Numbers –Tricky Tricky Numbers: Part 2

Guest Essay by Kip Hansen – 30 July 2022

One cannot average temperatures.

Let’s start with this simple statement – this statement is true but comes with some common-sense caveats.

Important Note:  The purpose of this essay is not to refute the basic underlying concepts of “global warming” or “climate change”.  Those concepts and their supporting data are an entirely different topic.  This essay is about a scientific point:  One cannot average temperature. This fact may affect your understanding of some of the supporting points of Climate Science.

Let’s say you run a web site for corporations interested in having conventions in Topeka, Kansas in August and you’d like to inform attendees what kind of weather, in terms of temperature, they should expect, so that they can pack clothes suitable for the trip. A chart like this is perfectly appropriate.  It shows the average of historical high and low temps for each day of the month and appropriately shows this as a range and not just a number.  It provides a common-sense answer to the corporate question:  “What’s the weather like in August in Topeka?”  Answer:  Hot days and pleasant warm nights.   So, speeches and presentations inside the air-conditioned auditorium during the day and in the evening, the  Tiki Bar Luau around the hotel pool is definitely on!

In this case, they have not really attempted to “average temperatures” —  they just averaged the numbers about temperatures to find an expected range of historic highs and lows – they don’t think this is a real temperature that could be measured – they acknowledge that it is a rather vague but useful range of expectable daily highs and lows.

This acceptable and reasonable approach is far different than taking the high temperature of San Diego, Los Angeles, Mohave and Palm Springs, adding them up, dividing by four, and pronouncing that you have produced the temperature average of the SW California Desert.   You may have an absolutely correct — precise to many decimal places — mathematical mean of the numbers used, but you will not have produced anything like a numerical temperature or a physically meaningful result.  Whatever numerical mean you have found will not represent the physical reality of “temperature” anywhere, no less the region of interest.

“But, but, but, but”  ….. no buts

One cannot average temperature

Why not?  Temperature is just another number, isn’t it?

Temperature is not just another number – temperature is the number of – the count or measurement of — one of the various units of temperature.

temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature). Temperature is not the equivalent of the energy of a thermodynamic system.  source ]

So, we can say that objects with temperatures with higher numbers, regardless of which scale one is using (°F, °C, K), are “more hot” and objects with temperatures with lower numbers (using the same scale) are “less hot” or “more cold”….and we can that expect that heat energy will  flow from the “hotter” to the “colder”.

Multiplying temperatures as numbers can be done, but gives nonsensical results partially because temperatures are in arbitrary units of different sizes but most importantly because the temperatures do not represent the heat energy of the object measured but rather relative “hotness” and “coldness”.  “Twice as hot” in Fahrenheit, say twice as hot as 32°F (freezing temperature of water) is 64°F – obviously warmer/hotter but only nonsensically “twice as hot”.  In Celsius degrees, we’d have to say 1°C (we can’t double zero) and we’d have 2°C or 35.6°F (far different than 64°F above).  Yes, that is because the unit sizes themselves are different.   However, if we wanted to know how much “heat” we are talking about, neither degrees Fahrenheit or degrees Celsius would tell us….temperature is not a measure of heat content or of heat energy.

A cubic meter of air at normalized sea level air pressure (about 1,013.25 millibars) and 60% humidity at a measured temperature of 70°F contains far less heat energy than a cubic meter of sea water at the same temperature and altitude.  A one cubic meter block of stainless steel at 70°F contains even more heat energy.  The relative hotness or coldness of a body of matter can be expressed as its temperature, but the amount of heat energy in that body of matter is not expressed by giving its temperature.

How is heat expressed – quantified – in science?:  the units of heat energy are calories, joules and BTUs.  [ source ]  We see that none of the units of heat are units of temperature (°F, °C, K). (Note:  If thermodynamics were easy, I wouldn’t have had to write this essay.)

Temperature is a property of matter – and temperature is specifically  an Intensive Property

Extensive properties can be added together – Volume:  Adding 1 cubic meter of topsoil to one new cubic meter of topsoil equals two cubic meters of topsoil and fills twice the volume the raised-bed garden in your yard.  Length:  Adding one mile of roadway to one mile of existing roadway gives two miles of roadway.

But for Intensive Properties, this does not work.  Hardness is an Intensive Property.  One cannot add the numerical Mohs scale hardness of apatite, which has a value of 5,  to the numerical Mohs scale hardness of diamond, which has a value of 10, and get any meaningful answer at all – certainly not 15 and likewise, not “5 plus 10 divided by 2 equals 7.5”.

Color is an Intensive Property.  Color has two measures, wavelength/frequency and intensity.  Most of us can easily discern the color of matter – our eyes tell our brains the generalized wavelength of the light reflecting off or emanating from an object which we translate to a color name.  Scientifically, the wavelength (or mixed wavelengths) of the reflected or emanated light can be measured as frequencies (in terahertz — terahertz, 1012 Hz ) and wavelengths (in nanometers).  Colors cannot be added as numbers.  In colored light, adding the three primary colors evenly results in “white” light.  In pigments, adding the three primary colors results in “black”, and other combinations, such as magenta and yellow, in surprising results.

Similarly, temperature, an Intensive Property, cannot be added.

“Intensive variables, by contrast, are independent of system size and represent a quality of the system: temperature, pressure, chemical potential, etc. In this case, combining two systems will not yield an overall intensive quantity equal to the sum of its components. For example, two identical subsystems do not have a total temperature or pressure twice those of its components. A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome. In special circumstances averaging might approximate the equilibrium temperature after mixing, but this is irrelevant to the analysis of an out-of-equilibrium case like the Earth’s climate.”    [ source:  Does a Global Temperature Exist?  By  Christopher EssexRoss McKitrick and Bjarne Andresen  ( .pdf ) ]

That is a wonderful, but dense, explanation.  Let’s look at the salient points individually:

1. Temperature, an intensive property, is independent of system size and represents a quality of the system.

2.  Combining two systems (such as the temperatures of two different cubic meters of atmosphere surrounding two Stevenson Screens or two MMTS units) will not yield an overall intensive quantity equal to the sum of its components.

3.  A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.

4.  Dividing meaningless totals by the number of components – in other words, averaging or finding the mean — cannot reverse this outcome, the average or mean is still meaningless.

5.   Surface Air Temperatures (2-meters above the surface) are all spot temperature measurements inside of mass of air that is not at equilibrium regarding  temperature, pressure, humidity, or heat content with its surroundings at all scales.

We can see that even at very small scales, the few meters surrounding the MMTS sensor at the Glenns Ferry weather station in Idaho, the air temperature system is far from being at equilibrium  — air over a hot transformer, frozen bare grasses, snow patches and brush, each absorbing heat energy from the sun and with differing heat content.  All these smaller sub-systems are actively out-flowing heat or absorbing heat energy from the unequal systems around them.  In a practical sense, if one was standing next to the sensor, you would know it was “cold” there, the air at the sensor being well below freezing – but in a pinch, you might be able to cuddle up to the transformer and feel warmer sharing its heat.  It is not, however,  scientifically possible to “average” the air temperatures even inside of the two-meters-on-a-side cube of air around the sensor.

One cannot average temperature.

# # # # #

Author’s Comment:

I am under no illusion that this essay will be widely accepted by all that read here.  It is, however, scientifically and physically correct and might shatter a lot of firmly held beliefs.

I will be writing a follow-up, Part 3, covering the excuses used in CliSci for pretending that they can validly average temperatures – including the lame excuses:  “We don’t average temperatures, we average anomalies”; “We don’t just find means, we find weighted means”; “We don’t average, we krig”; “We don’t make data up, we ‘use numbers from the nearest available stations, as long as they are within 1,200 kilometers’ [750 miles].” (Note:  This is the approximate distance from Philadelphia to Chicago or London to Marseille, which as we all know, do not share common climates, no less air temperatures); and many more.  In all cases, temperatures are inappropriately averaged resulting in meaningless numbers.

One can, however, average and work with heat content which is an extensive property of matter. It is the heat content of the “coupled non-linear chaotic system” which is Earth’s climate that Climate Science is concerned with when they insist that increasing atmospheric CO concentrations are trapping more heat in the Earth system.  But CliSci does not measure heat content of the system but instead insists on substituting the meaningless numbers various groups label as Global Average Surface Temperature.

Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about.  I will try to clarify if you ask specific questions.  If speaking to me, start your comment with something like “Kip, I wonder….”