January 11, 2018

Scary But Deceiving Climate Statistics

How many times do you see a headline or read an article about climate change, where you are told that threat of some scary extreme event (flood, heat waves, cold wave, etc.) has increased five or ten or 100 times due to global warming?

But as we will see, such scare statistics may not mean as much as the headlines suggest.  In fact, they can be quite deceptive.  Let me explain.

Many of the scary stories talk about the frequency of exceeding some extreme threshold, such as the number of times temperatures exceed 90F in Seattle during the summer, or the frequency of daily precipitation exceeding 20 inches during the winter in the Cascades--that kind of thing.

The nature of extremes is that they are unusual.  So a very small increase of their numbers can result in the number of occurrences above some threshold increasing radically.

So if there are normally one day a year with temperatures over 90F during the summer and there is two one year, the frequency has DOUBLED.   A 100% increase!  Huge.

Let me do this a bit more quantitatively.  The climatological distribution of temperature is often Gaussian (also called the normal and bell-shaped distribution).

Below is an example of such a distribution, whose mean and most probable value is 75F.  The x-axis is temperature and the y-axis is frequency.   A measure of the spread or width of the distribution is the standard deviation (greek letter sigma is often used to denote it).  67% of the observations should be within one standard deviation of the mean (I have assumed a 3F  standard deviation in the figure below)

You notice the frequency (or probability) of observations drops rapidly for values much larger and smaller than the mean.

Now let's think about extremes.  What is the probability of experiencing a temperature more than 85F?   According to the calculation shown above:  .00043 (.043%)  Not much

OK, now lets warm things up by 1F, so the mean becomes 76F (I am keeping the shape the same).  You might not even notice that.  Here is the new distribution.

The probability has increased to .00135 (.135%).  OMG!   The probability of exceeding 85F has gone up by 3.14 times!

But think about it a bit more.   Instead of the scary increase of 3.14 times, think about the actual increase of probability of getting about 85F.

The increase is ONLY .1%.  Yes, a tenth of a percent increased risk of such warm temperatures.  Doesn't seem so scary all of sudden.

I could give a dozen other examples of this...but hopefully you get the idea.

So be very cynical when you read about increases of extreme events due to global warming (or anything else) and particularly when the increases are for exceeding some threshold and given as a factor (5 or 10 or 100 times more). 

Such numbers can be extremely deceptive and imply a big increase in risk in situations with minor changes.  

And there is more.  Even if global warming results in a higher frequency of exceeding some threshold, its contribution might be quite small.  Consider Hurricane Harvey.   Global warming may have increased the precipitation by a few percent, but nearly all of the event was the result of natural processes.  When folks hear that global warming has increased the probability of an event by some factor they tend to assume that most of the event was due to global warming, when that is generally not the case.

Finally, thresholds are generally arbitrary and subjective.  For example, why is 90F more special than 91F?   The use of thresholds for such climate communication is essentially deceptive and should be used far less. 

What really counts is not the frequency of crossing some threshold but the increase of the amount of the threat (e.g., the increase in high temperature, precipitation).   For example, by the end of the century, the Northwest snowpack will probably be down by 30-50%.   That is scary.  Or the heaviest precipitation in atmospheric rivers could be 20-40% larger.  Again, a major issue.

Global warming is too serious of an issue for us to use questionable, if not deceptive, statistics for communications of its impacts.


  1. I think you need to start using Kelvin for your climate change postings. Degrees F or C are too scary sounding :-)

  2. I suppose many scientists are as prone to believing their priors and promoting their research as the rest of us would be. I mean no disrespect. It's tough being a scientist; no wonder there are so few

  3. Cliff, I have trouble following your logic here. The most extreme weather events may be very rare, but they are also by far the most devastating. For instance, would you argue that it's not a big deal if something like Hurricane Harvey becomes 6 times more likely? (That is the claim being made here.) I don't see why we should take that lightly.

    Or to give another example, about 171,000 people died in the Banqiao Dam failure. (The dam's design may have been to blame, but more than 40 inches of rain fell within a 24-hour period. I assume that would overwhelm the infrastructure in lots of places even if it was well-designed.) Again, I don't see why we should take it lightly when the chances of an event like that go up. Even a small increase in the risk of 171,000 people dying might weigh heavily on someone considering whether global warming deserves a robust government response.

  4. Cliff – It is not cynical to question these statements. It is intellectually honest. It is questioning and confirming and searching for truth. You know, like science once was.

    One of these days I would like to see you actually take the gloves off. But this is close enough for now, since you are the only scientist I know with the cajones to actually call out this garbage. Why is that?

  5. James..I have added some material in the blog to answer your question. Thresholds are arbitrary and have little real meaning. Real increases in threat are what count (say global warming increasing the storm total by 10 inches)...cliff

    1. Cliff, for someone who acknowledges global warming, it's interesting that anytime you wore about the issue it is to undercut those pointing to it's effects.

      Why do you spend absolutely no space in advocating to address the issue?

  6. Quite often those scary numbers are well within the margin of error for an attribute with variance. In other words, the real/actual value (whatever that means) jumps around a lot, and the measurements jump around a lot. A small change could be either measurement error or something real. Statistically there is NO way to determine that. Thus the margin of error.

  7. Is it only me or is more of you with me on how ridiculous the weather forecasting has gotten. Today was supposed to be blustery storm in Seattle, nothing of that sort in downtown. Sun was out mid-afternoon and never did it rain hard to call it 'blustery'.

  8. John Bennett...I have done a number of blogs talking about the serious implications of global warming. I believe it is too serious an issue to exaggerate/hype/distort. Society needs the unvarnished truth...thus, my attempts to correct bad information in the media or the web..cliff

  9. John Bennett...I have done a number of blogs talking about the serious implications of global warming. I believe it is too serious an issue to exaggerate/hype/distort. Society needs the unvarnished truth...thus, my attempts to correct bad information in the media or the web..cliff

  10. The difference between melting and freezing can be 0.1 degrees - and globally herein lies the real difference - as global warming continues, less and less snow pack and glaciers exist - these are the areas that respond to 0.1 degree changes - the change that is and will continue to occur in available fresh water as the snow melt finds higher and higher altitudes inexorably will be devastating to those downstream counting on that water for survival

    yes 0.1 degrees ain't much - over time its devastating - how much time? - maybe that's the real question

    the more we minimize global warming, which your article contributes to, the more humanity will suffer

  11. Threshold is an extreme example of a non-linearity. A tenth of a degree below 90F, nothing to see here. 90.1F, heat wave!

    Probability of extreme effects matters because there are other non-linearities, not quite as extreme, that are nevertheless economically significant. For example, wind storm damage might grow roughly with the square of wind speed.

    The insurance company sure as heck cares about the n-fold growth of the small probability of extreme values when computing the expected dollar value of wind storm damage, because that's the only part of distribution that contributes much to the integral, before or after the small shift in mean.

  12. Hi Cliff,
    The issue of how to communicate changes in extremes is worth discussing more but I don't think there is a unique best approach. For temperature, there are fixed thresholds that we care about (e.g., for heat stress). For snowfall, I wrote a paper a couple of years ago that focused on changes in the intensity of snowfall extremes (doi: 10.1038/nature13625) but I subsequently got feedback from engineers that changes in the probability of exceeding a fixed threshold were also important (e.g. for snow loading).
    Paul O'Gorman.

  13. Indeed society needs the unvarnished professional opinion of the scientific community. (Sorry the word "truth" is a bit "heavy" of a word.)

    Excellent post Cliff! IMHO you are really doing society a service with posts such as this.

    In order for society to grasp actual climate change, and take action when the time comes, it is imparitve we do not sensationalize the brevity of the now inevitable impacts of Climate change.

  14. Cliff,

    This type of post is why I enjoy your blog so much. Yes, as you note, the impacts of Climate Change will be pretty awful by the end of the century, but we can only deal with it by having rational, scientifically rigorous discussions.

    Hyperbole merely contributes to keeping the issue in the political realm where it cannot be effectively addressed. And in politics, the louder and bloodier you scream, the more likely someone will hear. Until you find the other guys are screaming just as loud, and then its just noise reinforcing noise. Which is where we are today.

    If the US cared as much about science as it did its obsession with politics, we would be much more likely to reduce (or at least be prepared) for the changes.

  15. Regarding the mention of the MIT article above - Richard Lindzen, noted MIT physicist and often regarded as one of the pioneers in the field of climatology, has often been a skeptic when it comes to the more outrageous predictions of his fellow colleagues. When he dared to express the heretical view that although he felt that the planet was warming but that humankind was not likely to be the primary cause, he was denounced and attacked 24/7. This example of PC/Orwellian thought police is prima facie evidence of why people like Dr. Mass must have their voices heard on this issue. The science is "never settled," and anyone demanding otherwise are the true denialists.

  16. Cliff,

    As someone trained in science and statistics myself, I always greatly appreciate your approach to transcending the bullshit of society and hype. This blog post is very good.

    Where my feedback for you might be:

    Although its true that global warming is currently only starting to affect "weather" by a seemingly small percentage (I think you say something around 10%?) we are still dealing with a VERY serious long-term threat to the survival of complex life on planet earth. Between climate change, ocean acidification, and habitat destruction, there is growing evidence that earth is entering the 6th great mass extinction event, and thus a new geologic epoc: "The Anthropocene".

    You have done a great job in previous posts and presentations about the critical importance of reducing carbon emissions immediately, however, I do think that you could focus on this key variable with more intensity and regularity.

    Holding the media accountable for exaggerating and / or negating facts is critical, however, the greatest challenge we face is in fact forcing political movement in the morally and ethically correct direction. Not to mention the evolutionary adaptive direction.

    From a mass media perspective, we really do need to be focused on getting the public as a whole pushed in the direction of even CARING about global climate warming.

    Right now, polls clearly show that environmental issues aren't even within the "Top 3" on most people's lists when it comes to voting for political candidates. This needs to change!

    Although you mention that we still have many good Cascade Mountain winter snowpacks left in our immediate future, I personally have witnessed PROFOUND changes in Cascade Glaciers within my lifetime. I also spend an enormous amount of time reading glaciology and climate journals, and the evidence on a global scale is as they say, "overwhelming and demands urgent action".

    Your blog is one of my favorite daily readings, and all I would say is that I do think you could be a tad bit more fervent about trying to outline all the reasons WE SHOULD CARE about global warming.

    A good example of this is simply the fact that I-732 failed so horribly. People just didn't care, and were very easily swayed by the negative marketing, even on the part of the environmental groups! (That being its own huge and charged discussion).

    So yes, perhaps lay out more of the science about why urgent and immediate action is so critical. Because as you yourself say, the end of the century will bring a "totally different world".


  17. The Arctic is twenty degrees above average. Is this normal?

  18. The Arctic is warming rapidly, with a good portion of that associated with anthropogenic greenhouse gases...cm

  19. It's not just about weather. Journalists frequently make misleading interpretations of other probability-based data -- for example, your chances of contracting an illness or chronic condition. "Three times the risk of cancer!" ... from 1 chance in a million to 3 chances in a million. I worked in the news business for 20 years, and the sad truth is that many reporters are nearly innumerate -- they struggle with simple arithmetic and have trouble calculating ratios and percentages.

  20. Problem with climate science is there is no real "control". The climate has been around for billions of years but only has the context of a human life span as far as interpretation. There is also the part where only the past few hundred years have been dedicated to understanding and recording climate data. Then there is what fits in a political term of office and matches an agenda....

  21. Better be careful! Seattle's "progressives" will have your head!

  22. It doesn't take a scientist to know we're in trouble. This leads to less than scientific arguments..

    In a generation or 2 they'll have some bigger numbers to look at, and then wonder how we were so blind to miss the small ones.

    It's not like we're missing them though. Just that nobody cares to change. Either way, we're at fault.

  23. Eric Blair - It would help sometime if you provided some substantiation, from credible sources that is, for your claims such as "science is never settled".

    Perhaps what you mean is science is never certain. That is true, being a judgement arrived at only through the skilled weighing of available evidence but when this occurs, the beliefs that arise with a vast majority of the expertise can be said to be "settled". The known physics of gravity is very well settled but it certainly isn't certain.

    It is important, unless one is inclined to undermine popular understanding rather than support it, to agree to a shared common use of language. A similar miss communication ( deliberate some might say) occurs with the claim "climate always changes". It has changed in the past you mean, but not at all like this on numerous significant factors not the least being rate.

    The 97% consensus among experts that climate change is primarily man made is settled. It is settled science. The beliefs of Richard Lindzen and a handful of others falls outside of the beliefs that the vast majority of their peers have settled on.

    The only really interesting question is why anyone who is not their peer, that is those like you or me and nearly anyone who lack validating skill, would chose to believe the tiny minority opinion.

  24. One of the problems with climate predictions based on Normal Distribution plots is that there is evidence that the Gaussian plots of recent extreme events have fat tails making predictions based on past events problematic. Ref: http://www.rff.org/files/sharepoint/WorkImages/Download/RFF-IB-10-12.pdf

  25. Ah yes, it wouldn't be a comment section if Bruce Kay weren't here to spew phony numbers.


  26. Bruce Kay - the more interesting question is that you again resorted to using a long - discredited meme that speaks volumes about either your credibility or gullibility. Here's just one of many that were published by that noted right - wing publication, Scientific American:


    Key Quote - "So far, no one has quantified the consensus among natural scientists on global warming. In fact, it cannot be done easily, said Jon Krosnick, a social psychologist at Stanford University who has been studying communication strategies for decades."

    Next you'll likely post something from noted fraudulent climate researcher Michael Mann, who's been laughed off the stage for his discredited "Hockey Stick Graph," that made it appear as if the earth's temperatures were increasing at double digit rates every decade. Or the IPCC's having to completely rejigger their earlier data when it was torn about by independent data analysis. Whoops.

  27. Placeholder - I made a comment that repeated what you had already posted. My bad.

  28. Thanks Place Slipper, I was pretty sure I'd trigger one of you guys!

    I'm not about to argue about how to rank something neither of us have any skill in so relax. I do think this s more pertinent -
    from the Fabius Maximus "about" page:

    "About the authors
    “Nor do we believe that any amount of author reputation is (or should be) able to prop up a bad piece. We credit our readers with the requisite intelligence and skepticism to do their own fact checking and assign their own credibility ratings to our content.”

    — From the Zero Hedge website.

    Exactly what Fabius Maximus's relationship is with the conspiracy blog Zero Hedge I'm not sure but it hardly matters. What does matter is that they slyly avoid establishing credibility for their authors by enlisting the standard ploy of any fraud artist, which is to stroke the ego of the reader in suggesting that if only they apply the magic and rare touch of wisdom and critical thinking , they can arrive at a reliable judgement on any subject set before them. They are literally suggesting that credibility for judgement lies entirely with the reader. Can you imagine shopping for a brain surgeon that way?

    Not only is this ploy the standard hook of any act of fraud in history It is also completely contrary to all substantive study on the reliability of human cognition. What Fabius Maximus encourages of their reader is an act of self delusion. - faith in your own common sense. The rule of thumb for common sense is it is only reasonably reliable for common problems - that is, problems that an average person is familiar and experienced with and which provide plenty of feedback, such as driving a car. As Cliff Mass has demonstrated with this very post, even basic statistical analysis is far from common to the average person. The average person will not make a reliable guess at the meaning of a polling of climate scientists nor will they reliably grasp the meaning of "5, 10 or 100 percent increase in precipitation". That is because statistical analysis are uncommon problems and the few times encountered, generally do not provide immediate feedback to prove or disprove the validity of your guess.

    Incidentally, the absence of feedback is a major reason why so many people are willing and eager to dispute the expert consensus opinion on climate change. As it is a forecasting problem, the proof of feedbacks are way off in the future. To put it in perspective, this is also why so few people behave similarly with something like flying a helicopter or brain surgery. Feedbacks are abundant and immediate. Not a good idea if you value your life!

  29. The science is settled: Eat margarine because it is better for your heart.

  30. Cliff, I would appreciate your thoughts on the article at the link. The author is Douglas Keenan, a former bond trader and peer-reviewed author on statistics. Among other things, his work caused the major banks of London and New York to be caught and prosecuted for making huge profits by illegally maniuplating LIBOR -- the London Interbank Offering Rate, the most world's influential interest rate benchmark.

    Keenan is a serious guy who does serious work. Some years back, he looked at the statistical underpinnings of the IPCC's Fifth Assessment, and demolished them. Since you've posted in detail here about statistics, I am genuinely interested in your view of this. Thanks.


  31. Also, Cliff, I will link to an article about a famous article by T.C. Chamberlain, the pre-eminent scientist, who was president of the University of Wisconsin, director of the Walker Museum at the University of Chicago, president of the American Association for the Advancement of Science, and the founder and editor of the Journal of Geology.

    In my opinion, the "climate science establishment" settled too quickly on one hypothesis, i.e. anthropogenic global warming. Had they paid attention to Chamberlain, they'd have entertained multiple working hypotheses. I think the establishment is so far into the hole that they'll never know how to get out.

    I offer this to you because, even though you're a "warmist," I don't think you're a nutcase. I just think you're wrong to have embraced AGW in any form. At least you aren't completely off the rails about it.


  32. Eric - Thank you for providing my requested substantiation. Here it is in its full context, :

    "One of the problems with Cook's appeal to authority is this: So far, no one has quantified the consensus among natural scientists on global warming. In fact, it cannot be done easily, said Jon Krosnick, a social psychologist at Stanford University who has been studying communication strategies for decades.
    While the Cook study may quantify the views expressed in published literature, it does not establish the beliefs of any defined group of scientists, Krosnick said.
    "How do you determine who qualifies to be surveyed and who doesn't qualify?" he asked. "Personally, I haven't seen anyone accomplish that yet."

    This reveals two things:

    1) There exists a not unusual disagreement from one specific specialist ( psychology/ communications) about the methodology used for the objective - a valid statistical sampling of individual beliefs, as opposed to study conclusions.

    2) The disagreement reveals that even among experts, navigating technical statistical representative nuances is difficult....... for non experts like you or me, it is proven repeatedly and consistently that we'd be better off spinning a bottle than rely on our common sense for such uncommon problems.

    The other obvious thing, if disinclined to cherry pick appealing little nuggets of straw man ambiguity that is, is to see that Cooks "97 %" study is one of only many, all arriving at different precise numbers of conclusion but all with the same general drift - a large majority of expertise form a strong consensus on AGW..... not surprising when different methodologies are employed yet still demonstrating that the hypothesis in question that is challenged does in fact pass the test into robust theory.

    Something that Richard Tol, another skeptical critic of methodology, does like most agree with yet we note you neglected to quote despite its prominence as the articles concluding sentence:

    "Tol has even said there is no doubt in his mind that there is an overwhelming scientific consensus, so everyone is a little bit amused by the fact that he agrees with our results and yet he has been attacking our research".

  33. BAMCIS said:

    "Problem with climate science is there is no real "control". The climate has been around for billions of years but only has the context of a human life span as far as interpretation."

    Strangely enough, we do actually have "controls" for running statistics on climate. This is called the geologic record... We have very precise data on Earth's climate and greenhouse gas concentrations that are as old as 1.5 million years, as dictated by microscopic bubbles in deep Antarctic ice cores, as well as ocean floor sediments et al sources.



Please make sure your comments are civil. Name calling and personal attacks are not appropriate.

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