Will a Small Change in Common Temperature Result in a Massive Change in Extremes? – Watts Up With That?

Guest Essay by Kip Hansen – 30 August 2022

One of the major misleading claims being pushed by The Climate Team and the various climate propaganda cabals is the “general mantra that has emerged in this area of ​​climate science: “A small change in the average means a large change in extremes.” (see also here and here).” Patrick Brown at The Breakthrough Institute wrote about the issue recently in “Effective Climate Communication on Extremes Should Not Sacrifice Clarity in the Name of Persuasion”.

This mantra is supported and promoted with images such as these (there are quite a few, readers can just scan down through them, but should notice the obvious differences):

Pretty convincing, isn’t it? That’s the problem – it’s convincing without being true.

What does the temperature distribution of a real weather station look like? I picked one at pseudo-random from the National Centers for Environmental Information feature called Daily Summaries map. I choose a station near the center of the United States – Atlanta Missouri, station code: USR0000MATL. I downloaded daily summaries (including TMAX, TMIN, and TAVG ) from August 2003 through August 2022, nineteen yearsand, after removing the error codes in the TAVG column (values ​​of 600 and 599) and converting values ​​(listed in tenths of a degree C) to degree C with decimals [ 241 to 24.1°C ] had MSExcel create a histogram of the values. I use a histogram, an “approximate representation of the distribution of numerical data”, with 2 degree C bins to clearly illustrate a real world example of the distribution of temperature data.

We are interested in hottest of the hot summer days. In 19 years, they have seen only 15 days with an average above 30°C (86 °F)…less than one day a year.

Let’s compare this actual station data distribution, above, to the theoretical “normal distribution” used by the climate enthusiasts in their graphics at the beginning of the essay —

Not a very good match is it? Not sure, page up to see the normal distributions used in the propaganda messages which all look like this. (image on left)

Seems right to the folks on the street, if they are not paying close attention.

This is the dw.com version, shifted to show “small increases in the average”. But what they show is moving the whole distribution a full 20 to 25% to the right. They fail to mention that this eliminates almost all very cold weather – but that wasn’t their point. The Climate Central folks use the same trick – shift the average a full 25% to the hot side.

If we are talking to them 1°C that is claimed for Global Warming in the last 100 years, this is what happens to real station data:

What changed when we added one degree centigrade to each and every daily average? The whole shifted to the right, to the warmer side. The long-term (all daily values) average also increased by 1 degree.

How many extra hot days – extreme hot days? NONE

Before the small increase in the average, there were 15 days above 30 °C (86 °F) only one of those above 33 °C (about 90 °F).

After the small increase, there would still have been only 15 days (out of 6860 days) with averages above 30 °C and still only one above 33 °C, still less than one per year.

Why? Two reasons: 1) a small change only produces a small change in linear systems like daily average temperature and 2) the shape of the real distribution looks like real temperatures in middle America and nothing like a normal distribution.

Summer days average between 21 and 29 °C (70 and 85 °F) with very few really hot days, with averages above 31 °C (88 °F), only 15 out of 6860. And, visually, Spring, Fall and some Winter days average 0 to 20 °C in about equal numbers. The cold days, 0 down to -21 °C far outnumber the hot days.

Long fat tail on the cold side, short steep tail on the hot side. Increasing the average by 2 °C doesn’t change the result very much…and the effect depends entirely on were one draws the line (in degrees) between hot summer days and extremely hot summer days. The hotter days are still only increased a single additional degree.

Looking at Tmax and Tmax+1, we see a slightly different shape, but similar overall pattern:

Very few (27 out of 6860) hot days greater than 37 °C (99 °F) for the 19 years shown (about 1.5 days per year) and when the average is increased by 1 °C, the same number of days (still about 1.5 days per year over 38 °C or 100 °F) but a highest temperature of 42 °C (107 °F), one day in 19 years.

To create a change that would be important to the people of Atlanta, Missouri, a big change in the number (or temperature) of hottest days per year, the daily average in Atlanta, Missouri would have to shift about 6 °C to the hot side; thus moving the taller column of 27 to 29 °C over into the 33 to 35 °C range and a similar shift of the Tmax hottest days into the high 90s and low 100s.


Looking at the real distribution of daily temperatures at an actual weather station, over a period of 19 years, we find that a small change in the average temperature causes only a small change in hotter days.

Small changes in the climate averages do not produce large changes in temperatures.

Temperature averages are not normally distributed.

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Frequent readers will know that I don’t think temperature averages are quite proper for evaluating climatic changes, even short term and local. Here I use a long-term average only to follow the conventions of CliSci and to illustrate the falsity of their meme.

A better way to look at temperatures, in my opinion, is to look at Tmax and Tmin shown on the same image. It is acceptable to show Tavg ( Tmax+Tmin/2 ) as a visual tool, although it is not particularly meaningful as it does not translate into the temperature profile of the day, which would be far more informative. Here is the year 2004 for Atlanta Missouri:

We see that Atlanta had a late December week-long thaw that year, which then dropped back into very cold temperatures -10 to -20 °C. An “Annual Average” would have missed this potentially agriculturally important fact.

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Author’s Comment:

Philosophically, the problem is the climate enthusiasts have pretended that the “climate average” (of any metric) is random normally distributed data. As in “A random variable with a Gaussian distribution is said to be normally distributedand is called a normally deviate.” There is no scientific reason to believe that is true, the evidence is to the contrary, and yet they use it to try and make a [false] point about changing climate.

Only in non-linear dynamics, in which systems can exhibit sensitive depending on initial conditions, do we find small changes producing large changes. For general climate temperature, the reverse is suspected, that is that temperature may exhibit uncanny long-term stability with variability that is self-similar over different time scalit.

Start comments with “Kip…” if addressing me.

Thanks for reading.

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