## 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.

J. Richard Wakefield has published three fiction novels, Blinding White Flash, Blinding White Flash Invasion and The Barn. The sequel to The Barn, The Cunningham Arrests, is going to the publisher in 2015. He was a firefighter for 22 years in Toronto, and a professional computer programmer for 25 years. He lives with his wife, Dorothy, in Southwestern Ontario.
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### 4 Responses to Why Mean Temp is meaningless

1. Anonymous says:

Interesting work. I would suggest that you remove %Diff from your table though–it is misleading and not very valuable information. Can you provide details on how you access temperature records for those interested in other station data?
Thanks

• jrwakefield says:

The links should be there, if you mean other places than Canada. The website I got the data from isn’t complete, it’s rather sporatic unfortunately, which limited the stations I could use. I was hoping the BEST data would solve that.

2. malagaview says:

Great to see you picking up on this (Tmin+Tmax) / 2 insanity…

Tracking the mid-point between the daily extreme outlier temperatures is simply meaningless…
Calling it a Daily Average is simply disingenuous…
It is a vaguely indicative, but statistically useless, Daily Outlier Mid-Point
Averaging these numbers in the monthly and annual averages is simply surreal…
Further obscuring these meaningless numbers by calculating Anomalies (with varying baselines) is simply hocus pocus

The how cold does it get Tmin values can be usefully analysed…
The how hot does it get Tmax values can be usefully analysed…
The analysis of the daily temperature range Tmax – Tmin is useful…

I am incredulous that seemingly intelligent minds can ignore this herd of elephants in the room.

3. BioBob says:

Agreed !

Actually, it seems to me that temperature itself is meaningless as well when one wants to know about climate. What you are actually after is the HEAT content of any system. So the actual numbers we should be after is joules, btu, watts, etc. as well as relative humidity, etc. and any other variables we can accurately collect to characterize heat itself. Temperature itself is only useful in defining boundaries where limits/phase changes/black swan events are encountered,

After all, you are trying to describe a portion of the global heat engine’s chaos which is more concerned with entropy and thermodynamics than evanescent temperatures.

The only problem is that getting heat numbers is much more work and climate “scientists” mostly seem inordinately lazy to me. LOL