Why Mean Temp is meaningless

This has been my theme throughout this blog. But it appears some do not understand why TMean as supplied is a meaningless number. So some specific examples of why it is meaningless is needed.

TMean as supplied by Environment Canada is simply (TMax+TMin)/2. That is, it's the half way point between the highest temp and the lowest temp of the day. If the hourly temperature profile were a perfect sine wave this would not be a problem. But the hourly temperatures are not a perfect sine wave. Far from it.

In a perfect sine wave the average of all the hourly temps and the TMean would be the same. But because the daily temperature trek is not a perfect sine wave the hourly average is not the same as the TMean. TMean could be more than the hourly average, it could be less. The point being the hourly average is a number that is closer to what is physically going on. TMean is not.

I download the hourly temp data for the month of November, 2010 for Station 4333 so you can see the difference. (For those who think I cherry pick, choose any station, any month, any days you want, you will see the same problem.)

This is the temperature profile for Nov 1 to 4:

Here are the numbers:

	Tmax	Tmin	Avg	Tmean	Diff	%Diff
Nov-01	4.4	-0.8	1.2	1.8	0.6	50%
Nov-02	7.1	-2.9	1.4	2.1	0.7	50%
Nov-03	8.1	-4.3	1.8	1.9	0.1	6%
Nov-04	6.7	1	3.7	3.85	0.15	4%

Notice TMean is more than the average, substantially more. Thus using TMean as an indicator of how much the planet is heating up is grossly overstating the case for these days at least.

This graph for the entire month of Nov shows the TMax, TMin, average and TMean. Notice TMean is mostly higher than the average:

This graph shows the difference, average subtracted from TMean:

Adding up the differences is 2.23, which indicates that TMean is higher most of the time than the average.

Here are two examples of two days with the same TMax, TMin, TMean but very different averages:

You can see a slight change in the hourly temperature profile can dramatically change the average, but not the TMean because TMax and TMin have not changed.

This means crucial data is lost with just the three daily numbers that come from EC. If one wants to see what is actually going on with temperatures, one should be counting the number of hours at each degree temp and see what shifts have been happening over time.

Thus, I maintain that TMean is a meaningless number as an indicator of trends in temperature over time. It's not a measurement, it's a course calculation. This leaves TMax and TMin as the only physical data points one can work with, even though the yearly highest and lowest of those two values may only represent 1 hour each for the entire year.

Hence, to get a better profile of what is happening you have to look at the range of TMax and TMin for the respective seasons. Tmax ranges in the summer (to see if the planet is really "getting hotter") and TMin in the winter to see if we are getting more or less cold. This is why I present such in this blog.