Sardeshmukh has weighed in on Curry’s blog:
The critic of our study is mistaken on all counts.
1) Contrary to his suspicion, we did correctly define the temperature extremes with respect to the same fixed temperature threshold in both periods at each geographical point. The formula in the math slide, which is for shape preserving changes of the distribution, is also for exceedances beyond a fixed threshold.
2) As already noted at the bottom of the math slide, “the situation gets even more complicated for non-Gaussian distributiions whose changes are not shape preserving”. And indeed they are not shape preserving for daily temperature. There were changes from 1901-1925 to 1981-2005 in both the skewness and kurtosis (a measure of tail heaviness) at most points on the globe, including the Indian ocean point discussed by the critic. I had mentioned these changes in my talk, but not shown them to save time, as the main point of the slide showing the change in daily temperature extremes from 1901-1925 to 1981-2005 had already been made. This was that the global pattern of the change in extremes does not look anything like that of the mean shift, and this is not surprising given the fractional changes in standard deviation. The point of this slide was not that one could deduce the numerical value of the change in the extremes from only the changes in the mean and standard deviation, but that the changes in standard deviation were clearly important, and opposed the changes in the mean in many regions.
I replied on Curry’s blog with this:
If what you say is true, then I have made a grave mistake. But perhaps you can understand my skepticism that an increase in mean by a full standard deviation, combined with an increase in standard deviation, would accompany no change in the probability of exceeding a fixed temperature threshold.
If you will share with me the data you used for that grid point in the Indian Ocean, I can confirm your results with my own eyes. Upon doing so, I will publish on my blog a prominent, unambiguous admission of my error. But until I see it with my own eyes, I remain skeptical.
I look forward to seeing the data
Tamino’s argument is essentially a quibble about how heat waves are defined, there are various definitions
My post was about the fact that both Sardeshmukh and Curry use two different definitions in order to downplay the impact of a change in the mean and standard deviation, without mentioning (or, apparently, even understanding) what they’re doing.
Look again at the second graph in Curry’s post:
That makes it crystal-clear that the IPCC report is talking about changes in extreme heat relative to a fixed temperature threshold. If he intended to study extreme heat relative to some threshold that changes as mean and standard deviation change, why does Sardeshmukh go on to ponder “what happens when they occur together?” (change in mean, standard deviation, and shape), then analyze it by completely eliminating the effect of change in mean and standard deviation.
That is, indeed, exactly what he does.
Take any probability distribution for a variable x, parametrized by its mean, standard deviation, and perhaps some “shape parameters.” Then compute the probability for exceeding some relative-to-the-standard-deviation threshold above the mean (e.g., two standard deviations above the mean) Then change the mean and standard deviation. Then compute the new probability. It will be the same. Exactly the same. Changing the mean and standard deviation can’t change the probability of exceeding the mean by some number of standard deviations. That’s a fact.
Changing the shape parameters can. Duh.
The really hilarious part is that Curry still doesn’t understand what Sardeshmukh did, or what she’s talking about. Consider this statement:
Sardeshmukh’s analysis uses two different baseline temps: one prior to 1950 and the other post 1950, and then calculates deviations from those means. His whole point is that the standard deviation and skewness changes can dominate, resulting in fewer large excursions from the mean.
Thanks for confirming that he did use different means for the two compared time spans. Too bad you didn’t also note that he uses two different standard deviations for the two different time spans.
Yet Sardeshmukh doesn’t seem to understand that by doing so, he eliminates the effect of both changes in mean and standard deviation. He expresses surprise, and even disturbance, when he says “The fact that changes in extreme anomaly risks cannot be deduced from the mean shiLs alone is disturbing, …” Of course they can’t — you deliberately eliminated its effect.
Clearly, Curry suffers from the same misconception when she says “Bottom line is that the intuitively reasonable attribution of more heat waves to a higher average temperature doesn’t work in most land regions.” Of course it can’t –Sardeshmukh deliberately eliminated its effect.
The only thing Sardeshmukh has shown is that if you eliminate the effect of changes in mean and standard deviation, then changes in mean and standard deviation don’t affect the result. Duh.
But he still makes a big deal about it — after having started off with the IPCC report about the impact of changes in mean and standard deviation as well as shape. He even states explicitly that he wants to know “what happens when they occur together?”, then tries to find out by eliminating all trace of the first two.
Judith, it’s obvious. Absobluminlutely obvious. The two of you used two different definitions of “extreme temperature,” one to give the impression of an “intuitively reasonable” effect of higher average temperature, then one which removes the effect of higher average temperature.
Please, oh please, deny that. As often as you can.
As for me, I don’t consider pointing this out to be a “quibble.”
While you’re at it, do tell us all why making heat waves hotter doesn’t exacerbate the problem (even if they don’t get more numerous when you move the goalposts defining “extreme”).
Curry closes with this:
The SD definition makes most sense for a global analysis, IMO
So … if the mean summertime daily temperature in Georgia increases to 200 degrees Fahrenheit with a standard deviation of 8 degrees, then we shouldn’t worry until the temperature hits 212?
Make your blood boil?