Numbers  — Tricky Tricky Numbers: Part 3

Guest Essay by Kip Hansen – 21 August 2022

This series of essays concerns Numbers.  Not the government-controlled lottery game type of numbers, or the older version run by crime organizations in every U.S. city, but just this: “A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.”   Much of science (in nearly all disciplines) concerns itself with measurements of all types – measurements most often expressed as numerical quantities – as numbers.

Part 1 of this series made the point that “Numbers are just Numbers”.   Lots of interesting things can be done with numbers and lots of even more interesting things can be done with sets of numbers – data sets and time series – through the magic of statistical analysis and statistical maths programs.  However, what can be done with the numbers is not the same of what can be done with the “things” that the numbers enumerate.  Such things as kilograms, hertz–frequency as cycles per second, lengths, temperatures in various degrees, color as frequency of light emitted or reflected, density, hardness – all the measurable properties of physical matter including those that are qualities.  When the numbers of a thing are treated as if they are (or are the same as) the thing(s) enumerated, troubles ensure – reification has taken place, someone has come to “…think of or treat something abstract as a physical thing.”   

Part 2 of this series dealt it the reasons why “One cannot average temperatures”.  This fact is a bit harder for most to understand as it is a common everyday practice to average temperatures, speak of “the average temperature” of some day, city, region, or even the whole globe.  Thus, when shown that the practice is scientifically improper and the results of such  are nonsensical (except in the most simplistic, daily pragmatic senses), confusion and objection results.

This third and final part of the series will expand on the reasons – the underlying why — that temperatures cannot be averaged and why when it is attempted, the results do not represent what they claim to represent. 

In this essay, I will limit the “averaging of temperatures” to its present-day use in Climate Science in which average surface temperatures, measured over time in disparate locations,  are used as evidence that the Earth’s climate, as a whole, is retaining more energy and thus “becoming hotter”.  As expressed at

 “By adding more carbon dioxide to the atmosphere, people are supercharging the natural greenhouse effect, causing global temperature to rise. According to observations by the NOAA Global Monitoring Lab, in 2021 carbon dioxide alone was responsible for about two-thirds of the total heating influence of all human-produced greenhouse gases.”

Or this from the NY Times section “The Science of Climate Change Explained: Facts, Evidence and Proof — Definitive answers to the big questions”:

“We know this is true thanks to an overwhelming body of evidence that begins with temperature measurements taken at weather stations and on ships starting in the mid-1800s. Later, scientists began tracking surface temperatures with satellites and looking for clues about climate change in geologic records. Together, these data all tell the same story: Earth is getting hotter.” 

There are a lot of varying opinions about the whether that statement is strictly factual, but my point in quoting it is only to show that “global temperature” is presented as a measure of “global heating”.  But as I showed in Part 2, temperature is not a measure of heat (or heat content).  So, even if global temperature (if there is such a thing) is rising that metric [“a system for measuring something“] will not tell us if the Earth’s climate is gaining heat or not.

[ Note:  As I have said before, it is my understanding that the Earth’s climate has been warming since the mid- or late 1700s – as the Earth comes up out of the Little Ice Age. ]

How is temperature not a measure of heat?

The following definitions and formulas are taken from an engineering site, BrightHubEngineering.

Total Heat Content of the Air  — The total heat content of the air is the sum of the sensible heat of the air and the latent heat of the air. Thus,

Total heat of the air = SH + LH

The sensible heat (SH) depends on dry bulb temperature of air while latent heat (LH) depends on dew point temperature of the air, hence the total quantity of heat in the air depends on the dry bulb and dew point temperature of the air. Further, for any combination of the dry bulb and dew point temperature, there can be only one wet bulb temperature, hence the total quantity of heat in the air also depends on the wet bulb temperature.”

The current versions of global mean surface air temperature  (and there are many) are often reported in “anomalies” (differences) of some current-period average temperature (daily, monthly, annual) over some previous 30-year base period average temperature (there is no standard – Earth Observatory – the previous link – uses 1951-1980 – other reported anomalies use 1981-2010 and 1991-2020).  These anomalies are difference of averages from some other average and used as if the numerical results can be reported in degrees (usually °F or °C) as if the number was an actual temperature.  In no case — even if the number actually represented a temperature — would the reported numerical figure represent any measure of heat, either greater or lesser.  As in the paragraph above, to find heat from temperature one needs more information.

[ Again, what follows are the formulas for determining the heat content of any quantity of air — think, maybe, the cubic meter of air surrounding a MMTS or Stevenson Screen at a weather station.  It is not strictly necessary to understand these formulas to understand the point of this essay – readers can glance through them if not particularly interested in the gory details. ]

We need to first determine Sensible Heat (most simply “the heat that can be felt”) which is done as follows:

The sensible heat of the air is calculated as follows:

SH = m*0.133*DBT

Where: m is the mass of the dry air, 0.133 is the specific heat of air in Kcal/kg and DBT is the dry bulb temperature of the air.

We need also to determine the Latent Heat:

The latent heat of the air is calculated as follows:

LH = m*w*hw

Where: m is the mass of dry air, w is the specific humidity of dry air, and hw is the specific enthalpy of water vapor taken from the steam tables as the enthalpy of water vapor at dew point temperature.

When we look at the temperature record of a weather station, we don’t always see the metrics we need to find out how much heat is in the air surrounding the Stevenson Screen or the MMTS weather sensor.

To calculate the Total Heat Content of Air (a specific volume of air) we need the following:

1. The mass of the air under question.   The mass of the air requires “volume” and “air pressure” — the mass of air in one cubic meter of air will increase with an increase in air pressure.

2.  The Relative Humidity – and here we are getting a little into the weeds as humidity is not simple.  But, we are saved by modern technology — as “there’s a web site for that.”    In order to sort out these metrics, we can use the handy calculator to Calculate Dewpoint, Wet-bulb Temperature from Relative Humidity.

I hope that readers aren’t expecting me to calculate the heat content of some air at some weather station at some particular time.  I just want you to be aware of the fact that it can be done, but that it isn’t being done – and because it isn’t being done, we don’t have a reliable metric for heat content of the air at any particular point and time thus cannot have a reliable measure of regional or global heat either. 

Let’s try to see why it isn’t calculated and used even though the calculator on your smartphone is powerful enough to do the math.  Here are the meteorological observations from a CO-OPS weather station, chosen because it reports Temperature, Barometric Pressure (air pressure) and Relative Humidity (not all stations do so or have the information publicly available).  Note that this particular weather station is right on the waterfront – literally just meters from the river’s edge. 

[Readers can just quickly scan the graphs and explanations – to the line of tildas (~~~)]

This weather station also reports wind speed and direction (hard to see direction in this image, see link above):

The wind speed is in meters per second.  Our one cubic meter of air surrounding the MMTS sensor is usually not the same from one six-second reading to the next, no less for the six-minute averages.

Just to see the relationship between the three important metrics, I have overlayed them:

Temperature (blue) and Relative Humidity (amber) look to be opposing one another, while Barometric Pressure (green) is more-or-less independent.  However, these relationships are tightly linked as this one-day graph shows:

That circled-in-red shift in barometric pressure is a front passing through around midnight causing a radical drop in temperature and a similar radical rise in relative humidity. 


Heat is an extensive property of matter – it is an amount of energy – and thus can be added, divided, and averaged.  This is in opposition to temperature, which is a qualitative intensive property.  Temperature cannot be added to temperature, thus cannot be averaged (see Part 2). 

Much of climate science is about energy retention in the climate system — which may be taking place — but of one thing be can be sure,  averaged temperature records are not evidence of such. 

Evidence of increasing heat content of the Earth climate requires scientific measurements of heat over the time period of climate – at least 30 years.  There are a lot of proxies which the IPCC and others believe are usable in that regard, including various forms of temperature averages, and even combined averages of the temperatures of different types of objects such sea surface skin temperature calculated from satellite observations and kriged surface air temperature anomalies from averaged thermometer readings.  None of these, of course, are valid in terms of the physics of thermodynamics (again, see Part 2).

[ Proxy:  “An entity or variable used to model or generate data assumed to resemble the data associated with another entity or variable that is typically more difficult to research.”  [ source ] ]

Some of these proxies for the heat (increasing or decreasing) in the Earth’s climate are known to be far from strictly scientific.  Sea Surface Skin Temperature, from satellite readings, measures the temperature of the top few millimeters of the sea.  It is not the temperature of some volume of sea water or the water below the surface, which changes temperature across depths. The actual temperatures of the sea are extremely complicated and some cannot even be measured

Obviously, averaging sea surface skin temperatures with 2-meter surface air temperatures doesn’t produce a measure of heat in the Earth climate system either.

Bottom Lines:

1.  To support a claim that the Earth’s Climate System is “getting hotter” one has to have a long-term time series of measurements of heat in the climate system.

2.  Current Global Mean Temperature data sets do not measure heat and thus can not supply evidence for #1.

3.  The lack of such a time-series doesn’t mean that the Earth’s climate isn’t gaining energy (heat) – it simply means we don’t have any reliable measure of it.

4.  Climate Science may have some evidence of long-term energy gain or what is commonly labelled “Earth’s Energy Budget” — energy in/energy out — but it doesn’t seem to be dominate in the ongoing climate controversy.  The latest paper shows that we can still cannot directly measure instantaneous radiative forcing.  “This fundamental metric has not been directly observed globally and previous estimates have come from models.  In part, this is because current space-based instruments cannot distinguish the instantaneous radiative forcing from the climate’s radiative response.”  It is possible that future satellite missions will be able to measure directly and accurately Earth’s incoming and outgoing energy.

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Author’s Comment:

This series has built upon the basics of quantification – counting the numbers of things.  Huge and serious scientific errors come about when the things counted are not really the thing one thinks one is counting.  One of these errors is the odd un-physical assertion that temperature a proxy for measured heat.

As for the insistence that the Earth is getting “hotter” — the global average temperature (such as it is claimed) currently runs just under 15°C — or about 58.8°F. Coolish by my standards, certainly not hot.

In this specific case, I have presented the concept that temperatures, temperature measurements in whatever degrees, are intensive properties of matter and not subject to being added, multiplied or subsequently divided, which precludes creating averages of temperatures.  One can surely find a number by adding the temperature of Los Angeles on noon today to the temperature of Chicago yesterday noon, and divide by 2 but the result will not be a temperature of any place or any time.  This extends to one of the problems of Global, Regional, State, National, weekly, annual temperatures and their anomalies over various periods of time and space.  

Temperature Averages (or their averaged anomalies) also share all the problems of averages in general (and Laws of Averages Part 2 and Part 3). 

A lot of people are real fans of Global Average Temperatures….but let me remind you of their true application, as illuminated by Steven Mosher:  “The global temperature exists. It has a precise physical meaning. It’s this meaning that allows us to say… The LIA was cooler than today…it’s the meaning that allows us to say the day side of the planet is warmer than the nightside…The same meaning that allows us to say Pluto is cooler than earth and mercury is warmer.”  [ source ]  And I agree wholeheartedly.  But, that and that alone.

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via Watts Up With That?

August 23, 2022 at 04:25PM

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