**UPDATE:**

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

**End Update**

Well, Judith Curry has “responded” to my last blog post … sort of. Here’s what she has to say about it:

Tamino’s argument is essentially a quibble about how heat waves are defined, there are various definitions

Bullshit.

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?

I suppose one person’s

quibbleis another’sbasic error that would be embarrassing in first-year undergraduates taking their first course in statisticsThis is on a par with Curry’s recent most, more than half or > 50% puzzler. Maybe it’s just one of those wicked problems that calls forth the uncertainty monster from the depths.

i believe the canonical term is “gremlins”.

I don’t think it can compete with her 50:50 posts. That was the most embarrassing nonsense I have seen from someone in her position, that has been so vocal against MS science. In particular, her admission that she did not realise the human contribution could be more than 100%, showing she had put so little effort in reading the IPCC reports that she argues against.

Not surprising that Dr Curry latched onto this as she seems to uncritically latch onto anything if it appears to sow uncertainty. But I am surprised that the original researcher thought he was onto something interesting about climate rather than a basic statistical property.

A new genera of climate denial?

“Don’t worry, no matter how hot it gets we’ll almost never get extreme 3 sigma heat waves”

Kind of a reverse Lake Woebegone where no matter how smart the children get in the future they only stay above average instead of turning into geniuses!

I’ve never seen “absobluminlutely” spelled out before.

Typical Curry. Her response to everything seems to be, “Meh, can’t be bothered to think about it since it doesn’t agree what I’m saying.”

I think you are not being fair to Sardeshmukh. All we have is Curry’s summary of a talk and some slides based on his unpublished work. Once Sardeshmukh’s paper is out we’ll know what he is really doing. His past work (http://cires.colorado.edu/index.php?cID=1095&pubid=2) indicates to me he is a serious scientist who understands statistics and is not a a climate change denier. For example, this paper http://onlinelibrary.wiley.com/doi/10.1002/grl.50425/abstract concludes “This independent data set reproduces both annual variations and centennial trends in the temperature data sets, demonstrating the robustness of previous conclusions regarding global warming.”

Well, here is his Google publication history:

https://scholar.google.com/citations?hl=en&user=rjl0EegAAAAJ&view_op=list_works&sortby=pubdate

His most recent paper (2015) is (paywalled):

Understanding the distinctively skewed and heavy tailed character of atmospheric and oceanic probability distributions

http://scitation.aip.org/content/aip/journal/chaos/25/3/10.1063/1.4914169

That paper looks to be somewhat relevant to the current discussion. If he has a working draft of a future (or submitted paper) with respect to the current topic, perhaps he might sent Tamino a draft copy (NDA review and comment purposes only)?

I was a talk of his recently (part of a bigger conference — IUGG) which used the same slides. Most in attendance were climate scientists, and it was specifically a session geared towards statistics and climate change. He got some arguments on his methods, but no one viewed him as someone with an agenda and some referenced his work in subsequent talks.

I usually like your posts, but this seems needlessly hostile. And you’re addressing his work via Curry’s presentation rather than it directly

[

Response:You’re right. I was wrong.]No, it’s because we and all other animal simply adapt our body chemistry to function at 40°C or whatever. No problem then with standard deviation heat waves.

May be a case to put a lot of money into genetic engineering!!!

This overlay might be of interest. Curry, of course, stated in a comment under her post this morning that different climatologies were used as you suspected. Another issue, of course is whether the distributions remain Gaussian.

I don’t think this is to difficult. If you use the concept of downtime.

This is sort of a time domain analysis, where one compares two different eras, say 1881-1910 and 1985-2014.

For a fixed temperature (and probably humidity, at least for places like the SE of the USA) of say 98.6F, what is the difference (or ratio) of time that exceeds said fixed temperature.

This would appear to be a means to test changes in ‘hot’ weather without making assumptions about statistical moments?

Anyways, just a thought.

Do people such as The Subject make these mistakes because they are actually ignorant of Substance in first-year Stats, which I agree this would be, or because they are writing for an audience which doesn’t understand such Substance, and are trying to convince them? I’ve often wondered that.

Note also that there are few probability distributions where the mean is statistically independent of the variance (or equivalently standard deviation). In other words, in the case of the Gaussian, you can shift the location — or mean — of the distribution all you want, leaving a variance alone. In, for instance, the case of a Gamma, as the mean approaches zero, that variance HAS to change, because it cannot go negative. In fact, the variance, in such instances, can be used to estimate the mean, because of this coupling.

The PSI function from the “math slide” can be rearranged to

((x1 + 2*sigma1) – (x0 + 2*sigma0))/sigma

i.e. it’s a difference of 2-sigma thresholds scaled by some (overall?) standard deviation. Given certain assumptions, I think that can be interpreted as the change in the point on a PDF above which 2.3% of the observations will be found. That’s somewhat consistent with their referencing Katz and Brown (1992).

When I first saw the “math slide”, I assumed it was not what they actually did because of the reliance on assumptions about well-behaved distributions. But then Sardeshmukh referenced it in his reply as representing what they actually did…

What is the sigma in that equation since there are different sigmas at to and t1? Not so easy to think about. If you look at just x1-x0 you get a very different pattern @ 2m than what he is showing at 860 kPa.

Do you mean the Math Slide on Judith’s blog? That seems okay to me as long as is fixed. However, as Tamino is pointing out (I think), if is fixed, and is fixed, then it’s hard to see how the probability doesn’t change if both and are both positive.

“The point of this slide was that… the changes in standard deviation were clearly important, and opposed the changes in the mean in many regions.”Prashant Sardeshmukh, via Judith CurryThat triggers a red flag with me with respect to potentially over-fitting noisy data. As Tamino says, I look forward to seeing the data and the final publication.

The graphs only deal with temperature – sensible heat. With AGW, there is also a greater likely-hood of higher levels of relative humidity – latent heat. High temperature/ high humidity events put much more stress on mammals including people. Loss of farm animals can mean later human deaths which is counted as “malnutrition” rather than being attributed to the heat wave. And, poor infant nutrition can reduce the intelligence of the the next generation. Thus, the repercussions of a heat wave can last 50 years.

Also, more recent heat waves tend to cover larger geographic areas and last longer.

Plots of number of people killed by heat waves does not reflect the full intensity and extent of heat waves as we are getting better at providing emergency services to prevent people from dying during acute heat events – e.g., helping people stay hydrated.

We are not yet recognizing the current costs of AGW.

In reading the Climate Etc post “Heat Waves Exacerbated by Global Warming” we see that before Dr. Curry gets to the Sardeshmukh presentation she cites several references that discuss heat waves in Europe. One is a peer reviewed paper by Horton and Diffenbaugh et al, “Contributions of Changes in Atmospheric Circulation Patterns to Extreme Temperature Trends”. She goes on to paraphrase one of the authors: “Diffenbaugh said the changes could be a result of random chance, or a side effect of climate change and melting sea ice as others have theorized” and provides a link Prof. Diffenbaugh’s YouTube discussion of the paper. She concludes with some editorializing: ” Because of the short time period of their analysis (since 1979), it is very difficult to attribute any trend in circulation patterns to AGW”.

The link provided is here:

But this seems to be a mistaken link because in this video Professor Diffenbaugh is discussing atmospheric circulation and drought, in particular drought in California. He is not discussing extreme heat or the paper she references. However accidental, this was something of a very nice find because it has significance for this blog although more appropriately under the CA H2O post. The video is he provides a highly informative summary of his research and causes of the drought. It is well worth a watch (only 7.5 minutes). His findings on the role of GHG’s in his research are notable and unequivocal “we also find that with very high statistical confidence that the warming that has occurred in California would not have occurred without greenhouse gases and the increase in co-occurrence of low precipitation and warm conditions (drought conditions) also would not have occurred without human emissions of greenhouse gases”.

I believe the paper that is the focus of the video is this one:

http://www.pnas.org/content/112/13/3931.full.pdf?with-ds=yes

So in place of this apparently mistaken video what video could have been referenced? I don’t know what she may have intended but here is an article and short video (3 min) from the Stanford Woods Institute for the Environment where the authors discuss their findings on contributions to extreme weather:

https://woods.stanford.edu/news-events/news/isolating-underlying-causes-extreme-weather

In this video at least, the authors comments seem to render her editorial remarks that “it is very difficult to attribute any trend in circulation patterns to AGW” as somewhat misleading. While the extent to which trends in circulation patterns are associated with rising GHG levels may not be completely understood at this point, the association of these levels with extreme weather is clearly stated. Lead author Daniel Horton: “Due to the continued accumulation of GHG’s in the atmosphere the heat content should increase and we can expect continued increases in extremely hot days and continued decreases in extremely cold days”. Prof. Diffenbaugh: “…the largest percentage of changes of extremely hot days and extremely cold days around the world is from the increasing heat and moisture in the atmosphere that comes with global warming”.

Meanwhile the howling at Climate Etc that AGW has nothing to do with extreme weather continues unabated.

Tamino we appreciate your work here and I enjoy reading your posts.

And of course Jeff Master’s newest post couldn’t have anything to do with this, could it?

“All-time July National Heat Records Fall on Three Continents”

http://www.wunderground.com/blog/JeffMasters/comment.html?entrynum=3033

“Same as it ever was”

Curry arranges

Same as it was

Everything changes

But nothing does

reminds me of Meehl and Tebaldi’s work way back in 2004.