Numbers  — Tricky Tricky Numbers: Part 3

Guest Essay by Kip Hansen – 21 August 2022

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

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

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

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

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

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

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

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

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

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

How is temperature not a measure of heat?

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

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

Total heat of the air = SH + LH

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

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

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

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

The sensible heat of the air is calculated as follows:

SH = m*0.133*DBT

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

We need also to determine the Latent Heat:

The latent heat of the air is calculated as follows:

LH = m*w*hw

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

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

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

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

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

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

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

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

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

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

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

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

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

~~~~~~~~~~~~~~~~~~~~~

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

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

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

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

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

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

Bottom Lines:

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

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

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

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

# # # # #

Author’s Comment:

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

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

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

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

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

# # # # #

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Carlo, Monte
August 23, 2022 2:11 pm

Oh, the trendologists will be out in force whining about this one, Kip.

Carlo, Monte
Reply to  Kip Hansen
August 23, 2022 4:45 pm

Kip—I use this word instead of climate science because the global average air temperature averages cannot tell you much of anything about climate. So instead of studying climate, many study nothing but trends.

Might as well be treading a hamster wheel, around and around it goes: nowhere.

And you are quite right about extrapolating into the future, many pretend that they don’t, but they do. Witness substituting “projections” for “predictions”.

Bellman
Reply to  Carlo, Monte
August 23, 2022 3:38 pm

Monckton doesn’t comment that often, apart from on his own posts.

Carlo, Monte
Reply to  Bellman
August 23, 2022 4:38 pm

Look, the Ship of Fools has docked.

Izaak Walton
August 23, 2022 2:32 pm

Kip,
how about a bit of consistency? You start by saying that you cannot average temperatures and thus global temperature doesn’t exist since you can’t average temperatures and you end by stating that you agree wholeheartedly with Steven Moshe that “The global temperature exists”.

So which is it? Does a global temperature exist or not?

Reply to  Kip Hansen
August 23, 2022 3:29 pm

Why not, in a manner of speaking? If one took a Fleer out into space to the Moon’s orbit and measured Earth’s temperature, what would it read?

Randy Stubbings
Reply to  Kip Hansen
August 23, 2022 9:53 pm

Kip: You said above that, “Earth, as a celestial object, must have a temperature.” In response to James you agreed that you could get a spot temperature with what he called a Fleer. (Did he mean FLIR?) What temperature would be measured? How would the measured value relate to the temperature at Earth’s core (~6000 degrees C), the temperature in Honolulu, or the air temperature at 10,000 metres above Honolulu? The idea that Earth has “a” temperature seems inconsistent with the premise of your three-part post.

I agree that a global average surface temperature (GAST), and even more so a global average temperature anomaly, is not a valid thermodynamic property. However, I also agree with what I believe is one of Nick Stokes’ points, which is that that an increasing GAST is a not-unreasonable indicator of “change.” To me, the problem with the GAST is less that it is thermodynamically invalid and more that it is touted by alarmists as a “doomsday” metric (“Earth has a fever,” etc.) and that the spatial and temporal structure of temperature changes is completely ignored by them. It’s hard to see much downside for humans from higher temperatures at high latitudes, during the winter, and/or at night. (Some might argue that a higher GAST means melting glaciers and sea-level rise, but an increase from -55 to -50 in Antarctica won’t melt any ice and tide-gauge data suggests no acceleration in the rate of rise due to CO2 emissions. Also, the Dutch solved sea-level rise hundreds of years ago.)

Jim Gorman
Reply to  Randy Stubbings
August 24, 2022 4:32 am

Part of the problem is that water vapor is not static nor does it stay in one place. So today I might have a high humidity but low temperature but tomorrow a low humidity and higher temperature. What has the heat done? Likewise, that humidity may have been moved by the wind and someplace else may be affected. Just averaging the temperatures won’t tell you where the “heat” is and what it is doing.

Randy Stubbings
Reply to  Kip Hansen
August 28, 2022 4:01 pm

Kip==> That’s what I expected you would say, and I agree. It just wasn’t clear to me what specific temperature you were referring to when you said Earth has “a” temperature. The clarification was helpful.

Reply to  Kip Hansen
August 23, 2022 3:37 pm

” Global Average Surface Temperature as a calculated number is a fantasy.”

But what you agreed with was
“The global temperature exists. It has a precise physical meaning. It’s this meaning that allows us to say… The LIA was cooler than today”

So how can it have that precise physical meaning if you can’t calculate it? How can you say that the LIA was cooler than today?

Rud Istvan
Reply to  Nick Stokes
August 23, 2022 3:39 pm

That is easy. The last Thames Ice Fair in London was in 1818.

Bellman
Reply to  Rud Istvan
August 23, 2022 3:51 pm

Which proves what about global temperatures?

The fact the Thames changed a lot in character since then, including removing the old London Bridge might have more to do with frost fairs than global temperatures.

Reply to  Rud Istvan
August 23, 2022 4:36 pm

That is easy. The last Thames Ice Fair in London was in 1818.”
And now we have 40°C in Lincolnshire. And buckling rails. Global warming is proved.

Carlo, Monte
Reply to  Nick Stokes
August 23, 2022 4:39 pm

HORRORS!

RUN AWAY!

Chris Hanley
Reply to  Nick Stokes
August 23, 2022 5:53 pm

Continuously welded rail lines are a post-ww2 development and introduced in UK only around 1960 so buckling due to heat is a poor proxy for temperature.

Carlo, Monte
Reply to  Chris Hanley
August 23, 2022 6:10 pm

And bad railroad engineering—the US has welded rail everywhere that doesn’t buckle.

observa
Reply to  Nick Stokes
August 23, 2022 6:10 pm

The Poms are hogging the missing heat Nick-
Snow cover and freezing temperatures hit Blue Mountains, Lithgow, Orange and Bathurst, as winter nears its end – ABC News
That’s bushfire country in summer but you and your clever mates will average it out for us all and save us from the sneaky plant food moving around and creating havoc like it does.

AndyHce
Reply to  Nick Stokes
August 23, 2022 9:46 pm

Global warming is proved.

The normal meaning of “global warming” in use today is ‘what humans done did’. No evidence of warming in itself can be considered evidence of any specific cause.

UK-Weather Lass
Reply to  Nick Stokes
August 24, 2022 12:07 am

The ‘unprecedented’ temperatures predicted gave rise to the fear that rails would buckle but I am not aware of any incident where a welded line actually suffered damage from the temperature peak recorded at an airfield in Lincolnshire.

On the day in question I recorded a 38C peak near my home but less than half a mile away, in a more rural setting nearby an ancient Thames tributary, the temperature only managed 34C. Which temperature tells us most about the state of our climate? Neither IMO.

Graemethecat
Reply to  Nick Stokes
August 24, 2022 12:10 am

Correction: we have 40C at RAF Coningsby measured at a station next to an asphalt road and a few meters from a runway.

Chaswarnertoo
Reply to  Graemethecat
August 24, 2022 1:09 am

As a flight of 4 Typhoons took off.
ah! Now I understand, that is AGW!

Chaswarnertoo
Reply to  Nick Stokes
August 24, 2022 1:07 am

As 4 Typhoons took off. Look at the bump in the data.

Jim Gorman
Reply to  Nick Stokes
August 24, 2022 5:22 am

But not AGW. I noticed you left out that salient descriptor.

Gerry, England
Reply to  Nick Stokes
August 24, 2022 5:30 am

And now we have 40°C in Lincolnshire

At an RAF airbase and I don’t think we had many of those in 1818. RAF Coningsby would have been a field just like Heathrow was a collection of fields and the western limit of London was Hyde Park. But hey, let’s just ignore all those changes to the landscape in the past 200 years to pretend global warming is real.

mkelly
Reply to  Nick Stokes
August 24, 2022 8:24 am

Nick are you saying that the Thames Ice Fair of 1818 was in the in the summer? Or are you comparing apples and oranges?

Reply to  mkelly
August 24, 2022 5:55 pm

You could insert a /sarc tag.

Loren C. Wilson
Reply to  Nick Stokes
August 27, 2022 8:00 pm

The point is not that an accurate measure of the earth’s surface temperature is invalid, it is that the raw data are manipulated and extended and estimated and infilled, etc. well beyond validity to produce the doomsday scenarios. Not to mention the malfeasance revealed by the ClimateGate emails. If that is as trustworthy as your associates are, I don’t trust them at all.

Reply to  Rud Istvan
August 23, 2022 5:40 pm

That is one winter in one city.
Not evidence of any global trend.

Bellman
Reply to  Rud Istvan
August 24, 2022 4:02 pm

A small correction; the last frost fair was February 1814.

According to CET, the winter that year was 0.4°C, 4th coldest on record. But still warmer than 1962/3 which was -0.3°C.

Bellman
Reply to  Kip Hansen
August 23, 2022 4:08 pm

Everything HAS a temperature

I’m confused. I thought the point of the paper from last time, was that “a” temperature didn’t exist unless unless everything was in equilibrium. Wasn’t that the point of the “proofs” on page six of the paper?

Bellman
Reply to  Kip Hansen
August 23, 2022 4:40 pm

I’m not trolling anyone. I’m just trying to figure out what’s being said. Either it’s possible to have a temperature representing a system that isn’t in equilibrium, or it’s not.

Jim Gorman
Reply to  Bellman
August 24, 2022 6:22 am

I’ll give you a concise answer but won’t argue with you.

If this is what you learned from Part 2, and all the messages exchanged with you, then you are absolutely incapable of dealing with thermodynamic questions.

Read the essay again and again until you learn what is being asserted.

Here is another site that may help.

https://www.e-education.psu.edu/earth103/node/1005

This is the important part.

If the energy lost in an interval of time is the same, the temperature of the cube of air will decrease much more than the water, and so in the next interval of time, the water will radiate more energy than the air, yet the air will have cooled even more, so it will radiate less energy. The result is that the temperature of the water cube is much more stable than the air — the water changes much more slowly; it holds onto its temperature longer.” (bold by me)

Jim Gorman
Reply to  Kip Hansen
August 24, 2022 11:07 am

You are welcome!

Bellman
Reply to  Jim Gorman
August 24, 2022 10:42 am

That’s not a concise answer. You just say I’m wrong and then giving a quote that has nothing to do with the question.

Is it possible for a system that is not in thermal equilibrium to have a single temperature representing that system?

Loren C. Wilson
Reply to  Bellman
August 27, 2022 8:14 pm

Sir, if the system is not in thermal equilibrium, then parts of it are at different temperatures by definition, and it would not be possible. Depending on the situation, you may be able to calculate some sort of weighted average or effective temperature that is representative of the whole system. For example, the radio tells me that the temperature in Houston is 93°F. Obviously, that is not the exact temperature for most of that city, but probably not too far off. For other systems, an average is not meaningful. One of the points being made in this series of essays is that the temperature is an indicator of the actual heat content of the system, which is what we should be monitoring.

Trick
Reply to  Kip Hansen
August 23, 2022 4:38 pm

Kip, writing on temperature in part 2: “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””.

Then in the top post “part 3” I observe Kip “Multiplying temperatures as numbers” in:

SH = m*0.133*DBT

So…why then is Kip’s SH result (and thus SH + LH for the “Total heat of the air” in Kip’s terms) NOT a “nonsensical result”? 

Last edited 1 month ago by Trick
Trick
Reply to  Kip Hansen
August 23, 2022 5:02 pm

No misunderstanding Kip, as Kip writes confirming again: “0.133 times dry bulb temperature.”

Kip thus is shown to be “Multiplying temperatures as numbers” which according to Kip in part 2: “gives nonsensical results”. 

Trick
Reply to  Kip Hansen
August 23, 2022 5:28 pm

So…according to Kip pretending “0.133 times dry bulb temperature.” is 0.133 times as hot a dry bulb temperature. No.

As Kip does correctly write, temperatures are an intensive property so cannot be added.

Correctly, the thermometer temperatures of the GHCN can be converted to effective temperatures to arrive at the global median Tse ~ 288K.

It does turn out that the same answer Earth’s global median Ts ~ 288K is obtained just by averaging relevant thermometer temperatures so the complex work to properly compute Tse each time does not change the global answer & is thus skipped by many authors.    

Last edited 1 month ago by Trick
Trick
Reply to  Kip Hansen
August 23, 2022 5:57 pm

Use the GHCN (or subset) thermometer temperatures for the period observed.

Kip, to be physically correct & more helpful, convert the top post essay in part 4 to only use enthalpy (H) which is an extensive property. LH and SH are archaic terms that have been more accurately replaced in modern times with the formula for H (the first letter of heat).

Kip will be more helpful to readers using enthalpies of vaporization, fusion, and sublimation. So-called heats of reaction are enthalpies of reaction. And so on.

The formula for Sensible Heat cannot be correctly given in the essay because as Kip correctly wrote earlier the formula “gives nonsensical results”.

Last edited 1 month ago by Trick
Trick
Reply to  Kip Hansen
August 23, 2022 6:27 pm

Where? Nowhere. Heat of the atm. would be its total thermodynamic internal (thermal) energy which cannot be known so is useless. Temperature is a useful measure of the local avg. thermal energy.

Last edited 1 month ago by Trick
Jim Gorman
Reply to  Trick
August 24, 2022 6:42 am

Temperature is not a good proxy.

Read this site.

https://www.e-education.psu.edu/earth103/node/1005

It tells you that air with a higher percent of water will both absorb more heat and conversely will lose heat slower.

Think about a site in a desert at 90 °F @ 10% humidity and one at 90 °F @ 70% humidity. Which one has more heat in a similar volume of air surrounding an LIG thermometer?

Old Cocky
Reply to  Trick
August 23, 2022 6:38 pm

You left out the mass. The 0.133 fudge factor is important to the whole equation, not just part of it. Dry air (principally N and O) has a known heat capacity per unit mass, so the mass x temperature x fudge factor is what is important.

Tim Gorman
Reply to  Trick
August 26, 2022 3:41 pm

As Kip does correctly write, temperatures are an intensive property so cannot be added.”

Multiplying is just consecutive addition. If you can’t add temps then you can’t multiply them together either.

Jim Gorman
Reply to  Kip Hansen
August 24, 2022 6:35 am

Not only that, but if you do a dimensional analysis, multiplying temperatures result in a power function. That is, °K * °K = (°K)^2

It may be enlightening to know that specific heat values are like:

J / (g*°K)
J / (kg*°C)

When multiplying by temperature the temperatures cancel. This is a functional relationship designed to use temperature as a measurement. Nowhere is Part 2 does it say that temperature can not be part of a functional relationship. There are many thermodynamic relations that do so.

Bellman
Reply to  Kip Hansen
August 24, 2022 8:47 am

Multiplying 60 F by 2 is not multiplying temperature by temperature. It’s either scaling the temperature by 2, or adding the temperature to itself.

And apart from the Essex paper, who says it will twice as hot. That paper claims it’s valid to square Celsius values, in order to take a geometric average. I pointed out why that was wrong.

Tim Gorman
Reply to  Bellman
August 26, 2022 3:44 pm

Multiplying 60 F by 2 is not multiplying temperature by temperature. It’s either scaling the temperature by 2, or adding the temperature to itself.”

Temperatures don’t add. 60F here and 60F there don’t add to 120F.

Bellman
Reply to  Tim Gorman
August 26, 2022 5:01 pm

It looks like I misread Kip’s post. He was talking about two different things, multiplying temperature by temperature, and scaling temperature.

Not sure who suggested multiplying temperature by temperature, or who thinks doubling temperature in Celsius would double the temperature. (Apart from that Essex paper).

Of course you can multiply temperature scales by arbitrary constants, how else would you convert Celsius to Fahrenheit?

AndyHce
Reply to  Trick
August 23, 2022 9:57 pm

Any particular numbers for temperature in different places under different conditions cannot be said to mean the same thing in terms of heat or energy, thus the numbers of those different places and times can’t be rationally used in calculations that are only meaningful in terms of heat or energy.

However, using a particular temperature in a particular place under a particular condition can be used in a calculation involving other measurements (humidity, wind speed, …, anything related to temperature) about that place at that time. This is not contradictory.

andic
Reply to  Trick
August 24, 2022 12:53 am

Willfully ignorant or stupid? A simple dimensional /units analysis shows that the formula is valid:

[kg] x [J/kg.Deg] x [Deg] after canceling out leaves units of energy

Bellman
Reply to  Kip Hansen
August 23, 2022 5:49 pm

This formula converts the intensive property “temperature” into an extensive property “sensible heat”.

Which was the point I was trying to make last time. The whole you cannot average intensive values is a red-herring, as you can always multiply them by an extensive property to get meaningful totals.

Multiply temperature by surface area to get the average surface temperature. Multiply temperature by time to get average monthly values.

Old Cocky
Reply to  Bellman
August 23, 2022 7:19 pm

The catch is that you have to have the figures (mainly moisture content) to calculate those extensive values. That can’t be assumed to be approximately equal in all places at all times.

Bellman
Reply to  Old Cocky
August 23, 2022 7:24 pm

I’m not talking about averaging enthalpy, just temperature.

Old Cocky
Reply to  Bellman
August 23, 2022 7:38 pm

Degree-hours sort of count for cold or warmth requirements for plant germination or flowering. if you’re using degree metres^2, how much area is allocated to each temperature reading? For of that matter, what does 500 Kelvin m^2 mean, and how do you average it? Is it 1 K over 500 m^2, 250K over 2m^2, 500K over 1m^2?, 1000 K over .5 m^2?

Jim Gorman
Reply to  Bellman
August 24, 2022 6:48 am

If you are not dealing in enthalpy then you are not dealing in HEAT, i.e., energy.

An average temperature is just that, temperature and only temperature. Temperature does not tell anything about the energy that is being radiated away at any one location.

Bellman
Reply to  Jim Gorman
August 24, 2022 7:39 am

That was my point. This post keeps talking about heat when it should be talking about enthalpy.

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

This is both confusing heat with enthalpy and with hotness.

Bellman
Reply to  Jim Gorman
August 24, 2022 3:53 pm

Heat is not enthalpy.

And I’m not interested in heat or enthalpy at this point, just temperature, the measure of hotness.

If you want to know if the world is hotter now than it was during the LIA, you need to know how the temperature has changed, not the enthalpy.

If you want to understand energy budgets or whatever, you might need to know about global enthalpy.

The irony is that whenever someone does try to show that enthalpy is rising, it’s immediately claimed to be a hoax to distract from “the pause”. Remember all Monckton’s “the oceans ate the warming” jokes?

lee
Reply to  Bellman
August 23, 2022 8:10 pm

Now all you have to do is show that this is in fact done. What size Stevenson Screen? That varies the column of air.

AndyHce
Reply to  Bellman
August 23, 2022 10:02 pm

Certainly you can get numbers that are arithmetically correct but what is the meaning of a termperature measure multiplied by (1200m x 1200m)?

bdgwx
Reply to  AndyHce
August 24, 2022 5:50 am

AndyHce: “Certainly you can get numbers that are arithmetically correct but what is the meaning of a termperature measure multiplied by (1200m x 1200m)?”

The most intuitive meaning is a barrier’s resistance to heat flow given one watt of power. Insulation effectiveness is typically specified by R-Value which has SI units of K.m2/W. The higher the K.m2 component the higher the R-Value. And the amount of heat transferred across the barrier is Q = A(Th – Tc) / R. Again, notice that higher K.m2 values increase R thus decreasing Q.

Reply to  bdgwx
August 24, 2022 7:47 am

LOL get out the handyman’s hand book bdgwx is in the house.

AndyHce
Reply to  bdgwx
August 24, 2022 1:17 pm

OK, but that has nothing to do with the practice of applying a thermometer reading to a large area and pretending the large area is at that temperature and pretending that the calculation tells something meaningful about the area in question.

Bellman
Reply to  AndyHce
August 24, 2022 7:51 am

It’s a description of temperature by area. Just as a degree day is a description of temperature by time.

The point is it allows you to determine an average temperature. The point of the previous post was that this wasn’t possible because intensive properties cannot be added and so cannot be averaged.

Bellman
Reply to  Kip Hansen
August 24, 2022 9:58 am

A degree day is a unit of temperature by time. You can use it for a specific purposes such as estimating the cost of heating or cooling, but my point is you can multiply any temperature by time to get a measure in degree days. An extensive property that can be added to get a meaningful sum, and the sum can be divided by time to get an average temperature over time.

Bellman
Reply to  Kip Hansen
August 24, 2022 4:03 pm

It is a number of degrees above or below 65°F the Tmax+Tmin/2 pseudo-average temperature (Tmean) for the day.

Better not let Tim hear you say that.

Tim Gorman
Reply to  Bellman
August 26, 2022 3:53 pm

It’s still the *OLD* method. The newer method is much more accurate, which results in more efficient in sizing HVAC systems – meaning less cost to the consumer!

Loren C. Wilson
Reply to  Trick
August 27, 2022 8:24 pm

This is the calculation of the energy stored in the dry air. M is the mass of the air (not a temperature) and 0.133 is the heat capacity of air (also not a temperature) in appropriate units for the mass and the dry bulb temperature (this is a temperature). So we haven’t violated the rule of not multiplying two temperatures together.

I use a different equation since I learned my thermodynamics as a chemical engineer, rather than as a meteorologist, but it does the same thing and gives the same answer.

Trick
Reply to  Loren C. Wilson
August 28, 2022 5:47 pm

Loren, Kip wrote in part 2: “Multiplying temperatures as numbers can be done, but gives nonsensical results” which is not your “multiplying two temperatures together.” Kip violated his own rule in part 3.

Izaak Walton
Reply to  Kip Hansen
August 23, 2022 5:21 pm

Kip,
What do you mean by saying that “Everything HAS a temperature”? You spent all of part 2 saying that it was not scientifically correct to average temperatures and that the results produced were nonsense. Now you are saying the opposite.

Take for example a sealed box that is half filled with water and with air in the remaining volume. Does it have a temperature?

What about if I take an iron rod and heat one end. Does the rod have a temperature and if so can I calculate it by averaging the temperature along the length?

Jim Gorman
Reply to  Izaak Walton
August 24, 2022 6:52 am

Your average would mean nothing except at equilibrium when the rod is at one temperature.

If you apply heat at one end, a gradient ensues controlled by conduction. Conduction is seldom a linear function, so again an average would mean nothing.

Do you know what a gradient or a diffusion equation looks like?

Reply to  Izaak Walton
August 24, 2022 7:49 am

OK IZAAKIE you tells us what is the earth temperature?

Reply to  Kip Hansen
August 23, 2022 5:42 pm

Hansen:  For a smart guy you wrote a stupid article.

Reply to  Kip Hansen
August 23, 2022 5:38 pm

Silly Hansen word games
Global average temperature is a statistic based on measurements, guessing (infilling) and adjustments. Any change of trend provides information that could be useful. Evidence that climates vary between warming or cooling trends. There is no “normal” temperature. Any unusual trend slope could be important.

The question of how accurate and useful that statistic is needs to be debated. To say that it is a fantasy is claptrap.

Geoff Sherrington
Reply to  Richard Greene
August 23, 2022 8:07 pm

Richard,
I have submitted Part 1 a relevant article in 2 parts for WUWT to consider. Your last line theme is addressed more in Part 2. Geoff S

AndyHce
Reply to  Richard Greene
August 23, 2022 11:05 pm

That brings up an interesting question.
Do a calculation based on one temperature measurement and some other relevant measurement(s) of the same place at the same time and you can get a real result. However, it has an uncertainty in value that involves the uncertainty of each measurement. Its precision and accuracy are, at best, limited to the least accurate and least precise of the individual measurements.

Combining a large number of different measurements (of surface temperature measurements) with different instruments in different places at different times (each value is +/- 0.5C), then finding the difference between the total’s average and some other multi-component average (an anomaly) gives a value that is very small relative to the temperature measurements’ uncertainty. That is, the anomaly’s uncertainty is far greater than the uncertainty of any individual measurement.

The interesting question is:
Ignore the particulars of the multiple uncertainties, but assume that the many measurements that have gone into the averages that were used to compute the anomalies were done consistently with the same instruments over time (i.e. by day, by month, by year, etc, but pick only one and stick to it). Then, if there is a trend in the values of the anomalies over a long period when many such anomalies have been calculated for their period’s duration, can that trend be reasonably interpreted, since its value is much smaller than the noise?

If not, is there any explanation of how a trend could persist (e.g. some particular figment of the particular statistical analysis)?

Jim Gorman
Reply to  AndyHce
August 24, 2022 6:58 am

Oh boy, did you step into a quick sand trying to explain this to some of the denizens of this site.

AndyHce
Reply to  Jim Gorman
August 24, 2022 1:21 pm

Do you mean my question is so poorly described that many will fail to understand it?

Tim Gorman
Reply to  AndyHce
August 26, 2022 4:01 pm

“Do you mean my question is so poorly described that many will fail to understand it?”

Combining a large number of different measurements (of surface temperature measurements) with different instruments in different places at different times (each value is +/- 0.5C), then finding the difference between the total’s average and some other multi-component average (an anomaly) gives a value that is very small relative to the temperature measurements’ uncertainty.”

You’re question is well posed. If the uncertainty overwhelms the anomalies then it also overwhelms any trend line developed from those anomalies.

Tim Gorman
Reply to  AndyHce
August 26, 2022 3:58 pm

+100

Solomon Green
Reply to  Richard Greene
August 24, 2022 6:18 am

“One can surely find a number by adding the temperature of Los Angeles on noon today to the temperature of Chicago yesterday noon, and dividing by 2 but the result will not be a temperature of any place at any time. This extends to one of the problems of Global, Regional, State, National, weekly, annual temperatures and their anomalies over various periods of time and space.  One can surely find a number by adding the temperature of Los Angeles on noon today to the temperature of Chicago yesterday noon, and dividing by 2 but the result will not be a temperature of any place at any time. This extends to one of the problems of Global, Regional, State, National, weekly, annual temperatures and their anomalies over various periods of time and space.” 

It seems that a number of those who have added to this discussion have either missed or misunderstood the above extract from Mr. Hansen’s paper. 

Tim Gorman
Reply to  Solomon Green
August 26, 2022 4:01 pm

One can surely find a number by adding the temperature of Los Angeles on noon today to the temperature of Chicago yesterday noon, and dividing by 2 but the result will not be a temperature of any place at any time.”

+100

Jim Gorman
Reply to  Richard Greene
August 24, 2022 6:56 am

Radiation is an important part of the earth’s system. So is conduction and convection.

Do you believe that temperature is a good proxy for HEAT, ie., energy?

Tim Gorman
Reply to  Richard Greene
August 26, 2022 3:57 pm

Does the temperature on top of Pikes Peak and the temperature in Denver tell you anything when you average them? No infilling, no homogenization.

When the uncertainty of the data overwhelms the differences used to establish a trend line what good is the trend line?

AndyHce
Reply to  Kip Hansen
August 23, 2022 9:43 pm

Of course, the Earth as a celestial object must have a temperature.

Surely the Earth has a large multitude of temperatures. Any single number must be some combination of those multiple tempreatures, whether average or some other calculation or selective measurement.

Reply to  AndyHce
August 24, 2022 7:53 am

Andy

from a light year away the earth would have an average temperature, good luck measuring it with any accuracy though.

AndyHce
Reply to  Kip Hansen
August 24, 2022 1:24 pm

But does that measurement have any real meaning?

Jim Gorman
Reply to  AndyHce
August 24, 2022 8:44 am

The problem is that the combination assumes that there is a “field” of temperatures where they all interact and that there is a an average.

Try this experiment find a temperature map of a big state. Try drawing a line between 3 fairly separated locations. Does the center of the line match the average of the two ends. You will find some that do, but many more that don’t. This simple experiment shows that temperatures don’t act together in unison to establish an “average temperature”. Now do the same thing with two cities, one in the northern hemisphere and one in the southern. Does the middle point have the average temperature?

Clyde Spencer
Reply to  Jim Gorman
August 24, 2022 12:46 pm

I think that is an argument against homogenization.

Jim Gorman
Reply to  Clyde Spencer
August 25, 2022 4:08 pm

It is. Part of the assumptions about temperature is that they are connected. They are not. They may be autocorrelated to a certain extent based upon things like zones, seasons, etc., but they don’t create the temperatures surrounding a location nor at a large distance from themselves, the sun and other interactions in the atmosphere does that.

AndyHce
Reply to  Jim Gorman
August 24, 2022 1:25 pm

That is my point. There are many different temperatures. What meaning does a single number for them have, no matter from where the measurement is made?

Reply to  Izaak Walton
August 23, 2022 3:22 pm

There is no global temperature that can be measured
There is a global temperature statistic.
It does not predict the future climate,
Not even trends that last 35 years, like the
global cooling from 1940 to 1975, which did not predict
the global warming from 1975 through 2022.

TheFinalNail
Reply to  Richard Greene
August 23, 2022 3:37 pm

The two periods are hardly comparable, either in duration or extent.

GISTEMP.png
Reply to  TheFinalNail
August 23, 2022 3:51 pm

That’s what I said.
One trend did not predict the next trend.
I did not say they were identical lengths.

In addition, the warming from 1910 to 1940, assuming the measurements made sense, did not predict the cooling frend from 1940 to 1975, which was much steeper when originally reported in 1975.

I could also add that the originally reported 1940 to 1975 cooling trend, as reported in 1975, did not predict the current much flatter 1940 to 1975 cooling trend, as reported in 2022 !

OweninGA
Reply to  Richard Greene
August 23, 2022 4:40 pm

I have often challenged people to look at the time series for the “Global Average temperature” for July 1935. When asked why, I suggest it must be a quantum number as it changes each time it is observed. Though I would think quantum changes would be more random, July 1935 has only ever gone down with each dataset release.

OweninGA
Reply to  Kip Hansen
August 24, 2022 5:25 am

Kip,
Someone posted the original on this site years ago and I downloaded a copy to my work and home computer. (Both crashed earlier this year and I now can’t find it on the site.) The plot in question was a moving GIF of the whole timeseries from the late 1800s to 1972. Each frame was the published timeseries advanced one month in publication. I was struck by the changes in the 1930s and so picked a July and recorded the number, frame-by-frame. I had a PowerPoint slide that showed the “temperature” for that date as published up through about 2010. Unfortunately, until I can find the graphic I got it from, I can’t recreate it. It didn’t convert the true believers, but it did peak the curiosity in some of my coworkers to start checking. They are all too busy with their teaching and personal research to spend much time on digging into it though.

It’s too bad the wayback machine doesn’t record database contents on the day of the snapshot. It would be nice to be able to pick the published output for each date of publication and compare. The person who made the original graphic (who was credited on my slide – my brain is fire and forget on names, so once I cited it, my brain decided it was done with it and purged it), had been actually saving the dataset to their computer for 20 years in separate files.

Reply to  OweninGA
August 23, 2022 5:47 pm

That’s because it is just as difficult to “predict” the past temperature as it is to predict the future temperature. Historical temperature data keep changing.

Frank from NoVA
Reply to  OweninGA
August 24, 2022 5:24 am

That’s because NASA GISS has been tampering with / adjusting the data.

bdgwx
Reply to  Frank from NoVA
August 24, 2022 6:46 am

Frank from NoVA said: “That’s because NASA GISS has been tampering with / adjusting the data.”

Would you mind showing me where in the code GISS is tampering with the data? I’ll modify that section of code and we’ll see what happens. You can download the code here. In fact, you get this up and running on your own machine in a just a few minutes and then run your own experiments where you disable or alter any sections of the code that you feel are nefarious. I have yet to find anything even remotely malicious or fraudulent.

OweninGA
Reply to  bdgwx
August 24, 2022 10:10 am

It really isn’t about tampering so much as the way homogenization checking works. For some reason, each time the dataset is homogenized it works with the whole set to the beginning of time and adjusts based on the new criteria. So even though all the new data is for the current month plus stragglers from the last year or so, homogenization changes stations all the way to the beginning. I really think the past should stand and the new data should be analyzed against it, but that isn’t the way it works. (That’s an analysis decision made by the senior scientists.)

Other changes to the past were due to the Time of Observation changes, but I am still not convinced that for a min/max thermometer it really matters whether it is read at 9AM or 5 PM or some other time altogether, other than a high or low temperature might get attributed to the wrong day once in a while. If the high for the day is at one minute past midnight due to a cold front passing, that is still the high for the day.

I don’t believe most of the folks working the issue are purposely increasing the trend. There are a few that are, but they tend to generate the policies the working scientists have to follow. Cooling the past readings happens due to groupthink and no one having the gumption to say “hey! this doesn’t smell right.” They all expect the modern record to be hotter and thus when they see it, no warning flags go up. History started yesterday, or maybe the day before, and we are the smartest ever, so those folks in the early 20th century couldn’t possibly tell us anything.

Tim Gorman
Reply to  OweninGA
August 26, 2022 4:06 pm

+100

Editor
Reply to  TheFinalNail
August 23, 2022 7:07 pm

Chart is dishonest since the cooling was much deeper than .1C

Mike
Reply to  Sunsettommy
August 23, 2022 8:27 pm

More than dishonest. Total garbage. 1960 and 2000 were the same temperature.

radiosonde.JPG
bdgwx
Reply to  Mike
August 24, 2022 6:22 am

That is HadAT2. At 500mb the 1960 value is 0.0 C vs 0.16 C in 2000. And the 5yr centered means are 0.03 C and 0.40 C respectively. You can download the data here.

Last edited 1 month ago by bdgwx
Robert B
Reply to  Izaak Walton
August 23, 2022 4:33 pm

“One of these errors is the odd un-physical assertion that temperature (is) a proxy for measured heat.”

It’s a good enough proxy for a qualitative argument like Mosher uses it. It’s not good enough for comparing the fractions of a degree changes of measurements of GTA with model predictions e.g. high confidence that at least half the 0.6 degree of warming since 1950 was due to fossil fuel use. That is treating a very poor proxy as a measure.

Or, for example, how the average temperature of the Moon is less than the Earth. Even without an atmosphere, the storage and transport of heat around the globe by the oceans should make the Earth have a mean of about 30 degrees greater than the moon even if everything else was equal (insolation, albedo, emissivity).
[I was tempted to write cooler and hotter]. In this case, it’s just due to the sum of T^4 over the whole surface area needs to be the same while T varies from 25K at the poles of the moon to 390 K at the equator at noon, and only a 30 K spread on the surface of oceans. That average does nothing to explain any average thermodynamics – it just indicates that the two worlds are very different.

And I’ll bring up my big bug bear. The modelling starts with what would the average temperature of a black-body orb would be this far from the Sun instead of what would the average be of a sphere made up of an infinite number of individual black bodies. My rough calculation suggests almost a factor of three warmer (sorry, larger) for the former with energy in and out being exactly the same.

The former would have a constant temperature over it’s surface, while the latter would be 0 K over half it’s surface, some illuminated areas would much hotter. If the illuminated area was a constant, T^4 would be twice of the black body to make up for being zero on the dark side, but T only 25% more. Divide 1.25 by 2 and the mean temperature should be a little over 60% of the black body. A bit more complicated to take into account the spread of temperatures on the illuminated side is not constant but spread from near 0 K at the poles, dawn and sunset, to much hotter at noon on the equator.

This is a theoretical emission temperature, so not the same as the daily mean from a weather station.

The dog is hassling me to take him to the beach, so apologies for not spending a bit more time on this comment.

Rud Istvan
August 23, 2022 2:40 pm

Excellent part three. You are of course correct. Anthropogenic global warming involves heat retention per air mass (via impaired radiative IR cooling). That is not the same as a temperature, or even temperature anomalies. At best, temperature is a poor proxy that is then improperly treated by ‘averaging’. And we also know there are still serious measurement problems with the temperature proxies.

IMO a worse ‘numbers’ sin is averaging the climate model spaghetti graphs and assuming the result is meaningful. It cannot be. Most of the models are provably wrong (having a tropical troposphere hotspot that does not exist in reality—the sole exception is the Russian INM CM4.8/5.0 in CMIP6 which means it is least wrong). Averaging provably wrong stuff does not make the resulting average meaningful, let alone ‘right’. And averaging anomalies hides the fact that the wrong models themselves also disagree by +/-3C at initialization. Judith had a post on that factoid years ago. I stuck her example into the ‘Climate models’ essay in ebook Blowing Smoke, with footnote attribution.

Ed Reid
Reply to  Rud Istvan
August 23, 2022 3:15 pm

The mean of meaningless models is a meaningless mean.

Ed Reid
Reply to  Kip Hansen
August 23, 2022 3:31 pm

Guilty as charged. 😉

Scissor
Reply to  Kip Hansen
August 23, 2022 4:19 pm

“I know what I know if you know what I mean.”

Michael S. Kelly
Reply to  Scissor
August 23, 2022 6:16 pm

“Don’t know much about history
Don’t know much biology
Don’t know much about a science book
Don’t know much about the French I took…

“Don’t know much about geography
Don’t know much trigonometry
Don’t know much about algebra
Don’t know what a slide rule is for…”

Huh…I’m pretty f*&#%@g stupid. Suddenly, I’m depressed.

Last edited 1 month ago by Michael S. Kelly
drh
Reply to  Kip Hansen
August 24, 2022 9:42 am

Odd tangent, but Edie Brickell and Paul Simon are married.

AndyHce
Reply to  Scissor
August 23, 2022 11:16 pm

Being unaware of so many things (true of everyone) strongly suggest that some unknow but probably not small number of those things that we “know” are not true. And, at least to some extent, the least able person to really understand an individual is that individual himself.

n.n
Reply to  Ed Reid
August 23, 2022 3:32 pm

And green in a green and greening world, albeit with anomalous Green local and regional blight.

bdgwx
Reply to  Kip Hansen
August 23, 2022 4:59 pm

And yet that is exactly what weather models like GEFS, GEPS, EPS, and NBM (which is an ensemble of ensembles) do to extend the useful skill of weather forecasts from 6-8 days to 8-10 days. The technique is so effective that the NWS uses NBM almost exclusively for their official forecasts now. It’s also why the NHC uses TVCN and IVCN almost exclusively for their official forecasts now. Averaging chaotic results is a very powerful technique for improving predictions.

Last edited 1 month ago by bdgwx
JonasM
Reply to  Kip Hansen
August 24, 2022 12:17 pm

Thanks for that – I read it when posted, but it’s one to bookmark.

Jim Gorman
Reply to  bdgwx
August 24, 2022 7:22 am

Have you ever kept track of the 10 day forecast for temperature and precipitation to see how correct they are?

Start on Jan 1 and write down what the previous 10 day said would happen, then write down what did happen. Do that every day of the year. You’ll be very sad.

Clyde Spencer
Reply to  Jim Gorman
August 24, 2022 12:52 pm

It is something I have been considering doing, making a matrix of false-positives and false negatives for the 5-day precipitation forecast, moving forward one day at a time. Sometimes the forecast is wrong even on the day of the forecast.

Temperatures appear to be more reliable, but then historical averages are usually available even if model outputs aren’t.

bdgwx
Reply to  Clyde Spencer
August 24, 2022 2:11 pm

This is already being done for us by the National Center for Environment Prediction here.

Reply to  Rud Istvan
August 23, 2022 3:31 pm

IMO a worse ‘numbers’ sin is averaging the climate model spaghetti graphs and assuming the result is meaningful.”

Averaging the climate model predictions presents the consensus view of the future climate. Every model is programmed to predict whatever the programmers want to predict, and whatever satisfies their “management”
The average is a consensus of opinions in numerical form..
The average is very meaningful.
The model average / consensus is numerical evidence that humans can not predict the future climate. If you looked at only one model, the Russian INM, you might think humans can predict the future climate. In my opinion that one less inaccurate prediction must be a lucky guess, or a 1975 to 2022 trend extrapolation. The knowledge of every climate change variable does not exist to build an accurate climate model by design. And that’s assuming the climate can be predicted. Maybe it can never be predicted?

Philip CM
August 23, 2022 2:51 pm

In my life time the world cooled, and then warmed, apparently having stopped warming after increasing global temperatures by ~0.8C. Plant life is prospering. Epidemic famines are a thing of the past. Grazing animals are procreating. Predator animals are feasting. Weather disasters are down from previous numbers. The only thing raging is the left’s hysteria about a world that might reject them is they don’t adopt authoritarian green orthodoxy. I really don’t see where the observance to the hysterical is worth several trillions in tax payer dollars.

OweninGA
Reply to  Philip CM
August 23, 2022 4:44 pm

They are coming back soon, but not due to climate but because the World Economic Forum wants to reduce the population by 6 billion or so. Government policy (looking at you Denmark and Canada) will provide the next epidemic famine.

Mr.
August 23, 2022 2:56 pm

So Kip, would it suffice to say, for the sake of an after-dinner discussion with family / friends, that Temperature value is NOT a physical reality, and therefore should not be being used to determine whether there are any concerning changes in the ambient sensible + latent heat present in Earth’s numerous climates?

Reply to  Mr.
August 23, 2022 3:36 pm

Just tell them you have lived with global warming for the past 47 years and you loved it. Tell them you are sure the climate will get warmer, unless it gets colder. If that doesn’t shake them up, tell them Trump was the greatest president in American history, and Biden is the worst. If they are leftists, they will go berserk.

Mr.
Reply to  Richard Greene
August 23, 2022 4:10 pm

Yes all of that works, but what I would also like to see are the spittle-flecked rants about “the science” when I say the temperature values they present in numerous colorful graphs are not physical realities of heat energy, and “so what else have ya got?”

Reply to  Mr.
August 23, 2022 5:56 pm

Here in Michigan we tell friends our property was under a mile of ice 20,000 years ago and all the ice melted in the next 10000 years in spite of no coal power plants and SUVs — no manmade CO2 emissions at all.

That usually ends the climate conversation. Leftist friends don’t want to hear about past climates. But they love scary predictions of the future climate.

To cheer them up I tell them scientists say the world is going to end from global warming in 27.85 years unless drastic actions are taken. And they believe it. Because “scientists say”. And two decimal places is “real science”. I have actually done this quite a few times in the past 25 years. I just make up some scary climate prediction and they believe it every time. Like children hearing a scary campfire story.

Mr.
Reply to  Richard Greene
August 23, 2022 6:33 pm

Yes that’s perplexing –

what are climate catastrophists so incurious about past climate behaviors, where we can physically observe (geology etc) what actually occurred, yet they are so fixated on conjectures about what might / could/ maybe / perhaps occur in the future?

Rationality seems to be the ONLY casualty of the AGW conjecture.

Doonman
Reply to  Mr.
August 23, 2022 7:48 pm

Same people who touch the woodwork if they see a wet paint sign.

Clyde Spencer
Reply to  Richard Greene
August 23, 2022 7:01 pm

One should consider the possibility that they are just being polite and don’t want to get into a confrontational exchange.

roaddog
Reply to  Clyde Spencer
August 23, 2022 9:31 pm

Life well-lived is all about confrontational exchange.

Clyde Spencer
Reply to  roaddog
August 24, 2022 8:22 pm

But, some people will avoid confrontation at all costs. You can draw your own conclusions about the quality of their life.

David Dibbell
August 23, 2022 3:13 pm

Good article, Kip. I would like to add a point. Computation-intensive models are good for some things, and in this case I see the value of the ERA5 reanalysis produced by the ECMWF (European Centre for Medium-Range Weather Forecasts). A wide range of hourly values of atmospheric properties are available, on a 1/4 x 1/4 degree grid.

This link below is to a time series plot of the hourly “vertical integral of total energy” per square meter for a gridpoint near where I live for all of 2019. Total energy includes internal energy (involving temperature), the latent energy of water vapor, kinetic energy, and potential energy due to altitude.

I have expressed the vertical axis in Watt-hours per square meter. The rapid and very large changes are obvious in the plot. The single-digit theoretical “forcing” commonly used for the direct radiative warming effect of a doubling of CO2 concentration since pre-industrial times is 3.7 W/m^2.

So what is the point? The very small incremental increase in the radiative coupling between the surface skin and the atmosphere vanishes in the vertical scale as total energy increases and decreases thousands of times more than that on short time scales in the column of air above the surface.

So just as you emphasize that from temperature alone one cannot infer heat gain or loss, neither can one assume that the incremental energy involved in the static GHG radiative warming effect experienced at the surface looking toward space MUST result in a reduction in outgoing longwave energy. The energy available in the vertical column of the atmosphere is huge in comparison and it is mostly from that stored energy that longwave emission is powered.

comment image?dl=0

David Dibbell
Reply to  Kip Hansen
August 23, 2022 5:36 pm

The reanalysis is fed a large volume of acquired data to keep it as close to the real thing as possible.

It suffices to illustrate that the energy content of the entire column of the atmosphere – which can only be computed, not directly measured – is huge and highly variable as best understood in numbers for comparison to the static GHG warming effect expressed in a number. This came to mind as you pointed out that it takes a computation involving not only temperature but also pressure and humidity to determine the heat content of air.

David Dibbell
Reply to  Kip Hansen
August 24, 2022 5:27 am

The ERA5 “vertical integral of total energy” is a computed estimate of a quantity that could indeed be summed and averaged and trended. But to what end? The reason I posted my comment was to jump to the logical extension of your valid point that temperature itself cannot be summed or averaged or trended to indicate accumulation or loss of heat content in the atmosphere. Even when you do estimate total energy properly, as in the ERA5 computations, you quickly discover that it varies so much and so rapidly above a location on the surface, as to make it absurd to claim a few watts per square meter of incremental static radiative warming effect can ever be isolated for reliable attribution. There is no suggestion here that the vertical integral of total energy would be or should be convertible into a temperature or a temperature trend.

bdgwx
Reply to  Kip Hansen
August 24, 2022 2:02 pm

ERA5 produces measured quantities. It just happen to use an extremely complex measurement model. Using the terminology from GUM JCGM 6:2020 it is a multi-stage measurement model. The fact that it is astonishingly complex does not make it any less of a measurement. It’s vertical integral of total energy is a measurement.

August 23, 2022 3:18 pm

“It is possible that future satellite missions will be able to measure directly and accurately Earth’s incoming and outgoing energy.:

So what?
They are not in balance
There are icehouse and greenhouse conditions
Lots of changes in between them
And a direct measurement on one day
that tells you nothing about the future climate

What percentage of people are living live with rising, falling or steady local temperatures over time?

How about local warming or cooling that affects real people where they live and work?

Changes of local weather over time?

Not just an average temperature — the TMAX trend. the TMIN trend, % days over 90 degrees F.. % days over 95 degrees F. etc.

Accurately measure Earth’s incoming and outgoing energy and you still don’t have the answer of how climate change is affecting people locally where they live and work. You don’t know if they like the changes in their local weather over time, or even if they have noticed. The local weather trend here in SE Michigan is warmer winters since the 1970s. We like that trend and want it to continue. We don’t live in the average temperature. No one does.

If I lived in Siberia and my TMIN was getting warmer, that’s good news. If I lived in the tropics and my TMAX was getting warmer, that’s bad news.

The theme of these articles: “One cannot average temperatures” is ridiculous. There are many monthly averages. So it can be done. And it is done. “Are they accurate averages” is another question. “Is a single global average useful” is another question.

Would a +1 degree C. increase in the average temperature over 100 years mean much? I doubt it. Would a +5 degree C. increase over one year mean much? You bet it would. These three articles serve no purpose in refuting the coming climate crisis fantasy or Nut Zero.

Reply to  Kip Hansen
August 23, 2022 3:43 pm

I stated the articles do not refute climate fantasies or Nut Zero. THAT IS A FACT. We climate realists are losing the climate change propaganda war and the even worse Nut Zero project is being launched at great expense to ruin electric grids. Our climate realist side need all the help we can get. When a good author like you devotes three articles to less important subjects, IMHO. that may make you happy, but doesn’t help win the propaganda battle.

Reply to  Kip Hansen
August 23, 2022 6:03 pm

Hansen
CAGW is just a prediction
It does not exist.
CAGW is barely related to the global average temperature statistic. It is mainly a wild guess of ECS multiplied by 2x to 4x by a water vapor positive feedback fantasy.
It is not an extrapolation of the global average temperature statistic. If it was, the prediction would be for future AGW (not scary, and a reasonable theory), not for CAGW (climate fantasyland)

Reply to  Kip Hansen
August 23, 2022 8:42 pm

The average temperature statistic is evidence of warming or cooling. It is used for that reason and used to define ECS, which has about 365 different guesses — one for every scientist. It is an imperfect statistic. It does not represent heat, but it does represent an average of temperature measurements infilling and adjustments.
It is a real statistic, not a fantasy.
It will keep being used long after this series of articles is forgotten.

There should be a debate on the accuracy the average temperature statistic. You could have pointed out that claimed margins of error are not reasonable margins of error. Or that margins of error can’t be calculated with infilling of numbers that can never be verified. But you did not.

And i suppose now we are armed with information to refute all the scientists in the world who use and debate the global average temperature statistic? I think not.

AndyHce
Reply to  Richard Greene
August 23, 2022 11:36 pm

I think that the real issue is that the tribe believes the shaman, not that the shaman is wrong or right. People in general believe their party or their tribe spokesman. Anything that challenges that is just noise unless it has immediate and direct consequences. The CO2 myth is even better than the rumbling of the gods for effectiveness. Any conflicting claims, no matter how presented, are like the proverbial water off a duck’s back..

Mr.
Reply to  Richard Greene
August 23, 2022 3:38 pm

So many questions, Grasshopper . . .

n.n
Reply to  Richard Greene
August 23, 2022 3:39 pm

They remove one scalpel from the climate anomaly quiver, which improves anthropogenic global probability of viability to breathe, to live another day amidst a social wash of wicked solutions.

Reply to  n.n
August 23, 2022 3:54 pm

Can you provide me with a gibberish decoder ring?

Reply to  Kip Hansen
August 23, 2022 6:03 pm

Hansen hired a joke writer !

H.R.
Reply to  Richard Greene
August 23, 2022 7:04 pm

“Drink more Ovaltine.”

~Annie

August 23, 2022 3:32 pm

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

This is just silly, and unsuccessful, playing with words. The whole essay is pointless. Hot does not mean that some object has high heat content, latent or otherwise. It means it has high temperature, as in red-hot etc. It is what burns you. It determines the speed of reactions.

The significance of temperature is that it moves heat around. It induces heat fluxes, which it is useful to be able to calculate, conserving energy. It will induce a heat flux into (or out of) you, which is the part of weather that we are most aware of.

Mr.
Reply to  Nick Stokes
August 23, 2022 4:26 pm

Nick, “hot” and “cold” mean different things to different people.

The Missus and I can never agree whether our bedroom feels “hot” enough to warrant the ceiling fan on 1 or 3 setting, or on at all.

Same with temperatures values.

Our neighbor gets the vapors if her weather app says that it’s 28 C outside.

Me, I reckon that’s ideal conditions for mowing the lawn.

Carlo, Monte
Reply to  Mr.
August 23, 2022 4:50 pm

Don’t ask Nick if the wind is blowing, and how fast.

Carlo, Monte
Reply to  Nick Stokes
August 23, 2022 4:49 pm

Oh, am I psychic or what?

Reply to  Kip Hansen
August 23, 2022 6:07 pm

Almost 8 billion first hand witnesses to up to 47 years of global warming since 1975 and no one asks them if they liked or hated their local climate change, or even if they noticed. We noticed here in SE Michigan and we love the small amount of warming (mainly the winters) since the 1970s.

Reply to  Kip Hansen
August 23, 2022 7:48 pm

Kip,
I quoted two statements to that effect.”
Neither of the statements you quoted was about gaining heat energy. They were both about temperature rise. They say so.

“to see the temperature and the humidity which will tell me how “hot” it will feel — because those two measurements will indicate relative heat content.”

They don’t. To echo the buzzword of a few days ago, they are intensive variables, and are potentials. Temperature sets up a gradient that conducts heat into your body, and humidity inhibits a moisture gradient that might take it away. Doesn’t involve the heat content of anything.

Reply to  Kip Hansen
August 24, 2022 1:07 pm

Kip,
You have it totally the wrong way around. Global warming, as the name says, is about gain in temperature. That is what affects us. To sustain a temperature difference, you need a flux of heat, a generally conserved quantity. That you can study and measure, and so work out energy retained. It tells you how the world works, but the end result is temperature.

Jim Gorman
Reply to  Nick Stokes
August 25, 2022 2:05 pm

Have you ever been to say Galveston when it is 90 and 90%. How about the desert when it is 90 and 10% humidity. If you have, you shouldn’t be saying it is all about temperature. It is not.

How do you ever expect to analyze the atmosphere properly if you ignore water vapor and its causes and results? You are just looking at part of the sun’s energy when you ignore water vapor.

Tim Gorman
Reply to  Nick Stokes
August 26, 2022 4:36 pm

It is energy content that drives the atmosphere, not temperature. It is energy content that tells you how many joules are available to drive a thunderstorm, i.e. how much moisture can you lift and how far you can lift it. Temperature won’t tell you that!

Why do you suppose there is a tornado alley and a hurricane alley? Why aren’t tornadoes common everywhere if it is only temperature that drives the climate. Minnesota has 80F temps just like Kansas but MN has few tornadoes. What’s the difference?

Jim Gorman
Reply to  Nick Stokes
August 24, 2022 8:59 am

Nick,

What are the units for incoming radiation? The last I looked it was W / m^2 or more explicitly, Joules per second per square meter. Now if the incoming energy is in Joules, don’t you think you should be dealing in Joules? That is enthalpy, and not temperature!

Bellman
August 23, 2022 3:34 pm

As I’m still learning about thermodynamics, could you be clear that when you say “heat” you actually mean enthalpy?

mkelly
Reply to  Bellman
August 24, 2022 6:47 am

Bellman, heat is energy in transit. Heat is only recognized as it crosses the system boundary. Heat is really internal energy that moves from one system to another due to a temperature gradient.

Enthalpy is H = U + PV.

U is internal energy and PV is pressure and volume. So no when they say heat they shouldn’t be meaning enthalpy.

I hope this helps. A web site called hyperphysics may help.

Rick C
August 23, 2022 3:39 pm

Kip ==> I get your point regarding averaging atmospheric temperatures where pressure and humidity mean equal temperatures don’t mean equal heat content. However, in the lab we frequently are required to precisely control temperatures in incubators, ovens, furnaces and baths. In most cases we need to control both average temperature and temperature distribution (uniformity). We therefore must measure temperature with a number of distributed sensors – e.g. a 4 x 4 x 4 grid of 64 sensors*. The data recorded from these at regular intervals can certainly be averaged since both pressure and humidity are equal throughout the space. Thus equal temperature between two sensors does imply equal heat content and variation in temperature implies proportional variation in heat content.

*Typically such gridded measurements are done in a calibration process and related to a single point control sensor so that the space is useable.

bdgwx
Reply to  Kip Hansen
August 23, 2022 5:20 pm

The books on my shelf Mesoscale Meteorology by Markowski and Richardson and Dynamic Meteorology by Holton and Hakim use average temperatures. And it’s not just temperature. It’s other intensive properties like density, pressure, vorticity, etc. The uses are prolific and encompass spatial extents of the atmosphere.

And I already mentioned this above but the ensemble models GEFS, GEPS, EPS, NBM, etc. all average temperature and all show superior forecasting skill as compared to their non-ensemble counterparts. Averaging temperature (plus hundreds of other properties) clearly works in the real world too. It’s why the NWS uses the NBM almost exclusively for their official forecasts now.

Last edited 1 month ago by bdgwx
Mr.
Reply to  bdgwx
August 23, 2022 5:49 pm

Short-term weather forecasting (< 4 days outlook) is reasonably reliable.
In places whose climates are fairly docile.
(It’s a lot trickier in climates like the American Pacific North West – ask Prof Cliff Mass).

But weathers are not climates.

Climates forecasting has been atrocious.

(The Farmers Almanac seems to have been somewhat useful, with ~ 50% near misses)

bdgwx
Reply to  Mr.
August 23, 2022 6:43 pm

I do enjoy reading Cliff Mass’ blog. He’s a smart guy.

andic
Reply to  bdgwx
August 24, 2022 2:47 am
  1. Appeal to authority. I don’t much care what books you own, or even if you have read them. I am using the 2018 Swagelock catalogue in Chinese as a monitor stand – does that make me an expert on little tubes?
  2. Averaging of models may appear to work but it is based on two fallacies – averaging temperature is not good practice as explained above and errors do not necessarily average out.
  3. Since weather forcasts are normally dire how are you quantifying this improvement is it real or by luck was there a marginal improvement, within the normal noise that has been claimed and is still claimed as an improvement but which may not still be apparent?
bdgwx
Reply to  andic
August 24, 2022 5:24 am

1) I’m not appealing to authority. I’m appealing to evidence. And I always cite my sources so that I’m not accused of making stuff up, so that I’m not accused of plagiarism, and so that others can quickly find, verify, and learn the details of the evidence themselves.

2) And yet averaging model outputs has proven to be so effective that ensembling techniques are used almost exclusively now for weather forecasts especially beyond 3 days.

3) Weather forecast skill is quantified by various skill scores including root mean squared error (RMSE), anomaly correlation coefficient (ACC), brier skill score (BSS), equitable threat score (ETS), etc. For example, notice that the GEFS (multi-model average) destroys the GFS (single-model counterpart) in forecast skill of 500mb height forecasts extending the useful skill (ACC > 0.6) from 7 days to 10 days in 2021. It is undeniable that averaging is an incredibly powerful tool for reducing prediction error and increasing prediction skill.

Last edited 1 month ago by bdgwx
roaddog
Reply to  Kip Hansen
August 23, 2022 9:36 pm

That seems the principle defect of the “Greenhouse Effect” itself. Believing an open system to behave like a small, contained one is inherently nonsensical.

Carlo, Monte
Reply to  Rick C
August 23, 2022 4:54 pm

As I tried to point out in the other threads, a triple-point bath in a laboratory is completely different from averaging air temperatures in Timbuktu and Kalamazoo. The average of the bath temperature is meaningful because it is not changing, or changing only tiny fractions of a degree. The bath temperature is needed for calibrating thermometers, for example.

Geoff Sherrington
Reply to  Rick C
August 23, 2022 8:29 pm

Rick C
Thank you for that comment, even though it represents a special set of paribus certeris type conditions.
If you have measurement data on the uncertainty of the constancy of temperature in a water bath, esp near room temperature, would be keen to see the results.
Interesting e.g. to compare with claims for Argo floats in open oceans.
Geoff S

andic
Reply to  Rick C
August 24, 2022 2:34 am

This is a special case because the medium is water, the system is close to equilibrium, small and well mixed. Therefore when calculating the heat content at each sensor position and then recalculating an average temperature from average thermal energy content everything would just drop out of the calculation and you are left averaging temperatures.

I think that the thrust of this essay is summed up very well by a quote from Goldratt’s The Goal:
‘I don’t check the calculations, the math is nearly always correct, if there are mistakes they are in the assumptions’ (or something like that)

Jim Gorman
Reply to  Rick C
August 24, 2022 9:27 am

Certainly small spaces make such an assumption more viable but let me point out a small logical inconsistency. If you assume the temperature between any two sensors is equal to the average, then you can eliminate two sensors and put only one in between where the two would have been. Then following that same assumption, you put one senor in between each of the remaining. What you end up with is one sensor located with the device being calibrated.

The only other conclusion is that there are gradients throughout the water bath and multiple sensors are needed to validate that a constant temperature has been achieved throughout. My surmise is that those gradients are in constant flux and an average doesn’t tell you how the middle is actually changing.

However, that is far from saying that we have constant temperatures throughout the globe.

Rick C
Reply to  Jim Gorman
August 24, 2022 10:05 am

Actually, the use of multiple sensors is often required to determine the magnitude of temperature gradients and variability. Often a test procedure specification with specify the required mean temperature, say X +/- 0.2 and the maximum deviation of any single location say X +/- .5. Or, in a standard calorimeter where high precision water bath temperature change is measured, the bath is constantly stirred to assure uniformity and a single sensor is used. In the old manual type a mercury in glass thermometer with graduations of 0.001 C read with a microscope was used.

Bellman
August 23, 2022 3:47 pm

“The LIA was cooler than today…” And I agree wholeheartedly.

How is possible for the LIA to be cooler than today if average temperatures don’t exist?

According to the Essex paper from the last post

In Sections 3.1.1 and 3.1.2 it was shown that objects out of equilibrium cannot necessarily be compared to each other as being ‘‘hotter’’ or ‘‘cooler’’. It makes problematic the claim that Earth’s temperature field is warmer or cooler today than it was a hundred years ago, or that one century is hotter than another century.

Mr.
Reply to  Bellman
August 23, 2022 4:19 pm

Well, these events aren’t held on the Thames any more for one thing –

comment image?itok=FTB303NA

Bellman
Reply to  Mr.
August 23, 2022 4:47 pm

Yes. Not even in December 2010 or the winter of 1962/3. Despite them being a lot colder than when some of these frost fairs were happening.

roaddog
Reply to  Mr.
August 23, 2022 9:37 pm

Fear of drowning.

Jim Gorman
Reply to  Bellman
August 24, 2022 10:49 am

What was intended was that you could not average, let’s say Lagos, Nigeria and somewhere in Iceland and arrive at an average temperature at a spot equidistant from each of the locations. TEMPERATURES do not act at a distance to warm or cool a spot far removed.

I’ll say it again, if you want to address the energy arriving at earth in terms of “joules per second per square meter”, then you must also address the spatial distribution of those joules. That means both sensible heat and latent heat.

Temperature only addresses sensible heat, guess what deals with both latent and sensible heat?

Clyde Spencer
Reply to  Jim Gorman
August 24, 2022 1:04 pm

“TEMPERATURES do not act at a distance to warm or cool a spot far removed.”

No, but temperatures do have spatial auto-correlation over short distances. That is why gridding programs for making isopleth maps use some form of inverse weighting that is a function of the distance from the interpolated point.

Last edited 1 month ago by Clyde Spencer
Clyde Spencer
Reply to  Clyde Spencer
August 25, 2022 7:45 pm

I would appreciate the minuscule amount of effort to at least point out what in the above the down-voter disagrees with.

Jim Gorman
Reply to  Clyde Spencer
August 26, 2022 5:46 am

Don’t know who downvoted but it was wrong to do so.

I thought more about what you said. Here is my take.

Temperatures are not fundamental properties that occur on their own. Temperatures are created out of other properties and thus can’t tell you anything about the properties that create them, nor define the properties of separate “objects”.

An example is PV = nRT. “T” becomes PV / nR. If you measure the same T at two locations, you still can’t determine the other values. Averaging T won’t even give you the averages of any of the other variables. Averaging T is simply a fruitless exercise.

August 23, 2022 4:57 pm

Temperature cannot be added to temperature, thus cannot be averaged
======
Speed is an intensive property like temperature. It can be averaged.

Speed = distance/time thus
Avg(speed) = total distance/ total time.

Reduce temp to energy/mass then it can be averaged

Geoff Sherrington
Reply to  ferdberple
August 23, 2022 8:31 pm

Speed is not a fundamental property, it is a combination of length and time which are.
Geoff S

Jim Gorman
Reply to  ferdberple
August 24, 2022 10:58 am

A more correct analogy would be

Avg Speed = (D1/T1 + D2/T2) / 2

This will give you an average speed, but it doesn’t actually exist. You are computing a number that is not real.

Nowhere in the distance traveled did that average speed exist. This is the equivalent of the Essex paper saying that the end points don’t work at a distance. Velocity 1 doesn’t determine the velocity at all points, and neither does Velocity 2.

August 23, 2022 5:08 pm

Take 2 cubic meters of dry air at 10C and 1 cubic meter of air at 20C, if tou mixed these the average temp of the resulting 3 cubic meters of dry air would be 1.33C

Intensive properties like speed, temperature and density can be averaged by converting rhem to extensive properties..

Trick
Reply to  Kip Hansen
August 23, 2022 6:21 pm

That would be energy in joules can be correctly averaged which can be known. Heat is the total thermodynamic internal energy which is not known. Temperature is a measure of local avg. energy. .

August 23, 2022 5:12 pm

A car travels for 2 hours at 10mph and 1 hour at 20mph. What is the average speed.

The average speed is D/T = 40/3.

This is the exact same problem I presented above using speed in place of temperature.

Note you cannot calculate average speed as (10+20)/2

The correct answer is (10+10+20)/3

Jim Gorman
Reply to  ferdberple
August 24, 2022 12:34 pm

It still gives you a number that is not real. Did you ever travel at 40/3 mph?

An average is 13.3 mph. Were you traveling at 13.3 mph @ the 20 mile midpoint in your journey? According to your problem you were traveling at 10 mph at 19.99999+ miles and 20 mph at 20.00001- miles. Now in real life you had a gradient from 10 to 20 mph. The average there would be 15 mph assuming a linear increase.

Your point is well taken. I am just trying to point out that there are other issues involved when solving physical problems. Simple arithmetic averages generally don’t work out well unless your data has a normal distribution.

August 23, 2022 5:23 pm

intensive properties of matter and not subject to being added, multiplied or subsequently divided,
=====

Most intensive properties are fractions created by dividing an extensive property by another extensive property.

You can add, subt, mult, div these so long as you first convert them to a common denominator.

For example, addition:

A/b + c/d is not (a+c)/(b+d)

It is (ad+bc)/(bd)

Thus you can add intensive properties. The rules of fractions can be used for +-/*

tygrus
August 23, 2022 5:32 pm

To be more technical, air can also have gravitational potential energy(height above earth) and kinetic energy (wind). The height & wind are less important because they don’t contribute to long term energy changes. The compression or decompression of air at varying altitudes & locations change temperatures while overall energy stays the same. Solar emissions & gravity from all other celestial bodies have some influence over water/atmospheric movement (fluctuations).
Being unable to model all the physics & influences accurately means the models resort to shortcuts, approximations, factors ignored & unscientific limits applied to parts of the models so the model gives sensible output with the semblance of possibility & scientific basis.

August 23, 2022 5:35 pm

Measuring the earths temperature from space relies upon the S-B law, which is a 4th power relationship.

Because this is non linear, the average temperature as measured from space will be affected by both the mean and the variance. Surface temperatures are not corrected fo this.

1^4+3^4=82
2^4+2^4=32

In the above exanole, thr average temp is 2 in both cases but there is a difference in outgoing radiation.

This also applies in reverse. For the exact same outgoing average radiation you can get different average surface temperature.

bdgwx
Reply to  ferdberple
August 23, 2022 6:56 pm

This is referred to as the rectification effect in academic literature like that of Trenberth et al. 2009. For Earth the rectification effect is about 1 K or 6 W/m2. You can avoid the rectification error by doing a spatial integration of the SB law. However, to do the reverse, determine the average temperature from the average outgoing radiation, you most know and apply a correction for the rectification effect.

Last edited 1 month ago by bdgwx
Reply to  bdgwx
August 31, 2022 12:16 am

Thanks for this, bdgwx!

“Rectification effect” — what an odd name for it.

But 6 W/m² = 1°C seems reasonable, to me. However, it seems surprising that Trenberth 2009 would acknowledge that such a large difference in RF makes such a small difference in temperature. I found where they estimate 6 W/m², but I didn’t find the 1K estimate:

comment image

 ‍‍‍‍‍‍ ‍‍
AR6 suggests a much smaller ratio (larger temperature difference):

comment image

Last edited 1 month ago by Dave Burton
August 23, 2022 7:17 pm

“One cannot average temperatures”

Actually it is not hard to do ;))

Reply to  E. Schaffer
August 23, 2022 8:25 pm

Three articles to prove heat and temperature are different?
Perhaps the author is being paid by the word?
The explanation should have required one paragraph:

Is temperature the same as heat?
Heat is a measure of change, never a property possessed by an object or system. Therefore, it is classified as a process variable. Temperature describes the average kinetic energy of molecules within a material or system and is measured in Celsius (°C), Kelvin(K), Fahrenheit (°F), or Rankine (R).

Steven
Reply to  Richard Greene
August 23, 2022 10:48 pm

Add to that Article 2’s erroneous assertion of what you cannot do sensibly with a meaningless sum of any Intensive variable (contra to what every empirical scientist knows that for example a useful statistic of the sample mean can be obtained by dividing by N) and that it ignored the fact that sums of Extensive variables can also be meaningless. Thus you get from Article 2 an Extensive vs Intensive “nothing-burger” and worse than that; mathematical nonsense.

Reply to  Steven
August 24, 2022 8:59 am

My disappointment is that one of the best authors here thought three articles on this subject were a valuable use of his time.

Fortunately, a new article here on Wednesday analyzed the uncertainty of temperature measurements themselves:

Uncertainty Estimates for Routine Temperature Data Sets. – Watts Up With That?

Steven
Reply to  Kip Hansen
August 24, 2022 4:06 pm

No read the statistical literature including text books. “Averaging averages is only valid when the sets of data — groups, cohorts, number of measurements — 
are all exactly equal in size (or very nearly so), contain the same number of elements, from…” 
https://wattsupwiththat.com/2017/07/24/the-laws-of-averages-part-3-the-average-average/.

This is WRONG. Where do I start? You could try reading this paper by colleagues of mine on averaging across random and fixed effects in Linear Mixed Models
(https://doi.org/10.1111/j.1467-842X.2004.00334.x). My paper here (https://doi.org/10.9734/arrb/2021/v36i1230460) uses a meta-analytic LMM approach using MCMC sampling to model (i.e. average via the LMM) means with unequal sample sizes at the first sampling level which is handled by
using an extra fixed variance component. I do not need to read your series I have seen enough of your amateur statistical theory prognostications.
I thought you were a science journalist. You have a penchant for lecturing the world on mathematical statistics principles and I saw a post where you threatened to lecture us on thermodynamics as well. What exactly are your qualifications to lecture us all on these technical areas? I have seen enough of your misconceptions in my field of
mathematical statistics (applied and theory) and your lack of knowledge of the peer-review literature (unless you can cite some references to your papers in peer-review literature or
 say a text book you have published) to be concerned about WUWT articles like these spreading fake-news statistical methods.

Last edited 1 month ago by Steven
Reply to  Steven
August 24, 2022 4:25 pm

Who are you talking to?
The appeal to authority logical fallacy won’t sway many opinions here. Why should it?

If the data are baloney, their average is baloney too. That’s my “statistics”

Steven
Reply to  Richard Greene
August 24, 2022 7:11 pm

I gave references to the statistical literature on why Kip’s statement I quoted was wrong. That is argument to peer-review literature that has been tested and validated by professional statisticians. That is how science works. Not argument to personal authority but to published authority. These blogs do not reference fairly the peer review literature.

Steven
Reply to  Steven
August 24, 2022 7:40 pm

That’s because they are just blogs. No discipline of fairly considering and referencing the published peer-review literature is required or even encouraged. Publishing in the peer-review literature is hard work and takes scholastic discipline unlike blogs like this.

Steven
Reply to  Kip Hansen
August 25, 2022 5:47 pm

Kip ==> “Statistics and modelling have their uses — but cannot perform magic such as making the “averaging of averages of averages” a valid mathematical scientific practice.”

Here is a simple 2-level nested model and Y_bar is the average of the sampling-level 1 averages (i.e. averaging of averages), assuming repeat sampling with n_i fixed then you get the following exact results. For n_i random an approximation can be used assuming say a truncated Poisson for the n_i. So what is mathematically invalid about the results below? (I can also post the truncated-Poisson n_i approximate version and its accuracy. NB approximations are a valid mathematical tool when their accuracy can be quantified).

Doc1.jpg
Last edited 1 month ago by Steven
Steven
Reply to  Steven
August 25, 2022 6:02 pm

There was a notational error in the last line. Corrected below.

Steven
Reply to  Steven
August 25, 2022 6:06 pm

Corrected below.

Doc1.jpg
Steven
Reply to  Steven
August 25, 2022 6:53 pm

In my paper modelling longterm trends in mean krill densities (which in terms of the nature of the data as unbalanced cross-sectional and longitudinal samples has similarities to weather station long term measurements where stations are added or removed, and there are confounding effects on the “true” longterm trend eg urban heat island effects etc) I considered the n_i fixed. There are justifiable reasons for doing this and statistical inference is all about making supportable assumptions for the inferences that are required. In this case what was of interest is the mean trend and its uncertainty given (i.e. conditional on) the realisation of the survey sampling design (with “design” used quite loosely for that particular multi-national dataset) which was not of interest in and of itself.

Steven
Reply to  Steven
August 25, 2022 7:28 pm

Statisticians and empirical scientists are always debating the merits or otherwise of the particular assumptions made for the required inferences given the data and competing models. What they do not debate, however, is patently incorrect generalised assertions such as “averaging averages is mathematically and/or scientifically invalid”.

Steven
Reply to  Steven
August 25, 2022 8:41 pm

In a consultancy I am currently working on, the mean is not of interest but the survey design and how it determines the variance of the mean for future surveys is the statistical inference of interest. In that case I am treating the n_i as random and using the zero-truncated Poisson approximation. Doesnt make a huge difference whether n_i is considered fixed or random but “horses-for-courses” as they say.

Jim Gorman
Reply to  Steven
August 26, 2022 5:57 am

It is incorrect when you are averaging intensive variables as a proxy for thermodynamic heat. There is nothing keeping one from averaging temperatures if all you are after is an average temperature. What you can’t do is then say, I know what the energy distribution of the earth is. Temperature is NOT a complete measure of energy nor can total energy be inferred from temperature, only enthalpy can give you that.

Trick
Reply to  Jim Gorman
August 26, 2022 9:14 am

Jim, intensive variable temperature (local avg. energy) can be converted to extensive variable energy then physically averaged as energy and converted back to temperature. That step isn’t needed when the emissivity at each thermometer site doesn’t vary much; nature is being kind in that regard.

If there are enough thermometers measuring local avg. thermodynamic internal energy in the total space of interest and they avg. higher after a certain time with enough statistical confidence, then the total thermodynamic internal energy in the space of interest will be confidently higher even though it is unknown. In that specific case as applied to climate, temperature is indeed a good proxy for whether the total thermodynamic internal energy in the space of interest has increased (or not) over climate timeframes. 

NB: FYI, I wasn’t the downvote on your 5:57 am noted at time of my reply. 

Last edited 1 month ago by Trick
Jim Gorman
Reply to  Trick
August 26, 2022 12:15 pm

If there are enough thermometers measuring local avg. thermodynamic internal energy in the total space of interest and they avg. higher after a certain time with enough statistical confidence, then the total thermodynamic internal energy in the space of interest will be confidently higher even though it is unknown.”

But you don’t have a clue about the value as compared to other distant locations. You can’t assume that everywhere increases the humidity the same. This was an assumption of the GHE theory and it hasn’t proven to be correct. The last time I checked, total global rainfall had not increased significantly.

The point of science is to eliminate change in as many variables as possible when dealing with just one. In other words a controlled experiment. If you do not include water vapor in your measurement, then all you are doing is guessing.