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