"Summers are cooling." Richard Wakefield Nov 8 2010

The story so far...

"2973 MUENSTER Saskatchewan 1904 2009 TMax flat trend" Richard Wakefield November 16 2010

Both the above quote and the one from the title of this post are from this thread at Coby's place. This led to my Fig. 1 below which demonstrated Tmax as a rising trend and I also showed summer Tmax rising. (See also here )

Turns out that when Richard says Tmax he (often, but not always) means highest Tmax, which is a little confusing.

I decided to look at the top 100 temperature records and they showed an interesting distribution. (Figs. 2 & 3). I was amused and amazed to see Richard attack this post so vociferously on his blog as they actually go some way to backing up his idea that summers aren't getting hotter - nearly half of the hottest days in the record are in the 1930s and 1940s (Fig. 3). I also used the Top Temps post to demonstrate the effect that extreme temperatures have on the naked eye estimation of a trend - if you remove the highest point the trend can look very different.

I moved on to looking at how well a polynomial fit to the data (Fig. 4). Again, this seems to back up Richard's claim but again he attacked it, which is rather strange.



Fig. 1



  


   





Fig. 2



Fig. 3





                                                           Fig. 4

 

What next? Let's try a spline. The best fit has 10 degrees of freedom (p<0.001) though still only accounting for 18.5% of the variance. More degrees of freedom lead to increasing p values - they hover around 0.001 - 0.002 until about 20 degrees of freedom then fall away rapidly. A 10 degree fit looks like this:

With the residuals looking pretty good too:

We can also test for autocorrelation:

Which shows that there is no autocorrelation in the series at all. One year does not even predict the next. The sample spectrum indicates that Highest Tmax is a pretty much random event.

This is borne out by a runs test (To do this you take the differences of consecutive pairs of observations (in time order) to give a set of values that are positives and negatives and then apply the test) : ( Number of runs:   65; expected number of runs:   52.83;  right sided P-value: 0.010;   left sided P-value: 0.994). This tells you that there are no significant trends in the data as a whole, p=0.994.There are 65 runs (+ves and -ves) altogether whereas the expected number is 52.83, so there are rather more runs than would be expected. If you had strong trends over time then you would observe fewer runs than expected. Adding a regression line through the raw data plotted against the time axis shows you whether there is an overall positive or negative trend, but note that this may be influenced by early and late points. A way around this is to bootstrap:

(Mean intercept is 1913, mean slope is +1.3)

That's about it for now, I'll return to this when real life has less demand on my time... But as things stand highest Tmax does not show any significant trend up or down. There were some high temperatures in the 1930s and 1940s that have a great influence on the shape of the data but in order to explain the data further I think the next step will be to look at mean Tmax to get a fuller picture of what temperature was doing outside the really hot days.