Hansen’s work is peer reviewed. Your work has been widely panned by scientists. Why should I listen to your unsupported opinions?

    You still do not mention your uncertainty when you discuss this subject, which is deceptive.

  8. 58
    cynicus says:

    Dutch climatologists Van Oldenborgh & De Laat who were recently quoted in a local newspaper (Volkskrant, August 11) saying:
    A) that Hansen is too easily assuming that temperatures are distributed in a Bell curve.
    B) that the climatological period 1951-1980 saw exceptionally few heatwaves.

    It is suggested that these critiques have significant effects on the paper’ outcome.

    Can anyone comment?

    [Response: The first is neither are true nor material. The incidence of 3 sigma + events in any one decade is independent of what might be the best fit to the distribution and the Gaussian approximation doesn’t come into any of the calculations above. The second is the basic result – but it is only a relative statement. The number of heat waves (as defined above) was only slightly higher in earlier decades, but has become significantly much higher recently. – gavin]

  9. 59
    J Bowers says:

    There’s no secret to success, there’s only a secret to failure: trying to please everyone.

  10. 60
    ralbin says:

    Prof. Mass – if you’re still participating. I can’t agree with your assessment that your proposed approach is the best way to communicate this type of information. You cite your personal experience in giving talks to lay audiences. I’m a physician-scientist with an active clinical practice. Issues of shifting probability distributions – disease risk factors, differential effects of competing treatments, natural history of disease – are common features of clinical practice. While I don’t use the term sigma in my practice (except when seeing engineers as patients and they usually raise the term), many, many patients have little difficulty in grasping verbal analogues of the type of analysis presented in the Hansen paper. Now, it may be that patients concentrate harder when the questions involved relate to their health than when attending talks on climate science but the Hansen-type approach is, in my experience, readily grasped by individuals from a variety of educational backgrounds.

  11. 61

    44 Cliff Mass

    “Folks…I know I am entering the lion’s den talking in this forum, but Hansen had no basis to say confidently that last summer’s heat wave was caused by global warming. …cliff”

    Right! The entire NH warms and there is no basis for Global Warming. Strong compelling nonsense. RC is not a Lion’s den but rather a reality check place, you will not get away with blank meaningless statements here.

  12. 62

    “(e., g., a catastrophic, 9-sigma event). ”

    A 7 sigma event would occur once in a 1.8 billion years. I can’t find reference to an 8 sigma event. It looks like one in 1.5 trillion. But even a 6 sigma event (1 in 6.5 million years) seems to me to be more exotic than meaningful. Milankovich cycles drastically change climate over a span of ~150,000 years so a 5 sigma event (1 in 58,000 years) is probably as rare as things can get.

    As for the Missouri farmer who dismissed AGW and blamed the heat on God, it’s interesting the number of people who don’t know math but who do know the mind of The One who Is.

  13. 63
    cliff mass says:

    Let’s try a different approach.

    Heat waves have an origin. They are the superposition of a background field and the effects of the upper atmospheric wave pattern. Generally heat waves, like the ones in the Midwest this year and last, are usually associated with high amplitude and persistent ridging. Now it is clear that GW can increase the background field—but the amplitude so far in the midlatitudes is modest (0 to 2 F perhaps, considering where you are). More in the Arctic. The background does not explain the amplitude Midwest heat waves. But there was clearly high amplitude and persistent ridge during the recent events. Now the question then becomes—is the excessive ridging the last two summers the result of GW? Was the large scale flow pattern somehow enhanced by GW? There is no reason to expect this…either from modeling or theoretical results. So the conclusion we must draw is that these events were mainly from natural variability.

  14. 64
    afeman says:

    The argument seems to be that attribution is spurious, and poorly communicated. The food is terrible and the portions small….

  15. 65
    David Lewis says:

    Does anyone know why PNAS editors required Hansen to drop any reference to “climate dice” in the title of this paper?

    Hansen has repeatedly drawn attention to the fact that his choice for a title included “climate dice”, e.g.: “the publishers eliminated that phrase from the paper’s title”, and “we were not allowed to keep Climate Dice in the title”.

  16. 66
    Ray Ladbury says:

    Ultimately, I think that what Cliff Mass fails to comprehend is that whether one is talking about “global mean” or “sigma”, one is talking summary statistics for a distribution. Merely saying that the mean has shifted by “x” is surely as potentially misleading as looking at the occurrence of 3 “sigma” events.

    If Cliff is truly interested in keeping things grounded in “physical reality,” then what matters are the extreme events, as these tend by far to cause the greatest damage. As risk is the product of probability of an event and its consequences, both the probability and the consequences are important.

    I do not agree that we must dumb down our discussion to the point where a high school dropout or an MBA could understand it.

  17. 67
    John E. Pearson says:

    I just saw this bit of stefan’s which was added some time later than Gavin’s response to Clifford Mass’s post 16. It’s worth repeating.

    [Response:I fully agree with Gavin, but here is an added simple point: if you prefer a temperature value rather than sigma, you could do the same analysis using the global mean of the sigma value (which is 0.6 degrees celsius). I.e., instead of plotting how often 3-sigma anomalies occur, you could plot how often anomalies exceeding 1.8 degrees occur. You’d get almost the same result as Hansen et al. Doing it that way would just be less sophisticated and informative, because in some places 1.8 degrees would just by nature of the local natural variability be exceeded much more easily than in some other places, so using that kind of threshold would not be as “fair” and even-handed as the 3-sigma threshold. -stefan]

  18. 68
    Charles Stanton says:

    Gavin’s reply at 58:
    “The first is neither are true nor material. The incidence of 3 sigma + events in any one decade is independent of what might be the best fit to the distribution and the Gaussian approximation doesn’t come into any of the calculations above.”

    I assume the “are” is a typo, but even without this statement is a bit difficult to parse. Certainly a non-Gaussian distribution will have different probabilities. For 3 sigmas, the best that can be said for a general distribution is that the probability is between 0 and 1/9 (Chebyshev). Even if the distribution is fairly close to Gaussian, I would not be surprised if the probabilities for 4+ sigma events to be considerably larger (“heavy tails”) than Gaussian probabilities.

  19. 69

    Professor Tony O’Hagan has just published online a summary of a discussion that occurred (raged?) at the International Society for Bayesian Analysis regarding the evidence for the Higgs Boson, and statistical means for demonstrating it. This is a follow-on to the references I posted at #35.

    This paper is available at

    It is interesting that while the Higgs is “new physics”, and demands experimental confirmation, climate change prediction and explication is the application of really well understood physics, by experiment, theory, and in engineering, albeit to complicated systems. To the degree to which sheer system complexity cannot cause conservation of mass and energy to be violated, climate change is inevitable and there is, to me, a strong sense in which Professor Trenberth’s case that if physics is true, that climate change must be so, and that must be here is just being consistent. (I’m paraphrasing and mistakes or distortions are my responsibility.) Hence, the idea of “demonstrating climate change” is a distraction. That’s because the point seriously asks what are we trying to do? Show that climate change’s effects exist contingent upon physics being wrong?

    Still I imagine that confirmation of effect, per Hansen, Sato, and Ruedy is a natural exercise, even if what’s available to be measured is an acceleration in the change, not before-and-after.

  20. 70
    M.F. Walther says:

    (@cynicus; Re: #58)
    I did recently some statistical experiments with temperature series. I looked at the GISS global temperature data (1880-2011), estimated a quadratic trend (R=0.91), removed the trend from the data and looked for the distributions of the residuals. The distribution is a nearly perfect example for a normal distribution as shown by a quantil-quantil-plot.

  21. 71

    Re: #63 (Galkowski)

    The paper by Professor Trenberth that makes this point is available at:

  22. 72
    Aaron Lewis says:

    Essentially, a 6-sigma (or higher) event means that the statistical baseline was in one system and very rare event means that the system is “out of control”. The system has inherently changed. See the work of Dr. Ed. Deming

    This summer’s North American drought is not that rare an event. Last winter’s South American drought was not that rare an event. Now, what are the odds that there will be another drought this year in SA? What are the odds that there will be another drought next year in NA next year?

    If we use the baseline data from the 20 th Century, then the odds of droughts in 4 successive agricultural crop seasons is near zero (eg 9 -sigma). However, if the loss of Arctic Sea ice has significantly changed global atmospheric circulation patterns, then we are dealing with a different system that has only been in existence since 2007, and we do not know how often to expect crop failures.

    Our agricultural production system is closely linked to the climate as we knew it in the 20 th century (and the 2,000 previous years). It the climate has gone out of control, then the results are likely to be bad for agriculture.

    Would somebody here, like to explain to me how we can lose Arctic Sea ice (in part or in whole) without changing the atmospheric circulation patterns? If reduced sea ice is changing circulation patterns, then we may have what a 20 th century weatherman would call a 9-sigma event every year. These are events that did not, and could not, happen in the old weather system.

    (In the course of the Milankovich cycles, the system changes, so one would either consider the variance in the system over the entire cycle, in which case the whole cycle is in control and at ~one-sigma; or, one would break system cycle up into shorter segments and look at the variance during those limited periods. If we look at the period from 1,000 to 2,000 CE, the weather was rather stable compared to the last 5 years.)

    Both IBM and Motorola insisted that I take Ed’s course on statistics and systems. So, I took it twice and passed it each time. However, my grandfather was a framer from the “Show me”! state

    Ladies and Gentlemen, we have a new weather system.

  23. 73

    “’s interesting the number of people who don’t know math but who do know the mind of The One who Is.”

    Yes, I’m often struck by such instances. False humility often conceals real arrogance… but I suppose that way lies OT Land.

  24. 74
    Unsettled Scientist says:

    Cliff Mass wrote > Folks…I know I am entering the lion’s den talking in this forum, but Hansen had no basis to say confidently that last summer’s heat wave was caused by global warming. …cliff

    He didn’t. You are being deceptive. Let’s actually quote what Hansen et al wrote.

    “It is not uncommon for meteorologists to reject global warming as a cause of these extreme events, offering instead a meteorological explanation. For example, it is said that the Moscow heat wave was caused by an extreme atmospheric “blocking” situation, or the Texas heat wave was caused by La Niña ocean temperature patterns. Certainly the locations of extreme anomalies in any given case depend on specific weather patterns. However, blocking patterns and La Niñas have always been common, yet the large areas of extreme warming have come into existence only with large global warming. Today’s extreme anomalies occur as a result of simultaneous contributions of specific weather patterns and global warming.”

    You see that detail Cliff? Hansen was talking about extreme events in general, not just last summer’s heat wave, and he clearly states the cause to be both specific weather patterns and global warming. What you wrote gives “an appearance or impression different from the true one.”

    This is only a lion’s den if you are here to misrepresent the literature, because here we actually read the primary sources. I’m sure elsewhere on the internet that claim you made is taken at face value as true, when clearly it is not. Details matter.

  25. 75
    sidd says:

    Prof. Mass seems disingenuous.

    1)Using distributions and sigmas is perfectly valid for a paper in PNAS aimed at an audience of scientists, who presumably are familiar with mathematical language. Are we to understand that all higher math is stripped from papers written by Prof. Mass ? A brief review shows this is not the case. So why does he attack Hansen for doing the same as he does ? If Hansen is to be branded deceptive, what shall we call Prof. Mass ?

    2)Hansen makes the case for increasing recurrence frequency of high temperatures in NH JJA. The argument is not about any single hot NH JJA, or the temperature of any particular NH JJA. This is important. Farmers, farming practices, indeed entire societies, have evolved in a climatology where a killing summer heat devastates more than a fraction f of yield every M years. Now the same society is subject to that killing heat destroying fraction f of the crop every M/10 years. The logic is simple, can the farmer or the society thrive or even survive when a heat wave that came one year in fifty year now comes once in five ?

    3)From the first graph on this post, it seems that the distribution has broadened, and more to the right (Prof. Rabett has pointed this out before), while moving to the right by 1 sigma. If the shape were unchanged, we would expect that the probability of a n sigma event for the baseline (1951-1980) would be the same as the probability of an (n+1) sigma event for 2001-2011. Not so, the latter is larger, the extreme heat events are coming more frequently than a simple shift in the distribution would calculate. This adds to my concerns raised in point 2) above.


  26. 76
    MARodger says:

    @44 Cliff Mass makes an issue of use of the word “bizarre” in an up-thread Response yet makes light of his own calling folk “deceptive.” Of course, there is a difference between a deceptive word and a deceptive person. But Cliff Mass makes plain he is playing the man not the ball when in his Aug 9 Blog Post he talks of the “…exaggerations of Hansen and his fellow travelers… …it is much worse that that.” “Let me prove to you now that Dr. Hansen’s claims are deceptive.

    And do we see here even in this one Blog Post of his, the dirty old pot calling the shiny electric kettle black? I think we do.
    Under a graphic in his Blog Post showing how easily it is for a tenfold increase in “extreme hot weather” to occur, Mass concludes “So the result is that you seem more warm temperature records and less cold temperature records. We are in fact seeing this. The earth is warming and there are more maximum temperature records than cold ones. Hansen and friends make a big deal about this.” (My emphasis.) The word “hot” appears to have slipped form Mass’s vocabulary.

    And his concluding assertion does make the attribution of extreme weather a serious issue, not something to dismiss out of hand as Mass appears to want happen. “Lets be clear here. Although the global warming signal is relatively weak today in most of the planet (outside of the Arctic), our best science indicates that the warming will greatly increase by the end of the century.” So if Texas 2011 was attributable to AGW (as Mass asserts it isn’t but with little supporting evidence), this intensity of event will have been relatively weak compared with what we should expect in the coming century.

    Cliff Mass has gone into the same argument prior to his Aug 9 piece. On July 29th he discussed climate extremes using the analogy of the 2011 Japanese tsunami to represent natural extreme weather & 10 centimetres of sea level rise to represent the AGW signature. He mentions this because folk are “twisting” the situation so as “…to make the case that global warming is making the weather more extreme. They cite the latest weather/climate disasters as proof: the current heat wave/drought in the Midwest, the Russian Heat Wave of 2010, the Hurricane Katrina in 2005, the list is endless. And headline-thirsty media are happy to amplify this message, to the detriment of their readership. ” (His emphasis.)
    Some organizations, like Climate Central and extremists like Bill McGibben, hype every major weather anomaly as proof of the profound effects of human-induced global warming. ” “They believe by hyping the relatively small impacts during the past few decades that they can motivate people to act. A lie for a good cause.” (My emphasis.) “If you believe in the seriousness of global warming in the future, it is essential to stick to the truth.

    And earlier again, Mass blogged on July 15th about Rupp et al 2012, ‘Did human influence on the climate make the 2011 Texas drought more probable?’ (on page 12 of link) saying “The trouble is that this study is flawed (I will explain why) and its scary conclusions are insupportable. This is important story: about the hyping of global warming, about poor research being published, about the media jumping on sexy, scary global-warming stories. And most worrisome of all..this is not an isolated incident.” (My emphasis.)

    Of course Mass may feel that a linear regression of average Texas summer temperatures since 1895 provides conclusive evidence for his case that AGW is currently far too weak to play a significant role in the Texas 2011 heatwave (an argument he recycles in his Aug 9 blog post), but it is strange Mass picks on Rupp et al 2012 without mentioning Massey et al 2012 in the same collection of papers that similarly finds AGW impacts in excess of Mass’s method (3 times in excess by my calculation).
    Cliff Mass presents arguments so utterly foolish that I have elsewhere called him a fool. The more I read of his work on this subject, the more I consider that my statement may have been fully justified.

  27. 77
    RobLL says:

    Actually to understand Cliff Mass’s web site it would help to have had an introductory year on weather or climate. I have had neither, but I like his site on Northwest weather for precisely that reason. It stretches my understanding. He has not addressed the question of how much global warming is locked in at current and likely CO2 emission levels, and oddly attacks people like Gore and Krugman who have accepted common projections.

  28. 78
    Susan Anderson says:

    Ray Ladbury @~64
    If we are looking for a layperson’s explanation, available to the untutored like myself, you’ve done it. Thanks.

    whether one is talking about “global mean” or “sigma”, one is talking summary statistics for a distribution. Merely saying that the mean has shifted by “x” is surely as potentially misleading as looking at the occurrence of 3 “sigma” events.

    … what matters are the extreme events, as these tend by far to cause the greatest damage. As risk is the product of probability of an event and its consequences, both the probability and the consequences are important.

  29. 79
    Douglas says:

    I read Mass’ blog regularly, and when he sticks to Pacific NW weather it’s a great read. I also thought he made some legitimate points about flaws in the Rupp/Mote study, though his presentation was way too acerbic for my tastes.

    Which leads to my criticisms: why he resorts to such over-the-top hyperbole re climate change “deception” is beyond me. Especially when he doesn’t (can’t?) back it up.

    For instance his comments on this post mainly have to do with presenting the data in a way that the general public will understand. A topic reasonable people can disagree on. But if you read Mass’ blog post and follow-up comments there it’s clear he doesn’t think the Hansen paper is suitable even for other scientists. I.e. it shouldn’t have been published to begin with. Needless to say that’s a very serious criticism of a fellow scientist, requiring a much greater burden of proof than anything he’s presented so far.

  30. 80

    I have a naive question about the first figure you use from the Hansen paper. Is there any simple way that doesn’t do violence to the data to plot temperature on the x-axis instead of standard distributions? I’d like to link the Hansen graph to the nice schematic graph that came from the University of Arizona (and they adapted it from the IPCC, I believe). The conceptual graph with temperatures on the x-axis is shown here ( and here (

    Your collected wisdom would be most appreciated.

  31. 81
    Toby Thaler says:

    Responding to comments 14, 25, and 56: I’m a policy analyst in Seattle, well-read on the impacts of climate change, but also other global resource constraints–like peak oil, peak phosphorus and the limits of industrial agriculture, waters supply (closely related to climate), and human systems/governance. I have lived and breathed forests, fish, and water issues in the Pacific NW for many years. (Cf. the work of EPA scientist Robert Lackey (Portland OR) on the interactions between population, governance/growth management policies, and salmonids.

    For years I have pressed my local governments to consider the very real limits to growth, with little success notwithstanding the clear degradation of the natural habitat and human quality of life in the region. Further, I have had to temper my lobbying with the realization that even if overall population stopped growing tomorrow, many could move from one place to another (America still being a democracy in terms of freedom of movement).

    Recently, it has become clear to me that global climate change (warming) is another looming force that will upset advocacy for more effective growth management in the PNW. All projections I’ve seen (e.g., UW CIG) indicate this region will remain pleasantly habitable for people for longer than other areas (think Texas, Oklahoma, Arizona) under the pressure of increasing numbers and extremes of weather “anomalies.” (Western Washington has the lowest annual insolation in the continental U.S.) In other words, we are likely to be the recipient of many climate refugees in coming decades, and we should start preparing for them. Unfortunately, I see that preparation happening about the same time as Aaron Lewis (#25) says we’ll deal with AGW generally—when it bites us in the ass.

    Regarding whether those ignorant in statistics can understand Hansen’s latest papers, I’m a perfect test case: My knowledge of stats is low (if I had ever heard the term “sigma” before, I don’t recall it), and only have a basic humanities major’s ability to grasp scientific arguments (well, maybe a little better since I work with scientists as expert witnesses). I would not have raised my hand in the audience Mass asked about knowledge of “sigma.” But that doesn’t mean I don’t get Hansen’s point. I’ll paraphrase what I think he said, and you all who know better can judge whether I “got it right”:

    The number of extreme summer heat events has increased (at least in the Northern Hemisphere) in recent decades; they now occur about ten times more often (i.e., increase from c. 1% to c. 10% of the time/area) than during the base period(s) of the early/mid Twentieth Century. Because these events were rare before human GHG emissions forced more energy (heat) into the atmosphere, it is reasonable to conclude that AGW is responsible for (is the cause of) the most extreme events.

    Is that close? I did it without rereading the abstract. The temporal and/or spacial extent of the increase is a little unclear to me…

  32. 82
    afeman says:

    Here’s a disturbing thought — it appears that over the past 30 years the distribution has shifted roughly up one sigma, so that what was 3 sigma is now about 2 sigma. Since it looks like the rise in mean temps is going to continue for at least another few decades, are we looking at what was 3 sigma events becoming 1 sigma and less? I know the there are calculations of the expected increase in the number of days above 90F or whatever, but this looks more frightening — somebody tell me what’s wrong with this reasoning. Please.

  33. 83
    sidd says:

    Mr. afeman asks on the 20th of August, 2012 at 4:22 PM:

    “…are we looking at what was 3 sigma events becoming 1 sigma and less?
    … somebody tell me what’s wrong with this reasoning.”

    I think you underestimate. See 3) in my comment at 1:25 pm


  34. 84

    #63 cliff mass

    Let’s try a different approach.

    If you subtract the calculated expected physical warming based on the current attribution analysis would the climate system be expected to produce the same number of heat records as are now occurring on trend?

    Survey says? No.

    If you subtract (anthropogenic GHG’s, sulfates, ozone) the mean increase in RF due to human influence the model rather strongly suggests that the extremes would not be occurring.

    As I said, reverse the null hypothesis. Prove current extremes are not human influenced. Good luck with that.

    Voltaire: Le mieux est l’ennemi du bien. (The best is the enemy of the good.)

    You seem to be foraging in the chaos of localized events in the noise to dissemble the significance of the anomaly trend in context of the historical trend. Do you really think that is scientifically wise when weighing the evidence in context of the supporting physics and probability analysis?

    In other words, you are picking on “high amplitude and persistent ridging” as the red herring (short term events) to distract from the probability analysis (regarding the long term anomaly trend attributable to increased RF). Like I said, write a paper and get it to pass muster in a relevant peer review. Good luck.

  35. 85
    afeman says:

    sidd says: 20 Aug 2012 at 4:58 PM

    It’s true the historical data are ugly enough, but my concern is whether the statistical shift in sigmas can continue in a way that is linear to the shift in the mean, if you know what I mean.

  36. 86
    Steve Bloom says:

    “Folks…I know I am entering the lion’s den talking in this forum, but Hansen had no basis to say confidently that last summer’s heat wave was caused by global warming. …cliff”

    Measurements of nature that affect human comfort are filled with value judgements like this (e.g. tropical cyclone strength categories). Technically all are arbitrary and approximate, yet they are useful.

    It seems to me that the problem with your approach is that by the time the standard of proof is met everyone but historical climatologists will have ceased to care.

    On your point about not wanting to give too much credit to global warming for the added increment of heat, here’s a very topical example where doing just that seems entirely appropriate. It turns out that the best metric of how the U.S. corn crop will do is the number of degree days exceeding 29C. The more of those there are, the worse the crop does. But the key point is that below that threshhold there is little damage. So in the instance of this season’s heat anomaly, why should global warming not get most of the credit?

  37. 87
    sidd says:

    Mr. afeman asks, insofar as i understand, if the NH JJA temperature distributions will continue evolving in a way similar to the last thirty years.

    That is asking for a model forecast of the future course of climate evolution. I do not know what the models say in hindcasts over the past from 1931-2011 for the NH JJA distribution, nor what they predict. I will note that previous forecasts have, if anything, underestimated the speed and ferocity of the changes we see today.


  38. 88
    Doug Bostrom says:

    cliff mass says: 20 Aug 2012 at 10:08 AM:

    …Generally heat waves, like the ones in the Midwest this year and last, are usually associated with high amplitude and persistent ridging. Now it is clear that GW can increase the background field—but the amplitude so far in the midlatitudes is modest (0 to 2 F perhaps, considering where you are). More in the Arctic. The background does not explain the amplitude Midwest heat waves. But there was clearly high amplitude and persistent ridge during the recent events. Now the question then becomes—is the excessive ridging the last two summers the result of GW?…

    An excellent question, and refreshingly worthwhile for taking this conversation forward. Restating Cliff’s question, are mechanisms at play helping to make additional energy in the atmosphere inhomogeneously distributed? Is any given spot on Earth only going to experience the mean increase in temperature, as Cliff implies in his blog post, or can we expect differently?

    Well, we know that energy is going appear in a lumpy form, at least if we accept that facts in the Arctic are not only accidentally coincident w/theory. But that’s not a matter of weather, it’s climate.

    So what about shorter-wavelength features, weather? A brief search suggests there’s reason to entertain the possibility:

    Heat Waves in Southern California:Are They Becoming More Frequent and Longer Lasting?

    More Intense, More Frequent, and Longer Lasting Heat Waves in the 21st Century

    and especially this business, which I stupidly only hinted at over at Cliff’s blog and which seems to complicate the matter:

    Warm Season Subseasonal Variability and Climate Extremes in the Northern Hemisphere: The Role of Stationary Rossby Waves

    We see from the Arctic that energy can “bulge” in the long term in certain regions of the planet. It seems incautious to baldly assert that on shorter time scales we can dismiss any such possibility.

  39. 89
    Susan Anderson says:

    It might be nice to stop letting Cliff Mass suck up all the oxygen in the room, but before I take my own advice I’d like to observe that he appears to be confusing weather with climate. Since his part of the world has been mostly rather cool, he seems to think he knows better. Since the strongest indicator of opinion on global climate change is individual’s weather experience, isn’t that all to likely?

  40. 90
    David B. Benson says:

    Toby Thaler @80 — You have it, close enough.

  41. 91
    Chris Dudley says:


    I don’t think you’ve got this quite right:

    “We have neither long enough nor good enough observational data to have a perfect knowledge of the extremes of heat waves given a steady climate, and so no claim along these lines can ever be for 100% causation, but the change is large enough to be classically ‘highly significant’.”

    We certainly have long enough duration observations to know what three sigma is. Asking for a longer set only allows you to find out if the distribution near four or five sigma is non-gaussian since those events may not be well enough sampled at this point to tell. The mean and sigma just won’t change much with more data. But that knowledge about the five sigma event frequency really says nothing about causation. In our current crop of above three sigma anomalies, finding one that was not caused by warming is like finding a needle in a haystack, because we know the distribution is gaussian with regard to what three sigma is. Trying to find a five sigma event not caused by warming is not really relevant to the argument.

    We don’t get to 100% causation because, over a long enough period of warming, we know there should be a needle in that haystack. Maybe one needle for every 30 straws of hay if we end emissions now. It does not have anything to do with trying to find a five sigma golden needle; for that you would need a very long period of warming indeed to get a large enough haystack to search through. Basically it is what we do know about the distribution, not what we don’t know (very rare wings) that tells us that we don’t get to 100% causation.

  42. 92
    Jim Larsen says:

    Susan, yeah. When one knows 7F + 1F = 8F (so the answer is 1/8, duh), then adding gobbledygoop just proves “you guys” don’t even know elementary school math, or you’re being deceitful. Yell, explain, teach all ya want, it’s not like you’re gonna prove 7F + 1F isn’t 8F. Unless…

    Perhaps a way to squash this belief would be to subtract the global average increase in temperature and then calculate the sigmas. If Cliff is right, shouldn’t every decade essentially match the base period?

  43. 93
    David B. Benson says:

    Doug Bostrom @87 asks are mechanisms at play helping to make additional energy in the atmosphere inhomogeneously distributed?

    I assume the question is rhetorical, but just in case some reader is not yet sure, the answer is yes.

    [reCAPTCHA agrees by proclaiming The yzeditu so now you know the reason.]

  44. 94
    Toby Thaler says:

    Susan Anderson (#88): You’re charitable. I live in Pugetopolis as well, and we do have electricity and computers. In fact, not long ago, Cliff Mass was quoted in newspaper predicting that we would have more dreary foggy summer days due to global warming: Seattle Times, August 1, 2012. It’s a pattern we’re all used to, “marine push”. Anyway, it’s been a fine summer, so no excuse: July 2012 actual cf. average and August 2012 actual cf. average.

    David Benson (#89): Thanks.

  45. 95
    John Brookes says:

    When one extreme event happens, we carry on, and recover. When two (or more) happen too close together, we struggle. When your house gets broken into, you think how unlucky you were. When it happens again, you start to question whether you should move to a different area, buy extra security etc.

    So if climate related disasters happen too frequently, we will struggle psychologically.

  46. 96
    John E. Pearson says:

    90 Jim Larson wrote: “Perhaps a way to squash this belief would be to subtract the global average increase in temperature and then calculate the sigmas. If Cliff is right, shouldn’t every decade essentially match the base period?”

    Yes. Similar to my 43 and 45. Clifford Mass’ hypothesis has nothing to do with “values”. It is fully calculable and the answer is sitting there in the data. The answer is in fact explicitly stated in Hansen’s PNAS in the first place: “In addition, the distribution has broadened, the shift being greater at the high temperature tail of the distribution.” and “This exposes the fact that the distribution is becoming broader and that there is a disproportionate increase of extreme hot outliers.”

    The onus is on Clifford Mass to show precisely why this result of Hansen’s is wrong. If the only consequences of global warming were a uniform constant shift of temperature by the mean then the whole issue would be much less worrisome. The distinction between a shift of mean and a change in the distribution was hashed out in the letters to the editor section of my local newspaper 2 decades ago by two scientists. I am surprised to see it coming up now.

  47. 97
    David M. Besonen says:

    can someone comment on Dan Miller’s reply (reply #19), where he says:

    > If this all wasn’t scary enough, +4-sigma events
    > are now happening about 5% of the time and
    > +5-sigma events, that formerly had a return time
    > of about a million years , are now occurring
    > about as often as 3-sigma events happened 50
    > years ago. With further warming, +4 and +5-sigma
    > events will become “normal”.


  48. 98
    John Monro says:

    Prokaryotes, thanks for the posting of the link to the NASA animation of Hansen’s work. You shouldn’t really need to have much understanding of bell curves to see what is happening with this animation. However in some ways I have to agree with Cliff about what the public does understand. I would wager that something approaching 2 standard deviations of the population haven’t got a clue what a bell curve is, and who’s scientific and mathematical understanding is so poor that you would have to take a good half hour of one on one time to get a majority of them to grasp what a bell curve is and how it can be interpreted, and some never will. . The other problem is of course, it doesn’t matter how brilliantly you describe these matters to the lay population, if the media won’t give you room to do so. This is particularly true of television, which is where about 70% of the population get almost all their news and current affairs information; most folk could watch television for a million years and they’d still be no wiser, of course by then their brains would have dribbled out of their ears.

  49. 99
    John Cartmill says:

    From Post #63
    Now the question then becomes—is the excessive ridging the last two summers the result of GW? Was the large scale flow pattern somehow enhanced by GW? There is no reason to expect this…either from modeling or theoretical results

    There is an excellent video explaining why this is the case here:

  50. 100
    Chris Dudley says:

    “Note that the change in spread shouldn’t be automatically equated with a change in climate variability, since a similar pattern would be seen as a result of regionally specific warming trends with constant local variability”

    This seems like a distinction without a difference. Under this description, if you were to take a cut across a hardiness zone, you’d find regions where the hardiness description is less reliable owing to increased spatial variability. So, that would in fact be a change in climate variability.

    Also, in the supporting link, the failure to reproduce the new paper’s results seem much more likely to be attributable to not using global data and not looking at summer time. If the mean shift is small compared to sigma then it is hard to say anything.