We had a talk at work today by a chap (eminent mathematician I think) about looking at the distribution of extremes in the temperature record and trying to say something about detection. The problem is that extremes are statistically rather unstable and all he could say was that he didn’t detect GW; he didn’t appear to understand that all that means is that his method isn’t very powerful…

[Update: JF points to http://www.arxiv.org/abs/physics/0509088 which is the paper]

And when I say global, actually he was looking at Philadelphia, daily data, last 125 years. He pretty well went out of his way to demonstrate his lack of met knowledge (didn’t know IPCC; didn’t know *where* the met station was in Philly; hadn’t managed to find many other longer records in the course of browsing the web; etc). Very much a mathematician picking up some met data and playing with it. Which is fair enough *unless* you start taking his conclusions seriously.

Anyway, what he was doing (via some maths) was noting that if you have a stationary record, then record-breaking highs (or lows) get less and less frequent as time goes on. Whereas if you have a trend, then the frequency tends to a constant. Unfortunately… when testing his method, the “trend” he tried fitting was 0.6 oC/C, which isn’t a very good approx to the temperature record. Whether this matters is unclear. More significantly, his results were simply inconclusive: he failed to detect a trend, but he also failed to rule out a trend.

It was pointed out to him (by me and others) that if you really want to detect a trend… err… why not just look at the trend? All the record-fitting its fun maths, but (as a detection method) really very weak. It wasn’t quite clear whether this had never occurred to him, or if he knew it perfectly well but wasn’t going to mention it first on the off chance that no-one else would think of it. There seemed to be some suggestion that he was confusing (not in his maths, but perhaps in his motivation) the difference between GW-will-lead-to-more-extremes and extremes-are-useful-for-monitoring-GW.

[Incidentally, this is my first-ever scheduled post. Hope it works. I wrote far too many yesterday. Like the London buses]


  1. #1 Matt McIrvin

    There was a nice post by Rasmus Benestad explaining this on RealClimate a while ago (but you probably saw it).

    [Yes (I drew the picture!) but I’d forgotten it. Thanks for reminding me -W]

    One reason people may be drawn to use extremes is that extremes get attention; they’re the things that nonspecialists will hear about and ask you about. That’s why it’s so frustrating to have to say that one extreme data point doesn’t necessarily say anything about the reality or unreality of a trend.

    One good way to deal with it is to make the reversal you mentioned, and talk more about the trend leading to more extremes than about the use of extremes as an indicator. Nevertheless, it’s nice to have readily comprehensible indicators.

  2. #2 Mark Paris

    I’m not sure why the trend is not the most important and understandable indicator, since what we are talking about is a trend in global average temperatures. Of course there is a tendency (a trend?) in general media to concentrate on the remarkable, like, “Record high temperature today!” It’s more interesting that a day’s temperature was the highest on record for that date than that the average temperature is climbing by an amount that most people’s thermometers can’t read accurately. Forget the fact that it’s the small change in average that counts rather than an individual data point. Oh well. Playing with the data is fun, and it’s even possible that you might find something remarkable in them.

  3. #3 John Fleck

    Was it Sydney Redner and/or Mark Peterson?

    [He was introduced as “Sid”, but whether with a Y or not I don’t know. I was hoping someone would know who I meant, thanks John. MP may have been a collab -W]

  4. #4 Roman Werpachowski

    It was pointed out to him (by me and others) that if you really want to detect a trend… err… why not just look at the trend? All the record-fitting its fun maths, but (as a detection method) really very weak.

    Yeah, but it still is nice to have some well defined quantity passing some sort of mathematical test giving a YES/NO answer to the question “do we have GW?”. (I think we do, but would like to see some kind of a numerical argument for it).

  5. #5 James Annan

    I think it’s an entirely reasonable question to ask both whether extremes will change by more than or less than the mean, and whether or not model predictions on this issue are detectable in the data. Not that I’m a great fan of D&A, as I’ve said before. And of course this comment doesn’t have much bearing on whether this mystery mathematician was doing anything sensible or not.

    [He wasn’t really looking at the point you’re talking about, he was effectively trying to use extrems for detection. I think. Speaking of models, another comment he got was, why not run your method on model data? Then you know perfectly well whether you have a trend or not, you have no missing data points, and you can test how powerful it is. He was distinctly unkeen on the idea -W]

  6. #6 John Fleck

    OK, I’m familiar with this then. I’ve acutally interviewed him about some other work he’s done (an analysis of why soccer/football is a more interesting sport – Google it – delightful bit of business) and we talked some about his Philedelphia climate paper:


  7. William – Completely OT, but I have yet to see much from the experts on recent news about the warm Arctic 55 Myr ago. This is new in the NYT, but I assume has been in the community for a while. One claim I’ve seen in that the Arctic was something like 13 C warmer than models retrodicted. Is anything known about this?

    [Hmm, don’t recall that -W]

    Also, Joel Achenbach had a column in the Washington Post magazine last week that is causing a stir. He profiled Bill Gray, with minor roles for some other skeptics. Have you seen it, and if so, do you have any comment.

    [I saw it. I thought it was fine… I posted a comment on someone elses blog – JFs? I think Chris Mooneys take was about right… but I can’t find that now. Anyway, Gray etc come across as ranters, which seems fair -W]

  8. #8 James Annan

    Having now read the paper, it seems pretty overblown for such a simple point. Will be interesting to see if it makes it into print in this form.

  9. #9 Eli Rabett

    One of the interesting things about an extreme is that the probability is higher (50%) for reaching a further extreme starting from that point.

  10. #10 Q

    Global Warming or Global WARNING. Love the Krakatoa eruption on top of the page. Laters…

  11. #11 James Killus

    There was a similar discussion several months ago on the Compuserve Sci/Math Forum (nostalgist that I am), only it featured the NYC rainfall time series.

    The greatest problem with any historical data set such as the Philadelphia and NY series is observational stability. Did the instruments change? If so, when? How about the local area? New buildings? Less greenery? And so forth.

    It’s not an insurmountable set of problems, but it isn’t something that can be addressed by mathematics alone.

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