# 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 Essex, Ross 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.

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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 CO2  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….”

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August 9, 2022 6:04 pm

Some thoughts from Roy Spencer in WUWT: Top Ten Skeptical Arguments that Don’t Hold Water
9. THERE IS NO SUCH THING AS A GLOBAL AVERAGE TEMPERATURE Really?! Is there an average temperature of your bathtub full of water? Or of a room in your house? Now, we might argue over how to do the averaging (Spatial? Mass-weighted?), but you can compute an average, and you can monitor it over time, and see if it changes. The exercise is only futile if your sampling isn’t good enough to realistically monitor changes over time. Just because we don’t know the average surface temperature of the Earth to better than, say 1 deg. C, doesn’t mean we can’t monitor changes in the average over time. We have never known exactly how many people are in the U.S., but we have useful estimates of how the number has increased in the last 50-100 years. Why is “temperature” so important? Because the thermal IR emission in response to temperature is what stabilizes the climate system….the hotter things get, the more energy is lost to outer space.”

Sparko
August 9, 2022 6:40 pm

Specific heat capacity is needed to make any average meaningful.
Also for the purposes of SB avg(T^4) really isn’t the same as Tavg^4, and come to think of it, emissivity varies with temperature anyway, and you really need to know what the area of the surface is to calculate precisely.
Seems to be a hell of a lot of bad averaging in climate science

observa
August 10, 2022 12:20 am

Seems to be a hell of a lot of bad averaging in climate science

Nick will set you straight and put you onto the right ones-
Trillions of dollars at risk because central banks’ climate models not up to scratch (msn.com)

Geoff Sherrington
August 10, 2022 2:50 am

observa,
The Reserve Bank of Australia has a recent letter suggesting it might be prudent to conduct an exercise in due diligence on the climate science on which they rely. An answer is awaited.

Joao Martins
August 10, 2022 3:26 am

Seems to be a hell of a lot of bad averaging in climate science

Yes, that is the point. By DEFINITION, an average is NOT a REAL entity. An average does NOT exist in the physical world: it is ALWAYS a human construct. A discretionary construct: it depends on what is chosen to be averaged.

August 10, 2022 8:36 am

“an average is NOT a REAL entity.”

An average is a statistic, not a measurement.

Is it useful?
How accurate is it?
Useful for what?
How useful?

Those are four good questions

Richard Page
August 10, 2022 9:11 am

Those are 2 good questions and a bit of waffle that should have been answered in the first question.
You’re welcome.

August 10, 2022 1:42 pm

A global average temperature increase of +1 degrees C. in 50 years may be nothing important, but a global average temperature increase of +1 degree C. in 10 years could be a very important statistic.

Richard Page
August 10, 2022 2:35 pm

You’re wrong. Statistics in specific areas of, say, a companies production or turnover can be useful for that company – global statistics for production are not. Similarly, a 1C rise in temperature globally tells us bugger all – where and when did it occur? Was it a gradual or incremental increase in one or multiple regions, or was it an artefact of error ranges? Your figure answers none of those questions. Having regional temperatures and comparing them against historical and other regional temperatures may be useful as it tells you something about the changing area. Homogenising everything into one big averaged clump says nothing except that someone has far too much spare time on their hands.

August 10, 2022 11:57 pm

Virtually every scientist in the world is wrong and you are right? Don’t make me laugh.

I saidcould be a very important statistic.”

It is a high level statistic that could be a leading indicator of global, regional or local climate changes that need detailed analysis. It is a simple statistic that ordinary people can understand.

Consider the Dow Jones Industrial Average stock market index. 30 large cap stocks. If you are a stock investor who does not own any of those stocks, or even any large cap stocks, the DJIA can still be a useful indicator. If it goes down 20% in six months, there’s a high probability your own stocks also went down. Even though the average has no direct connection with your investments, it can be a useful statistic for stock investments in general.

Similarly, no one lives in the global average temperature, but that statistic can be a useful indicator of changes in regional and local climates — the climates we live in.

August 11, 2022 7:16 am

Yah, well… If you do climate science the way you understand stocks, I have to warn you urgently of the sandstorm approaching from Lapland…
Or maybe your investment strategy relies on siting your heat probes next to tarmac, electric transformers, volcanoes and other places that will increase sales of your prefab snow flakes.

Tim Gorman
August 11, 2022 11:30 am

Similarly, no one lives in the global average temperature, but that statistic can be a useful indicator of changes in regional and local climates — the climates we live in.”

Once again, the average gives you *NO* information concerning the temperature profile. And it is the *entire* temperature profile that determines the climate we live in. Since multiple combinations of different temperatures can give the same “average” value the average gives you no way to differentiate between the combinations in order to judge anything to do with climate.

Averages *LOSE* important data. Averages don’t gain important data as you calculate them.

This is as true for local and regional climates as well as the global climate.

Jim Gorman
August 13, 2022 8:40 am

Lets keep in mind you are not really discussing the end result of all the averaging of temperatures. The Global Average Temperature is an average of “anomalies” which is even worse. Invariably the people that say it is warming are referencing anomalies and not absolute temperatures.

August 10, 2022 3:43 pm

No, those are four good questions. They are what can be called a “NAND gate cascade.” (Any of the earlier questions that are answered “no” make proceeding with the cascade meaningless.)

Jim Gorman
August 10, 2022 5:47 pm

An average is one statistical descriptor of a distribution. How meaningful it is in reference to the distribution must be stated by other descriptors like variance, standard deviation, kurtosis, and skewness. Confidence intervals are very much affected by the distribution shape which these descriptors attempt to show.

When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.

August 10, 2022 7:57 pm

When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.”

As I’ve been noting, WUWT posts global average and US average on its front page. No mention of kurtosis. Articles here (eg Spencer, Monckton) are full of temperature series without those statistics.

Tim Gorman
August 11, 2022 6:27 am

As I’ve been noting, WUWT posts global average and US average on its front page. No mention of kurtosis. Articles here (eg Spencer, Monckton) are full of temperature series without those statistics.”

So what? This is no defense. Once again, it is the argumentative fallacy of Appeal to Authority.

Winter temps have a different variance than summer temps. Yet the SH and NH temps get mixed together every single month with apparently no attempt to reconcile the different variances! Using anomalies doesn’t help at this at all!

Can you actually address the ISSUES at hand instead of just resorting to argumentative fallacies.

August 11, 2022 1:33 pm

“it is the argumentative fallacy of Appeal to Authority”

It is surprising to me to be slammed for appealing to the Authority of WUWT. But the original query was

“When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.”

To which I say, when was the last time anyone showed any of those things? Anyone at all? WUWT doesn’t. You are dismissing a lot of WUWT content as meaningless, including the reference pages.

It isn’t “Appeal to Authority“; it is Reductio ad Absurdum.

August 11, 2022 6:07 pm

No, I’m saying, in effect, why pick on me? This often happens – I post a graph, just like the thousands that have been posted at WUWT without demur, and I’m told that I have left out essential things and the graphs are meaningless.

August 11, 2022 7:16 pm

It’s basically mindless heckling. If you really believe that temperature graphs should not be displayed without a whole lot of other information, take it up with WUWT, where it is done all the time. If it’s something that only bothers you when I do it, well, maybe you have identified the cause.

That’s why it is relevant to mention how often folks here invoke average temperature to promote some narrative like the Pause. If you really believe all this stuff, some kind of protest has to be made about that.

Carlo, Monte
August 11, 2022 8:43 pm

take it up with WUWT

Who is the gatekeeper of all things WUWT?

b.nice
August 12, 2022 4:18 pm

“It’s basically mindless heckling.”

A great description of Nick’s comments !!

Tim Gorman
August 12, 2022 2:55 pm

This is the argumentative fallacy of “woe is me” or Appeal to Pity.

Carlo, Monte
August 11, 2022 8:42 pm

I posted some just a few days ago, where were you?

Jim Gorman
August 11, 2022 9:14 am

Two wrongs don’t make a right. Don’t make excuses, make facts.

Robert B
August 10, 2022 4:28 pm

You can average the concentration of solutions to get something meaningful. Concentration is also an intensive property, quantity of a component divided by the total quantity of the sample.

You need to ensure that;
it’s the same component you measure the concentration for,
same extensive component for the quantities, e.g. amount that is measured in moles for the solute and volume for the sample, using constant units e.g. mole per litre or M
and the quantities of the samples are exactly the same.

The average will be the same as the total quantity of the component in all samples divided by the total quantity of all samples.

If you only partially sampled what you are analysing, it is also correct if the composition is constant (pointless averaging it, as well, except to reduce uncertainty due to random error). It’s an estimate that could be utterly useless if not. Possibly useful if you took many samples, evenly throughout, and if the profile of the composition doesn’t vary greatly. If the profile varies considerably, you can fit polynomials to what data you have to get an estimate of the profile and average that as if it’s an average of sampling the whole (Krigging).

It’s tempting to view temperature as the amount of heat energy that went into the system divided by the heat capacity (an extensive property while specific heat capacity is the intensive property ie. per unit of mass) because of the basic definition of heat capacity, but that definition is for a very small change in temperature of the system and the heat capacity can change dramatically with phase changes.

Now I wouldn’t argue against using the average of temperature measurements, even just minimum and maximum rather than continuous measurements, as a proxy of net flow of energy into the system. I say proxy because you are not taking into account so many things. It’s the temperature of a probe influenced by its environment and I could write an essay on the issues with equating it with the extra heat energy accumulated by the region.

That is if the temperature record to do it existed ie. if this profile that was made by Krigging what data exists was the actual record. This is the difference in opinions here, because nobody acknowledges that it’s a proxy only marginally better than tree rings, and that is if it were actually measurements rather than an estimated profile.

The average global surface temperature might be a meaningful estimate of the flux of energy out from the Earth if the emissivity was proportional to temperature rather than temperature to the power of 4. And still a proxy rather than a measure as what happens above the surface will make a much bigger difference than a degree change to the flux from that patch of Earth. The small range of temperatures of sea surfaces means you can ignore that if you are just using SST as an indicator of climate change, or the surfaces needing to warm to get that flux back to equal the energy coming in. It can’t be used as a meaningful measure (or modelled).

And if you use the average surface temperature like that, a 1% increase in flux only requires a 0.25% increase in the average surface temperature of 0.7°C. So an extra 100 ppm gave an extra third of a percent downwelling, corresponding to about two to three tenths of a degree.

I can’t believe that we are making major policy decisions on this because academia is defending the science.

Jim Gorman
August 10, 2022 6:10 pm

You must be careful what you do with this. Temperatures are not a good proxy for heat energy. There are too many other variables that enter into determining the heat energy in a volume of air. Water vapor for one, and it is a big one. Is it reasonable to average temps over a month when you have no idea how water vapor changed during the month? Is it reasonable to average a desert temperature with one from Miami considering the difference in heat capacities of the two different locations?

Robert B
August 10, 2022 9:16 pm

I used the analogy with tree rings because they really are a proxy for how good the growing season was rather than average temperature of the region. Extremely poor thermometers.

Tim Gorman
August 11, 2022 8:00 am

Tree rings depend on a lot of things, precip, insect infestation, shade from surroundings, and temp. That’s why they are such a poor thermometer.

Tim Gorman
August 11, 2022 5:23 am

The average will be the same as the total quantity of the component in all samples divided by the total quantity of all samples.”

What does the average tell you about each sample individually? Just like with temperature you will be unable to identify which samples have a high concentration and which have a low concentration.

“total quantity of the component”

In other words you are calculating an *extensive* value, the total quantity of the component, and then calculating an intensive property using that value.

How do you get a “total quantity of temperature”? And what do you divide it by in order to calculate some “thing”.

Robert B
August 11, 2022 4:38 pm

I’m just looking at why some scientists are adamant that the average has some physical meaning. So you add up a number of samples x1/y + x2/y + xn/y and divide by n then you get (x1 + x2 + ….xn) / ny. Pretty straight forward.

X is delta Q and y is heat capacity. A lot of problems with that simplification, same as why thinking of a proxy as a measure of a variable is wrong.

The idea of using a proxy comes from psychology. You believe a variable that you can measure shows similar trends that have occurred in variables that you can’t measure. In this case, if everything else was the same, an average of the real temperature for all the infinitesimal areas that make up the whole surface should show any trends of increasing Q due to the GHE, is the BELIEF.

So there are two arguments.

Is it a good proxy for delta Q?

Is it sane to use Krigging with a proxy?

Scissor
August 9, 2022 6:53 pm

I doubt that the average temperature of an average room can be determined to within a couple of degrees (especially if kids are going in and out).

Measuring an average of the earth is a slightly bigger challenge.

Mr.
August 9, 2022 8:45 pm

Yeah what might serve your purpose in a laboratory environment can lead you up a garden path when you test it outdoors with life-size quantities of substances, materials and equipment.

It’s the classic “academic” result vs real-world outcomes.

August 10, 2022 12:54 am

Only the scientific point that temperatures cannot be averaged to produce any kind of a meaningful result”
So what of your figure showing averages for Topeka. You seemed to think that meaningful. You might think averages over time are meaningful, but not over space. Well, first if the newcomers to Topeka find the quoted average helpful, they are doing spatial extrapolation. Infilling even (at that bar). But suppose you were to arrive in Kansas by balloon, which might land at a random point. What then? The Kansas average is your best estimator.

Geoff Sherrington
August 10, 2022 2:58 am

Nick,
Then we have William S Briggs, statistician, writing this:
“Now I’m going to tell you the great truth of time series analysis. Ready? Unless the data is measured with error, you never, ever, for no reason, under no threat, SMOOTH the series! And if for some bizarre reason you do smooth it, you absolutely on pain of death do NOT use the smoothed series as input for other analyses! If the data is measured with error, you might attempt to model it (which means smooth it) in an attempt to estimate the measurement error, but even in these rare cases you have to have an outside (the learned word is “exogenous”) estimate of that error, that is, one not based on your current data.”
Do not smooth times series, you hockey puck! – William M. Briggs (wmbriggs.com)
This advice is relevant also for Kip’s Topeka figure, which has a type of smoothing.
If the advice of Briggs is accepted, it raises the issue of how to measure and process errors. And uncertainty. Question – are the uncertainty limits around a time series of “anomaly” daily temperatures smaller or larger than those around a time series of measurements as observed? Geoff S

August 10, 2022 8:41 am

Smoothing is very useful if shown on the same chart as the raw data. It helps make a trend visible that may have otherwise been invisible. It can also make a trend visible that is really nothing more than meaningless random variations.

Jim Gorman
August 10, 2022 6:21 pm

I think the term is spurious.

Carlo, Monte
August 10, 2022 5:43 am

So what of your figure showing averages for Topeka.

Sophistry—the Topeka graph is not a single-number average.

Tim Gorman
August 10, 2022 6:21 am

Kip’s graph is showing the VARIANCE of the maximum and minimum temperatures along with their average allowing the person viewing to make a judgement about the WEATHER at a location, not the climate! There is no “averaging” being done in the guise of a *mid-range* value or an anomaly derived from the “mid-range” values.

When you find the “mid-range” value you have lost *all* of the pertinent data required to judge what the actual climate is. The climate is the entire temperature profile. The mid-range value can be the same while the climate is significantly different! That’s one of the major problems with the “global average temperature”, it gives exactly zero information on the actual changes in climate!

Richard Page
August 10, 2022 9:20 am

No. The most useful information for Topeka would be a descriptor giving an indication of, say, warm days and cooler nights with a small chance of rain: most people have an entirely subjective view of temperature anyway so using those figures may be a dodge for meteorologists to get information across in the shortest possible time but means very little to most people. Frankly ‘temperature’ is only an indicator of what heat energy has done to the physical surroundings anyway – do a proper job and measure the heat directly instead.

ih_fan
August 10, 2022 11:24 am

The Kansas average is your best estimator.

We expect more than just averages of what it “feels” like outside from a “science” that receives billions of dollars per year and influences decisions at national and even global levels.

Jim Gorman
August 10, 2022 6:20 pm

You’ll note that WE only showed a graph of temperatures. He did not attempt to show humidity levels. The weather stations do give a heat index for a reason. I live in Topeka. Two days ago we had a morning temp of 70 @ 94% and an evening temp of 84 @ 84%. Today we had a morning temp of 58 @ 96% and an evening temp of 91 @ 25%.

Do you think there was a big difference in the heat index between the two evenings? And, BTW, the 84% humidity was around that for the whole day.

Temperature is NOT a good proxy for heat energy. It might be ok for determining radiation values per S-B but that is all. The global climate has more to it than radiation.

Hoyt Clagwell
August 9, 2022 9:57 pm

“Why is “temperature” so important? Because the thermal IR emission in response to temperature is what stabilizes the climate system….the hotter things get, the more energy is lost to outer space.”

Nick, no part of this statement relates to a “global average temperature.” IR is emitted differently all around the globe just as temperatures are different and constantly changing all around the globe. The last part of your statement is just a description of equilibrium. The more water going into the pond, the more water goes over the weir. If more energy is lost to space because things get hotter, how are they getting hotter, and what’s the problem?

August 10, 2022 12:30 am

The last part of your statement”
It is Roy Spencer’s statement (vla WUWT) not mine.

“Nick, no part of this statement relates to a “global average temperature.” I”

Roy says a global average temperature is meaningful. So it’s hard to say an average isn’t. Plus, of course, Roy calculates one every month, and WUWT runs an article about it, closely followed one from Lord M about the “pause”. Pause of what? Global average temperature, of course.

Geoff Sherrington
August 10, 2022 3:00 am

And Australian temperatures, which by UAH v6.0, have not warmed for a decade, to this month of August 2022. Geoff S
http://www.geoffstuff.com/uahaug2022

Geoff Sherrington
August 10, 2022 5:58 am
Carlo, Monte
August 10, 2022 5:45 am

Appeal to authority—more sophistry.

Tim Gorman
August 10, 2022 6:27 am

Roy says a global average temperature is meaningful.”

That’s no answer! It’s an argumentative fallacy called the Appeal to Authority. An assertion isn’t correct merely because some states it, it must be shown to be true – WHICH YOU HAVEN’T DONE!

None of the global average temperatures can tell you if maximum temps are going up, if minimum temps are going up, or if a mixture of both are going up. Yet that information is VITAL for actually judging whether or not changes are pointing to significant changes in climate that will affect humankind.

Suppose the global average temperature goes from 15C to 15.1C. Can *YOU* tell us what caused it to go up? Can you tell us *where* a change happened that caused it to go up? If *YOU* can’t then why do you think it is important?

Hoyt Clagwell
August 10, 2022 8:35 am

Then I disagree with Roy Spencer, and you for quoting him. Nothing in your response refutes my point. I think most of the people contributing to WUWT will agree that a “global average temperature” is just an abstract concept which exists merely as a calculation with little to no ability to predict future climate states around the world. It is primarily used on this site to refute the people who popularize the notion that if the GAT goes up, catastrophe must necessarily ensue and man must be the cause.

August 10, 2022 3:49 pm

@Kip – more precisely, “argument from consensus.”

Hoyt Clagwell
August 10, 2022 9:29 pm

Kip, I wasn’t arguing that a GAT as a meaningless abstract is proved by the number of people here who believe that. I simply observe that most contributors here do seem to feel that way more or less, rightly or wrongly. I was merely pointing out that the concept of a GAT appears on this website frequently (as Nick points out) but for reasons other than what Nick thinks is the reason.

Tim Gorman
August 10, 2022 9:51 am

Hoyt,

The CAGW people can’t even use the GAT to tell you if minimum temps are going up, whether max temps are going up, or if it is a combination. They just all assume that it is maximum temps going up and they will keep going up forever with no limit, thus turning the earth into a cinder.

What a joke!

Jim Gorman
August 11, 2022 4:01 am

A GAT may or may not be useful depending on the uses made of it. However, one failure for climate science is to attempt to use a “mean”, i.e., a statistical descriptor of a distribution, without also quoting the other necessary descriptors to allow one to judge just how well the mean represents the distribution. Even Dr. Spencer fails to do this.

Tell us the other descriptors that are associated with any of the so-called Global Average Temperature determinations. What are the variance, standard deviation, kurtosis, and skewness? Is the distribution normal? Is it bimodal? Don’t just quote some SEM calculation that tells how close the estimated mean is to the population mean. Give us the details of the population distribution.

If you want to deal with statistics these things are necessary to evaluating the information. These shouldn’t be hard for a mathematician to calculate.

Redge
August 9, 2022 11:33 pm

Whilst it is feasible to calculate a global average temperature, I would suggest the amount of adjustment to raw data and interpolation across vast areas makes a global average temperature irrelevant and likely inaccurate

August 10, 2022 12:32 am

I calculate the average using unadjusted temperatures. It makes very little difference.

You can calculate using just half the data points, then the other half (or any other large subset that you like). You get the same answer.

Geoff Sherrington
August 10, 2022 3:11 am

But Nick,
Should you use adjusted or raw? Here is a comparison of raw Tmax Alice Springs, Australia, with 4 versions of ACORN-SAT adjusted data and an earlier one.. Kip, the daily numbers have been averaged into annual, for convenience of data handling, not because it is the fundamentally correct act.
What error or uncertainty summary would you draw from this?

Geoff S

August 10, 2022 5:36 am

The right questions are:

Do you trust the people who do the infilling and compile the global average temperature?

Is there evidence they are biased?

I would not trust NASA-GISS or NOAA to tell me the time.

Jim Gorman
August 11, 2022 4:15 am

I don’t think folks appreciate that temperatures are MEASUREMENTS and not simple old numbers on a number line to be manipulated. The goal for GAT is to obtain a number that is NOT A MEASUREMENT. The best you see for uncertainty is a Standard Error which is a number that describes how well a sample mean predicts a population mean. It is not uncertainty.

What WE is trying to do here is laudable. Too much of climate science has revolved around finding an unreal measurement from statistical analysis. They need to go back to the beginning and realize that they are dealing with physical measurements, not just numbers. They need to reevaluate how to treat measurements to obtain an accurate description of temperature. One of the uses of krigging is to arrive at a map describing the geophysical phenomena being evaluated. Why don’t we see contour maps of temperature (or anomalies) so they can be evaluated? How about contour maps of IR leaving the earth and entering the surface? How about contour maps of humidity so people can see the heat distribution?

August 10, 2022 5:34 am

The 194- to 1975 global average temperatures have changed considerably from 1975 to 2022. Science fraud !

August 10, 2022 6:27 am

That’s 1940 to 1975.
not 194- to 1975.

Richard Page
August 10, 2022 9:26 am

People have been telling him that for ages, although a lot of comments were concerned with the complete ignorance of errors. Climate ‘Scientists’ are little more than statisticians – they have no idea how those numbers relate to anything whatsoever but they do like playing with them!

Jeff Alberts
August 10, 2022 3:55 pm

I’ve been saying this often for years here, usually any time a graph with a single line for “global temp” is presented.

August 10, 2022 3:56 pm

Mathematics is only a tool – it MIGHT produce useful results, and it might not.

I can average the number of crickets I heard last night with the length in centimeters of the skirt that my wife wore to work this morning. I can be very honest and also compute the error bars for my average (I might have missed a chirp, or some other noise in the house sounded like one; my length measurement is only as accurate as the tape measure I used, and the amount of annoyance my wife showed at my apparent insanity).

The resulting number, with its error range, is a perfectly good number, calculated with mathematical rigidity. It is also absolutely and entirely meaningless.

Jim Gorman
August 11, 2022 4:24 am

Very good!

Trying to map a temperature versus time along with a CO2 concentration versus time hoping to see some way to tie them together is exactly your description.

If time is the common independent variable, the best you can get is a correlation of 1. That is not proof of causation. Climate science must establish CO2 as an independent variable and temperature as the dependent variable. That will let one develop a functional relationship that allows verification of predictions. It also will show one temperature for a given CO2 concentration.

However, don’t hold your breath. Lots of studies showing CO2 follows temp instead of the other way around. Finding an actual relationship will be hard. Probably too hard to get much funding!

Solomon Green
August 10, 2022 6:52 am

Ten days ago, at about 12.30 the thermometer on a North facing wall by our stone patio at the back of our house registered 104.6 F. Within a minute or two the temperature on our tree-shaded brick patio at the bottom of our garden was 86.0 F. The distance between the patios is around 60ft.

Can we say that the average temperature in our garden was 95.3 F?

Do we need to record that at the time there was a pleasant breeze blowing?

August 10, 2022 5:32 am

We know there has been warming for 300+ years
The alternative is cooling
We should be thrilled we got warming
The people living in the 1690s would have lived todays’ climate.
The last half of the 1600s was too cold.
Some famines in Europe back then.

Now let’s get to important questions:

Is the current climate pleasant?
— Yes

Can humans predict the climate in 50 to 100 years?
— No

If the1975 to 2022 global warming continued for another 47 years, would that be a problem?
— No. Unless you object to warmer winter nights in Siberia and more
greening of the planet.

Are leftist Climate Howlers climate science fools, or do they have devious political motives for climate scaremongering?
— I say both. Leftists are the Forrest Gumps of climate science.

Is Al Gore a rich doofus?
— Yes

August 10, 2022 6:29 am

Not true
Depends on the accuracy of the data and global average
+ 0.5 degrees C. might be meaningless
+ 5 degrees C. would be meaningful

August 10, 2022 8:47 am

You are wrong again
A +5 degree C. increase of the global average temperature would most likely be a very important statistic, assuming decent accuracy of the underlying temperature data. How you could argue with that statement escapes me.

Tim Gorman
August 10, 2022 12:49 pm

Decent accuracy? Uncertainty accumulates when it is associated with independent, random variables. Just like variances add when combining them. They both get treated in a similar manner.

What would you consider decent accuracy when you are combining a 1000 independent measurements with uncertainty?

Jeff Alberts
August 10, 2022 4:16 pm

If you have a room with 5 people that are 5′ tall, and a 6’5″ guy walks in, has everyone in the room gotten taller?

Tim Gorman
August 10, 2022 12:47 pm

If the aggregate uncertainties from the base absolute numbers is greater than +5C then how would you know if it is meaningful?

If you average 30 numbers whose uncertainty is +/- .7 using root-sum-square then you get sqrt(30) * 0.7 = +/- 4C. If you then average 12 groups of 30 (i.e. monthly to get annual) you get sqrt(12) * 4C = +/- 14C of uncertainty!

I know the CAGW crowd thinks all uncertainty cancels and the stated temperature values are all 100% accurate but that just isn’t reality at all!

andic
August 10, 2022 8:28 pm

Very well put.

“I know the CAGW crowd thinks all uncertainty cancels”
It is rare to find someone who understands what UoM actually is actually describing.

It is not a measure of fluctuation about a true value.

I have on my desk a Certified Reference Material 24X07001 (batch C). The Ti content is 3.14% +/- 0.02% (95% CI)

So if I measure stick it in my XRF and measure it ten times will I obtain results which average to 3.14%? Nope, of course not, but why?

one factor is:
CRMs are certified based on multiple analyses of a number of samples from the batch to be certified, but the material is not perfectly homogeneous therefore the samples will be different, the likelihood that my sample is exactly 3.14% is vanishingly small, the same is true of all of the CRMs which were used to calibrate the methods used to certify 24X07001C. And so the situation arises that all we can say is that the Ti content of my piece is somewhere between 3.12% and 3.16% (probably (95% certainty)). Now if I calibrate an instrument with 24X07001C I have no choice but to use 3.14% as a best estimate, but am knowingly introducing a bias of up to 0.02% (and there is an estimated 5% chance its greater) into my future measurements of this alloy.
This type of bias is not averaged out over multiple measurements over time and cannot be assumed to be averaged out by measurements from different sources.

Tim Gorman
August 11, 2022 5:58 am

Wow! You pegged it perfectly!

Your ten measurements *should* average out to the true value for that one sample (assuming zero systematic bias in the measurement device) but will it come out to 3.14%? Like you say, probably not.

Using the stated value in subsequent calculations is fine – as long as the uncertainty is propagated along as well!

Tim Gorman
August 10, 2022 6:33 am

It’s not just meaningless because it is an intensive property. It actually tells you nothing about climate. Climate is a function of the entire temperature profile at a location, including daily and seasonal profiles of maximum and minimum temperatures. An average, especially of anomalies, gives you *NO* clue to the actual temperature profiles associated with the anomalies – thus no information about the climate either.

August 10, 2022 8:59 am

WRONG
A significant global average temperature change is high level statistical evidence that there may be significant changes to local temperatures, where people actually live.

A small average temperature change probably reveals nothing of use. The dabate is how much of an average temperature change is important. My guess is +/- 1 degree C. is not important. A +2 degree C. increase ,ight indicate that more informasltion is needed about the temperature change –changes by latitude, local changes, TMIN and TMAX changes — seasonal changes, time of day changes, etc.

The GLOBAL AVERAGE TEMPERATURE CAN BE AN INDICATOR OF SOMETHING IMPORTANT HAPPENING TO THE GLOBAL CLIMATE OR A STATISTIC THAT HIDES IMPORTANT DETAILS. OR BOTH

The 2020 election bellwether county poll showed Trump won 18 or 19 counties,yet lost the election. The bellwether statistic result in 2020 was unprecedented in polling history. It does not prove election fraud in 2020, and does not change a single vote, but is high level statistical evidence of election fraud that needs further investigation.

Tim Gorman
August 10, 2022 12:56 pm

“WRONG
A significant global average temperature change is high level statistical evidence that there may be significant changes to local temperatures, where people actually live.”

Malarky! The uncertainty of the global average temperature is so high you can’t tell if there is a significant change or not!

Each temperature measurement is of a different thing made by a different device. The uncertainty in such a distribution can *NOT* cancel. Thus any average of the distribution inherits the total uncertainty of the elements in the distribution.

I would defy you to go outside from a 70F house to an outside temp of 75F and be able to tell the difference. If you can’t tell what that difference is then how would you have any chance of being affected by a 4F change over 100 years?

The GLOBAL AVERAGE TEMPERATURE CAN BE AN INDICATOR OF SOMETHING IMPORTANT HAPPENING TO THE GLOBAL CLIMATE OR A STATISTIC THAT HIDES IMPORTANT DETAILS. OR BOTH”

Only if you buy into the CAGW claim that all temps are 100% accurate. If each temp is actually “stated value +/- uncertainty” that simply can’t be possible.

Redge
August 9, 2022 11:38 pm

The average human has one tit and one ball but you’d be hard pressed to find an average person

M Courtney
August 10, 2022 12:17 am

But if the average human is measured consistently and the average increased the number of tits while decreasing the number of balls you could tell that the ratio of women to men is changing. And in which direction.

An average not being a physical property does not mean the average has no meaningful descriptive function.

You can average temperature (in theory, the practice is hard). And you can make meaningful statements about that average.

However, Kip is right to say that the meaningful statements do not include what the temperature actually is at any given time and place.

Tim Gorman
August 10, 2022 6:35 am

M.,

I disagree. The most likely cause is a change in the ratio of men and women but that is not the only possible cause of a change. Besides, physical attributes are an extensive property, not intensive properties.

August 10, 2022 12:33 am

The average human has one tit and one ball”
If you want to know how many tits and balls there are in a country, that is a useful statistic.

Derg
August 10, 2022 1:50 am

But what would it tell you?

Geoff Sherrington
August 10, 2022 3:13 am

Derg,
That the woke police will be at your door, like they did to US President Trump. Geoff S

AlanJ
August 10, 2022 5:38 am

If the average number of breasts and testicles was found to be changing over time that might be something worth looking into, though.

ih_fan
August 10, 2022 11:30 am

… and if you are a biologist

August 10, 2022 6:29 am

Thaks for elevating the comments to the Ph.D. level

DMacKenzie
August 10, 2022 10:23 am

A fine example of why one is easily misled when doing “statistics” on quantized phenomenon…

Jim Gorman
August 11, 2022 4:31 am

“The average human has one functional tit and one ball but you’d be hard pressed to find an average person”

Fixed for you!

Brent Wilson
August 11, 2022 11:37 am

Wrong. Males also have two mammary glands, albeit vestigial. Females also have two gonads.

Graemethecat
August 10, 2022 3:32 am

Any fool like Nick Strokes can average temperatures. That doesn’t mean such averages have any meaning. Only enthalpy (an extensive property) can have a physically meaningful average. Without knowledge of heat capacity and mass, averaging is completely meaningless, save for climate “scientists”.

Thought experiment for Strokes: an incandescent speck of iron of mass 1mg at 1500K lands on a 1Kg iron block at 300K. What is the average temperature?

Similarly, a 1Kg iron at 400K is placed on the preceding 1Kg block at 300K. What is the average temperature? Would it change if one of the blocks were made of lithium (heat capacity per gram about 8 times that of iron)?

Graemethecat
August 10, 2022 6:51 am

I presume GAST stands for “Global Average Surface Temperature”. If Climate “Scientists” used Global Average Surface ENTHALPY instead, that would be perfectly meaningful and indeed valuable in detecting real climate change.

Tim Gorman
August 10, 2022 1:04 pm

The problem is where do you measure the enthalpy? At 6′ above land? Above and below that the enthalpy value will be different, it is a gradient as you move up and down because of the change in pressure and humidity. How about the ocean? Right at the surface or at some distance above the surface? How would you combine those values with the land values?

Take a look at the attached pressure map. These gradient lines change from hour-to-hour, day-to-day, etc. How do you capture an average>?

August 10, 2022 3:23 pm

“Any fool like Nick Strokes can average temperatures”

So if it is so foolish, why does WUWT display on its front page the global average of UAH? Or the US average derived from USCRN? What’s with Monckton and Co going on about the new Pause, to much local cheering? What is the Pause without a global average temperature?

Graemethecat
August 11, 2022 12:29 am

WUWT allows you freely to post your stupidity on its platform, so why not global average temperature?

Duane
August 10, 2022 5:11 am

There certainly is such a thing as average daily global temperature, but such is meaningless. It’s meaningless because it cannot be measured (it is literally impossible to measure the temperature of every cubic centimeter of the earth’s atmosphere in real time and compute an “average” … and the average even if computed would by itself be meaningless, because the entire atmosphere is not a population with shared attributes.

Tim Gorman
August 10, 2022 6:37 am

Temperature is also a time varying property, day/night, winter/summer, cloudy/clear, etc.

What does the average of a time varying, intensive property tell you?

Jeff Alberts
August 10, 2022 4:20 pm

It’s meaningless because it cannot be measured (it is literally impossible to measure the temperature of every cubic centimeter of the earth’s atmosphere in real time and compute an “average” “

That’s not why it’s meaningless.

August 10, 2022 5:20 am

Hard to understand why a Roy Spencer quote would get “thumbs down” votes
and surprising that the Stroker would quote him.

Hoyt Clagwell
August 10, 2022 9:02 am

Because this statement is just wrong:

“Because the thermal IR emission in response to temperature is what stabilizes the climate system”

These things don’t ’cause’ the climate to be stable, these things are the ‘effect’ of a stable system. They are examples of equilibrium which is the nature of the universe.

Also, IR emissions don’t occur in response to any ‘average global temperature.’ They happen to a greater or lesser extent depending entirely on local, real time, conditions. Averages have nothing to do with it.
One could calculate the average temperature of different planets to come up with a universal average planetary temperature but, what could that possibly mean? Remember, even the calculated GAT isn’t ‘global.’ It is just a small sliver of atmosphere 2 meters in thickness, representing just a tiny percentage of an atmosphere that is 62 miles thick. That still ignores all of the temperature variations in the oceans and beneath the crust.

August 10, 2022 1:57 pm

THERE ARE ALSO ALMOST 8 BILLION FIRST HAND WITNESSES TO SOME OR ALL OF THE GLOBAL WARMING SINCE 1975.

Every average temperature compilation says there was warming.

I felt warmer winters here in SE Michigan,

The only other possibility is global cooling, since a flat temperature trend over 47 years would be unusual.

But Hansen is here pontificating that the average temperature statistic is worthless,
AND HE IS WRONG.
If he is right, virtually every climate scientist in the world is wrong, including “skeptic” scientists. Your choice.

How useful the global average temperature statistic is remains open to debate. I say it is useful if there is a large change in a short period of time, AND NOT USEFUL if there is a small change over a long period of time.

August 10, 2022 4:26 pm

I’ve experienced warmer winters here in SE Arizona – AND colder ones. That time period encompasses the year we had a real White Christmas in TUCSON (6″ on the ground). The several other years we had a succession of < 20 degree nights. Generally, I’ve experienced more “colder than ‘normal'” winters for here since I moved here in 1985, than I did 100 miles north of here where I grew up.

THIS summer is quite a bit “cooler” than last year’s, in fact. Going by the high temperature readings, that is. The ENTHALPY is just about the same – a very weak monsoon flow last year, and a stronger than normal one this year.

I once did, for a statistics class, an analysis of the “average temperatures” for Tombstone and for Tucson. That was back in 2010 – but the Tombstone temperatures showed NO change (a statistically insignificant drop, actually) – and the Tucson temperatures plotted a classic “hockey stick.” What was the temperature of SE Arizona (Cochise, Santa Cruz, and the eastern half of Pima Counties)? Averaging these two would give you a number – that is completely wrong for either locality, and irrelevant to, say, Bisbee or Benson or Nogales.

Hoyt Clagwell
August 10, 2022 9:38 pm

“The only other possibility is global cooling, “

Richard, have you considered the possibility that some parts of Earth are cooling, some are staying the same, and some are warming. And the further possibility that those trends could change starting tomorrow, or next week, or next year? Why should the entire Earth be experiencing the same climate trends when the entire Earth doesn’t experience the same climates? What happens in Bristol isn’t necessarily the same thing that happens in Waikiki, or on top of Mt. Everest. Different variables all over. Climate is by definition local.

andic
August 11, 2022 12:30 am

Not useful for what?

Scare mongering presumably?

Tim Gorman
August 10, 2022 6:13 am

“Is there an average temperature of your bathtub full of water?”

Actually there isn’t, at least not in the short term. The temperature at the end of the bathtub away from the spigot will be colder than the water entering the bathtub from the spigot. This is the correct analogy to the air temperature – both are constantly changing! The water in the bathtub only reaches a constant temperature (i.e. an average) after a period of time. That is not the case with air temp, it never reaches an equilibrium point. That is also the problem with homogenization, even when using anomalies. The air temperature at two different points with different microclimates is never the same, it is constantly changing with time. The difference in air temperature between the two stations is dependent on distance, elevation, pressure (weather fronts, etc), terrain, and geography. Spatial averaging isn’t sufficient to account for the differences in microclimate, especially when you are trying to identify differences in the hundredths digit. There simply isn’t any way to account for this in developing an “average” air temperature. Using anomalies doesn’t doesn’t help. The temperature at the bottom of a valley will have a different variance then one at the top of an adjacent mountain top thus the anomalies and their variance will be different and trying to average them is a lost cause!

Tim Gorman
August 10, 2022 8:29 am

I see we both got a downcheck – but no actual refutation!

AZeeman
August 10, 2022 8:11 am

How about the average temperature of ice cubes and the drink they are in?

Kevin kilty
August 10, 2022 8:21 am

the hotter things get, the more energy is lost to outer space.”

Gosh, no. The hotter something gets, the more energy is being stored in that something. This statement doesn’t tell us enough to conclude that more energy is lost or gained by any means.

August 10, 2022 1:19 pm

You might make an argument that measuring the temperature of a tub with a constant amount of water over time, although technically wrong, still gives some information.
Maybe averaging the temp of two cities or comparable size, although technically wrong, has SOME value- specifically TRENDS.
(I averaged errors across manufacturing facilities of different types to give a trend on how the company was progressing on our “quality improvement” program and got constant objections from our PhD statisticians.)

Use of such averages to approximate a trend is only justifiable if the two (or more) items being measured are comparable in other respects (same tub of water, two similar urban cities).

But measure the temperature at the top of a flame on a matchstick – pretty hot.
Then take the temperature of a lukewarm bathtub.
Now average them. What meaning does that result have? THE FIGURE CERTAINLY DOES NOT HAVE ANY MEANING IN HEAT CONTENT, OR IN CHANGE IN HEAT CONTENT WHEN MEASURED OVER TIME.

When we measure temps 2 feet over land and 2 feet over an ocean we are not measuring relative heat content, yet that is supposedly the purpose of the exercise. (I’ll leave the WHY of that statement to more learned commenters.)

Carlo, Monte
August 11, 2022 7:12 am

This is why I call all of this “trendology”: they study “trends”, not climate.

Jim Gorman
August 10, 2022 5:36 pm

You betray your lack of physical laboratory experience. Read this reference and pay attention to temperature uniformity and temperature accuracy of a manufactured water bath. The device the author talks about has both a uniformity and accuracy specification of ±0.2°C.

Temperature Specifications Explained: Accuracy, Uniformity, Stability | Blog | WaterBaths.net

A little off topic, but do you a weather station to have a better specification than a laboratory water bath.

Did you not read Willis say that heat energy depends on more than temperature. How much heat energy does 1 cu meter of soil have vs a column of air 1 sq meter to say 30,000 feet?

August 10, 2022 6:17 pm

You betray your lack of physical laboratory experience”
Wearily, again, it is a quote from Roy Spencer, writing in WUWT, as linked.

Graemethecat
August 11, 2022 5:20 am

Why are you arguing from authority again?

Tim Gorman
August 11, 2022 5:38 am

Wearily, again, it is a quote from Roy Spencer, writing in WUWT, as linked.”

So what? Address the issue, don’t use an argumentative fallacy!

August 11, 2022 12:35 pm

I’m simply pointing out that whatever you make of what Spencer says, it doesn’t reflect my supposed lack of lab experience.

b.nice
August 12, 2022 4:15 pm

An ex-CSIRO lemming ought to know better !.

Nick obviously doesn’t !

Basic measurement and its comprehension seem to be beyond him.

Tom Halla
August 9, 2022 6:20 pm

Well, neither Fahrenheit or Celsius temperatures are ratio scale measurements, while Kelvin is.
But radiation is on a cube of the Kelvin temperature, so using linear increases is deceptive as to the effect.

August 10, 2022 4:59 pm

It’s not the scale used that makes temperature an intensive property.

I can express the temperature of my back yard in Fahrenheit, Celsius, or Kelvin – and it still tells me nothing useful about the energy content in Joules / meter^3 (an extensive property).

DaveW
August 11, 2022 2:00 am

I think I understood that, so I’m giving you a thumbs up.

So energy content of the atmosphere could be measured, in theory at least, and if so then changes could be tracked over time.

However, ‘average air temperature’ is an abstraction that gives no reliable estimate of the energy in the system.

Close enough or am I still confused? But thanks for putting it simply enough for me to try to think about it.

I do understand about how people get distracted by averages – e.g. they are often used as if they were intrinsic characteristics of organism such as an average length. You can calculate average length, but it isn’t much use because so many factors can affect how large an organism grows. There may be an intrinsic genetic limit to size, but even that tends to be variable over time and space. A range of observed sizes is usually the most useful information – like the graph of the range of temperatures observed in Topeka.

Tim Gorman
August 11, 2022 5:32 am

I’d say you understand it pretty well. The only comment I would make is that the energy content of the atmosphere is a gradient vertically. It changes with altitude. So one model with one output can only give a view of a part of the atmosphere. Other parts may be different.

August 9, 2022 6:33 pm

“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.”

This essay seems to drift toward saying that measured temperatures don’t tell you anything about the environment. And yet it starts out by saying that you can usefully use measured temperatures in Topeka for something. In fact climate scientists did not invent the use of measured temperatures to represent an environment. Newspapers have been telling people about the temperature in their town for at least a century.

” temperatures do not represent the heat energy of the object measured”
Well, they do if multiplied by the specific heat. And remember, climate science does not generally deal with temperatures but anomalies, which are temperature differences. This draws attention to the main role of temperature – it is a potential for heat flow. That is, heat flows down a temperature gradient. In this role conductivity is the parameter that matters, not specific heat. The average temperature is what a system gets to when all these fluxes have sorted themselves out. Conductive heat fluxes work out to reduce the temperature gradient, and so approach – wouldn’t you know – the average (weighted, it is true, by specific heat).

Meab
August 10, 2022 10:19 am

Kip, You are correct, humidity and air pressure are the two other factors along with temperature needed to determine the heat content of an air mass. Even if you had the TPH information for every surface measurement you would still have a very large error in computing the heat content of the global atmosphere as the temp, pressure, and humidity of the vertical profile above the surface varies widely, so the surface TPH does not give you the total heat content of the overlying column of air.

Add to that, you need the heat content of land and sea, and a knowledge of how that total varies throughout the year and between years before you know if the total heat content is truly changing. The average temperature is truly a meaningless quantity.

The total integrated microwave emission from microwave sounding satellites is a more useful measure, but still error prone. The sea level adjusted for subsidence/land rebound is perhaps the best semi-quantitative indicator of a total heat gain.

hiskorr
August 9, 2022 7:49 pm

I would be very dissatisfied with my “Newspapers” if they included only projections of expected “average temperature” in their “Weather Report” and left out the temperature range, and expectations of sun/clouds, precipitation, and winds, wouldn’t you?

H. D. Hoese
August 9, 2022 8:07 pm

It may not be an adequate comparison, but biologists sometimes talk about heat budgets. Organisms have developed all sorts of tricks to keep systems going because a lot operates on either side of the mean unless you are at ocean depths with tiny deviations. Averages are used, but not with much symmetry around a mean beyond generalities. How many times is it necessary to take a temperature in a 24 hour period to get an accurate mean and do they mean the same thing every day? Meteorologists need to quit using “normal” temperatures.

pls
August 9, 2022 10:27 pm

I don’t know about where you are, Kip. But here is Phoenix the various weather people very often give 5 day forecast as “15 degrees above normal” or “5 degrees below normal”. Even the NWS does that on their web site.

AGW is Not Science
August 10, 2022 4:13 am

Actually they should say “a little warmer than average” since THERE IS NO :normal” or “usual” temperature. What they’re talking about is a 30-year average, not a “normal” or “expected” temperature.

They misuse language in weather reporting in a manner that is simply deceptive.

Jeff Alberts
August 10, 2022 5:05 pm

waetherman/woman”

I just use Weatherthing. Since you can’t even know who’s what these days.

August 10, 2022 12:36 am

In fact meteorologists usually speak of average Tmax and Tmin.

Tim Gorman
August 10, 2022 6:46 am

Then why don’t climate scientists do the same? Why don’t the climate models output Tmax predictions and Tmin predictions instead of some kind of hokey average?

Mr.
August 9, 2022 8:52 pm

the main role of temperature – it is a potential for heat flow

A proxy for heat flow?

August 10, 2022 2:46 am

No, potential
Flux=-k ∇T
k=conductivity

michel
August 10, 2022 1:03 am

This essay seems to drift toward saying that measured temperatures don’t tell you anything about the environment.

No, it does not, and neither does the paper its summarizing. It says that taking a bunch of temperature readings across the Earth over time and calculating the average over time, tells us nothing about the environment, specifically, tells nothing about whether its getting hotter or colder on planet Earth.

The paper is very interesting (though I am unqualified to assess the mathematical detail) because it addresses the problem of attribution, and this is the heart of the question.

It is commonly argued that a given weather event is attributable to global warming. For instance, the recent Arkansas floods. The current long hot and dry summer in the UK.

We supposedly know that there has been global warming because the statistic of global average temperature has risen. But the connexion to the local phenomena, for instance the current UK summer, and the unusually high peak temperatures in some UK locations, is never demonstrated or even evidenced.

Its taken for granted that if the average global temperature has risen, this must make local rises in peak temperatures more likely. So we hear people saying that 40c+ could not have happened in the UK without global warming, by which they mean, a rise in global average temperature. That after all is the way we measure whether there has been any global warming.

But as Essex, McKitrick and Andresen point out, the average global temperature is not a meaningful concept – its not a physical quantity, it cannot be cited as the cause or explanation of anything. In addition they suggest that there are multiple plausible inconsistent ways of calculating it which will yield completely different answers to the apparently simple question: is the planet warming or cooling and if so by how much?

While it is impossible to prove that such averages are not useful in any manner whatsoever, it can be shown that temperature field averages cannot be useful in certain specific roles in which they are cited. For example, upward trends in X are said, uncritically, to indicate trends in underlying dynamics, such as changes in the numbers or severity of storms, and trends in rainfall, not to mention melting of glaciers or many other local physical dynamical processes.

What connection exists between these dynamical processes and such averages? No physically precise reasoning has been proposed as the basis of such a connection. Indeed, it is unlikely that there is any such connection because intensive variables, like temperature, do not generally drive dynamics, and in particular do not drive the dynamics of the atmosphere and oceans, whose dynamics are caused by gradients, or di¤erences in thermodynamic intensities, rather than the intensities themselves.

Recently its been alleged that global warming, again as measured by average global temperature changes, are impacting and will impact illnesses, their frequency and severity. Exactly the same problem is obvious: what exactly is the causal relationship, and between what entities. It cannot be that a rise in global average temperatures is the causal factor, because its not a physical entity. Any causal chain must start with something local, and be tied to (for instance) Wuhan market.

But this is never done, the lazy assumption is that if its warmer than usual at a given location it must be caused by average global temperature rising. Which it cannot be. And the average is then used. Its not argued that it was hotter than usual in Wuhan, and this led in defined ways to increased risk of interspecies transmission. Usually what happens is global warming is invoked as a sort of proxy for local conditions. Hotter measurements in Australia in this way can be invoked as causing a disease outbreak in Wuhan, without having to allege a specific and obviously implausible causal connexion.

They also make the important point that the global average is made up by taking as one continuous series the average of very different observations. To take one example, there have been changes in stations, both in location and perhaps more importantly the total number of them. This makes it even less meaningful.

If, for instance, I persuade 20 of my village neighbors to keep weather stations and record daily temps, and over the next 20 years two thirds of them drop out, then for me to publish the average of all observations on a monthly basis as if they were one continuous series would not be legitimate. This is what is being done. The sections in the paper which discuss this are very enlightening.

The authors also very amusingly point out, drawing on the way the global average temperature is calculated, that attributions of the sort commonly being made this summer involve temperature action at a distance, and in some cases an absurd relation between past temperatures and present weather events.

The paper, and Kip’s summary, get to the heart of the attribution problem. If we are claiming that climate change and global warming are causing (for instance) the recent UK heat wave, what exactly do we mean by global warming? How exactly has some measured quantity caused the heat wave, or modified its intensity or duration?

There’s no answer to this. Because nothing has been cited that could be a causal agent. What has happened, in Arkansas and in the UK, is rare weather events, and that’s all that has happened.

Geoff Sherrington
August 10, 2022 4:29 am

Michel,
You write: “Its taken for granted that if the average global temperature has risen, this must make local rises in peak temperatures more likely. So we hear people saying that 40c+ could not have happened in the UK without global warming, by which they mean, a rise in global average temperature.”
You cannot take that for granted. I have calculated many cases where it has not happened over time spans of many decades. But, I also have cases where it happens.
The question might have to wait an answer until we know more about mechanisms.
The ocean surface temperature seems no to show peaks rising in rhythm with background. All surface sea temperatures over open ocean come to an abrupt stop at 30 degrees C. The mechanism is being clarified in terms of cloud motion and properties. I do not think anyone knows if land temperatures are also limited.
But this is drifting away from Kip’s central thesis here. Geoff S

Tim Gorman
August 10, 2022 6:43 am

This essay seems to drift toward saying that measured temperatures don’t tell you anything about the environment.”

When you take an average you LOSE the information the measured temperatures tell you!

“And remember, climate science does not generally deal with temperatures but anomalies, which are temperature differences.”

The anomaly between 1C and 2C is the same as between 15C and 16C yet are generated by vastly different climates. So exactly what does the anomaly tell you about the change in climate? 1C/!C is a 100% change. 1C/15C is only a 7% change. Does a 100% change versus a 7% change represent the same impact on climate?

hiskorr
August 9, 2022 7:31 pm

Thank you! Thank you! Thank you! I’ve been saying the same thing, less succinctly, for decades! Now, if you will agree that your useful chart of expected Topeka temperature says little useful about August Topeka “expected weather” (I.e., climate), which would include humidity, winds, clouds, rain, etc., then we can dispense with the “Climate Change” nonsense and go back to laughing at what is actually being calculated– minuscule differences in Average Global Temperature!!

August 10, 2022 5:10 pm

I hope you mean the weather forecast as a whole, Kip.

There was one June when the wife and I traveled back to New England for a friend’s wedding – and had to dash into Walmart to buy sweaters. Her lifetime of living there, and my six years, told us that “normal” June was warmish, not usually hot – but never 55 degrees for a high.

JAK
August 9, 2022 7:38 pm

Kip,

You’re trying to make your point the hard way. I believe you’re trying to make the point that knowing the condition of a system is rather difficult with limited samples. Averaging more samples isn’t likely to correct that problem particularly if the further samples are equally unrepresentative. The average (linear, log-normal, etc.) of uninformative is still uninformative.

If I dip a temperature probe in the ocean, all I really know is the temperature of the probe. Likely that measurement is representative of the water adjacent to the probe. Fifty-foot away? Now we’re getting sketchy. Ok, I could grid the surface on five-foot centers for a mile around. I could properly average those numbers and I would have a valid average temperature, for that mile. However, that’s only likely applicable of a span of inches to a foot in depth.

So, if I want that average temperature to mean something (say the sensible heat content of that volume of water), then I need to make sure that my measurement system properly samples that volume. All the statistical tools in the world cannot reverse the inadequacies of measurement system.

So, while I agree with your general conclusions, you thermodynamic arguement doesn’t hold water. Given a properly measured temperature of a system (even averaged), I can tell a lot about the system. Using heat capacity and properly measured temperatures, I can tell you the final temperature of mixing cottage cheese with cotton candy.

Sampling the temperature of bucket of water is actually more challenging then most people realize. Sampling a cubic mile of ocean would be majorly hard IF it were standing still and unchanging. Normal, dynamic ocean conditions? Good luck storming the castle.

JAK
August 11, 2022 5:36 pm

Actually, if they had all of that data (since air density can be determined quite accurately from that) one still wouldn’t be able to accurately calculate sensible heat beyond so many feet from that point. One could then estimate the heat between here and the next station by taking an average, but that has many intrinsic assumptions that would be imprudent if the system was even steady-state let alone dynamic as you and Mr. Gorman observe.

Since both the atmosphere and oceans are quite dynamic, the assumptions become dubious. Since climate modeling is by definition an exercise in heat balance, not being able to even remotely estimate the heat content of even a few thousand cubic meters of air or water is rather a serious impediment. One might be able to live with the broad confidence interval around the estimate (why not invoke more statistics?) if the heat imbalance under dispute were even larger; but, we’re trying to tease-out a watt or two per square meter. Please.

As one of my instructors observed, if one has to make so many assumption to make a calculation, you might as well assume the answer.

Tim Gorman
August 10, 2022 6:53 am

So, while I agree with your general conclusions, you thermodynamic arguement doesn’t hold water. Given a properly measured temperature of a system (even averaged), I can tell a lot about the system. Using heat capacity and properly measured temperatures, I can tell you the final temperature of mixing cottage cheese with cotton candy.”

The problem is that the atmosphere is constantly changing. You are describing an equilibrium condition between cottage cheese and cotton candy. What is the average temperature of the mixture when cottage cheese and cotton candy is continually added/removed from the mixture in time varying amounts?

RickWill
August 9, 2022 8:14 pm

Anyone with knowledge of energy and temperature know they are different.

What is more difficult to explain to most is that increasing the average temperature of the oceans above 2000m is the result of reduced evaporation due to lower surface heat input. Lower surface heat input actually translates to higher ocean temperature. That is counter-intuitive.

There is a subtle difference between increasing ocean heat content due to surface heating and increasing heat content due to reduced surface heating slowing the ocean circulation from high latitudes to the equator. The greater the surface area of the oceans regulating at 30C means less surface heat input and less evaporation.

The simple fact is that oceans are coolest in December when the surface heat input is at a maximum.

So there is a HUGE misunderstanding that oceans can be heated from the surface in a matter of decades. That is another physical impossibility embodied in all coupled climate models.

Bob boder
August 10, 2022 3:33 am

This is why I always say, if the oceans warming it ain’t CO2 in the atmosphere doing it.

Geoff Sherrington
August 10, 2022 4:40 am

Bob boder,
In May 2022 there were a couple of linked papers from respected mathematician and hydrologist Demetris Koutsoyiannis and colleagues. The studied causality including puzzles of the type “Which came first, the hen or the egg?”. They use global climate as one test case for their theory and conclude (my summary) that changes measured in air temperatures cause changes in atmospheric CO2 levels. This conflicts with the Establishment view that it works the other way round.
Personally, I regard these as being of fundamental importance.
Geoff S
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2021.0835
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2021.0836

Graemethecat
August 10, 2022 11:07 am

We all knew that the CAGW alarmists had the CO2/warming causality the wrong way round from the Vostok and Law Dome ice core temperature series, which showed that temperatures always changed BEFORE CO2 levels.

August 10, 2022 1:34 pm

That is the result of natural climate change (ice cores)

It does not reveal the effects of manmade climate change

Both happen at the same time but are different.

Graemethecat
August 11, 2022 5:22 am

How does the effect of anthropogenic CO2 differ from that of natural CO2?

John Hultquist
August 9, 2022 8:14 pm

Kip,
your comment [ I will not be arguing the point – it is just too basic ]
is on a T-shirt that an ad keeps pushing to me with a pretty lady wearing it, namely
“I’m not arguing with you, I am just telling you why I am right.”

I like the idea of plants as integrators of climate. There are no Palm Trees where I live, but there are Ponderosa Pines. The pines have been here a long time – and continue.  The temperature will go from -20F to 115F in some years, but thankfully not every year.

H.R.
August 9, 2022 9:32 pm

Fauna as integrators of climate are useful indicators as well. I’ll be firmly convinced that Climate Change™ has occurred when iguanas, an invasive species in Florida** have expanded their range to Minnesota.

The average temperature of a region doesn’t tell us as much as iguanas can tell us about a region. There are States a little North of Florida that have a similar average temperature because of higher highs and lower lows that work out to about the same average. But they have no iguanas because the slightly lower lows are enough to k!ll iguanas whereas the lows in Florida usually just stun the iguanas.

**They actually issue “Falling Iguana Warnings” in parts of Florida when the overnight lows are forecast to be in the low 50s(F). It’s kind of weird when the evening weather forecast is “Clear and colder tonight with a chance of falling iguanas.”

H.R.
August 10, 2022 6:42 am

Kip – I’m really enjoying this series of yours.

I blame John. He started it. 😉 The constraint you put on the discussion is contrasted by all the other factors that go into climate. You did address what your presentation is NOT in your first post, and you have emphasized all along how narrow it is and why.

I can’t speak for John, but my comment was just meant to be an amusing (and true!) way to illustrate how much more climates consist of than just an average temperature. Average temperature alone doesn’t tell the whole story. Iguanas and palm trees and Ponderosa pines go a long way towards painting the whole picture.

So, my bad. I was just “a little outside” with that comment.

H.R.
August 10, 2022 7:31 am

Nope. Didn’t take it as critical nor too serious at all. 👍

The follow-up was a “why I dunnit” just in case someone didn’t know why iguanas had anything to do with anything.

Even the “my bad” was a little cheeky with that reference to the clip of Bob Uecker calling a totally wild pitch that Eric(?) or David(?) includes in their posts sometimes.

Macusn
August 10, 2022 2:39 pm

Armadillos, they also can be used.

Alexy Scherbakoff
August 9, 2022 8:28 pm

I’m waiting for the day when someone comes up with Earth’s average wind speed.

Alexy Scherbakoff
August 9, 2022 8:37 pm

What a wonderful world that would be and we could all live an average life.

Clyde Spencer
August 9, 2022 9:16 pm

And only have above average children.

Alexy Scherbakoff
August 9, 2022 9:54 pm

With above-average genders.

Geoff Sherrington
August 10, 2022 4:41 am

Alexy,
Like it. Geoff S

August 10, 2022 9:06 am

The average IQ is 100/
I’d expect them to be smart, however.

RicDre
August 10, 2022 2:49 pm

Kip==> You must live in Lake Wobegon.

RickWill
August 9, 2022 8:58 pm

No need to wait. You can get it now.

According to the research the global average windspeed has increased from about 7mph to about 7.4mph since 2010. The findings could be a boon for wind power with the speed increase translating to a 17% rise in potential energy for wind turbines.

As you can see, it is used here to encourage more wind turbines. Get them while the going is good. You do not want to be building wind turbines if the global average windspeed is tanking.

The power of wind is function of the cube of the speed so, as they point out, an increase from 7 to 7.4 of 5.7% results in power up 17%.

Alexy Scherbakoff
August 9, 2022 9:30 pm

Therefore an increase in average evaporation, average cloud cover and average rainfall. Which may result in the lowering efficacy of PVs. It’s all too complicated for me. I’ll mix another drink and watch some anime.

Retired_Engineer_Jim
August 9, 2022 10:33 pm

But that is an increase in kinetic energy, not potential energy.

Mr.
August 9, 2022 9:06 pm

If they do, don’t accept anything under 3 decimal points of one metre / second.

Otherwise, you’re being bullshitted to.

Retired_Engineer_Jim
August 9, 2022 10:32 pm

42

August 10, 2022 9:05 am

And when they do, I predict a climate emergency will be predicted too

Clyde Spencer
August 9, 2022 9:37 pm

One cannot add the numerical Mohs scalehardness 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.

Part of the problem is that Mohs Hardness is a ranking, not a continuous ratio scale. There is no mineral with a hardness of zero, and the resistance to scratching varies with the planes in the crystallographic structure. That is, hardness is vectorial. There are minerals with a scratch resistance intermediate to the integer Mohs values, but there is no defined way of assigning a number other than arbitrarily appending a one-half to the softer standard, thus calling something intermediate to Apatite and Orthoclase as having a Mohs Hardness of 5 1/2, sometimes inappropriately stated as 5.5, implying that the scratch hardness can be measured to a tenth of a unit.

On the other hand, there is a measure of resistance to indentation known as the Vicker’s Hardness that is calculated by taking the mid-range value of the widths of a diamond-shaped indentation, and then averaging several mid-range values to discern outliers, and improve the accuracy and precision, hopefully.

August 9, 2022 9:55 pm

Kip, nice article, and I endorse the science presented. One little nit to pick–a cubic meter of stainless steel at 70 degrees does not have more heat energy than a cubic meter of sea water at the same temperatures, although is does have the potential to transfer its contained heat energy more rapidly through conduction.

Alexy Scherbakoff
August 9, 2022 10:00 pm

I didn’t bother looking anything up or performing a calculation, but mass plays a big part. He was referring to a volume and not a mass.
Specific heat is based on mass, although a conversion based on volume is possible.

August 10, 2022 3:41 pm

Alexy, I ran the numbers, and although I had not considered the density difference between stainless steel and sea water, it turns out the specific heat difference is even larger, so the two ultimately have about the same heat capacity per unit of temperature. See my numbers in the comment to Kip below.

August 10, 2022 3:36 pm

You are right that I had not considered the difference in masses of a cubic meter of the two substances, Kip. But I may (accidentally) still be right that their heat content per degree is about the same. The density of stainless steel is about 7.5 to 8 g/cm3, and it’s specific heat is about c = 0.5 J/gK, while pure water has density 1 g/cm3, but specific heat of c = 4.18 J/gK. Joules of heat content is q=mc delta T, so if delta T is the same, for a cubic centimeter of stainless the quantity mc=(1cm3)(7.5g/cm3)(0.500J/gK) is between 3.75 and 4 J/K, while for a cm3 of water the quantity mc is (1g)(4.18 J/gK) = 4.18 J/k. So pure water has a slightly higher heat content per unit of temperature change. But I just looked up sea water, and found it’s specific heat is a bit lower than water, about 3.85 J/gK, but it’s density is a bit more, about 1.025g/cm3, giving
a value for the quantity mc for one cm3 of sea water of about 3.95 J/K. So I think a cubic meter of stainless steel and of sea water have about the same heat content per unit of temperature. As a teacher of high school chemistry for many years, I learned that iron is a pretty poor material for students to use for experiments determining specific heat, because it’s low value gave relatively high error. Water is amazing for its ability to store heat.

steven candy
August 9, 2022 10:09 pm

Your constraint that the sum of a set of sample values has to be a useful value in itself having a common sense interpretation in order for a statistic measuring central tendency, such as the mean or median to also have any useful common sense interpretation. This is an artificial constraint you have imposed with many counter-examples. Take one such; a tide gauge measuring sea level at a given site, where daily high and low tide measurements are taken each day of the year for a range of years and average annual sea-level height is obtained by summing the gauge measurements for the year and dividing by the sample size giving the mean height on that gauge at that site in that year. That total used to obtain the mean has no useful interpretation but the trend in mean sea-level height for that site does have a useful practical interpretation. Another example I am very familiar with. Samples of fish lengths taken in research surveys are important to monitor the average length over fishing seasons or differences between types of fishing method for fisheries management. The sum of the sample of fish lengths has no useful physical interpretation but measures of central tendency do. Bottom line is the mean as a measure of central tendency can have a useful physical and practical interpretation even if the sum used to obtain it does not. In this paper I modelled the complete empirical distribution of fish lengths using sample quantiles and cubic smoothing splines (https://doi.org/10.1016/j.fishres.2014.05.002)

steven candy
August 10, 2022 9:32 pm

Lengths of a sample of fish can be added for what purpose? To represent one mega-fish OR the fish all lined up head to tail. As ridiculous as it sounds. You are too enamoured by your own definitions. Submit your essays or bits of them for peer-review in scientific journals.

Tim Gorman
August 11, 2022 8:02 am

Samples of fish lengths”

You are the one that brought up fish lengths. Why?

Clyde Spencer
August 10, 2022 10:46 am

The sum of the sample of fish lengths has no useful physical interpretation but measures of central tendency do.

For purposes of setting a size limit for fish catches, a mean might be very misleading. The mean can be shifted by a few very large fish, or a large number of small fish. It is probably better to look at a distribution by size rather than trying to reduce the population to one or two numbers.

Tim Gorman
August 10, 2022 3:25 pm

A multi-modal distribution can’t be described using the average and standard deviation. You must use something like a 5-number statistical description.

steven candy
August 10, 2022 9:26 pm

Exactly what my paper published in Fisheries Research was about
“A nonparametric model of empirical length distributions to inform stratification of fishing effort for integrated assessments” 2014, http://dx.doi.org/10.1016/j.fishres.2014.05.002. Setting catch limits that incorporate size limits is typically done using integrated assessments (see my paper CCAMLR Science, Vol. 15 (2008): 1–34, https://www.ccamlr.org/en/system/files/science_journal_papers/01candy-constable.pdf).

Editor
August 11, 2022 9:34 pm

Steven Candy, you say “The sum of the sample of fish lengths has no useful physical interpretation.” YOU have put the word “useful” into the criterion. The sum of the sample of fish length absolutely has a physical interpretation. You line the fish up on the dock, nose to tail, and you get the total length laid out on the dock.

The key is the word “total”. If you have 10 kg of water and 40 kg of water, they have a total weight of 50 kg with a physical meaning. You can put them both on the scale and weigh them together. Total weight. The average weight is 50/2 = 25 kg.

Same with volume. If you have ten liters of water and 40 liters of water, they have a total volume of 50 liters. You can measure it in a large container. Total volume. The average volume is 50/2 = 25 liters.

But what if we have a ten liters of water at 10°C, and forty liters at 40°C … we know the average volume, 10 liters plus 40 liters divided by 2 = 25 liters. And we know the average mass, (10 kg + 40 kg) / 2 = 25 kg.

But is the average temperature (10°C + 40°C) / 2 = 25°C? Well … no. And we can prove that. We pour the two containers of water into one container, and we find that the resulting temperature is 34°C … what’s the problem here?

The problem is that while the two amounts of water have an actual total weight (50 kg) or an actual total volume (50 liters), there is no such thing as total temperature. It doesn’t exist. And because of that, we think the average temperature of the water is 25°C, whereas in fact it’s 34°C.

HOWEVER (and it’s a big however), this does NOT mean that this type of incorrect average is useless. This is because of a peculiar property. If the actual average temperature of 34° (determined by mixing the two units of water together) goes down because one of the units of water is cooling, so does our incorrectly calculated “average. And the same is true if one or both of the units warm. Both the correct and the incorrect average temperatures increase. They always move up or down together.

So they are not useful or meaningful for the value, but they are useful for the direction of change over time in the value.

Hope this clarifies some things.

w.

Bellman
August 12, 2022 5:44 am

But is the average temperature (10°C + 40°C) / 2 = 25°C?

No. Because it’s (10kg X 10°C + 40kg X 40°C) / (10kg + 40kg) = 34°C

The problem is that while the two amounts of water have an actual total weight (50 kg) or an actual total volume (50 liters), there is no such thing as total temperature.

The problem here is you didn’t work out the average correctly, and the fact that it is possible to get the correct value suggests the argument about total temperature is invalid.

Tim Gorman
August 12, 2022 4:32 pm

ROFL!

What is kg * temperature? Is it an intensive or extensive property. It certainly isn’t temperature!

Bellman
August 12, 2022 4:57 pm

It’s extensive – the result is intensive. It’s another example of how you can average intensive values and get a meaningful result. Even Essex et al acknowledge this.

Tim Gorman
August 12, 2022 6:37 pm

So, once again, you are arguing that you can average intensive properties while using extensive properties as proof.

Unfreakingbelievable!

Bellman
August 12, 2022 7:07 pm

Yes, that was the point of what I said dozens of comments ago. If you think that is unacceptable explain why, rather than just making an argument by personal incredulity.

Tim Gorman
August 13, 2022 8:34 am

Where does he acknowledge this? Quote please!

Bellman
August 13, 2022 1:55 pm

There’s the mixing example, and also this

Personal income and height are meaningful at the individual level, and no conceptual problems emerge when adding or averaging over a population.

That again depends on whether you regard personal height as being an intensive property or not.

Editor
August 15, 2022 12:09 pm

Height is obviously extensive, by definition—it’s measuring the extent of something.

w.

Jim Gorman
August 15, 2022 12:12 pm

Ha! Not only that, but if you cut someone in half, the two halves aren’t the same height!

Bellman
August 15, 2022 12:58 pm

Depends on which way you cut them.

Bellman