Guest Essay by Kip Hansen – 30 July 2022
One cannot average temperatures.
Let’s start with this simple statement – this statement is true but comes with some common-sense caveats.
Important Note: The purpose of this essay is not to refute the basic underlying concepts of “global warming” or “climate change”. Those concepts and their supporting data are an entirely different topic. This essay is about a scientific point: One cannot average temperature. This fact may affect your understanding of some of the supporting points of Climate Science.
Let’s say you run a web site for corporations interested in having conventions in Topeka, Kansas in August and you’d like to inform attendees what kind of weather, in terms of temperature, they should expect, so that they can pack clothes suitable for the trip. A chart like this is perfectly appropriate. It shows the average of historical high and low temps for each day of the month and appropriately shows this as a range and not just a number. It provides a common-sense answer to the corporate question: “What’s the weather like in August in Topeka?” Answer: Hot days and pleasant warm nights. So, speeches and presentations inside the air-conditioned auditorium during the day and in the evening, the Tiki Bar Luau around the hotel pool is definitely on!
In this case, they have not really attempted to “average temperatures” — they just averaged the numbers about temperatures to find an expected range of historic highs and lows – they don’t think this is a real temperature that could be measured – they acknowledge that it is a rather vague but useful range of expectable daily highs and lows.
This acceptable and reasonable approach is far different than taking the high temperature of San Diego, Los Angeles, Mohave and Palm Springs, adding them up, dividing by four, and pronouncing that you have produced the temperature average of the SW California Desert. You may have an absolutely correct — precise to many decimal places — mathematical mean of the numbers used, but you will not have produced anything like a numerical temperature or a physically meaningful result. Whatever numerical mean you have found will not represent the physical reality of “temperature” anywhere, no less the region of interest.
“But, but, but, but” ….. no buts!
One cannot average temperature
Why not? Temperature is just another number, isn’t it?
Temperature is not just another number – temperature is the number of – the count or measurement of — one of the various units of temperature.
temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature). Temperature is not the equivalent of the energy of a thermodynamic system. [ source ]
So, we can say that objects with temperatures with higher numbers, regardless of which scale one is using (°F, °C, K), are “more hot” and objects with temperatures with lower numbers (using the same scale) are “less hot” or “more cold”….and we can that expect that heat energy will flow from the “hotter” to the “colder”.
Multiplying temperatures as numbers can be done, but gives nonsensical results partially because temperatures are in arbitrary units of different sizes but most importantly because the temperatures do not represent the heat energy of the object measured but rather relative “hotness” and “coldness”. “Twice as hot” in Fahrenheit, say twice as hot as 32°F (freezing temperature of water) is 64°F – obviously warmer/hotter but only nonsensically “twice as hot”. In Celsius degrees, we’d have to say 1°C (we can’t double zero) and we’d have 2°C or 35.6°F (far different than 64°F above). Yes, that is because the unit sizes themselves are different. However, if we wanted to know how much “heat” we are talking about, neither degrees Fahrenheit or degrees Celsius would tell us….temperature is not a measure of heat content or of heat energy.
A cubic meter of air at normalized sea level air pressure (about 1,013.25 millibars) and 60% humidity at a measured temperature of 70°F contains far less heat energy than a cubic meter of sea water at the same temperature and altitude. A one cubic meter block of stainless steel at 70°F contains even more heat energy. The relative hotness or coldness of a body of matter can be expressed as its temperature, but the amount of heat energy in that body of matter is not expressed by giving its temperature.
How is heat expressed – quantified – in science?: the units of heat energy are calories, joules and BTUs. [ source ] We see that none of the units of heat are units of temperature (°F, °C, K). (Note: If thermodynamics were easy, I wouldn’t have had to write this essay.)
Temperature is a property of matter – and temperature is specifically an Intensive Property.
Extensive properties can be added together – Volume: Adding 1 cubic meter of topsoil to one new cubic meter of topsoil equals two cubic meters of topsoil and fills twice the volume the raised-bed garden in your yard. Length: Adding one mile of roadway to one mile of existing roadway gives two miles of roadway.
But for Intensive Properties, this does not work. Hardness is an Intensive Property. One cannot add the numerical Mohs scale hardness of apatite, which has a value of 5, to the numerical Mohs scale hardness of diamond, which has a value of 10, and get any meaningful answer at all – certainly not 15 and likewise, not “5 plus 10 divided by 2 equals 7.5”.
Color is an Intensive Property. Color has two measures, wavelength/frequency and intensity. Most of us can easily discern the color of matter – our eyes tell our brains the generalized wavelength of the light reflecting off or emanating from an object which we translate to a color name. Scientifically, the wavelength (or mixed wavelengths) of the reflected or emanated light can be measured as frequencies (in terahertz — terahertz, 1012 Hz ) and wavelengths (in nanometers). Colors cannot be added as numbers. In colored light, adding the three primary colors evenly results in “white” light. In pigments, adding the three primary colors results in “black”, and other combinations, such as magenta and yellow, in surprising results.
Similarly, temperature, an Intensive Property, cannot be added.
“Intensive variables, by contrast, are independent of system size and represent a quality of the system: temperature, pressure, chemical potential, etc. In this case, combining two systems will not yield an overall intensive quantity equal to the sum of its components. For example, two identical subsystems do not have a total temperature or pressure twice those of its components. A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome. In special circumstances averaging might approximate the equilibrium temperature after mixing, but this is irrelevant to the analysis of an out-of-equilibrium case like the Earth’s climate.” [ source: Does a Global Temperature Exist? By Christopher Essex, Ross McKitrick and Bjarne Andresen ( .pdf ) ]
That is a wonderful, but dense, explanation. Let’s look at the salient points individually:
1. Temperature, an intensive property, is independent of system size and represents a quality of the system.
2. Combining two systems (such as the temperatures of two different cubic meters of atmosphere surrounding two Stevenson Screens or two MMTS units) will not yield an overall intensive quantity equal to the sum of its components.
3. A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.
4. Dividing meaningless totals by the number of components – in other words, averaging or finding the mean — cannot reverse this outcome, the average or mean is still meaningless.
5. Surface Air Temperatures (2-meters above the surface) are all spot temperature measurements inside of mass of air that is not at equilibrium regarding temperature, pressure, humidity, or heat content with its surroundings at all scales.
We can see that even at very small scales, the few meters surrounding the MMTS sensor at the Glenns Ferry weather station in Idaho, the air temperature system is far from being at equilibrium — air over a hot transformer, frozen bare grasses, snow patches and brush, each absorbing heat energy from the sun and with differing heat content. All these smaller sub-systems are actively out-flowing heat or absorbing heat energy from the unequal systems around them. In a practical sense, if one was standing next to the sensor, you would know it was “cold” there, the air at the sensor being well below freezing – but in a pinch, you might be able to cuddle up to the transformer and feel warmer sharing its heat. It is not, however, scientifically possible to “average” the air temperatures even inside of the two-meters-on-a-side cube of air around the sensor.
One cannot average temperature.
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Author’s Comment:
I am under no illusion that this essay will be widely accepted by all that read here. It is, however, scientifically and physically correct and might shatter a lot of firmly held beliefs.
I will be writing a follow-up, Part 3, covering the excuses used in CliSci for pretending that they can validly average temperatures – including the lame excuses: “We don’t average temperatures, we average anomalies”; “We don’t just find means, we find weighted means”; “We don’t average, we krig”; “We don’t make data up, we ‘use numbers from the nearest available stations, as long as they are within 1,200 kilometers’ [750 miles].” (Note: This is the approximate distance from Philadelphia to Chicago or London to Marseille, which as we all know, do not share common climates, no less air temperatures); and many more. In all cases, temperatures are inappropriately averaged resulting in meaningless numbers.
One can, however, average and work with heat content which is an extensive property of matter. It is the heat content of the “coupled non-linear chaotic system” which is Earth’s climate that Climate Science is concerned with when they insist that increasing atmospheric CO2 concentrations are trapping more heat in the Earth system. But CliSci does not measure heat content of the system but instead insists on substituting the meaningless numbers various groups label as Global Average Surface Temperature.
Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about. I will try to clarify if you ask specific questions. If speaking to me, start your comment with something like “Kip, I wonder….”
Thanks for reading.
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Some thoughts from Roy Spencer in WUWT: Top Ten Skeptical Arguments that Don’t Hold Water
“9. THERE IS NO SUCH THING AS A GLOBAL AVERAGE TEMPERATURE Really?! Is there an average temperature of your bathtub full of water? Or of a room in your house? Now, we might argue over how to do the averaging (Spatial? Mass-weighted?), but you can compute an average, and you can monitor it over time, and see if it changes. The exercise is only futile if your sampling isn’t good enough to realistically monitor changes over time. Just because we don’t know the average surface temperature of the Earth to better than, say 1 deg. C, doesn’t mean we can’t monitor changes in the average over time. We have never known exactly how many people are in the U.S., but we have useful estimates of how the number has increased in the last 50-100 years. Why is “temperature” so important? Because the thermal IR emission in response to temperature is what stabilizes the climate system….the hotter things get, the more energy is lost to outer space.”
Specific heat capacity is needed to make any average meaningful.
Also for the purposes of SB avg(T^4) really isn’t the same as Tavg^4, and come to think of it, emissivity varies with temperature anyway, and you really need to know what the area of the surface is to calculate precisely.
Seems to be a hell of a lot of bad averaging in climate science
Seems to be a hell of a lot of bad averaging in climate science
Nick will set you straight and put you onto the right ones-
Trillions of dollars at risk because central banks’ climate models not up to scratch (msn.com)
observa,
The Reserve Bank of Australia has a recent letter suggesting it might be prudent to conduct an exercise in due diligence on the climate science on which they rely. An answer is awaited.
” Seems to be a hell of a lot of bad averaging in climate science ”
Yes, that is the point. By DEFINITION, an average is NOT a REAL entity. An average does NOT exist in the physical world: it is ALWAYS a human construct. A discretionary construct: it depends on what is chosen to be averaged.
“an average is NOT a REAL entity.”
An average is a statistic, not a measurement.
Is it useful?
How accurate is it?
Useful for what?
How useful?
Those are four good questions
Those are 2 good questions and a bit of waffle that should have been answered in the first question.
You’re welcome.
A global average temperature increase of +1 degrees C. in 50 years may be nothing important, but a global average temperature increase of +1 degree C. in 10 years could be a very important statistic.
You’re wrong. Statistics in specific areas of, say, a companies production or turnover can be useful for that company – global statistics for production are not. Similarly, a 1C rise in temperature globally tells us bugger all – where and when did it occur? Was it a gradual or incremental increase in one or multiple regions, or was it an artefact of error ranges? Your figure answers none of those questions. Having regional temperatures and comparing them against historical and other regional temperatures may be useful as it tells you something about the changing area. Homogenising everything into one big averaged clump says nothing except that someone has far too much spare time on their hands.
Virtually every scientist in the world is wrong and you are right? Don’t make me laugh.
I said “could be a very important statistic.”
It is a high level statistic that could be a leading indicator of global, regional or local climate changes that need detailed analysis. It is a simple statistic that ordinary people can understand.
Consider the Dow Jones Industrial Average stock market index. 30 large cap stocks. If you are a stock investor who does not own any of those stocks, or even any large cap stocks, the DJIA can still be a useful indicator. If it goes down 20% in six months, there’s a high probability your own stocks also went down. Even though the average has no direct connection with your investments, it can be a useful statistic for stock investments in general.
Similarly, no one lives in the global average temperature, but that statistic can be a useful indicator of changes in regional and local climates — the climates we live in.
Yah, well… If you do climate science the way you understand stocks, I have to warn you urgently of the sandstorm approaching from Lapland…
Or maybe your investment strategy relies on siting your heat probes next to tarmac, electric transformers, volcanoes and other places that will increase sales of your prefab snow flakes.
“Similarly, no one lives in the global average temperature, but that statistic can be a useful indicator of changes in regional and local climates — the climates we live in.”
Once again, the average gives you *NO* information concerning the temperature profile. And it is the *entire* temperature profile that determines the climate we live in. Since multiple combinations of different temperatures can give the same “average” value the average gives you no way to differentiate between the combinations in order to judge anything to do with climate.
Averages *LOSE* important data. Averages don’t gain important data as you calculate them.
This is as true for local and regional climates as well as the global climate.
Lets keep in mind you are not really discussing the end result of all the averaging of temperatures. The Global Average Temperature is an average of “anomalies” which is even worse. Invariably the people that say it is warming are referencing anomalies and not absolute temperatures.
No, those are four good questions. They are what can be called a “NAND gate cascade.” (Any of the earlier questions that are answered “no” make proceeding with the cascade meaningless.)
An average is one statistical descriptor of a distribution. How meaningful it is in reference to the distribution must be stated by other descriptors like variance, standard deviation, kurtosis, and skewness. Confidence intervals are very much affected by the distribution shape which these descriptors attempt to show.
When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.
“When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.”
As I’ve been noting, WUWT posts global average and US average on its front page. No mention of kurtosis. Articles here (eg Spencer, Monckton) are full of temperature series without those statistics.
“As I’ve been noting, WUWT posts global average and US average on its front page. No mention of kurtosis. Articles here (eg Spencer, Monckton) are full of temperature series without those statistics.”
So what? This is no defense. Once again, it is the argumentative fallacy of Appeal to Authority.
Winter temps have a different variance than summer temps. Yet the SH and NH temps get mixed together every single month with apparently no attempt to reconcile the different variances! Using anomalies doesn’t help at this at all!
Can you actually address the ISSUES at hand instead of just resorting to argumentative fallacies.
Tim ==> Nick is fooling with you — poking you (and skeptics in general) with a stick to get a reaction.
His point is “If you lousy skeptics don’t think GAST (or other temperature models) are any good, why do you hold up UAH as a good example opposing BEST or GISTemp?”
Bascially, trolling-lite.
“it is the argumentative fallacy of Appeal to Authority”
It is surprising to me to be slammed for appealing to the Authority of WUWT. But the original query was
“When was the last time Nick Stokes ever showed any of these when providing a Global Average Temperature? Without them the number is meaningless.”
To which I say, when was the last time anyone showed any of those things? Anyone at all? WUWT doesn’t. You are dismissing a lot of WUWT content as meaningless, including the reference pages.
It isn’t “Appeal to Authority“; it is Reductio ad Absurdum.
Nick ==> Come on….you are doing the same thing the worst commetners here do — You lump all WUWT authors and Readers as have a common reality/opinion just like the readers here often lump all Cli Sci researchers.
Not true at all, and you know it well.
No, I’m saying, in effect, why pick on me? This often happens – I post a graph, just like the thousands that have been posted at WUWT without demur, and I’m told that I have left out essential things and the graphs are meaningless.
Nick ==> They pick on you because of the manner in which you comment here…
besides, they identify you as “the enemy” or “a climate alarmist”. LOL
It’s basically mindless heckling. If you really believe that temperature graphs should not be displayed without a whole lot of other information, take it up with WUWT, where it is done all the time. If it’s something that only bothers you when I do it, well, maybe you have identified the cause.
That’s why it is relevant to mention how often folks here invoke average temperature to promote some narrative like the Pause. If you really believe all this stuff, some kind of protest has to be made about that.
Who is the gatekeeper of all things WUWT?
Nick ==> You are absolutely right, most of the responses to your comments are mindless heckling. That exactly what I meant.
I did not say that temperature graphs should not be displayed, with or without a whole lot of information.
As far as I recall, you did not display any graphs in this comment section, and it does not bother me when you or anyone else does it.
I am almost positive that you know that there is no “WUWT” to “take anything up with”. Your site, moyhu, is that way because your site it YOU. WUWT is not that way, Anthony is far too busy with other things– I doubt he even reads most of the stuff posted here.
I think you also know that WUWT is happy to post ALL of the usual GAST/GAT graphs without prejudice in its reference section.
If you has started out with a serious science-based comment about the topic of the essay, showed that you had read or considered the narrow science point being raised — in other words, acted like an adult in the room, you would have fared better.
And, please, remember that the comment section is a free for all and only very loosely monitered — we have a lot of young Junior Climate Skeptic Warriors here and fewer serious adults with science backgrounds. Try to be one of the later.
“It’s basically mindless heckling.”
A great description of Nick’s comments !!
This is the argumentative fallacy of “woe is me” or Appeal to Pity.
I posted some just a few days ago, where were you?
Two wrongs don’t make a right. Don’t make excuses, make facts.
You can average the concentration of solutions to get something meaningful. Concentration is also an intensive property, quantity of a component divided by the total quantity of the sample.
You need to ensure that;
it’s the same component you measure the concentration for,
same extensive component for the quantities, e.g. amount that is measured in moles for the solute and volume for the sample, using constant units e.g. mole per litre or M
and the quantities of the samples are exactly the same.
The average will be the same as the total quantity of the component in all samples divided by the total quantity of all samples.
If you only partially sampled what you are analysing, it is also correct if the composition is constant (pointless averaging it, as well, except to reduce uncertainty due to random error). It’s an estimate that could be utterly useless if not. Possibly useful if you took many samples, evenly throughout, and if the profile of the composition doesn’t vary greatly. If the profile varies considerably, you can fit polynomials to what data you have to get an estimate of the profile and average that as if it’s an average of sampling the whole (Krigging).
It’s tempting to view temperature as the amount of heat energy that went into the system divided by the heat capacity (an extensive property while specific heat capacity is the intensive property ie. per unit of mass) because of the basic definition of heat capacity, but that definition is for a very small change in temperature of the system and the heat capacity can change dramatically with phase changes.
Now I wouldn’t argue against using the average of temperature measurements, even just minimum and maximum rather than continuous measurements, as a proxy of net flow of energy into the system. I say proxy because you are not taking into account so many things. It’s the temperature of a probe influenced by its environment and I could write an essay on the issues with equating it with the extra heat energy accumulated by the region.
That is if the temperature record to do it existed ie. if this profile that was made by Krigging what data exists was the actual record. This is the difference in opinions here, because nobody acknowledges that it’s a proxy only marginally better than tree rings, and that is if it were actually measurements rather than an estimated profile.
The average global surface temperature might be a meaningful estimate of the flux of energy out from the Earth if the emissivity was proportional to temperature rather than temperature to the power of 4. And still a proxy rather than a measure as what happens above the surface will make a much bigger difference than a degree change to the flux from that patch of Earth. The small range of temperatures of sea surfaces means you can ignore that if you are just using SST as an indicator of climate change, or the surfaces needing to warm to get that flux back to equal the energy coming in. It can’t be used as a meaningful measure (or modelled).
And if you use the average surface temperature like that, a 1% increase in flux only requires a 0.25% increase in the average surface temperature of 0.7°C. So an extra 100 ppm gave an extra third of a percent downwelling, corresponding to about two to three tenths of a degree.
I can’t believe that we are making major policy decisions on this because academia is defending the science.
You must be careful what you do with this. Temperatures are not a good proxy for heat energy. There are too many other variables that enter into determining the heat energy in a volume of air. Water vapor for one, and it is a big one. Is it reasonable to average temps over a month when you have no idea how water vapor changed during the month? Is it reasonable to average a desert temperature with one from Miami considering the difference in heat capacities of the two different locations?
I used the analogy with tree rings because they really are a proxy for how good the growing season was rather than average temperature of the region. Extremely poor thermometers.
Tree rings depend on a lot of things, precip, insect infestation, shade from surroundings, and temp. That’s why they are such a poor thermometer.
Robert ==> That is correct. The question is “What are they really counting?”
https://wattsupwiththat.com/2015/12/05/what-are-they-really-counting/
Is the thing they really counted the same as the thing they say they counted? Is a tree ring width graph a graph of historical temperature? Absolutely not.
“The average will be the same as the total quantity of the component in all samples divided by the total quantity of all samples.”
What does the average tell you about each sample individually? Just like with temperature you will be unable to identify which samples have a high concentration and which have a low concentration.
“total quantity of the component”
In other words you are calculating an *extensive* value, the total quantity of the component, and then calculating an intensive property using that value.
How do you get a “total quantity of temperature”? And what do you divide it by in order to calculate some “thing”.
I’m just looking at why some scientists are adamant that the average has some physical meaning. So you add up a number of samples x1/y + x2/y + xn/y and divide by n then you get (x1 + x2 + ….xn) / ny. Pretty straight forward.
X is delta Q and y is heat capacity. A lot of problems with that simplification, same as why thinking of a proxy as a measure of a variable is wrong.
The idea of using a proxy comes from psychology. You believe a variable that you can measure shows similar trends that have occurred in variables that you can’t measure. In this case, if everything else was the same, an average of the real temperature for all the infinitesimal areas that make up the whole surface should show any trends of increasing Q due to the GHE, is the BELIEF.
So there are two arguments.
Is it a good proxy for delta Q?
Is it sane to use Krigging with a proxy?
Robert ==> “I can’t believe that we are making major policy decisions on this” — neither can I.
I doubt that the average temperature of an average room can be determined to within a couple of degrees (especially if kids are going in and out).
Measuring an average of the earth is a slightly bigger challenge.
Yeah what might serve your purpose in a laboratory environment can lead you up a garden path when you test it outdoors with life-size quantities of substances, materials and equipment.
It’s the classic “academic” result vs real-world outcomes.
Nick ==> Thanks for supplying one of the main Lame Excuses for averaging of an Intensive Property that simply cannot be scientifically averaged. Knowing the averaged temperature or its changes over time does not inform us whether the heat content of the climate system is increasing or not. It does does not inform us if it is “getting hotter”.
I have not made any claim about the other foundational claims of Climate Change or Global Warming. Only the scientific point that temperatures cannot be averaged to produce any kind of a meaningful result.
“Only the scientific point that temperatures cannot be averaged to produce any kind of a meaningful result”
So what of your figure showing averages for Topeka. You seemed to think that meaningful. You might think averages over time are meaningful, but not over space. Well, first if the newcomers to Topeka find the quoted average helpful, they are doing spatial extrapolation. Infilling even (at that bar). But suppose you were to arrive in Kansas by balloon, which might land at a random point. What then? The Kansas average is your best estimator.
Nick,
Then we have William S Briggs, statistician, writing this:
“Now I’m going to tell you the great truth of time series analysis. Ready? Unless the data is measured with error, you never, ever, for no reason, under no threat, SMOOTH the series! And if for some bizarre reason you do smooth it, you absolutely on pain of death do NOT use the smoothed series as input for other analyses! If the data is measured with error, you might attempt to model it (which means smooth it) in an attempt to estimate the measurement error, but even in these rare cases you have to have an outside (the learned word is “exogenous”) estimate of that error, that is, one not based on your current data.”
Do not smooth times series, you hockey puck! – William M. Briggs (wmbriggs.com)
This advice is relevant also for Kip’s Topeka figure, which has a type of smoothing.
If the advice of Briggs is accepted, it raises the issue of how to measure and process errors. And uncertainty. Question – are the uncertainty limits around a time series of “anomaly” daily temperatures smaller or larger than those around a time series of measurements as observed? Geoff S
Geoff ==> Ah, Cmdr. Briggs. Thanks for the quote.
The Topeka figure illustrates the correct way to talk about “average temperatures”.
Smoothing is very useful if shown on the same chart as the raw data. It helps make a trend visible that may have otherwise been invisible. It can also make a trend visible that is really nothing more than meaningless random variations.
I think the term is spurious.
Sophistry—the Topeka graph is not a single-number average.
Nick ==> You conflate vague practical weather features with scientific mispractice.
Kip’s graph is showing the VARIANCE of the maximum and minimum temperatures along with their average allowing the person viewing to make a judgement about the WEATHER at a location, not the climate! There is no “averaging” being done in the guise of a *mid-range* value or an anomaly derived from the “mid-range” values.
When you find the “mid-range” value you have lost *all* of the pertinent data required to judge what the actual climate is. The climate is the entire temperature profile. The mid-range value can be the same while the climate is significantly different! That’s one of the major problems with the “global average temperature”, it gives exactly zero information on the actual changes in climate!
No. The most useful information for Topeka would be a descriptor giving an indication of, say, warm days and cooler nights with a small chance of rain: most people have an entirely subjective view of temperature anyway so using those figures may be a dodge for meteorologists to get information across in the shortest possible time but means very little to most people. Frankly ‘temperature’ is only an indicator of what heat energy has done to the physical surroundings anyway – do a proper job and measure the heat directly instead.
We expect more than just averages of what it “feels” like outside from a “science” that receives billions of dollars per year and influences decisions at national and even global levels.
You’ll note that WE only showed a graph of temperatures. He did not attempt to show humidity levels. The weather stations do give a heat index for a reason. I live in Topeka. Two days ago we had a morning temp of 70 @ 94% and an evening temp of 84 @ 84%. Today we had a morning temp of 58 @ 96% and an evening temp of 91 @ 25%.
Do you think there was a big difference in the heat index between the two evenings? And, BTW, the 84% humidity was around that for the whole day.
Temperature is NOT a good proxy for heat energy. It might be ok for determining radiation values per S-B but that is all. The global climate has more to it than radiation.
“Why is “temperature” so important? Because the thermal IR emission in response to temperature is what stabilizes the climate system….the hotter things get, the more energy is lost to outer space.”
Nick, no part of this statement relates to a “global average temperature.” IR is emitted differently all around the globe just as temperatures are different and constantly changing all around the globe. The last part of your statement is just a description of equilibrium. The more water going into the pond, the more water goes over the weir. If more energy is lost to space because things get hotter, how are they getting hotter, and what’s the problem?
“The last part of your statement”
It is Roy Spencer’s statement (vla WUWT) not mine.
“Nick, no part of this statement relates to a “global average temperature.” I”
Roy says a global average temperature is meaningful. So it’s hard to say an average isn’t. Plus, of course, Roy calculates one every month, and WUWT runs an article about it, closely followed one from Lord M about the “pause”. Pause of what? Global average temperature, of course.
And Australian temperatures, which by UAH v6.0, have not warmed for a decade, to this month of August 2022. Geoff S
http://www.geoffstuff.com/uahaug2022
Make that
http://www.geoffstuff.com/uahaug2022.jpg
Appeal to authority—more sophistry.
Nick ==> You are falling back on “Authority” as an argument. Personally, I like Roy Spencer, have spoken with him, shared jokes, but only as a casual, passing acquaintance. He and Monckton disagree about lots of stuff as well…I have watched them discuss their disagreements off in a corner quietly between themselves.
None of that is pertinent to the scientific fact that it is not possible to average Intensive Physical Properties, including temperature and arrive at a meaningful physical result.
“Roy says a global average temperature is meaningful.”
That’s no answer! It’s an argumentative fallacy called the Appeal to Authority. An assertion isn’t correct merely because some states it, it must be shown to be true – WHICH YOU HAVEN’T DONE!
None of the global average temperatures can tell you if maximum temps are going up, if minimum temps are going up, or if a mixture of both are going up. Yet that information is VITAL for actually judging whether or not changes are pointing to significant changes in climate that will affect humankind.
Suppose the global average temperature goes from 15C to 15.1C. Can *YOU* tell us what caused it to go up? Can you tell us *where* a change happened that caused it to go up? If *YOU* can’t then why do you think it is important?
Then I disagree with Roy Spencer, and you for quoting him. Nothing in your response refutes my point. I think most of the people contributing to WUWT will agree that a “global average temperature” is just an abstract concept which exists merely as a calculation with little to no ability to predict future climate states around the world. It is primarily used on this site to refute the people who popularize the notion that if the GAT goes up, catastrophe must necessarily ensue and man must be the cause.
Hoyt ==> Just a note: That “most of the people contributing to WUWT will agree” is yet another “argument from authority”.
The simple scientific fact (from the physics of thermodynamics) that the Intensive Property we call Temperature cannot be added (or the result of an addition of temperatures divided to create an “average”) is not subject to argument from authority.
@Kip – more precisely, “argument from consensus.”
WO ==> Yes, I was using “most of the people here” as a group expert.
Kip, I wasn’t arguing that a GAT as a meaningless abstract is proved by the number of people here who believe that. I simply observe that most contributors here do seem to feel that way more or less, rightly or wrongly. I was merely pointing out that the concept of a GAT appears on this website frequently (as Nick points out) but for reasons other than what Nick thinks is the reason.
Hoty ==> Sorry, I get a little pedantic sometimes….
As you may have gathered from the comments following this essay — the WUWT crowd does think GAST/GAT is wrong, not a good measure, nonsense, jiggered, faked etc etc etc.
But very few understand intensive/extensive properties or why one cannot average temperature.
Hoyt,
The CAGW people can’t even use the GAT to tell you if minimum temps are going up, whether max temps are going up, or if it is a combination. They just all assume that it is maximum temps going up and they will keep going up forever with no limit, thus turning the earth into a cinder.
What a joke!
A GAT may or may not be useful depending on the uses made of it. However, one failure for climate science is to attempt to use a “mean”, i.e., a statistical descriptor of a distribution, without also quoting the other necessary descriptors to allow one to judge just how well the mean represents the distribution. Even Dr. Spencer fails to do this.
Tell us the other descriptors that are associated with any of the so-called Global Average Temperature determinations. What are the variance, standard deviation, kurtosis, and skewness? Is the distribution normal? Is it bimodal? Don’t just quote some SEM calculation that tells how close the estimated mean is to the population mean. Give us the details of the population distribution.
If you want to deal with statistics these things are necessary to evaluating the information. These shouldn’t be hard for a mathematician to calculate.
Whilst it is feasible to calculate a global average temperature, I would suggest the amount of adjustment to raw data and interpolation across vast areas makes a global average temperature irrelevant and likely inaccurate
I calculate the average using unadjusted temperatures. It makes very little difference.
You can calculate using just half the data points, then the other half (or any other large subset that you like). You get the same answer.
But Nick,
Should you use adjusted or raw? Here is a comparison of raw Tmax Alice Springs, Australia, with 4 versions of ACORN-SAT adjusted data and an earlier one.. Kip, the daily numbers have been averaged into annual, for convenience of data handling, not because it is the fundamentally correct act.
What error or uncertainty summary would you draw from this?
http://www.geoffstuff.com/aliceadjust.docx
Geoff S
The right questions are:
Do you trust the people who do the infilling and compile the global average temperature?
Is there evidence they are biased?
I would not trust NASA-GISS or NOAA to tell me the time.
I don’t think folks appreciate that temperatures are MEASUREMENTS and not simple old numbers on a number line to be manipulated. The goal for GAT is to obtain a number that is NOT A MEASUREMENT. The best you see for uncertainty is a Standard Error which is a number that describes how well a sample mean predicts a population mean. It is not uncertainty.
What WE is trying to do here is laudable. Too much of climate science has revolved around finding an unreal measurement from statistical analysis. They need to go back to the beginning and realize that they are dealing with physical measurements, not just numbers. They need to reevaluate how to treat measurements to obtain an accurate description of temperature. One of the uses of krigging is to arrive at a map describing the geophysical phenomena being evaluated. Why don’t we see contour maps of temperature (or anomalies) so they can be evaluated? How about contour maps of IR leaving the earth and entering the surface? How about contour maps of humidity so people can see the heat distribution?
The 194- to 1975 global average temperatures have changed considerably from 1975 to 2022. Science fraud !
That’s 1940 to 1975.
not 194- to 1975.
Nick ==> You can get a numerical answer — it just is not physically meaningful.
People have been telling him that for ages, although a lot of comments were concerned with the complete ignorance of errors. Climate ‘Scientists’ are little more than statisticians – they have no idea how those numbers relate to anything whatsoever but they do like playing with them!
I’ve been saying this often for years here, usually any time a graph with a single line for “global temp” is presented.
Mathematics is only a tool – it MIGHT produce useful results, and it might not.
I can average the number of crickets I heard last night with the length in centimeters of the skirt that my wife wore to work this morning. I can be very honest and also compute the error bars for my average (I might have missed a chirp, or some other noise in the house sounded like one; my length measurement is only as accurate as the tape measure I used, and the amount of annoyance my wife showed at my apparent insanity).
The resulting number, with its error range, is a perfectly good number, calculated with mathematical rigidity. It is also absolutely and entirely meaningless.
Very good!
Trying to map a temperature versus time along with a CO2 concentration versus time hoping to see some way to tie them together is exactly your description.
If time is the common independent variable, the best you can get is a correlation of 1. That is not proof of causation. Climate science must establish CO2 as an independent variable and temperature as the dependent variable. That will let one develop a functional relationship that allows verification of predictions. It also will show one temperature for a given CO2 concentration.
However, don’t hold your breath. Lots of studies showing CO2 follows temp instead of the other way around. Finding an actual relationship will be hard. Probably too hard to get much funding!
Ten days ago, at about 12.30 the thermometer on a North facing wall by our stone patio at the back of our house registered 104.6 F. Within a minute or two the temperature on our tree-shaded brick patio at the bottom of our garden was 86.0 F. The distance between the patios is around 60ft.
Can we say that the average temperature in our garden was 95.3 F?
Do we need to record that at the time there was a pleasant breeze blowing?
Solomon ==> A very common sense question.
We know there has been warming for 300+ years
The alternative is cooling
We should be thrilled we got warming
The people living in the 1690s would have lived todays’ climate.
The last half of the 1600s was too cold.
Some famines in Europe back then.
Now let’s get to important questions:
Is the current climate pleasant?
— Yes
Can humans predict the climate in 50 to 100 years?
— No
If the1975 to 2022 global warming continued for another 47 years, would that be a problem?
— No. Unless you object to warmer winter nights in Siberia and more
greening of the planet.
Are leftist Climate Howlers climate science fools, or do they have devious political motives for climate scaremongering?
— I say both. Leftists are the Forrest Gumps of climate science.
Is Al Gore a rich doofus?
— Yes
Redge ==> One can calculate a “number” for Global Average temperature, but it will be meaningless.
Not true
Depends on the accuracy of the data and global average
+ 0.5 degrees C. might be meaningless
+ 5 degrees C. would be meaningful
Richard ==> The NUMERICAL result of such an exercise is meaningless.
If the Earth climate system were to actually warm — real world warming, not a change in a calculated number — it would be meaningful.
But we will not learn that from GAST calculations.
You are wrong again
A +5 degree C. increase of the global average temperature would most likely be a very important statistic, assuming decent accuracy of the underlying temperature data. How you could argue with that statement escapes me.
Richard ==> One would first have to have a physically correct quantity that physically (as in physics) represents “increase of the global average temperature”.
Decent accuracy? Uncertainty accumulates when it is associated with independent, random variables. Just like variances add when combining them. They both get treated in a similar manner.
What would you consider decent accuracy when you are combining a 1000 independent measurements with uncertainty?
If you have a room with 5 people that are 5′ tall, and a 6’5″ guy walks in, has everyone in the room gotten taller?
If the aggregate uncertainties from the base absolute numbers is greater than +5C then how would you know if it is meaningful?
If you average 30 numbers whose uncertainty is +/- .7 using root-sum-square then you get sqrt(30) * 0.7 = +/- 4C. If you then average 12 groups of 30 (i.e. monthly to get annual) you get sqrt(12) * 4C = +/- 14C of uncertainty!
I know the CAGW crowd thinks all uncertainty cancels and the stated temperature values are all 100% accurate but that just isn’t reality at all!
Very well put.
“I know the CAGW crowd thinks all uncertainty cancels”
It is rare to find someone who understands what UoM actually is actually describing.
It is not a measure of fluctuation about a true value.
I have on my desk a Certified Reference Material 24X07001 (batch C). The Ti content is 3.14% +/- 0.02% (95% CI)
So if I measure stick it in my XRF and measure it ten times will I obtain results which average to 3.14%? Nope, of course not, but why?
one factor is:
CRMs are certified based on multiple analyses of a number of samples from the batch to be certified, but the material is not perfectly homogeneous therefore the samples will be different, the likelihood that my sample is exactly 3.14% is vanishingly small, the same is true of all of the CRMs which were used to calibrate the methods used to certify 24X07001C. And so the situation arises that all we can say is that the Ti content of my piece is somewhere between 3.12% and 3.16% (probably (95% certainty)). Now if I calibrate an instrument with 24X07001C I have no choice but to use 3.14% as a best estimate, but am knowingly introducing a bias of up to 0.02% (and there is an estimated 5% chance its greater) into my future measurements of this alloy.
This type of bias is not averaged out over multiple measurements over time and cannot be assumed to be averaged out by measurements from different sources.
Wow! You pegged it perfectly!
Your ten measurements *should* average out to the true value for that one sample (assuming zero systematic bias in the measurement device) but will it come out to 3.14%? Like you say, probably not.
Using the stated value in subsequent calculations is fine – as long as the uncertainty is propagated along as well!
It’s not just meaningless because it is an intensive property. It actually tells you nothing about climate. Climate is a function of the entire temperature profile at a location, including daily and seasonal profiles of maximum and minimum temperatures. An average, especially of anomalies, gives you *NO* clue to the actual temperature profiles associated with the anomalies – thus no information about the climate either.
WRONG
A significant global average temperature change is high level statistical evidence that there may be significant changes to local temperatures, where people actually live.
A small average temperature change probably reveals nothing of use. The dabate is how much of an average temperature change is important. My guess is +/- 1 degree C. is not important. A +2 degree C. increase ,ight indicate that more informasltion is needed about the temperature change –changes by latitude, local changes, TMIN and TMAX changes — seasonal changes, time of day changes, etc.
The GLOBAL AVERAGE TEMPERATURE CAN BE AN INDICATOR OF SOMETHING IMPORTANT HAPPENING TO THE GLOBAL CLIMATE OR A STATISTIC THAT HIDES IMPORTANT DETAILS. OR BOTH
An example about another subject:
The 2020 election bellwether county poll showed Trump won 18 or 19 counties,yet lost the election. The bellwether statistic result in 2020 was unprecedented in polling history. It does not prove election fraud in 2020, and does not change a single vote, but is high level statistical evidence of election fraud that needs further investigation.
“WRONG
A significant global average temperature change is high level statistical evidence that there may be significant changes to local temperatures, where people actually live.”
Malarky! The uncertainty of the global average temperature is so high you can’t tell if there is a significant change or not!
Each temperature measurement is of a different thing made by a different device. The uncertainty in such a distribution can *NOT* cancel. Thus any average of the distribution inherits the total uncertainty of the elements in the distribution.
I would defy you to go outside from a 70F house to an outside temp of 75F and be able to tell the difference. If you can’t tell what that difference is then how would you have any chance of being affected by a 4F change over 100 years?
“The GLOBAL AVERAGE TEMPERATURE CAN BE AN INDICATOR OF SOMETHING IMPORTANT HAPPENING TO THE GLOBAL CLIMATE OR A STATISTIC THAT HIDES IMPORTANT DETAILS. OR BOTH”
Only if you buy into the CAGW claim that all temps are 100% accurate. If each temp is actually “stated value +/- uncertainty” that simply can’t be possible.
The average human has one tit and one ball but you’d be hard pressed to find an average person
But if the average human is measured consistently and the average increased the number of tits while decreasing the number of balls you could tell that the ratio of women to men is changing. And in which direction.
An average not being a physical property does not mean the average has no meaningful descriptive function.
You can average temperature (in theory, the practice is hard). And you can make meaningful statements about that average.
However, Kip is right to say that the meaningful statements do not include what the temperature actually is at any given time and place.
M.,
I disagree. The most likely cause is a change in the ratio of men and women but that is not the only possible cause of a change. Besides, physical attributes are an extensive property, not intensive properties.
“The average human has one tit and one ball”
If you want to know how many tits and balls there are in a country, that is a useful statistic.
But what would it tell you?
Derg,
That the woke police will be at your door, like they did to US President Trump. Geoff S
If the average number of breasts and testicles was found to be changing over time that might be something worth looking into, though.
AlanJ ==> But not too closely…..
… and if you are a biologist
Thaks for elevating the comments to the Ph.D. level
A fine example of why one is easily misled when doing “statistics” on quantized phenomenon…
“The average human has one functional tit and one ball but you’d be hard pressed to find an average person”
Fixed for you!
Wrong. Males also have two mammary glands, albeit vestigial. Females also have two gonads.
Any fool like Nick Strokes can average temperatures. That doesn’t mean such averages have any meaning. Only enthalpy (an extensive property) can have a physically meaningful average. Without knowledge of heat capacity and mass, averaging is completely meaningless, save for climate “scientists”.
Thought experiment for Strokes: an incandescent speck of iron of mass 1mg at 1500K lands on a 1Kg iron block at 300K. What is the average temperature?
Similarly, a 1Kg iron at 400K is placed on the preceding 1Kg block at 300K. What is the average temperature? Would it change if one of the blocks were made of lithium (heat capacity per gram about 8 times that of iron)?
Graemethecat ==> CliSci “GAST” should be a study of heat energy (by whatever name). But CliSci uses an scientifically improper measure, “average temperature”.
I presume GAST stands for “Global Average Surface Temperature”. If Climate “Scientists” used Global Average Surface ENTHALPY instead, that would be perfectly meaningful and indeed valuable in detecting real climate change.
Graeme ==> Yes, GAST is “Global Average Surface Temperature” but not a specific one — there are lots of versions from any groups using many different models to determine a single number result.
The basic point of Global Warming science deals with the question of increasing (or not) heat content of the Earth climate system…So, quite right, enthalpy [ a thermodynamic quantity equivalent to the total heat content of a system ] is what they should be using. Enthalpy is an Extensive Property.
a thermodynamic quantity equivalent to the total heat content of a system.
The problem is where do you measure the enthalpy? At 6′ above land? Above and below that the enthalpy value will be different, it is a gradient as you move up and down because of the change in pressure and humidity. How about the ocean? Right at the surface or at some distance above the surface? How would you combine those values with the land values?
Take a look at the attached pressure map. These gradient lines change from hour-to-hour, day-to-day, etc. How do you capture an average>?
“Any fool like Nick Strokes can average temperatures”
So if it is so foolish, why does WUWT display on its front page the global average of UAH? Or the US average derived from USCRN? What’s with Monckton and Co going on about the new Pause, to much local cheering? What is the Pause without a global average temperature?
WUWT allows you freely to post your stupidity on its platform, so why not global average temperature?
There certainly is such a thing as average daily global temperature, but such is meaningless. It’s meaningless because it cannot be measured (it is literally impossible to measure the temperature of every cubic centimeter of the earth’s atmosphere in real time and compute an “average” … and the average even if computed would by itself be meaningless, because the entire atmosphere is not a population with shared attributes.
Temperature is also a time varying property, day/night, winter/summer, cloudy/clear, etc.
What does the average of a time varying, intensive property tell you?
Tim ==> That’s a trick question — one cannot average the numerical values of intensive properties.
“It’s meaningless because it cannot be measured (it is literally impossible to measure the temperature of every cubic centimeter of the earth’s atmosphere in real time and compute an “average” “
That’s not why it’s meaningless.
Jeff ==> Thank you, quite right! That is NOT why it is meaningless.
Hard to understand why a Roy Spencer quote would get “thumbs down” votes
and surprising that the Stroker would quote him.
Because this statement is just wrong:
“Because the thermal IR emission in response to temperature is what stabilizes the climate system”
These things don’t ’cause’ the climate to be stable, these things are the ‘effect’ of a stable system. They are examples of equilibrium which is the nature of the universe.
Also, IR emissions don’t occur in response to any ‘average global temperature.’ They happen to a greater or lesser extent depending entirely on local, real time, conditions. Averages have nothing to do with it.
One could calculate the average temperature of different planets to come up with a universal average planetary temperature but, what could that possibly mean? Remember, even the calculated GAT isn’t ‘global.’ It is just a small sliver of atmosphere 2 meters in thickness, representing just a tiny percentage of an atmosphere that is 62 miles thick. That still ignores all of the temperature variations in the oceans and beneath the crust.
Hoyt ==> Well, only maybe a foot (0.3 meters) thick — the inside height of a Stevenson screen. Less for MMTSs, which are maybe 8 inches. And the temperature records is not continuous — it is made up of thousands of individual measurements made at very small spots in a system that is out of equilibrium at almost all conceivable scales.
THERE ARE ALSO ALMOST 8 BILLION FIRST HAND WITNESSES TO SOME OR ALL OF THE GLOBAL WARMING SINCE 1975.
Every average temperature compilation says there was warming.
I felt warmer winters here in SE Michigan,
The only other possibility is global cooling, since a flat temperature trend over 47 years would be unusual.
But Hansen is here pontificating that the average temperature statistic is worthless,
AND HE IS WRONG.
If he is right, virtually every climate scientist in the world is wrong, including “skeptic” scientists. Your choice.
How useful the global average temperature statistic is remains open to debate. I say it is useful if there is a large change in a short period of time, AND NOT USEFUL if there is a small change over a long period of time.
I’ve experienced warmer winters here in SE Arizona – AND colder ones. That time period encompasses the year we had a real White Christmas in TUCSON (6″ on the ground). The several other years we had a succession of < 20 degree nights. Generally, I’ve experienced more “colder than ‘normal'” winters for here since I moved here in 1985, than I did 100 miles north of here where I grew up.
THIS summer is quite a bit “cooler” than last year’s, in fact. Going by the high temperature readings, that is. The ENTHALPY is just about the same – a very weak monsoon flow last year, and a stronger than normal one this year.
I once did, for a statistics class, an analysis of the “average temperatures” for Tombstone and for Tucson. That was back in 2010 – but the Tombstone temperatures showed NO change (a statistically insignificant drop, actually) – and the Tucson temperatures plotted a classic “hockey stick.” What was the temperature of SE Arizona (Cochise, Santa Cruz, and the eastern half of Pima Counties)? Averaging these two would give you a number – that is completely wrong for either locality, and irrelevant to, say, Bisbee or Benson or Nogales.
WO ==> Ever sleep under the stars at Joshua Tree National Monument — I have and experience hotter than Hades days, and frost on top of my sleeping bag at night.
“The only other possibility is global cooling, “
Richard, have you considered the possibility that some parts of Earth are cooling, some are staying the same, and some are warming. And the further possibility that those trends could change starting tomorrow, or next week, or next year? Why should the entire Earth be experiencing the same climate trends when the entire Earth doesn’t experience the same climates? What happens in Bristol isn’t necessarily the same thing that happens in Waikiki, or on top of Mt. Everest. Different variables all over. Climate is by definition local.
Not useful for what?
Scare mongering presumably?
Richard ==> Have you read the referenced paper: Does a Global Temperature Exist? By Christopher Essex, Ross McKitrick and Bjarne Andresen ( .pdf ) ?
When you’ve read the paper, check back in.
When you’ve read he second paragraph of this essay, which points out that I am not saying what you claim but rather that the science, called physics and the sub-specialty called thermodynamics, says “one cannot average temperature”, when you’ve understood that, check back in.
“Is there an average temperature of your bathtub full of water?”
Actually there isn’t, at least not in the short term. The temperature at the end of the bathtub away from the spigot will be colder than the water entering the bathtub from the spigot. This is the correct analogy to the air temperature – both are constantly changing! The water in the bathtub only reaches a constant temperature (i.e. an average) after a period of time. That is not the case with air temp, it never reaches an equilibrium point. That is also the problem with homogenization, even when using anomalies. The air temperature at two different points with different microclimates is never the same, it is constantly changing with time. The difference in air temperature between the two stations is dependent on distance, elevation, pressure (weather fronts, etc), terrain, and geography. Spatial averaging isn’t sufficient to account for the differences in microclimate, especially when you are trying to identify differences in the hundredths digit. There simply isn’t any way to account for this in developing an “average” air temperature. Using anomalies doesn’t doesn’t help. The temperature at the bottom of a valley will have a different variance then one at the top of an adjacent mountain top thus the anomalies and their variance will be different and trying to average them is a lost cause!
Tim ==> There is a lot of trying to justify a scientific error using practical, everyday understandings and definitions.
Those doing so either are being duplicitous or are truly ignorant of the scientific issue.
I see we both got a downcheck – but no actual refutation!
How about the average temperature of ice cubes and the drink they are in?
AZeeman ==> It is easy to cunfuse the common-sense practical ideas of “average temperature” with the inappropriate, nonsensical, practice of averaging temperatures in science.
Gosh, no. The hotter something gets, the more energy is being stored in that something. This statement doesn’t tell us enough to conclude that more energy is lost or gained by any means.
You might make an argument that measuring the temperature of a tub with a constant amount of water over time, although technically wrong, still gives some information.
Maybe averaging the temp of two cities or comparable size, although technically wrong, has SOME value- specifically TRENDS.
(I averaged errors across manufacturing facilities of different types to give a trend on how the company was progressing on our “quality improvement” program and got constant objections from our PhD statisticians.)
Use of such averages to approximate a trend is only justifiable if the two (or more) items being measured are comparable in other respects (same tub of water, two similar urban cities).
But measure the temperature at the top of a flame on a matchstick – pretty hot.
Then take the temperature of a lukewarm bathtub.
Now average them. What meaning does that result have? THE FIGURE CERTAINLY DOES NOT HAVE ANY MEANING IN HEAT CONTENT, OR IN CHANGE IN HEAT CONTENT WHEN MEASURED OVER TIME.
When we measure temps 2 feet over land and 2 feet over an ocean we are not measuring relative heat content, yet that is supposedly the purpose of the exercise. (I’ll leave the WHY of that statement to more learned commenters.)
George ==> Much of what you say is correct. The standard CliSci answer is that they are only interested in temperature anomaly trends — which they think means “is it getting hotter or colder”.
This is why I call all of this “trendology”: they study “trends”, not climate.
You betray your lack of physical laboratory experience. Read this reference and pay attention to temperature uniformity and temperature accuracy of a manufactured water bath. The device the author talks about has both a uniformity and accuracy specification of ±0.2°C.
Temperature Specifications Explained: Accuracy, Uniformity, Stability | Blog | WaterBaths.net
A little off topic, but do you a weather station to have a better specification than a laboratory water bath.
Did you not read Willis say that heat energy depends on more than temperature. How much heat energy does 1 cu meter of soil have vs a column of air 1 sq meter to say 30,000 feet?
“You betray your lack of physical laboratory experience”
Wearily, again, it is a quote from Roy Spencer, writing in WUWT, as linked.
Why are you arguing from authority again?
“Wearily, again, it is a quote from Roy Spencer, writing in WUWT, as linked.”
So what? Address the issue, don’t use an argumentative fallacy!
Tim ==> Come on, Nick is just saying that the quote represents what Spencer thinks, not what he (Stokes) thinks….
The real question is why he quoted Spencer, with whom he disagrees,
I’m simply pointing out that whatever you make of what Spencer says, it doesn’t reflect my supposed lack of lab experience.
An ex-CSIRO lemming ought to know better !.
Nick obviously doesn’t !
Basic measurement and its comprehension seem to be beyond him.
Well, neither Fahrenheit or Celsius temperatures are ratio scale measurements, while Kelvin is.
But radiation is on a cube of the Kelvin temperature, so using linear increases is deceptive as to the effect.
Tom ==> Clarify? More words maybe….(I don’t disagree — but not sure I really get it…)
It’s not the scale used that makes temperature an intensive property.
I can express the temperature of my back yard in Fahrenheit, Celsius, or Kelvin – and it still tells me nothing useful about the energy content in Joules / meter^3 (an extensive property).
I think I understood that, so I’m giving you a thumbs up.
So energy content of the atmosphere could be measured, in theory at least, and if so then changes could be tracked over time.
However, ‘average air temperature’ is an abstraction that gives no reliable estimate of the energy in the system.
Close enough or am I still confused? But thanks for putting it simply enough for me to try to think about it.
I do understand about how people get distracted by averages – e.g. they are often used as if they were intrinsic characteristics of organism such as an average length. You can calculate average length, but it isn’t much use because so many factors can affect how large an organism grows. There may be an intrinsic genetic limit to size, but even that tends to be variable over time and space. A range of observed sizes is usually the most useful information – like the graph of the range of temperatures observed in Topeka.
I’d say you understand it pretty well. The only comment I would make is that the energy content of the atmosphere is a gradient vertically. It changes with altitude. So one model with one output can only give a view of a part of the atmosphere. Other parts may be different.
Dave ==> “However, ‘average air temperature’ is an abstraction that gives no reliable estimate of the energy in the system.” This is correct.
“Surface Air Temperatures (2-meters above the surface) are all spot temperature measurements inside of mass of air that is not at equilibrium regarding temperature, pressure, humidity, or heat content with its surroundings at all scales.”
This essay seems to drift toward saying that measured temperatures don’t tell you anything about the environment. And yet it starts out by saying that you can usefully use measured temperatures in Topeka for something. In fact climate scientists did not invent the use of measured temperatures to represent an environment. Newspapers have been telling people about the temperature in their town for at least a century.
” temperatures do not represent the heat energy of the object measured”
Well, they do if multiplied by the specific heat. And remember, climate science does not generally deal with temperatures but anomalies, which are temperature differences. This draws attention to the main role of temperature – it is a potential for heat flow. That is, heat flows down a temperature gradient. In this role conductivity is the parameter that matters, not specific heat. The average temperature is what a system gets to when all these fluxes have sorted themselves out. Conductive heat fluxes work out to reduce the temperature gradient, and so approach – wouldn’t you know – the average (weighted, it is true, by specific heat).
Nick ==> Yes,it would be possible, if one had enough other information to work with, such as air pressure and humidity, to work out the heat content for the point measured by a MMTS. But, as neither temperature nor humidity nor air pressure can be considered in equilibrium over even fairly small distances (air pressure tends to have larger area of general equilibrium), one cannot generalize even that heat content.
Yes, if we could throw a box that was totally thermally insulating, passing no heat at all in either direction in or out, around the cubic meter of air surrounding a MMTS, leaving it to reach equilibrium, then one could calculate the heat energy inside that cube.
But the heat energy in that cube would not be the same as the heat energy in a meter cube of air 40 feet or 100 feet or 1/2 mile away — except accidentally.
In order to determine if a 1° Grid was gaining or losing heat, one would have to throw that insulting box around all the air from 1.5 to 2.5 meters above the surface, all six sides of that giant perfectly insulated box, and allow all the factors to equalize (air density, humidity, temperature) — then you could get an average of the heat content for that Grid, for that one moment. Doing that every six minutes, for every 1° Grid on Earth might give you a single heat content/heat energy base figure say, for an hour or a day.
Read Does a Global Temperature Exist? By Christopher Essex, Ross McKitrick and Bjarne Andresen ( .pdf )
You may not agree, but they are correct accoding to physics and thermodynamics.
You may come up with some other metric to show the Earth is gaining heat, fair enough, but GAST is not it.
Kip, You are correct, humidity and air pressure are the two other factors along with temperature needed to determine the heat content of an air mass. Even if you had the TPH information for every surface measurement you would still have a very large error in computing the heat content of the global atmosphere as the temp, pressure, and humidity of the vertical profile above the surface varies widely, so the surface TPH does not give you the total heat content of the overlying column of air.
Add to that, you need the heat content of land and sea, and a knowledge of how that total varies throughout the year and between years before you know if the total heat content is truly changing. The average temperature is truly a meaningless quantity.
The total integrated microwave emission from microwave sounding satellites is a more useful measure, but still error prone. The sea level adjusted for subsidence/land rebound is perhaps the best semi-quantitative indicator of a total heat gain.
Meab ==> Yes, even at that, one would have spot calculations of heat content that might not apply at distances even up to several meters (see the photos of weather stations in Anthnony’s new Surface Stations Project. ) no less out miles.
I would be very dissatisfied with my “Newspapers” if they included only projections of expected “average temperature” in their “Weather Report” and left out the temperature range, and expectations of sun/clouds, precipitation, and winds, wouldn’t you?
hiskorr ==> You want a weather report? Have at it!
You want a report of Earth’s “averaged temperature”, no can do.
It may not be an adequate comparison, but biologists sometimes talk about heat budgets. Organisms have developed all sorts of tricks to keep systems going because a lot operates on either side of the mean unless you are at ocean depths with tiny deviations. Averages are used, but not with much symmetry around a mean beyond generalities. How many times is it necessary to take a temperature in a 24 hour period to get an accurate mean and do they mean the same thing every day? Meteorologists need to quit using “normal” temperatures.
H.D. ==> Now, using “normal” temperatures for a specific day of the year is a really asking for the expected temperature for that particular time of year…..to the day. It is silly to for the waetherman/woman to say “five degrees above normal….” rather than a simple statement that “it will be a little warmer than usual today:.
I don’t know about where you are, Kip. But here is Phoenix the various weather people very often give 5 day forecast as “15 degrees above normal” or “5 degrees below normal”. Even the NWS does that on their web site.
Pls ==> Yes, but it is just a shorthand for “It is gonna be hotter than usual”…..
Actually they should say “a little warmer than average” since THERE IS NO :normal” or “usual” temperature. What they’re talking about is a 30-year average, not a “normal” or “expected” temperature.
They misuse language in weather reporting in a manner that is simply deceptive.
“waetherman/woman”
I just use Weatherthing. Since you can’t even know who’s what these days.
In fact meteorologists usually speak of average Tmax and Tmin.
Then why don’t climate scientists do the same? Why don’t the climate models output Tmax predictions and Tmin predictions instead of some kind of hokey average?
A proxy for heat flow?
No, potential
Flux=-k ∇T
k=conductivity
No, it does not, and neither does the paper its summarizing. It says that taking a bunch of temperature readings across the Earth over time and calculating the average over time, tells us nothing about the environment, specifically, tells nothing about whether its getting hotter or colder on planet Earth.
The paper is very interesting (though I am unqualified to assess the mathematical detail) because it addresses the problem of attribution, and this is the heart of the question.
It is commonly argued that a given weather event is attributable to global warming. For instance, the recent Arkansas floods. The current long hot and dry summer in the UK.
We supposedly know that there has been global warming because the statistic of global average temperature has risen. But the connexion to the local phenomena, for instance the current UK summer, and the unusually high peak temperatures in some UK locations, is never demonstrated or even evidenced.
Its taken for granted that if the average global temperature has risen, this must make local rises in peak temperatures more likely. So we hear people saying that 40c+ could not have happened in the UK without global warming, by which they mean, a rise in global average temperature. That after all is the way we measure whether there has been any global warming.
But as Essex, McKitrick and Andresen point out, the average global temperature is not a meaningful concept – its not a physical quantity, it cannot be cited as the cause or explanation of anything. In addition they suggest that there are multiple plausible inconsistent ways of calculating it which will yield completely different answers to the apparently simple question: is the planet warming or cooling and if so by how much?
Recently its been alleged that global warming, again as measured by average global temperature changes, are impacting and will impact illnesses, their frequency and severity. Exactly the same problem is obvious: what exactly is the causal relationship, and between what entities. It cannot be that a rise in global average temperatures is the causal factor, because its not a physical entity. Any causal chain must start with something local, and be tied to (for instance) Wuhan market.
But this is never done, the lazy assumption is that if its warmer than usual at a given location it must be caused by average global temperature rising. Which it cannot be. And the average is then used. Its not argued that it was hotter than usual in Wuhan, and this led in defined ways to increased risk of interspecies transmission. Usually what happens is global warming is invoked as a sort of proxy for local conditions. Hotter measurements in Australia in this way can be invoked as causing a disease outbreak in Wuhan, without having to allege a specific and obviously implausible causal connexion.
They also make the important point that the global average is made up by taking as one continuous series the average of very different observations. To take one example, there have been changes in stations, both in location and perhaps more importantly the total number of them. This makes it even less meaningful.
If, for instance, I persuade 20 of my village neighbors to keep weather stations and record daily temps, and over the next 20 years two thirds of them drop out, then for me to publish the average of all observations on a monthly basis as if they were one continuous series would not be legitimate. This is what is being done. The sections in the paper which discuss this are very enlightening.
The authors also very amusingly point out, drawing on the way the global average temperature is calculated, that attributions of the sort commonly being made this summer involve temperature action at a distance, and in some cases an absurd relation between past temperatures and present weather events.
The paper, and Kip’s summary, get to the heart of the attribution problem. If we are claiming that climate change and global warming are causing (for instance) the recent UK heat wave, what exactly do we mean by global warming? How exactly has some measured quantity caused the heat wave, or modified its intensity or duration?
There’s no answer to this. Because nothing has been cited that could be a causal agent. What has happened, in Arkansas and in the UK, is rare weather events, and that’s all that has happened.
Get the paper. https://www.fys.ku.dk/~andresen/BAhome/ownpapers/globalTexist.pdf
Michel,
You write: “Its taken for granted that if the average global temperature has risen, this must make local rises in peak temperatures more likely. So we hear people saying that 40c+ could not have happened in the UK without global warming, by which they mean, a rise in global average temperature.”
You cannot take that for granted. I have calculated many cases where it has not happened over time spans of many decades. But, I also have cases where it happens.
The question might have to wait an answer until we know more about mechanisms.
The ocean surface temperature seems no to show peaks rising in rhythm with background. All surface sea temperatures over open ocean come to an abrupt stop at 30 degrees C. The mechanism is being clarified in terms of cloud motion and properties. I do not think anyone knows if land temperatures are also limited.
But this is drifting away from Kip’s central thesis here. Geoff S
Michel ==> Thank you. I have suggested that Nick actually read the paper referenced. I’m glad someone did!
“This essay seems to drift toward saying that measured temperatures don’t tell you anything about the environment.”
When you take an average you LOSE the information the measured temperatures tell you!
“And remember, climate science does not generally deal with temperatures but anomalies, which are temperature differences.”
The anomaly between 1C and 2C is the same as between 15C and 16C yet are generated by vastly different climates. So exactly what does the anomaly tell you about the change in climate? 1C/!C is a 100% change. 1C/15C is only a 7% change. Does a 100% change versus a 7% change represent the same impact on climate?
Tim ==> I’m not sure Stokes is always being serious — sometimes he seems to be just poking others with various sharp sticks and not talking science anymore.
Thank you! Thank you! Thank you! I’ve been saying the same thing, less succinctly, for decades! Now, if you will agree that your useful chart of expected Topeka temperature says little useful about August Topeka “expected weather” (I.e., climate), which would include humidity, winds, clouds, rain, etc., then we can dispense with the “Climate Change” nonsense and go back to laughing at what is actually being calculated– minuscule differences in Average Global Temperature!!
hiskorr ==> Conventioneers may well worry about “just the expected temperature” when packing clothes. I always check how hot or cold it can be expected to be in a distant city when travelling….
I hope you mean the weather forecast as a whole, Kip.
There was one June when the wife and I traveled back to New England for a friend’s wedding – and had to dash into Walmart to buy sweaters. Her lifetime of living there, and my six years, told us that “normal” June was warmish, not usually hot – but never 55 degrees for a high.
WO ==> That’s the trouble with weather — it is even more chaotic (read: unpredictable) than climate.
Kip,
You’re trying to make your point the hard way. I believe you’re trying to make the point that knowing the condition of a system is rather difficult with limited samples. Averaging more samples isn’t likely to correct that problem particularly if the further samples are equally unrepresentative. The average (linear, log-normal, etc.) of uninformative is still uninformative.
If I dip a temperature probe in the ocean, all I really know is the temperature of the probe. Likely that measurement is representative of the water adjacent to the probe. Fifty-foot away? Now we’re getting sketchy. Ok, I could grid the surface on five-foot centers for a mile around. I could properly average those numbers and I would have a valid average temperature, for that mile. However, that’s only likely applicable of a span of inches to a foot in depth.
So, if I want that average temperature to mean something (say the sensible heat content of that volume of water), then I need to make sure that my measurement system properly samples that volume. All the statistical tools in the world cannot reverse the inadequacies of measurement system.
So, while I agree with your general conclusions, you thermodynamic arguement doesn’t hold water. Given a properly measured temperature of a system (even averaged), I can tell a lot about the system. Using heat capacity and properly measured temperatures, I can tell you the final temperature of mixing cottage cheese with cotton candy.
Sampling the temperature of bucket of water is actually more challenging then most people realize. Sampling a cubic mile of ocean would be majorly hard IF it were standing still and unchanging. Normal, dynamic ocean conditions? Good luck storming the castle.
JAK ==> “Using heat capacity and properly measured temperatures, I can tell you the final temperature of mixing cottage cheese with cotton candy.” That much is in the essay — but CliSci does not do that — we do not know, because it is not measured, what the heat capacity of the cubic meter of air surrounding an MMTS (weather temp station) was at the moment that the temperature was recorded. One needs density (basically for air, air pressure) and humidity (which changes heat capacity). If CliSci were reporting heat content of air at each moment at each weather station, then we could average that — but only maybe. Only maybe because the atmosphere is too dynamic and too far out of equilibrium to generalize from our one 6-minute measured temperature and calculated heat content.
Actually, if they had all of that data (since air density can be determined quite accurately from that) one still wouldn’t be able to accurately calculate sensible heat beyond so many feet from that point. One could then estimate the heat between here and the next station by taking an average, but that has many intrinsic assumptions that would be imprudent if the system was even steady-state let alone dynamic as you and Mr. Gorman observe.
Since both the atmosphere and oceans are quite dynamic, the assumptions become dubious. Since climate modeling is by definition an exercise in heat balance, not being able to even remotely estimate the heat content of even a few thousand cubic meters of air or water is rather a serious impediment. One might be able to live with the broad confidence interval around the estimate (why not invoke more statistics?) if the heat imbalance under dispute were even larger; but, we’re trying to tease-out a watt or two per square meter. Please.
As one of my instructors observed, if one has to make so many assumption to make a calculation, you might as well assume the answer.
“So, while I agree with your general conclusions, you thermodynamic arguement doesn’t hold water. Given a properly measured temperature of a system (even averaged), I can tell a lot about the system. Using heat capacity and properly measured temperatures, I can tell you the final temperature of mixing cottage cheese with cotton candy.”
The problem is that the atmosphere is constantly changing. You are describing an equilibrium condition between cottage cheese and cotton candy. What is the average temperature of the mixture when cottage cheese and cotton candy is continually added/removed from the mixture in time varying amounts?
Anyone with knowledge of energy and temperature know they are different.
What is more difficult to explain to most is that increasing the average temperature of the oceans above 2000m is the result of reduced evaporation due to lower surface heat input. Lower surface heat input actually translates to higher ocean temperature. That is counter-intuitive.
There is a subtle difference between increasing ocean heat content due to surface heating and increasing heat content due to reduced surface heating slowing the ocean circulation from high latitudes to the equator. The greater the surface area of the oceans regulating at 30C means less surface heat input and less evaporation.
The simple fact is that oceans are coolest in December when the surface heat input is at a maximum.
So there is a HUGE misunderstanding that oceans can be heated from the surface in a matter of decades. That is another physical impossibility embodied in all coupled climate models.
RickWill ==> I am not as familiar with ocean heating and heat content, but thanks for the comment.
This is why I always say, if the oceans warming it ain’t CO2 in the atmosphere doing it.
Bob boder,
In May 2022 there were a couple of linked papers from respected mathematician and hydrologist Demetris Koutsoyiannis and colleagues. The studied causality including puzzles of the type “Which came first, the hen or the egg?”. They use global climate as one test case for their theory and conclude (my summary) that changes measured in air temperatures cause changes in atmospheric CO2 levels. This conflicts with the Establishment view that it works the other way round.
Personally, I regard these as being of fundamental importance.
Geoff S
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2021.0835
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2021.0836
Geoff ==> Thanks for sharing the links to those papers.
We all knew that the CAGW alarmists had the CO2/warming causality the wrong way round from the Vostok and Law Dome ice core temperature series, which showed that temperatures always changed BEFORE CO2 levels.
That is the result of natural climate change (ice cores)
It does not reveal the effects of manmade climate change
Both happen at the same time but are different.
How does the effect of anthropogenic CO2 differ from that of natural CO2?
Kip,
your comment [ I will not be arguing the point – it is just too basic ]
is on a T-shirt that an ad keeps pushing to me with a pretty lady wearing it, namely
“I’m not arguing with you, I am just telling you why I am right.”
I like the idea of plants as integrators of climate. There are no Palm Trees where I live, but there are Ponderosa Pines. The pines have been here a long time – and continue. The temperature will go from -20F to 115F in some years, but thankfully not every year.
John ==> Hmmmm. California?
John ==> Additionally, I am right!
Fauna as integrators of climate are useful indicators as well. I’ll be firmly convinced that Climate Change™ has occurred when iguanas, an invasive species in Florida** have expanded their range to Minnesota.
The average temperature of a region doesn’t tell us as much as iguanas can tell us about a region. There are States a little North of Florida that have a similar average temperature because of higher highs and lower lows that work out to about the same average. But they have no iguanas because the slightly lower lows are enough to k!ll iguanas whereas the lows in Florida usually just stun the iguanas.
**They actually issue “Falling Iguana Warnings” in parts of Florida when the overnight lows are forecast to be in the low 50s(F). It’s kind of weird when the evening weather forecast is “Clear and colder tonight with a chance of falling iguanas.”
H.R. ==> You are now speaking of Environmentally Important Climatic differences. A shift in Frost Free Days, a major shift in First and Last Killing Frosts, a major shift is week-long low temperatures below -20°F — that kind of climate change.
Kip – I’m really enjoying this series of yours.
–
I blame John. He started it. 😉 The constraint you put on the discussion is contrasted by all the other factors that go into climate. You did address what your presentation is NOT in your first post, and you have emphasized all along how narrow it is and why.
–
I can’t speak for John, but my comment was just meant to be an amusing (and true!) way to illustrate how much more climates consist of than just an average temperature. Average temperature alone doesn’t tell the whole story. Iguanas and palm trees and Ponderosa pines go a long way towards painting the whole picture.
–
So, my bad. I was just “a little outside” with that comment.
H.R. ==> Oh, I wasn’t being critical of your comment — I have experienced Falling Iguanas.
My response may have been a little too serious.
Nope. Didn’t take it as critical nor too serious at all. 👍
The follow-up was a “why I dunnit” just in case someone didn’t know why iguanas had anything to do with anything.
Even the “my bad” was a little cheeky with that reference to the clip of Bob Uecker calling a totally wild pitch that Eric(?) or David(?) includes in their posts sometimes.
I will now return to our regular programming.
Armadillos, they also can be used.
Macsun ==> Armadillos are an alien species introduced from a far distant planet where things are even weirder than they are here….(that’s just my opinion….)
I’m waiting for the day when someone comes up with Earth’s average wind speed.
Alexy ==> Maybe the Berkeley project will produce it for you….
What a wonderful world that would be and we could all live an average life.
And only have above average children.
With above-average genders.
Alexy,
Like it. Geoff S
Clyde ==> All of MY children are above average!
The average IQ is 100/
You may have inadvertantly insulted your children.
I’d expect them to be smart, however.
Kip==> You must live in Lake Wobegon.
RicDre ==> Well, grew up there….
No need to wait. You can get it now.
As you can see, it is used here to encourage more wind turbines. Get them while the going is good. You do not want to be building wind turbines if the global average windspeed is tanking.
https://www.meteorologicaltechnologyinternational.com/news/climate-measurement/after-decades-of-slowing-down-global-windspeeds-are-picking-up.html
The power of wind is function of the cube of the speed so, as they point out, an increase from 7 to 7.4 of 5.7% results in power up 17%.
Rick ==> Thanks for the link — incredible, quite literally.
Therefore an increase in average evaporation, average cloud cover and average rainfall. Which may result in the lowering efficacy of PVs. It’s all too complicated for me. I’ll mix another drink and watch some anime.
But that is an increase in kinetic energy, not potential energy.
If they do, don’t accept anything under 3 decimal points of one metre / second.
Otherwise, you’re being bullshitted to.
42
Retired ==> Thank you.
And when they do, I predict a climate emergency will be predicted too
Part of the problem is that Mohs Hardness is a ranking, not a continuous ratio scale. There is no mineral with a hardness of zero, and the resistance to scratching varies with the planes in the crystallographic structure. That is, hardness is vectorial. There are minerals with a scratch resistance intermediate to the integer Mohs values, but there is no defined way of assigning a number other than arbitrarily appending a one-half to the softer standard, thus calling something intermediate to Apatite and Orthoclase as having a Mohs Hardness of 5 1/2, sometimes inappropriately stated as 5.5, implying that the scratch hardness can be measured to a tenth of a unit.
On the other hand, there is a measure of resistance to indentation known as the Vicker’s Hardness that is calculated by taking the mid-range value of the widths of a diamond-shaped indentation, and then averaging several mid-range values to discern outliers, and improve the accuracy and precision, hopefully.
Clyde ==> Thanks — every substance, I suppose, will fall somewhere in these scales….but they are Intransitive Properties and not subject to being added together, and certainly not averaged.
Kip, nice article, and I endorse the science presented. One little nit to pick–a cubic meter of stainless steel at 70 degrees does not have more heat energy than a cubic meter of sea water at the same temperatures, although is does have the potential to transfer its contained heat energy more rapidly through conduction.
I didn’t bother looking anything up or performing a calculation, but mass plays a big part. He was referring to a volume and not a mass.
Specific heat is based on mass, although a conversion based on volume is possible.
Alexy, I ran the numbers, and although I had not considered the density difference between stainless steel and sea water, it turns out the specific heat difference is even larger, so the two ultimately have about the same heat capacity per unit of temperature. See my numbers in the comment to Kip below.
Wayne ==> Are you sure? SS is far denser than water…..
You are right that I had not considered the difference in masses of a cubic meter of the two substances, Kip. But I may (accidentally) still be right that their heat content per degree is about the same. The density of stainless steel is about 7.5 to 8 g/cm3, and it’s specific heat is about c = 0.5 J/gK, while pure water has density 1 g/cm3, but specific heat of c = 4.18 J/gK. Joules of heat content is q=mc delta T, so if delta T is the same, for a cubic centimeter of stainless the quantity mc=(1cm3)(7.5g/cm3)(0.500J/gK) is between 3.75 and 4 J/K, while for a cm3 of water the quantity mc is (1g)(4.18 J/gK) = 4.18 J/k. So pure water has a slightly higher heat content per unit of temperature change. But I just looked up sea water, and found it’s specific heat is a bit lower than water, about 3.85 J/gK, but it’s density is a bit more, about 1.025g/cm3, giving
a value for the quantity mc for one cm3 of sea water of about 3.95 J/K. So I think a cubic meter of stainless steel and of sea water have about the same heat content per unit of temperature. As a teacher of high school chemistry for many years, I learned that iron is a pretty poor material for students to use for experiments determining specific heat, because it’s low value gave relatively high error. Water is amazing for its ability to store heat.
Wayne ==> Well, if your calculations are correct, then they are. But, a hot rock stays hot far longer than hot water….
Your constraint that the sum of a set of sample values has to be a useful value in itself having a common sense interpretation in order for a statistic measuring central tendency, such as the mean or median to also have any useful common sense interpretation. This is an artificial constraint you have imposed with many counter-examples. Take one such; a tide gauge measuring sea level at a given site, where daily high and low tide measurements are taken each day of the year for a range of years and average annual sea-level height is obtained by summing the gauge measurements for the year and dividing by the sample size giving the mean height on that gauge at that site in that year. That total used to obtain the mean has no useful interpretation but the trend in mean sea-level height for that site does have a useful practical interpretation. Another example I am very familiar with. Samples of fish lengths taken in research surveys are important to monitor the average length over fishing seasons or differences between types of fishing method for fisheries management. The sum of the sample of fish lengths has no useful physical interpretation but measures of central tendency do. Bottom line is the mean as a measure of central tendency can have a useful physical and practical interpretation even if the sum used to obtain it does not. In this paper I modelled the complete empirical distribution of fish lengths using sample quantiles and cubic smoothing splines (https://doi.org/10.1016/j.fishres.2014.05.002)
Steven ==> Length is an Extensive Property and can be added, averaged, etc.
Lengths of a sample of fish can be added for what purpose? To represent one mega-fish OR the fish all lined up head to tail. As ridiculous as it sounds. You are too enamoured by your own definitions. Submit your essays or bits of them for peer-review in scientific journals.
“Samples of fish lengths”
You are the one that brought up fish lengths. Why?
Tim ==> Averaging fish lengths is an important part of fishery management science….I’m not sure (haven’t been paying attention to this fish topic) why this has become a point of discussion.
For purposes of setting a size limit for fish catches, a mean might be very misleading. The mean can be shifted by a few very large fish, or a large number of small fish. It is probably better to look at a distribution by size rather than trying to reduce the population to one or two numbers.
A multi-modal distribution can’t be described using the average and standard deviation. You must use something like a 5-number statistical description.
Exactly what my paper published in Fisheries Research was about
“A nonparametric model of empirical length distributions to inform stratification of fishing effort for integrated assessments” 2014, http://dx.doi.org/10.1016/j.fishres.2014.05.002. Setting catch limits that incorporate size limits is typically done using integrated assessments (see my paper CCAMLR Science, Vol. 15 (2008): 1–34, https://www.ccamlr.org/en/system/files/science_journal_papers/01candy-constable.pdf).
Steven Candy, you say “The sum of the sample of fish lengths has no useful physical interpretation.” YOU have put the word “useful” into the criterion. The sum of the sample of fish length absolutely has a physical interpretation. You line the fish up on the dock, nose to tail, and you get the total length laid out on the dock.
The key is the word “total”. If you have 10 kg of water and 40 kg of water, they have a total weight of 50 kg with a physical meaning. You can put them both on the scale and weigh them together. Total weight. The average weight is 50/2 = 25 kg.
Same with volume. If you have ten liters of water and 40 liters of water, they have a total volume of 50 liters. You can measure it in a large container. Total volume. The average volume is 50/2 = 25 liters.
But what if we have a ten liters of water at 10°C, and forty liters at 40°C … we know the average volume, 10 liters plus 40 liters divided by 2 = 25 liters. And we know the average mass, (10 kg + 40 kg) / 2 = 25 kg.
But is the average temperature (10°C + 40°C) / 2 = 25°C? Well … no. And we can prove that. We pour the two containers of water into one container, and we find that the resulting temperature is 34°C … what’s the problem here?
The problem is that while the two amounts of water have an actual total weight (50 kg) or an actual total volume (50 liters), there is no such thing as total temperature. It doesn’t exist. And because of that, we think the average temperature of the water is 25°C, whereas in fact it’s 34°C.
HOWEVER (and it’s a big however), this does NOT mean that this type of incorrect average is useless. This is because of a peculiar property. If the actual average temperature of 34° (determined by mixing the two units of water together) goes down because one of the units of water is cooling, so does our incorrectly calculated “average. And the same is true if one or both of the units warm. Both the correct and the incorrect average temperatures increase. They always move up or down together.
So they are not useful or meaningful for the value, but they are useful for the direction of change over time in the value.
Hope this clarifies some things.
w.
“But is the average temperature (10°C + 40°C) / 2 = 25°C?”
No. Because it’s (10kg X 10°C + 40kg X 40°C) / (10kg + 40kg) = 34°C
“The problem is that while the two amounts of water have an actual total weight (50 kg) or an actual total volume (50 liters), there is no such thing as total temperature.”
The problem here is you didn’t work out the average correctly, and the fact that it is possible to get the correct value suggests the argument about total temperature is invalid.
ROFL!
What is kg * temperature? Is it an intensive or extensive property. It certainly isn’t temperature!
It’s extensive – the result is intensive. It’s another example of how you can average intensive values and get a meaningful result. Even Essex et al acknowledge this.
So, once again, you are arguing that you can average intensive properties while using extensive properties as proof.
Unfreakingbelievable!
Yes, that was the point of what I said dozens of comments ago. If you think that is unacceptable explain why, rather than just making an argument by personal incredulity.
Where does he acknowledge this? Quote please!
There’s the mixing example, and also this
That again depends on whether you regard personal height as being an intensive property or not.
Height is obviously extensive, by definition—it’s measuring the extent of something.
w.
Ha! Not only that, but if you cut someone in half, the two halves aren’t the same height!
Depends on which way you cut them.
Probably, but the question was “individual height”. Do three people have three times the individual height?
I know! You should be averaging the number of angels on the head of the pin that are dancing with the unicorns!
w. ==> What do you make of this seemingly endless back and forth? Think it will ever stop?
I watch in astonishment!
It has descended into ridiculousness. We’re being told that the CMB temperature is meaningless, total solar irradiance is meaningless, convective available potential energy is meaningless, the Stefan-Boltzmann law is meaningless, the hypsometric equation is meaningless, the QG height tendency equation is meaningless, the albedo of Earth is meaningless, and I’m sure others that I’ve missed as well. And now we’re being told that averages of extensive properties are meaningless as well. So that means the average height of humans and countless other examples are meaningless too. Astonishing indeed!
Quite the collection of strawmen you have blazing away in the night sky here. No, you’ve been told that the global average temperature is meaningless, which is antithetical to your CO2 religion.
Not saying they are meaningless unless they are AVERAGES of intensive measurements. Even averages of intensive measurements may have meaning if the controlling measurements are the same. But the conundrum is that then, the temperatures would be the same. You wouldn’t need an average then would you?
AVERAGES of extensive measurements may or may not be meaningless. Have you ever built a deck? Have you bought and had delivered 2″x8″x12′ boards and found some so warped they won’t reach the hangers and would make a terribly warped floor? The average of the extensive measurements are meaningless! The list is endless and keeps quality engineers employed, if a little insane.
I’m sorry. It is getting ridiculous, and I should be prepared to just ignore the Gormans, but being constantly told to shut up, take remedial classes, whilst being presented by a barrage of questions, just makes me feel I have to continue or it will be assumed I’m accepting their points.
I know nothings going to change, this has been going on for years, but I do occasionally have fun, and sometimes learn things.
Translation:
WHAAAAAAAAAAA!
It is of course a lot easier to ignore Carlo’s attention seeking.
Which of course you don’t, and can’t.
W. ==> Good point — and if we were only interested in valueless “direction of change” for any single measurement — today’s temperature vs. yesterday’s temperature — we would set.
But last year’s “global average surface temperature” vs. the year before?
You touch on a crucial point. Just because you can write out (10 C + 40 C) / 2 = 25 C and get the wrong answer does not mean that an average temperature, when computed correctly, is not meaningful, useful, and actionable.
Yet the Essex et al. 2007 paper does just that. That is they compute the global average temperature using a generalized mean with R > 1 without spatial weighting and proclaim that because it gives a different result than when R = 1 with spatial weighting then the concept of an average must therefore be meaningless in general regardless of the method.
It’s the same with your example. Just because I can erroneously compute the average as [(10C^2 + 40C^2)/2]^(1/2) = 29 C like Essex et al. do it does not mean that (10 kg * 10 C + 40 kg * 40 C) / (10 kg + 40 kg) = 34 C is automatically wrong.
Did you bother to read Page 6 of the Essex paper where he provided a general proof that you can’t average intensive properties?
And yet there are several real world examples where an intensive property like temperature is averaged and produces a meaningful, useful, and actionable quantity.
Willis, the only problem I see with your explanation is that even temperature differences don’t tell you about the changes in enthalpy. Enthalpy is the only value that can be used to determine the amount of heat energy in a location. That even lets you deal with convection and conduction properly.
Temperature differences, i.e., anomalies are no better in determining actual heating and cooling than averaging absolute temps.
Jim ==> But I like his fish story — because temperature changes, temperature ranges, temperature fields are important in biology.
Pip. You propose that that the sum of a set of sample values has to be a useful value in itself having a common sense interpretation in order for a statistic measuring central tendency, such as the mean or median to also have any useful common sense interpretation. This is an artificial constraint you have imposed with many counter-examples. Take one such; a tide gauge measuring sea level at a given site, where daily high and low tide measurements are taken each day of the year for a range of years and average annual sea-level height is obtained by summing the gauge measurements for the year and dividing by the sample size giving the mean height on that gauge at that site in that year. That total used to obtain the mean has no useful interpretation but the trend in mean sea-level height for that site does have a useful practical interpretation. Another example I am very familiar with. Samples of fish lengths taken in research surveys are important to monitor the average length over fishing seasons or differences between types of fishing method for fisheries management. The sum of the sample of fish lengths has no useful physical interpretation but measures of central tendency do. Bottom line is the mean as a measure of central tendency can have a useful physical and practical interpretation even if the sum used to obtain it does not. In this paper I modelled the complete empirical distribution of fish lengths using sample quantiles and cubic smoothing splines (https://doi.org/10.1016/j.fishres.2014.05.002)
A further proof that your argument that we can calculate meaningful estimates of central tendency like the mean only for random variables that have so-called “Extensive properties” that “.. can be added together ” is wrong is to consider the median. The sample median is often close to the sample mean for large samples from symmetric distributions (and has exactly the same expectation as that for the sample mean for a normal distribution) and the median does not involve a sum at all but the rank order of the sample. So the median, as is the mean, is a meaningful statistic even if the random response variable a researcher is studying may be rubbish. You are trying to propose a new fundamental statistical theory/logic/inference along with a good smattering of arrogance (“One cannot average temperatures.”…“I am under no illusion that this essay will be widely accepted by all that read here. It is, however, scientifically and physically correct and might shatter a lot of firmly held beliefs”). Send me a reprint/preprint of your paper published/submitted to a theoretical or even applied statistics journal on your theory…
Steven ==> Have you read to paper :
referenced in the essay? :
https://www.fys.ku.dk/~andresen/BAhome/ownpapers/globalTexist.pdf
I will read it.
“The sample median is often close to the sample mean for large samples from symmetric distributions (and has exactly the same expectation as that for the sample mean for a normal distribution) and the median does not involve a sum at all but the rank order of the sample. So the median, as is the mean, is a meaningful statistic even if the random response variable a researcher is studying may be rubbish. ” (bolding mine, tg)
Really? If I collect random boards I see in the roadside ditch as I travel around and then find their mean and median lengths that will give me a meaningful statistic? A statistic that I can use to design a doghouse?
Your restriction that you have a symmetric distribution simply doesn’t apply to temperatures collected from around the globe. I can find no justification for assuming that this will result in a “symmetric distribution”. When you combine southern hemisphere temperatures with northern hemisphere temperatures all from the same month you actually wind up with a bi-modal or multi-modal distribution. The mean and median statistical descriptor for that distribution is likely not very meaningful or useful.
In metrology there is a vast difference between a distribution derived from multiple measurements of the same thing using the same device and a distribution derived from multiple measurements of different things using different devices. The first can (not always but many times) result in a symmetric distribution. The second very seldom does (see the board example above),
I didnt imply temperatures have a symmetric distribution I was simply making the point that valid and practically useful inferences can be drawn from sample statistics like the mean or the median and their further modelling also inferentially useful even if the sum over the sample of the response values is not. That’s the general thrust of my rebuttal of his new unpublished statistical “theory”.
If you have a non-normal distribution then it should not be described using mean and standard deviation. It should be described using something like the 5-number description: minimum value, first quartile, median, third quartile, and maximum. The mean is truly a misleading statistical description for anything but a symmetrical distribution like a normal one or a uniform one. Even the median by itself tells you nothing, it’s not even inferentially useful without other information.
Take the daily temperature curve for instance. It closely approximated a sine wave. Climate scientists use the formula (Tmax-Tmin)/2 as an “average” or “mean” value for the entire daily curve. Yet the equivalent power of a sine wave is the root-mean-square value or 0.7 * Tmax. And the average value of the daytime curve is .64 * Tmax (or substitute Tmin for Tmax for nightime). Thus their value for the mean is already a mathematical fiction from the beginning!
If they were to use the true rms or average for a sine wave you could at least get some indication of what the actual climate impact of the value would be. Not so with the mid-range value, it is pretty much meaningless since multiple Tmax/Tmin combinations can give the same mid-range value. That makes it impossible to “infer” anything from such a value.
Admittedly the temperature curve is not a pure sine wave and it changes from day-to-day, season-to-season, and year-to-year. But it *could* be subjected to Fourier or wavelet analysis each day to get a far better approximation than the mid-range value, at least since the use of digital measurement devices.
Steven ==> Please read the referenced paper by Essex et al so we can be talking about the same thing…..
Means (averages) have no meaning without knowing the statistical descriptors surrounding it.
In mathematics one counter example to a general theory proves the general theory wrong:
Pip’s general theory: “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome” = the sample mean has no valid interpretation if the sum of sample values used to calculate the mean has no valid interpretation
Counter-example: For a normal distribution the expectation of the sample median equals the expectation of the sample mean and since the sample median is not based on the sum of sample values but their rank order it is interpretable as a measure of central tendency and therefore so does the sample mean irrespective of the interpretability of the sum of sample values.
(See “The expected value of the order statistic L(r), and there-fore the quantile L(pr), is mu(pr) …” (Appendix A of my senior author paper http://dx.doi.org/10.1016/j.fishres.2014.05.002). Note mu(pr=0.5) is the population median = mu population expected value, which is the expected value of the sample mean.
See “On the distribution of the sample median” The Annals of Mathematical Statistics
Vol. 26, No. 1 (Mar., 1955), pp. 112-116 (5 pages)
.
“For a normal distribution”
Temperature values are not a normal distribution, especially when they are from different locations and are taken with different devices.
During the day the temperature curve is pretty close to a sine wave. The mean of the sine wave is not the median. The median is Tmax (equal number of values below and above). The mean is .64 * Tmax.
Nighttime is pretty much an exponential decay. The mean for such a curve is approximately .37 * T0. The median is approximately ln(2)/k where k is the rate of decay (sorry, I don’t remember the typical range for k).
Tim ==> Daily local temperatures tend to have a sine-wave like distribution only because of Earth’s day/night cycle.
Real world daily temperatures often have wildly non-sine wave distributions, even during the day-time hours. I’ll be showing some graphs of this in Part 3 of this series. (eg: Three days ago my wife and I were sailing when a line squall hit….temps dropped 15 degrees in an instant.)
I agree with you generally, but we do have to deal with the fact that even simple things, like the temperature tends to go up through the day and down through the night are “rule of thumb” and not scientific at all.
I agree with you, the temperature curve is not an ideal sine wave or exponential decay. But it *is* close enough to suggest that the mid-range value is neither the median or mean of the temperature curve. It’s also why I suggested that a Fourier or wavelet analysis could be done for the distorted sine wave or exponential decay in order to get a more accurate measurement of median and mean. Would that make it far more complicated to analyze the biosphere? Yep! But it would be far better than what we have today which is a hokey as all git out!
Temperatures are a poor metric for climate. Mid-range temperatures are far worse!
Tim ==> Maths/statistics vs s reality.
Steven ==> Think this comment got posted twice.
The Incorrect Use Of Centigrade & Fahrenheit
Most readers of this site will understand that mathematics places limitations on how certain numbers can be manipulated. Unfortunately this is not so for the population as a whole.
There are three kinds of data :- Ratio, Ordinal and Nominal.
Nominal: Is for instance a yes/no question in a survey where Male=1 and Female=0 if the average of the survey is 0.5 we can conclude only that half the population that answered were male and half female or if the average was 0.6 we can conclude that 60% of the respondents were male.
You cannot conclude the sample was slightly female – although marketing types do use such expressions. There is no such answer as 0.5 only what the number infers.
Ordinal: Is for instance a question in a survey where a range of answers are permitted, such as “On a scale of Zero to 10 rate the quality of our service where 0=terrible and 10 = exceeded my expectations.
If we get an average answer of say 6.23 – it is meaningless unless we calibrate it against what it meant to respondents.
Even if we were to ask the same question of a competitors service and got 6.10, we cannot conclude we are doing 2% better than our competitor (divide one by the other) as we are not necessarily comparing apples with apples.
So you have to be very careful when using Nominal and Ordinal data when you attempt to manipulate them mathematically.
Only Ratio data can be freely manipulated – true numbers that are infinitely divisible.
Unfortunately Centigrade and Fahrenheit scales are in fact Ordinal based on the freezing and boiling points of water and alcohol respectively to an arbitrary 100 divisions.
Thus if you say something like “what temperature is twice the boiling point of water” :-
You might try 100°C multiplied by two is 200°C – you would be seriously wrong!
Let’s try that with Fahrenheit 2 x 212°F = 424°F wrong again – translate it to centigrade and we get 217.7°C – Oh dear – that does not align with my prior calculation. Why ? – Because we have applied ratio data mathematics to ordinal data.
All thermodynamic calculations are done in Kelvin which starts at absolute zero (-273.15°C) so it becomes perfectly true to state that an object at 400°K is twice as hot (or contains twice the thermal energy) of the same object at 200°K.
Kelvin still uses the centigrade divisions but that does not cause problems – it could be anything but keeping the same divisions makes conversion simpler.
Now lets go back to the prior question “what temperature is twice the boiling point of water” first we need to know the boiling point of water in Kelvin which is :-
373.15°K = 100°C = 212°F
Multiply by 2, we get :-
746.3°K which converts to 473.15°C or converts to 883.67°F Which is correct (believe it or not).
So when you find “Climate Scientists” multiplying the Centigrade or Fahrenheit scales by any factor, there can only be two reasons :-
1) They deliberately want to overemphasize (or underemphasise) their findings – which is misrepresentation or fraud.
2) They don’t actually understand what they are doing and you should ignore the accolade “scientist” if they are ignorant of such scientific basics.
So a scientist saying that 2°C is double 1°C is talking out of his hat.
Of course, displaying results in Centigrade or Fahrenheit is completely acceptable – but doing thermodynamic calculations in those scales isn’t.
“So when you find “Climate Scientists” multiplying the Centigrade or Fahrenheit scales by any factor“
You don’t. All sorts of scientists and engineers multiply temperature differences by factors. For example, heat flux through a slab is conductivity*(temp difference).
They don’t usually (for good reason) average temperatures that are not differences (anomalies). But you can, and your argument does not apply. If you add an offset to the numbers, you add the same offset to the average, keeping the scale consistent.
Nick ==> They do, however, add temperatures and then divide the result by the number of components…..even “anomalies”.
You can do that, and the result is consistent over units. The average of 0C and 100C is 50C. The average of 32F and 212F is 122F, which is in fact 50C. That was my point in the last sentence.
“The average of 0C and 100C is 50C”
Actually it isn’t. That’s a mid-range value. It tells you NOTHING about the temperature curve itself which is what defines climate. You could get the same mid-range value from 30C and 70C, a far different climate than represented by 0C and 100C.
If we are talking about daytime temps which closely approximate a sine wave the average is .64 * Tmax. Nighttime temps are more exponential than sine but the same thing applies. Thus your average value would be 100C * .64 = 64C and 70C * .64 = 45C. *Those* values actually tell you something about the daytime climates!
If you *really* want something useful then the climate scientists should move to using cooling degree-days and heating degree-days to describe the climate. That’s what HVAC engineers use and they actually have to understand climate in order to get paid and not sued! I would love to see a climate model that spits out heating and cooling degree day prognostications for the next 100 years!
The Fahrenheit or Celsius gets canceled out via the dimensions used only the dimensionless number is used.
I.e. k = W/ m * C. m is meter and C is Celsius
Ken ==> I’ll take your Kelvin statements at face value — though I am not sure that “twice as hot” Kelvin or not, means the same thing thermodynamically as “contains twice the heat energy”.
“so it becomes perfectly true to state that an object at 400°K is twice as hot (or contains twice the thermal energy) of the same object at 200°K.” (bolding mine, tg)
You used a restriction that simply doesn’t apply to temperature measurements of the atmosphere. You are *NEVER* measuring the same object at any point, either by location or by time. Even if you took measurements at 6 ms intervals in a Stevenson screen you would be measuring different objects because of the air flow through the screen.
Thanks for that article. An illustration that might illustrate your point or illustrate that I missed a key element:
Imagine two bottles, both half full of water. In bottle A the water is 10 deg c and the air in the rest of the bottle is 90 deg c. In bottle B the water is 90 deg c and the air is 10 deg c.
It is possible to say that the average temperature inside the two bottles is 50 deg c, but to do so would be misleading and unhelpful.
We could then suggest the method of forming an average is unhelpful. “Alex scored 10% on test A, and 90% on test B; Ben scored 90% on test A and 10% on test B – their average score was the same. However test A was a mid-term exam worth 25% of the total, while test B was the final exam worth 75% – so we need to weigh them accordingly” – the equivalent weighting method for temperature is (among other things?) mass and specific heat capacity. But once you’ve done that weighting all you’ve done is worked out energy, not temperature.
Perhaps I’ve missed something? It seems to me that it must be possible to gain an average temperature: a thermometer doesn’t tell the temperature at a spot, but tells the average temperature of the glass that the thermometer is made from.
There is at least one attempt that studies the atmospheric heat content instead of just the temperature. The article “It’s the Heat and the Humidity: The Complementary Roles of Temperature and Specific Humidity to Recent Changes in the Energy Content of the Near-Surface Atmosphere” by Stoy, Roh and Brommley published in Geophysical Research Letters includes humidity as part of their analysis. My takeaway from this article is that even though lower atmosphere results point towards an increase in energy, there is not enough knowledge of the humidity to come to solid conclusions.
Art ==> Thank you for the link. As I have mentioned to Nick S, it would be possible, if one could totally isolate a piece of the atmosphere, to calculate its heat content if one had measurements of the other factors necessary for that calculation. Air pressure, humidity being required.
It is not my intention to make any claim about whether or not the Earth’s climate system is gaining heat overall — this is just about the improper practice of averaging the intensive property temperature.
Kip, thanks for an interesting post. Two comments.
1st, you are right that you cannot average measurements of intensive properties. To average something, first you add the values and divide by the count. For extensive properties like mass, this works—3 kg + 1 kg = 4 kg, and that has a physical meaning.
But if we add 78°F and 74°F and 76°F, we get 228°F … which is meaningless.
However, the change in the value of the numerical mean of a number of measurements of an intensive property can be very useful.
I used to fish commercially for albacore. They typically run along an isotherm, 51°F from memory.
A thermometer is dragged through the water. Since the thermometer takes time to respond to changing temperature, this, of course, averages the temperature of the water the boat is passing through. And here’s the point.
If the thermometric average of the water temperature is 49°F and dropping, the boat is going the wrong way to catch the fish … but if it is 49°F and rising, Bob’s your uncle. The change can be very meaningful even though the raw average is not.
Second, in your graphic at the top, I was amused to see the diamond demonstrating that “lust” is an intensive quality … made perfect sense to me, can’t argue with that.
Well done,
w.
“For intensive properties like mass . . . ”
Typo: Mass is an extensive property.
Dan ==> Yes, a typo only.
Thanks, Dan, fixed.
w.
Willis,
“Lust” is not only intensive, it is also expensive. Geoff S
Hence the diamond used to symbolize it.
w.
W. ==> You meant to write that Mass was an Extensive Property, and thus can be added etc. Which is correct.
Intensive Properties are useful — of course they are. All physical properties have uses, and all their changes can be useful….that’s why we measure them.
Your change in water temperature is an indicator of an environmental characteristic useful to fishermen but I note that it is still a series of spot measurements.
Are you averaging in this case or are you differentiating? It would seem you are finding the slope of the temperature gradient, not really the average of the temperature.
I really hate to pick nits here but there are a couple that are actually so big that they need attention.
Whatever you are doing by dragging a thermometer with appreciable thermal inertia through the water it’s not “of course, averaging the temperature”. It’s actually low pass filtering the temperature of its surroundings – that is, it’s filtering out / not responding to any rapid changes in temperature. This cannot be averaging as there is no backward processing involved, the thermometer just has a simple transfer function with one pole which is the system time constant (I’m assuming that what you’re viewing the result on has no lag in display.)
Just imagine that the thermometer has a very large lump of metal on its bead and is towed across a block of water which changes temperature slowly between say ten degrees and forty degrees and back again. Then imagine what the display would look like – it would just change very slightly, if at all – responding to the low frequency / slow changes in temperature – not at all an average of the temperature.
You are, of course, right about the changes being meaningful if the temperature measurement device has little inertia – what your eyes and brain are doing is extracting the first ( and possibly second) derivative of the change in displayed value to see how rapidly it is changing and hence, in this situation, how narrow the junction between the isotherms actually is. This is, incidentally, why meters with needles are often far more useful that numerical displays because it’s much easier to see how fast a needle is flicking rather than how fast a group of numbers is varying. (and also, of course, why thermocouples and thermometers have heads as small and low mass as possible.)
PS
Thanks for the information about fishing – I never knew that fish liked such a specific temperature environment
Dave
Thanks, Dave. It’s an average. Not a simple average, a decaying trailing average … but an average nonetheless.
As you point out, the value of the decaying trailing average has little meaning … but my point was, the CHANGES in that average are meaningful enough to help us catch fish. The story of those voyages is here. Upon re-reading it I see the preferred temperature for albacore is 58°-64°F.
w.
W. ==> Alas, the endless argument of the common-sense practical vs. the scientific view.
We’ve got one professional statistician commenting here who is so upset that anyone might say “one cannot average….” that he has written a book’s worth of comments that say nothing other than “Yes you can….”
But, that’s the game (which is what the comments section is for far too many….)
If you mean me, I am not a professional statistician. I wouldn’t even call myself an amature one.
This is all very known to physicists, but unknown or unwelcome in climate science. We used to say that calculating Earth’s average temperature is about as meaningful as calculating the average telephone number in a phone book.
Take two equally sized bodies of air both with temperature of 30 C. One is placed in a humid location like Thailand while the other is in desert like Sahara. The body of air in Thailand contains much more energy than the body of air in Sahara. This shows the futility of averaging temperatures.
Agreed but to Nicks point the earth is a closed system so averages will average out over the whole system. Not a true picture but a useful piece of information. Big problem is that the human factor is not accounted for, the fingers on the scale, and since there are few “climate scientists” that aren’t bias there is little hope objectivity. Nick being one of the examples, he knows there is no climate emergency but his income depends on one so he fights the fight and deceives him self.
Bob ==> The Earth’s climate is known, even to the IPCC, to be a “coupled non-linear chaotic system” — which also means that it is not, and will not be, in equilibrium — not at (almost) any scale.
In a closed system averages tell you almost nothing. It is the gradients, minimums, and maximums that are important. Averages of intensive properties tell you almost nothing. You can have a closed system with very different environments within the system. The entire earth s a closed system, no mass in or out (or at least an insignificant amount). But the actual enthalpy of the parts, e.g. ocean vs land, can be quite different. The “average” temperature of the two tells you what?
The Earth is an open system, not closed. It receives energy from the sun and radiates energy to space.
Most people don’t seem to know that enthalpy is the correct way to measure heat energy – temperature is a rather poor proxy.
I think a typical thermodynamic closed system is one that doesn’t exchange mass externally but can exchange energy externally. Am I wrong? Are you perhaps thinking of an isolated system?
thanks for the correction. Yes, I was conflating closed and isolated systems.
Old cocky ==> Yes, sir, that is correct. Any tiny changes in a poor proxy are not adequate for major societally altering political decisions.
Frank (no relation) ==> Thank you for the support. As you use “we” when speaking of physicists, can I assume that you are one?
Not for the obtuse, those who are slow to understand.
Climate alarmists are simplistic. We usually expect it to be warm or hot at midday when the sun is shining and colder or cold at midnight. Sometimes we find the temperatures reversed because of other factors. In the winter along the southern Cape coast of South Africa a Berg wind (katabatic wind) from the interior pushes up the midnight temperature.
In Ireland we find that in winter some night temperatures can be much warmer at midnight than in the day because of factors like sea currents and winds. Then we also have local variations between where the temperature is being officially measured and a few miles away in different directions. This all adds layer upon layer of complexity. When we are given an average temperature we could ask “where was this measured and how was it averaged?” We could ask for temperature measurements from other weather stations in the same geographic area and compare them.
At the end of the day having masses of data is relatively unimportant. What matters more is are we able to adapt to the conditions and even use them to our benefit. We know that nearly four thousand years ago people observed and farmed accordingly. In Israel with its dry summers they had two markers: the early and late rains. They wisely built cisterns thousands of years ago to help them through the dry summers. We would be better able to flourish today if we apprectiate how much we can adapt rather than stoking alarmism with all the numbers and foolishly trying to engineer climates.
The question that should be asked is, “What information can one obtain from an average temperature?” or, alternatively, “Of what utility is the average temperature?”
While the physiological effects of temperature can be important, the humidity can modulate those effects. Therefore, it is important to know not just the temperature, but rather the Heat Index.
There is a very simple truth associated with climate ‘science’, which is that climate ‘scientists’ do not understand statistics. If they did they would understand that any model of climate is just that, a model, and they wouldn’t make ridiculous claims about the results that come out of them.
There’s nothing remotely magical or difficult about this. In fact it’s incredibly basic stuff. If you take the errors involved in any climate model, regardless of the power of the supercomputer running it or the ‘accuracy’ of the model itself, you very quickly realise that any forecast made from it will have confidence intervals so large that the results are effectively meaningless in real terms.
This thread confirms this point. Any average is little more than a number, which approximates to the real world in varying degrees of reliability. But you have to be incredibly careful when interpreting averages because they can lead you to very misleading conclusions.
Average global temperature is a very good example of this. As a number it is useful, but as a representation of the real world it is worse than useless. Worse because while something that is useless has no value and will therefore be ignored, global temperature leads to incorrect and very misleading conclusions, which aren’t ignored but used to make absurd and very misleading claims.
Climate ‘scientists’ do themselves no favours by ignoring this. Anyone who knows anything about statistics and computer models can challenge a climate ‘scientist’ about confidence intervals associated with models and point out that modelling any non-deterministic system, such as climate, that involves so many variables, such as climate, means the results they produce looking at any length of time into the future are no more accurate than you’d get from tossing a pair of dice.
I’ve challenged a number of climate scientists about this and never received a remotely satisfactory answer. I’ve also challenged Nick Stokes and never received a response. This isn’t surprising because there is no satisfactory answer. There isn’t and never will be a solution to this because of the fundamental properties of probability, of which averages are just one small part.
While Joe Public instinctively understands this — anyone with an ounce of common sense can do so — the vested interests of climate ‘scientists’, politicians and environmentalists exploit these misunderstandings to their advantage. 150 years from now there will numerous text books about “the great climate change scam” of the 21st century and how trillions were wasted addressing the wrong problem. But none of us will be around then to say “we told you so”.
And averaging the spaghetti from a whole bunch of climate model outputs is also alleged to mean “something”.
Of course it does. The range of predictions and the average model prediction represent the overall consensus of government bureaucrat climate scientists. The “best” model (least inaccurate Russian model) could represent a better understanding of climate science, or a lucky guess.
“If you take the errors involved in any climate model, regardless of the power of the supercomputer running it or the ‘accuracy’ of the model itself, you very quickly realise that any forecast made from it will have confidence intervals so large that the results are effectively meaningless in real terms.”
The climate models are iterative. As Pat Frank has shown, a small error in the initial input accumulates uncertainty across each iteration and after a number of iterations overwhelms any output – i.e. your “confidence interval”.
‘As Pat Frank has shown, a small error in the initial input accumulates uncertainty across each iteration and after a number of iterations overwhelms any output.’
Even worse than that, the incremental ‘uncertainty’ overwhelms the incremental ‘output’ across each iteration.
Frank ==> The first is the initial conditions problem of non-linear systems (in short, Chaos), the second is statistics…(I think). depending on the model, uncertainty is either additive or multiplicative.
Predictions and average temperatures are two different things
Climate models are not based on data for the future climate because there are no data for the future climate. They are based on unproven climate theories, some historical data (maybe) and speculation, Since they consistently over predict the rate of global warming, on average, the unproven theories appear to be wrong.
The average temperature is an imperfect statistic that allows us to estimate if the climate model predictions make any sense. So far it appears they don’t, except for the Russian IMN model. which might make sense or is a lucky guess.
You are assuming the future forecasts of average global temperature means something. It doesn’t. You don’t even know if Tmax or Tmin is driving any change.
The article keeps saying you cannot do something, then showing you can. I’m guessing the author means you shouldn’t do it, not that you cannot.
Pedantry aside, the argument is still wrong. Ignoring all the technical points about intrinsic properties and whatever, the average temperature does tell you something. If it’s meaningless, it would be impossible to know if California is hotter than Iceland, or if summers are hotter than winters. You don’t need to have a correct understanding of thermodynamics to know that a place with an average temperature of 40°C is on average hotter than a place with an average of 10°C.
Bellman,
Before the thermometer was invented, people seem to have migrated according to hot or cold climates, as in colonization of Greenland. One might say that they used their bodies for thermometers as guides to locations they liked. Their bodies did not provide temperature numbers. Therefore I would agree with your assertion that “You don’t need to have a correct understanding of thermodynamics to know that a place with an average temperature of 40°C is on average hotter than a place with an average of 10°C.” But I do not know what we should learn from this comment. Geoff S
One might say that the successful harvesting of crops was of more importance to the Vikings than the average temperature. Extreme temperatures are more important than averages because extreme temperatures kill plants and animals.
The focus on average temperatures ignores the fact that Earth’s temperature distribution is skewed, with a long tail on the cold side. That is why I have advocated for analyzing the changes in Tmax and Tmin instead of the mid-range value.
Bravo! Testify brother!
Bellman ==> This is a continuation of a series of essays….about NUMBERS.
Mathematicians can and do average numbers: numbers as “just numbers”.
When those numbers are numerical values of physical properties, the rules of their manipulation change as they are no longer “just numbers” but something quite different.
You use practical everyday understandings to support misuses of mathematics applied to thermodynamic properties.
Temperature is the measure of relative “hotness and coldness”. So, California’s climate, expressed in some practical sense of expected winter temperatures (say at San Diego) is surely warmer than Icelands winter expected temperatures.
Nothing whatever to do with the topic of this essay, except as covered in the Topeka Kansas example.
Your example was averaging 4 locations toget an estimate of the average temperature of California. Even if one were to accept the claim that the average temperature means nothing in terms of the scientific definition of temperature, my point is that it still has a practical everyday meaning. If that isn’t the point of your essay, why use it as an example?
Bellman ==> No, that is not the point of the essay. We are talking about a specific scientific point of physics.
The everyday observation that the deserts of Southern California tend to have hotter days than the steppes of Minnesota is nothing more than a true observation. It does not involve a calculation from temperatures measurements.
But the fact that the averages support the “true observation” show that the average is not meaningless.
Do you dress for the average temp or for the max and min temps?
Would you dress differently in the desert then in Kansas even if the average temp is the same?
Bellman ==> The fact that one cannot average temperature is an interesting and rather technical issue of physics and thermodynamics.
One you have yet to demonstrate, yet keep insisting is a fact because you said so and no “buts” are allowed.
I’ve searched on line for any clue that this might be true or false, and found nothing, apart from the fact that as I suspected the final temperature of two identical substances is the average of the two temperatures.
To me it makes no sense to say that you cannot average a heterogeneous intensive property. It’s just common sense and I’ve given examples where it is done, e.g. density.
It clearly is possible to determine the average of an intensive property. It’s just a question of if you can then say that average temperature is the temperature of the system or if it’s just the average temperature of the system.
Read the wiki at:
https://en.m.wikipedia.org/wiki/Intensive_and_extensive_properties
It is a very detailed discussion.
It would help if you could post some reference(s) for your position.
I’m guessing he didn’t make it much past the first paragraph of the introduction, where they stated:
He believes that the act of averaging reduces measurement uncertainty.
Thanks, but the wiki entry was the first place I checked yesterday. It makes no mention of whether you can average intensive quantities or not, so I’m not sure how it helps.
“Consider a homogeneous system, divided into two halves; all its extensive properties, in particular its volume and its mass, are each divided into two halves. All its intensive properties, such as the mass per volume (mass density) or volume per mass (specific volume), must remain the same in each half.“
Intensive and extensive properties – Wikipedia
This is how you determine if a property is intensive or extensive.
Your formula picked from your reference have exacting assumptions before you can simply average temperatures. One is that mass and specific heat capacities be the same. That is what I showed you without even reading the reference.
(c1=c2=c), (m1=m2=m)
The underlined is a very well defined property. You can see the units for both extensive and intensive types of specific heat values. The units are different. For “specific heat capacity”, the units are J/(kg·K)
Now ask yourself, do these properties exist in the atmosphere in equal quantities at any two station locations? If they don’t, then you can’t use the simple formula.
Further more, That formula is how you determine if a property is intensive or not. If both objects are identical, including temperature, the final temperature doesn’t change, whereas the volume and mass would double.
Lastly, quit scanning stuff for equations to prove your point. That is cherry-picking without understanding the assumptions needed to use certain equations. That is part of an engineering background, i.e., recognizing the physical properties involved in making assumptions.
“Consider a homogeneous system”
“homogeneous” being the operative word.
If the temperature in a system is homogeneous the question of averages is not an issue, all temperatures are the average.
“This is how you determine if a property is intensive or extensive.”
That is not the full story, as it doesn’t work if the intensive property is not homogeneous. You can’t simply cut simply cut something in half, see the property is different in each half and claim the property is not intensive.
“Your formula picked from your reference have exacting assumptions before you can simply average temperatures.”
Which I mentioned. It doesn’t alter the fact that refutes the claim that averaging temperatures can have no physical meaning. A single falsification is all it takes to refute the claim.
” If they don’t, then you can’t use the simple formula. “
I’m not saying you can. It’s just showing the premise of this argument is flawed.
“Lastly, quit scanning stuff for equations to prove your point. That is cherry-picking without understanding the assumptions needed to use certain equations”
Seriously, you think finding evidence that the claim you made can’t be correct is cherry-picking now? I didn’t scan for equations to prove my point. I was actually looking for examples that would help me understand the argument better. I was mainly looking for anything saying it was or was not possible to average intensive properties.
“ That is part of an engineering background, i.e., recognizing the physical properties involved in making assumptions. ”
I pointed out those assumptions at the beginning.
Moreover, the formula for mixing substances with different heat capacities are still averaging the temperatures, just with different weightings.
Bellman, I tell you what, you find a reference to support your position and that shows the math derivation copy and paste here and I’m sure folks will be happy to critique it. There are at least four references here on this thread supporting that intensive properties can’t be averaged. I for one, will be happy to see one that falsifies these.
By “true observation” I suspect you are meaning “true value”. There are several prerequisites for this to be true. The big one is that random errors must have a normal distribution. An assumption is that multiple readings of the same thing will provide a normal distribution. This must be proven by determining if the plot of readings is normal.
Temperature readings of different stations will not do this. One single reading of a temperature won’t provide this.
I was quoting Kip.
It really helps if you click on the name of the person being replied to, so you can see the context.
You didn’t address the true value issue. Why is that?
Because I’m trying to keep these discussions on topic, and every time I spend time trying to correct some irrelevant nonsense from you two, I’m accused of being a troll.
Does knowing the average temperature inform you as to whether or not you should wear a coat when you leave your house in the morning? It is more important to know the probable extreme temperatures for a particular day.
“. You don’t need to have a correct understanding of thermodynamics to know that a place with an average temperature of 40°C is on average hotter than a place with an average of 10°C.” (bolding mine, tg)
You are missing the point. You may be right about a place. But if you average two different places then what does that average actually tell you?
Or take a place in the southwest desert. The average temperature may be higher than a place in Kansas. But that still doesn’t tell you that it can get colder at night in the desert place than it does at a place in Kansas. Or that the heat index in Kansas (a function of humidity) can be higher than in the desert. So which place is actually hotter and which is colder?
The average enthalpy might give you an indication but temperatures can be very deceiving.
A place can be bigger than a spot. By place I was usingfollowing this article talking about the average temperature in a region of California.
Whatever the point of this article is, it’s not about the concept of averaging multiple points to estimate the average. Rather it seems to be something about whether an average temperature represents some definition of temperature.
Bellman ==> Read the just the numbered points about 2/3rds of the way through the essay.
OK,
I’m not sure why you think temperature is a quality rather than a quantity. But, yes it is an intensive quantity.
Why would you expect it to. You’ve just said it’s an intensive property, so what’s the point of summing them?
Again, yes that’s the point of intensive properties. But just because something has no physical meaning doesn’t mean it’s impossible to do, or that it can’t be used as an intermediate value towards a meaningful result.
Say I have 3 sheep and give away 5 sheep. I can subtract 5 from 3 to get the value -2. With regard to sheep that has no physical meaning, but I can do it and the result might have meaning beyond the physical reality of negative sheep.
In particular if I have 3 sheep give away 5, but someone else gives me 4. The sum (3 – 5 ) + 4 is just as valid as 3 + (4 – 5), or (3 + 4) – 5. They all give me a valid result, but two involve partial results that are physically meaningless.
See above regarding meaningless results.
However, when I’m talking about the average temperature, I’m imagining an ideal concept of that average, based on an integral of all values. Averaging components is just a way of using statistics to estimate the true average.
So can you integrate intensive properties? You could argue it still involves adding increasingly small values which can only be done with extensive values, but you are tending it to the limit where all values have zero width, so everything tends to spot values.
As an example, velocity is an intensive property, and I’ve never seen a suggestion that you cannot integrate velocity.
Even if you don’t like that idea, there seems to me to be an obvious workaround. Convert the intensive property to an extensive one. You can do that with time using degree days. As Tim Gorman keeps pointing out the advantage of looking at degree days is they can be added. But once you’ve added your degree days over a month say, you can divide them by 30 days, and the time dimension vanishes, leaving just degrees. I see no reason why you couldn’t do the same using spacial dimensions. Measure your temperature in units of Cm^3, then there’s nothing stopping you adding all the components and finding the average temperature per cubic meter.
5. Surface Air Temperatures (2-meters above the surface) are all spot temperature measurements inside of mass of air that is not at equilibrium regarding temperature, pressure, humidity, or heat content with its surroundings at all scales.
This is just getting back to the practical issues of sampling and measuring temperature. I don’t think it helps to mix this up with the more fundamental issue of whether an average temperature is a physical thing.
Here for example is formula for the final temperature when mixing two identical substances at different temperatures
and if the two have the same mass this becomes
The first could shows it is possible to convert temperature to temperature times mass to get an extensive average, the second doesn’t even do that, just averages the temperature.
Is this allowed if it’s impossible to average temperature?
So, didn’t read the paper. Obvious.
Was there any specific bit of the paper that particularity impressed you? Did you like the parts where they show that if you use different averaging you can turn a warming trend into a cooling one. Did you not think that was dubious, or did you not see a problem?
Look at this link, it describes your example exactly, except for the conclusion. Can you figure out why temperature in your example simply shows that temperature is intensive?
http://www.thoughtco.com/intensive-vs-extensive-properties-604133
I can’t see where that page explains my example, exactly or otherwise. Maybe if you provide the quote you think does, we could see if you are understanding it correctly.
Do the math. If:
m1 = m2 = m, and
T1 = T2 = T
then you get,
(m • 2 • T) / 2 • m, which ,
= T.
This is intensive!
And now what do you get if T1 does not equal T2?
You need to show your reference so the assumptions for the equation are known.
https://www.tec-science.com/thermodynamics/temperature/richmanns-law-of-final-temperature-of-mixtures-mixing-fluids/
There’s also the passage from Essex et al quoted in this essay.
You missed the words “MIGHT” and “APPROXIMATE“!
Nope. They are right there in my quote.
But you apparently didn’t bother reading them!
I did. They are irrelevant to the argument. I don’t care how approximate Essex et al think the formulae for mixing are, it directly contradict the claim that temperatures can not, under any circumstances, averaged to give a meaningful result.
You are doing what you keep accusing me of, nit picking in order to distract from the argument.
This is nothing more than a mathematician showing no knowledge of physical science.
When you remove the masses from the equation you no longer have any idea of what the equilibrium temperature will be.
T_f = (T_1 + T_2)/2 is *NOT* a standalone equation. It only applies if you have identical masses. If you don’t include the masses in the equation then how do you know they are equal?
“It only applies if you have identical masses.”
Hence why I said “and if the two have the same mass”.
Bellman ==> You are welcome to comment here but it is annoying that you continue to do so without having done your homework or paid close attention to the essay.
The remedy is this: Read the links and references.
“Say I have 3 sheep and give away 5 sheep. I can subtract 5 from 3 to get the value -2. With regard to sheep that has no physical meaning, but I can do it and the result might have meaning beyond the physical reality of negative sheep.”
Physics exists to describe the REAL world. There is no such thing as a negative sheep in the real world.
“In particular if I have 3 sheep give away 5, but someone else gives me 4. The sum (3 – 5 ) + 4 is just as valid as 3 + (4 – 5), or (3 + 4) – 5. They all give me a valid result, but two involve partial results that are physically meaningless.”
Is a sheep an intensive or extensive property? If I have one sheep and add another I have two sheep. If I have one steel bar of temp T1 and add a second steel bar of temp T2 do I now have T1 + T2 degrees of temperature?
It’s not obvious that you have internalized the difference between intensive and extensive properties. You keep trying to justify adding intensive properties using examples of things that are extensive properties.
“I’m imagining an ideal concept of that average, based on an integral of all values.”
Your calculus ignorance is showing again. An integral of a function is not an average!
“Averaging components is just a way of using statistics to estimate the true average.”
Do you mean “true value”? There is no true value for a distribution of measurements taken from different things using different devices. You haven’t yet internalized that yet either!
“So can you integrate intensive properties? You could argue it still involves adding increasingly small values which can only be done with extensive values, but you are tending it to the limit where all values have zero width, so everything tends to spot values.”
Integration finds the area under a curve, not an average. What does that buy you with intensive properties?
“you can divide them by 30 days”
You can but why would you? HDD and CDD are used to create energy usage values so you can compare changes in energy usage to maintain a base temperature, i.e. kWh per degree-day figures. If max temperatures are going up kWh per degree-day for cooling will go up. If min temps are going down kWh per degree-day for heating will go up. If min temps are going up the kWh per degree-day for heating will go down. If we are seeing global climate change then the energy usage per degree-day *will* change. If the climate change is so small that it doesn’t affect energy usage then why should we be so alarmed about it?
It is the *sum* of degree-days above and below a base that is useful, not the average. And, yes, you *could* calculate an annual average degree-day value over a time span of years but, again, what would it tell you? As with temperature you would lose the min and max data which is so important for discerning what is actually happening!
I’ll try to be brief as I don’t want to be accused of more trollish behavior.
There is no such thing as a negative sheep. That was the point. Physically impossible calculations can lead to physically correct results.
I talked about deriving an average based on an integral, not that an integral is an average. If you take an integral a to b and divide it by b – a you get an average.
No, I meant true average. The point of that comment was that taking samples to determine an average is trying to estimate the true average, by which I mean the average obtained by integration.
My point about degree-days stands. By definition they are an extensive property, you can add them and so you can average them.
“There is no such thing as a negative sheep. That was the point. Physically impossible calculations can lead to physically correct results.”
If you can’t have a negative sheep in the real world then how can your calculation be correct in the real world?
“I talked about deriving an average based on an integral, not that an integral is an average”
No, you keep calling an integral an average. Apparently you’ve finally figured out you are wrong.
“If you take an integral a to b and divide it by b – a you get an average.”
You get an average what?
“No, I meant true average. The point of that comment was that taking samples to determine an average is trying to estimate the true average, by which I mean the average obtained by integration.”
You keep claiming that the mid-range value of a sine wave is the “true average”. Have you finally figured out that is wrong?
“My point about degree-days stands. By definition they are an extensive property, you can add them and so you can average them.”
No, you claimed they were an intensive property and by dividing by the number of degrees you could get an intensive property that you could then average. Your conclusion: you can average intensive values. I pointed out that you were calculating an intensive value using an extensive value.
Congrats for finally learning something. You can’t average intensive properties.
“If you can’t have a negative sheep in the real world then how can your calculation be correct in the real world?”
Yet strangely enough it is.
“You get an average what?”
The average of the value you are integrating.
“You keep claiming that the mid-range value of a sine wave is the “true average”.”
I’m not sure when I’ve claimed it, but it’s obviously true – the median and the mean of a sine from 0 to 2pi are the same.
“Have you finally figured out that is wrong?”
No I haven’t. Could you explain?
“No, you claimed they were an intensive property and by dividing by the number of degrees you could get an intensive property that you could then average.”
I did not. Here’s what I said
See the difference. A degree is a measure of an intensive property, temperature. Multiplying it by an extensive property, time, produces an extensive property with units degree days.
“You can’t average intensive properties.”
And yet I have. Do you want me to show you how to get an average density, or velocity?
“Yet strangely enough it is.”
You live on a strange planet if you think negative sheep actually exist.
“The average of the value you are integrating.”
For at least the fifth time an integral does not give you an average, it gives you the area under a curve.
“I’m not sure when I’ve claimed it, but it’s obviously true – the median and the mean of a sine from 0 to 2pi are the same.”
For at least the fifth time, take a remedial calculus course.
“See the difference. A degree is a measure of an intensive property, temperature. Multiplying it by an extensive property, time, produces an extensive property with units degree days.”
And how does that prove you can average an intensive property?
“And yet I have. Do you want me to show you how to get an average density, or velocity?”
No, you averaged an extensive property and then calculated the intensive property. How does that prove you can average intensive properties.
YES! Show me how you can integrate velocity and get an average velocity!
“You live on a strange planet if you think negative sheep actually exist. ”
Does the sound of points flying over your head keep you awake at night?
I do not think negative sheep exist. I think the final answer which gives you a positive number of sheep.
“For at least the fifth time an integral does not give you an average, it gives you the area under a curve.”
Whoosh! There goes another one.
If you integrate a value and divide by the difference of the limits you get the average of that value.
“For at least the fifth time, take a remedial calculus course.”
Why, will it teach me that the median is actually the maximum of the sine wave? If so I’ll ask for my money back.
“And how does that prove you can average an intensive property?”
Beginning to think I should just ignore anything written in all caps or bold.
I’ve taken an intensive property (temperature), I’ve calculated an average for that intensive property (still temperature). I’ll leave the rest of the proof as an exercise for the reader.
If it is meaningless why would you want to use it in further calculation?
The last I knew the Global Average Temperature is an AVERAGE. Averages use a sum. The sum of meaningless numbers is meaningless. Therefore, the average of meaningless numbers is also meaningless.
I take it you do not have a weather station nor do you keep track of its information. If you did, you would recognize that morning low temperatures have a much different humidity than the afternoon high temperatures. That means the enthalpy of each vary considerably. Temperature averages just aren’t a good proxy for the heat content of the atmosphere.
“region of California”
What does an average of a region of CA tell you? It can’t tell you anything about a specific location. So what can it tell you?
“Whatever the point of this article is, it’s not about the concept of averaging multiple points to estimate the average. Rather it seems to be something about whether an average temperature represents some definition of temperature.”
Go study up on intensive properties vs extensive properties. An average temp does *NOT* represent any definition of temperature. You can’t actually even calculate a daily mid-range average at a specific point because you can’t add intensive properties in order to create an average. Between Tmax and Tmin humidities can change, pressures can change, wind can change, etc. So what does an average of Tmax and Tmin tell you? It’s a meaningless number!
“What does an average of a region of CA tell you?”
You keep asking these inane questions, and always ignore the answer.
It tells you the average temperature in that region. There’s a clue in the words average, temperature and region.
“It can’t tell you anything about a specific location.”
How specific a location do you want? We are talking about a specific region in California.
“So what can it tell you?”
Already answered, but again, it can tell you things like is this region on average warmer than another region, is this day on average warmer than the previous day and has there on average been any long term change in the temperature in that region.
“An average temp does *NOT* represent any definition of temperature.”
That’s the nub of Kip’s claim. I don’t agree, but even if true it doesn’t matter. I don’t care if you think of the average temperature as being a measure of temperature or of average of varying temperature. It’s still telling you something about temperature of the region.
It’s like claiming the average family size is not the size of a family. That’s correct but it doesn’t matter if what you want to know is the average family size rather than the size of a family.
“You can’t actually even calculate a daily mid-range average at a specific point because you can’t add intensive properties in order to create an average.”
Your record’s stuck again. The argument in this article is not about averages in time, but in space. But you are still wrong.
“Between Tmax and Tmin humidities can change, pressures can change, wind can change, etc.”
I don’t care.
“So what does an average of Tmax and Tmin tell you?”
It’s an estimate of the mean temperature during the day.
Go on, now tell me how changing this to degree days gets rid of all the changes in humidity and pressure, and gives you an extensive temperature you can add.
“It tells you the average temperature in that region. There’s a clue in the words average, temperature and region.”
So what? How is that average value useful? The average value for San Diego, CA and Romana, CA is useless! It would describe what is going on in either location let alone somewhere in the middle.
Or how about Colorado Springs, CO and Pikes Peak, CO? Would the average between the two locations tell you what to wear at each location?
“How specific a location do you want? We are talking about a specific region in California.”
Tell me what you would wear when travelling from Stratton, CO to Granby, CO based on the average temperature in each location!
“Already answered, but again, it can tell you things like is this region on average warmer than another region, is this day on average warmer than the previous day and has there on average been any long term change in the temperature in that region.”
How do you tell that from an average? A region with a range of 0F to 100F gives an average of 50C. A region with a range of temps from 30F to 70F gives the same average. Which region is warmer and which is colder based on an average value of 50F for both?
“That’s the nub of Kip’s claim. I don’t agree, but even if true it doesn’t matter. I don’t care if you think of the average temperature as being a measure of temperature or of average of varying temperature. It’s still telling you something about temperature of the region.”
The issue is CLIMATE! It’s why the models are called “CLIMATE MODELS“! And the mid-range temp (it’s not even an average!) tells you nothing about the climate in a location or a region or the globe!
“It’s like claiming the average family size is not the size of a family.”
You analogy is wrong! The size of a family is an EXTENSIVE property, not an intensive property! The size can be measured directly, it doesn’t have to be calculated!
“Your record’s stuck again. The argument in this article is not about averages in time, but in space. But you are still wrong.”
Temperature *is* a time varying value whether you are looking at a specific location or a region. It is also a pressure varying value, a humidity varying value, a terrain varying value, a geography varying value, and other varying values!
If the temperature curve approximates a sine wave then the at one location you have a curve T = Tmax1 * sin(t) and at the other Tmax2 * sin(t + ⱷ)
The correlation between the two is cos(ⱷ). ⱷ is a function –
ⱷ(vector distance, elevation, pressure, humidity, wind, terrain, geography, etc)
Unless the function ⱷ() is the same for both locations then the average of the two really doesn’t tell you a whole lot!
“I don’t care.”
Yep, you have faith in your religious dogma and nothing will shake it!
“It’s an estimate of the mean temperature during the day.”
It’s actually not. The mean is .64*Tmax during the day. Go take a remedial calculus class!
“Go on, now tell me how changing this to degree days gets rid of all the changes in humidity and pressure, and gives you an extensive temperature you can add.”
Degree-days are an integral of the temperature curve. They are not averages or means or anything. They are the area under a temperature curve. Can you tell everyone what that implies? I doubt it.
“So what? How is that average value useful?”
See my previous 999 explanations.
“The average value for San Diego, CA and Romana, CA is useless!”
Would you say it was more or less useful than knowing just San Diego?
” It would describe what is going on in either location let alone somewhere in the middle.”
And why would you expect it to? You keep getting hung up on the idea that an average has to be the same as a specific value. The purpose of an average is not to tell you the temperature at every location, it’s to tell you the average – again there’s a clue in the name.
“Or how about Colorado Springs, CO and Pikes Peak, CO? Would the average between the two locations tell you what to wear at each location?”
I would not. Nor would I use just one location to tell me about another. But I would prefer to know an average based on many measurements in preference to nothing at all.
“Tell me what you would wear when travelling from Stratton, CO to Granby, CO based on the average temperature in each location!”
Why are you obsessed with what I’m wearing?
“How do you tell that from an average?”
Your question is how would I tell if one average is hotter than another when all I know is the average temperature. Think about it.
“A region with a range of 0F to 100F gives an average of 50C. A region with a range of temps from 30F to 70F gives the same average. Which region is warmer and which is colder based on an average value of 50F for both?”
If they both have the same average than on average they are both the same. Which is heavier 1kg of lead or 1kg of feathers?
“If they both have the same average than on average they are both the same. Which is heavier 1kg of lead or 1kg of feathers?”
You are KIDDING me, right?
The climate in the desert with a range of 100F is the same as the climate in Colorado where the range is 40F? Where the minimums range from 0F to 30F? Where the max temps range from 70F to 100F?
You’ll say anything to keep from having to admit the average temp tells you nothing! A true religious fanatic.
I didn’t say the ranges were the same. I was answering your question “Which region is warmer and which is colder based on an average value of 50F for both?”
You didn’t answer the question. What would you wear based on the average temperatures?
Why do you want to know? This is getting quite sinister.
Seriously, why would I wear something based on an average temperature?
“Seriously, why would I wear something based on an average temperature?”
You are the one claiming that average temperature is a useful value!
Why are you now trying to claim that it isn’t?
You’re creating a false dichotomy. Just because an average temperature isn’t useful in all conceivable situations does not make it meaningless.
Do you think just because NASA did not design JWST to operate only in a ~2.7 K environment that the average temperature of the CMB is totally meaningless and useless?
Strawman Extraordinaire. What do you think the enthalpy would be at 2.7 K? You reckon there is a lot of heat surrounding it at that temperature?
Here is the exchange I’m responding to.
TG said: “What would you wear based on the average temperatures?”
Bellman said: “why would I wear something based on an average temperature?”
TG said: “You are the one claiming that average temperature is a useful value! Why are you now trying to claim that it isn’t?”
Note that Bellman is not saying either way if an average temperature is useful for planning his attire. Yet Tim jumps to the conclusion that this means an average temperature isn’t useful.
The argument I’m challenging is Tim’s. I didn’t create that argument. He did. I’m just challenging it using the JWST and the CMB average temperature as a real world example of the ridiculousness of it.
If an average is not useful then it isn’t useful. There’s simply no way to hide that fact using a word salad.
bellman was the one that said it wasn’t useful.
And you have yet to disprove the mathematical proof on Page 6 of the Essex paper. No amount of word salad will change that fact.
So that’s how it is eh? Tim Gorman unilaterally declares the CMB temperature useless?
Oh, and Bellman said no such thing. You and few contrarians are ones saying that.
So climastrology’s air temperature anomaly graphs are on a par with the cosmic background?
I don’t thinkso.
Not me. Lot’s of others.
You *STILL* haven’t proved the Essex paper math to be wrong. Till you can prove it wrong, it sure seems to be correct to me!
bellman said the average temp wasn’t of any use in selecting clothes to wear. And he, nor you, can give any situation where it is useful.
Learn it, love it, live it.
Let me make sure I’m understanding your final argument here. Your argument is that because the average of an intensive property does not equal the value of the property at each and every location within the body being discussed it is therefore a meaningless and useless value. Is that correct?
The pH of the ocean is useless and meaningless?
The CMB temperature is useless and meaningless?
The atmospheric pressure at sea level is useless and meaningless?
The MLCAPE at a specific location is useless and meaningless?
The albedo of the planet is useless and meaningless?
The TSI of the planet is useless and meaningless?
All of the above involve averaging intensive properties. Do you really think all of them including the countless others I did not mention are useless and meaningless? And all because each of these does not equal the corresponding value for every part of the whole?
Really? Is that how far you’re going to take this?
Can you take two points several miles apart in the ocean, average their ph and *always* find someplace in between with that average value of ph?
CMB *is* an extensive value. It is a measure of the power in an EM wave. The “temperature” of that is calculated, not measured!
MLCAPE is a measure of energy. Energy is an extensive property.
How do you have an average albedo? It has the same problem as assuming that everyplace on earth gets the same amount of sun insolation at the same time. It has the same problem as temperature. Albedo doesn’t act at a distance. If you measure the albedo at point A and at point B, there is no causal connection between point A and B so there can’t be a causal connection to an average either.
TSI is, once again, energy – an extensive property. Even so, the value of useful TSI at any specific point on the earths atmospehre is related to the sin(a), the angle of incidence. Since the earth is spinning the impact of the TSI at any point on the earth also changes during the day, it’s a time function, another sin(a). So it isn’t something you can just “add up” in order to find an average. And since TSI only makes sense by considering its impact on the atmosphere and the surface of the earth, it’s impact at any point in time and space will be dependent on the makeup of the atmosphere, a function which the climate models handle very, very badly – think clouds for one thing.
The CMB temperature is intensive. The canonical ~2.7 K figure is computed by averaging the temperature of the sky.
MLCAPE is intensive. It is computed from subtractions of average temperatures which is also intensive. The units are j/kg.
TSI is intensive. The canonical ~1360 W/m2 figure is computed by averaging the perpendicular solar flux over at least one orbital cycle.
As with the average of all intensive properties an average of K, j/kg, W/m2, pH, etc. will not equal the value at every point within in the body.
Anyway, unless you tell me otherwise and based on your posts in this article I’m going to assume you think the average of an intensive quantity is meaningless and useless in all circumstances.
“The canonical ~2.7 K figure is computed by averaging the temperature of the sky.”
No, the 2.7 K figure is CALCULATED from the average of the received EM radiation!
“MLCAPE is intensive. It is computed from subtractions of average temperatures which is also intensive. The units are j/kg.”
from NOAA.gov:
“MLCAPE (Mixed Layer Convective Available Potential Energy) is a measure of instability in the troposphere. This value represents the mean potential energy conditions available to parcels of air located in the lowest 100-mb when lifted to the level of free convection (LFC). No parcel entrainment is considered.” (bolding mine, tg)
Potential energy is EXTENSIVE!
Here’s another definition:
CAPE: “Convective available potential energy, or CAPE, is a measure of the available or potential energy that may fuel a thunderstorm. Specifically, CAPE is a measure of the energy that is available for convection, or the movement of gas and liquid during the formation of weather phenomena.” (bolding mine, tg)
from wikipedia: “In meteorology, convective available potential energy (commonly abbreviated as CAPE),[1] is the integrated amount of work that the upward (positive) buoyancy force would perform on a given mass of air (called an air parcel) if it rose vertically through the entire atmosphere.”
Work is dependent on mass. As mass changes the amount of work to move the mass changes also. Therefore it can’t be an intensive property, it must be an extensive property. j/kg merely denotes an index or constant used to determine actual energy required from a mass of air. Wet air has more mass so when you multiple the mass times j/kg you get the total number of joules required to move that mass. The wetter the air the larger the number of joules required to move it.
I guess TSI could be considered to be the same thing as density, an intensive value. But its main use is as a conversion constant to get the number of watts being dumped into a receiver. But you simply can’t average a conversion constant – just like you can’t average density. Neither value is dependent on an amount of anything, you can’t take some of it away or add more at any point without changing an extensive attribute in the radiation source.
The CMB is not at 2.725 K everywhere. The CMB is not in equilibrium. The canonical value of 2.725 K is the average. That’s the point. BTW…the fact that the CMB is not at the same temperature everywhere is profound. It is one of the the most important observations in all of cosmology.
The units for CAPE is j/kg. It is convective available potential energy per unit mass. It is most like a density metric. However, unlike a density this value can actually be negative. When negative it is often referred as convective inhibition. It is an intensive property. When you partition a parcel with CAPE = 2000 j/kg each of the parts still has 2000 j/kg of CAPE. And I’ll remind you that the equation is CAPE = g * integral[(Tparcel – Tenv)/Tenv, LFC, EL, dz] where Tparcel and Tenv can either be a spot value or an average value through an atmospheric layer.
bellcurveman apparently truly believes that the operator 1/N performs the transformation of meaningless into meaningful!
“You are the one claiming that average temperature is a useful value! Why are you now trying to claim that it isn’t?”
It’s not an either / or statement. Something can be useful, without being useful in all circumstances. Knowing the average temperature can be useful, but won’t tell me if it’s raining, or windy, or what the local dress code is.
Two things you will never grasp from your time spent typing into WUWT:
The global average temperature is a meaningless number, and averaging does not reduce measurement uncertainty.
Actually, if one is wanting to know about “heat”, using just temperature increases uncertainty by leaps and bounds.
Nor will it tell you the amount of heat that has been added/subtracted at a single point.
“See my previous 999 explanations.”
Your examples are all using extensive properties trying to prove you can average intensive properties and come up with something useful!
“Would you say it was more or less useful than knowing just San Diego?”
It’s neither. It’s useless! You need to know the Tmax/Tmin for both in order to judge the climate at each place and every place in between! And my guess is that you don’t have a clue as to why!
“And why would you expect it to? You keep getting hung up on the idea that an average has to be the same as a specific value”
And if I have two boards, one 6′ and on 8′ then what does the average tell me? Of what use is it in the real world? I *need* the specific value of each in order to have something useful! It’s no different with temperature. If the temperature in Phoenix is 100F and in Galveston it is the same, 100F, does the average tell me anything? Why is one described as a dry heat and one as a wet heat?
“Nor would I use just one location to tell me about another. But I would prefer to know an average based on many measurements in preference to nothing at all.”
Cognitive dissonance at its finest. You think something that is of no use is useful!
“Why are you obsessed with what I’m wearing?”
I didn’t ask what you are wearing. I asked what you *would* wear. And you refused to answer. That tells me you know you’ve been caught out.
“Your question is how would I tell if one average is hotter than another when all I know is the average temperature. Think about it.”
NO, *YOU* think about it! And then answer the question. How would you know which is hotter when all you know is the average?
“The issue is CLIMATE!”
The issue of this essay is temperature.
“The size of a family is an EXTENSIVE property, not an intensive property!”
Either I’m misunderstanding the terms, or that is seriously wrong. Granted, it’s a bit ambiguous as to what family size means, but if we are talking about a typical nuclear family and not say a commune, family size is intensive. You cannot join a family with 2 children to a family with 5 to get a family with 7 children. The number of children are extensive, but the family size is intensive.
“The size can be measured directly, it doesn’t have to be calculated!”
Is that what you think the difference between extensive and intensive is?
“The issue of this essay is temperature.”
Yes, and you have still not shown how you can add or subtract intensive properties. All have done is try to use extensive properties to prove you can add/subtract intensive properties!
“Either I’m misunderstanding the terms, or that is seriously wrong”
Uh huh. And which do you think it is?
“Granted, it’s a bit ambiguous as to what family size means, but if we are talking about a typical nuclear family and not say a commune, family size is intensive.”
Can you add/subtract members from a family? Can family members be born or die? Even the term “family” is extensive. If I turn my basement into an apartment and rent it out then there are two families living here, not one.
“You cannot join a family with 2 children to a family with 5 to get a family with 7 children”
Why not? I have a dear friend with 1 child who married a widow with 3 children. They are now a family of 6.
“The number of children are extensive, but the family size is intensive.”
So in your world no one ever dies and no one is ever born. That’s typical for you. You have no understanding of the real world.
“Is that what you think the difference between extensive and intensive is?”
Again, intensive is a property that is qualitative, not quantitative, e.g. density. It doesn’t matter how much gold you have, the density of gold remains the same. An intensive property is a magnitude that is independent of system size.
The term “family” is both intensive and extensive. You can have a family without regard to the number of members in the family. But it is *also* extensive in that the number of families you can have living in a home is additive. The temperature of a substance is intensive in that it doesn’t matter how much of the substance you have. But that temperature is *not* additive. If you hold two bars, one in each hand, the first being at 70F and the second at 75F the total temperature is *NOT* 145F. If you combine them then at equilibrium you will have a new substance whose temperature is still not additive with a different substance.
Far too much of this discussion has been based on thermodynamic process, e.g. mixing two solutions, which is a totally different subject than whether the final temperature is an intensive property of the new substance created from the mixing or whether that final temperature is an extensive property additive with the temperature of something else. A thermodynamic process is neither intensive or extensive, it is not a “property” of a substance.
“Uh huh. And which do you think it is?”
I’m quite prepared to accept my understanding on intensive properties is wrong, but considering your answers I wouldn’t put money on it.
(Note, I’m only using family size as an analogy, I doubt anyone would really call it an intensive property, that’s really for physical properties, but it seems to me closer to an intensive one then extensive.)
“Can you add/subtract members from a family?”
Of course, what has that got to do with anything?
“If I turn my basement into an apartment and rent it out then there are two families living here, not one. ”
Which is my point. Two families, but not twice the family size.
“Why not? I have a dear friend with 1 child who married a widow with 3 children. They are now a family of 6. ”
As I sad last time, the concept of family size is ambiguous. That’s why I said I was only considering regular nuclear families and not extended families. Please stop trying to take this crude analogy too literally.
“So in your world no one ever dies and no one is ever born. That’s typical for you. You have no understanding of the real world. ”
You keep leaping to these ridiculous conclusions, mainly I suspect because you don’t understand what intensive means. You seem to think it means constant. Whereas I think it means not depending on the system size. In this analogy number of families is the system size, and the average family size does not depend on the number of families.
“Again, intensive is a property that is qualitative, not quantitative, e.g. density.”
Do you have a definition of what you mean by qualitative verses quantitative, because to me that makes no sense. Density is a quantitative value, so is temperature. Qualitative would mean to me that you couldn’t attach a numerical value to it.
“I’m quite prepared to accept my understanding on intensive properties is wrong, but considering your answers I wouldn’t put money on it.”
Uh huh. You won’t abandon your religious dogma.
“Of course, what has that got to do with anything?”
Didn’t figure you would get it.
“Which is my point. Two families, but not twice the family size.”
You still don’t get it. If it was an intensive property then you would still have ONE family! Extensive properties can be divided, intensive properties can’t. Cut a metal bar in half and you you half the mass in each half but you don’t get half the temperature. Stick the half-bars back together and you get twice the mass of each but still the same temperature. If family size was intensive then family size would stay the same – one family!
“You seem to think it means constant. Whereas I think it means not depending on the system size.”
Nope. See the paragraph above. You don’t even recognize that you just refuted yourself. If you add two objects together and get double (i.e. two families) that is extensive. If you add two objects together and get the same (i.e. one family) that is intensive.
You are trying to have it both ways!
“Do you have a definition of what you mean by qualitative verses quantitative, because to me that makes no sense. Density is a quantitative value, so is temperature. Qualitative would mean to me that you couldn’t attach a numerical value to it.”
An intensive property is a quality of the object. It may have a value but it is a *quality* of the object, it doesn’t depend on how much of the object you have. The density of gold is a quality of gold even if it has a quantitative value. The mass of the gold depends on how much gold you have, it is not a *quality* of the gold.
“If it was an intensive property then you would still have ONE family!”
Family size – not family, is what I was using as an analogy to an intensive property.
“If you add two objects together and get double (i.e. two families) that is extensive.”
The number of families is extensive, the family size isn’t. For the purpose of this analogy, if I stick two families together I do not have one big family, I have two families each retaining their own size.
“An intensive property is a quality of the object. It may have a value but it is a *quality* of the object”
I was asking for your definition of quality. I’m just curious as to where this idea comes from, and if it’s accepted in some fields. I was curious as to why the Essex paper talks about temperature as being a quality.
To me, quantity means something that can be measured, whereas quality is something that can only be described. Some intensive properties may be qualities, such as hardness and colour, but temperature seems like it should be a quantity.
The wiki page says
“Temperature *is* a time varying value whether you are looking at a specific location or a region.”
It may be, but that’s not what this essay is about.
“If the temperature curve approximates a sine wave then the at one location you have a curve T = Tmax1 * sin(t) and at the other Tmax2 * sin(t + ⱷ)”
How many times have I had to explain to you why this is wrong. You even seem to accept it’s wrong at some points, but then a few months later you are back to square one.
Those equations are only correct if you think the mid point of the daily temperature range is zero.
“ⱷ(vector distance, elevation, pressure, humidity, wind, terrain, geography, etc)”
Hold on. Are you saying all those things effect the frequency of the daily cycle? Or did you mean to put the ⱷ outside the brackets? But in that case
Tmax2 * sin(t ) + ⱷ
would mean that the maximum temperature could be more or less than Tmax2.
“It’s actually not. The mean is .64*Tmax during the day. Go take a remedial calculus class!”
Here we are again!
First, and this should be really obvious even to you, when I said it’s an estimate of the mean temperature during the day, I mean day in the sense of a 24 hour period, not the hours of daylight.
Second, no it isn’t. I’ve explained many many times why it isn’t and it just doesn’t stick in your long term memory.
You can multiply the amplitude of a sine wave by ~0.64 to get the average value from 0 to pi provided the sine wave has a mid point on zero. For your “the mean is 0.64Tmax during the day” to be correct you have to assume the average temperature is zero (using whatever measurement system you want) and assume that “day” is defined as the point’s where the temperature is above zero.
If by “day” you mean from sunrise to sunset, this is not going to be correct. The length of the day changes with the season and the maximum temperature is not usually mid way between sunrise and sundown.
“It may be, but that’s not what this essay is about.”
Of course it is! How do you add time-varying functions?
“How many times have I had to explain to you why this is wrong. You even seem to accept it’s wrong at some points, but then a few months later you are back to square one.”
BS! Major BS! You have *NEVER* explained how this is wrong nor have I ever accepted that it is wrong!
I guess that you believe one or all of the following:
So, tell us which one of these you do *NOT* believe is true.
Heck, even the slope of the temperature curve, whose curve is estimated by the travel of the sun as approximately Asin(θ), is Acos(θ). So the slope of the temperature curve is not the same everywhere. It depends on A which is not the same everywhere. The *direction* of the slope may be the same, plus or minus, but that doesn’t determine the actual correlation.
“Those equations are only correct if you think the mid point of the daily temperature range is zero.”
Nope. Show me *YOUR* derivation of the correlation between sin(x) and sin(x + ⱷ). My guess is that you can’t. You’ll make up some excuse.
“Hold on. Are you saying all those things effect the frequency of the daily cycle? Or did you mean to put the ⱷ outside the brackets? But in that case”
Your lack of calculus knowledge is showing again! ⱷ is a PHASE DIFFERENCE. Did you somehow see an ω in the equation? (ω -small omega – is typically used to denote frequency) You are pretty good at seeing things that aren’t actually there. sin(t) is a normalized equation with no frequency implied.
“First, and this should be really obvious even to you, when I said it’s an estimate of the mean temperature during the day, I mean day in the sense of a 24 hour period, not the hours of daylight.”
So what? The median of the daytime temp is Tmax. The mean is .64 * Tmax if it is assumed to be a sine wave. The temperature curve at night is more approximately an exponential decay function. It’s mean is .37 * T0 where T0 starts at sundown. It’s median is ln(2)/k where k is the rate of decay.
So how do you combine those to get an actual average temperature? The mid-range value is certainly not the average temperature for the entire 24 hour period!
I’ve showed you with graphs over and over again that when you integrate a sine curve between two points on the curve you can set the baseline where ever you want. The area between the curve (T) and the baseline (T – Tb) remains the same no matter what T is as long as T – Tb remains constant. You just refuse to believe that. If you compute the area of a tire between its top and the axle it simply doesn’t matter if the tire is sitting on the ground or is on a lift 6′ in the air. That area between the top of the tire and the axle remains the same.
“Your lack of calculus knowledge is showing again! ⱷ is a PHASE DIFFERENCE.”
Yes, my mistake. No excuses.
But I still don’t get why you think vector distance, elevation, pressure, humidity, wind, terrain, geography, etc will all result in a phase shift.
“So, tell us which one of these you do *NOT* believe is true”
None of the above. My point is that you keep thinking a daily temperature cycle is a sine wave with a center amplitude of zero. From that you claim that the mean is 0.64 * Tmax.
“The median of the daytime temp is Tmax.”
What? How can the max be the median?
“The mid-range value is certainly not the average temperature for the entire 24 hour period!”
If as you keep claiming it’s a perfect sine wave then yes it is. I see you are now claiming night time temperatures are not part of the sine wave, but the point is still that the mean of tmax and tmin is a reasonable estimate of tmean, given that they are often the only data you have.
Certainly better than just multiplying tmax by 0.64.
“The area between the curve (T) and the baseline (T – Tb) remains the same no matter what T is as long as T – Tb remains constant.”
And I keep explaining to you why that is meaningless. If by baseline you mean Tmean, all you are saying is the temperature minus the mean is constant. As I keep telling you, if you want to calculate the “daytime” mean assuming a sine wave the correct formula would be
0.64*(tmax – tmean) + tmean.
But the period of that mean is only the period when temperature is above the mean, not the period when the sun is up.
“But I still don’t get why you think vector distance, elevation, pressure, humidity, wind, terrain, geography, etc will all result in a phase shift.”
Does the sun shine on the entire Earth’s surface the same at the same time?
Do weather fronts impact all points on the Earth at the same time?
Does the wind blow the same everywhere on the earth?
Does the east side of a mountain get the same sun insolation as the west side?
Does the atmosphere above a soybean field get the same sun insolation as in a forest at the same height of measurement?
Does Montreal get the same sun insolation as Miami?
All of these factors, and probably others, affect the relationship between one point on the surface and a different point. A phase shift is not just a shift in time but a change in relationship. You’ve obviously convinced yourself that a sine wave can only define frequency of oscillation. You always wind up trapping yourself in a small box. A velocity profile can be a sine wave between a start point and an end point. The shape of the velocity profile can be different for two different objects while still starting and ending at the same point. That difference can be described by sin(t) and sin(t + ⱷ) in many cases.
“Does the sun shine on the entire Earth’s surface the same at the same time?
Do weather fronts impact all points on the Earth at the same time?
Does the wind blow the same everywhere on the earth?
Does the east side of a mountain get the same sun insolation as the west side?
Does the atmosphere above a soybean field get the same sun insolation as in a forest at the same height of measurement?
Does Montreal get the same sun insolation as Miami?”
What does any of this have to do with a phase shift? Temperatures will be different because of all of this, but I don;t know how your model says that in each case it will simply shift a sine wave along.
“What? How can the max be the median?”
What is a median?
“It is the point above and below which half (50%) the observed data falls, and so represents the midpoint of the data.”
So how can Tmax *NOT* be the median?
You think half the day is warmer than the maximum?
Take a remedial calculus course! I gave you the definition of what a median is. And how can Tmax be less than Tmax?
Better yet, just go away troll!
If you weren’t so obsessed with everyone else’s education, you might be able to learn something yourself.
The median temperature in a day is the mid point of all temperatures, it’s the temperature that half the day will be above and half below. That you think the maximum temperature will also be the median is unfathomable. That you persist in this belief after someone points out the obvious problem just shows what happens when you are so sure you must be right, that you just insult anyone who tries to correct you.
I doubt if this will help you, but here’s the Wikipedia page on Medians
Note the need for the median to separate the higher half from the lower half. That means the median temperature needs to be cooler than half the distribution. Can you explain how the maximum temperature (by definition the hottest temperature) can be cooler than half the day?
So you *DO* believe the correlation between sin(t) and sin(t+ⱷ) is cos(ⱷ)?
So you *do* believe that latitude has an impact on temperature? Then how do you design a functional relationship that describes that without using something like sin(t) and sin(t+ⱷ)?
So you *do* believe that elevation has an impact on temperature? How do you design a functional relationship that describes that without using something like sin(t) and sin(t+ⱷ)?
So you *do* believe that terrain has an impact on temperature? How do you design a functional relationship that describes that without using something like sin(t) and sin(t+ⱷ)?
So you *do* believe that geography has an impact on temperatue? How do you design a functional relationship that describes that without using something like sin(t) and sin(t+ⱷ)?
So you *do* believe that the sun doesn’t hit every point at the same time. So how do you design a functional relationship other than by using a sinusoid?
I’ve given you the answer multiple times. You just keep forgetting it, purposefully I guess.
The heat pushed into the earth from the sun happens during daylight hours. The temperature from that driver approximates the positive half of a sine wave. The average value of that curve is .63 * Tmax. The actual power is the root-mean-square value which is .7 * Tmax. That’s the constant value of temperature that would result in the same amount of power.
The heat lost during nighttime hours is an exponential decay. It’s mean is .37 * T0 where T0 starts at sundown. It’s median is ln(2)/k where k is the rate of decay.
It should be obvious to even you that the average temperature is *NOT* (Tmax+Tmin)/2!
“So you *DO* believe the correlation between sin(t) and sin(t+ⱷ) is cos(ⱷ)?”
Yes. So what? You keep getting so wrapped up in your games that the meaning should be obvious.
“So you *do* believe that latitude has an impact on temperature? Then how do you design a functional relationship that describes that without using something like sin(t) and sin(t+ⱷ)?”
Of course latitude has an impact on temperature. Int he Norther Hemisphere in general the higher the latitude the colder it is. But I wouldn’t assume it makes the time of maximum and minimum temperatures later. Any function is more likely to be ⱷsin(t) or sin(t) + ⱷ.
And the same answer to all your other questions.
“I’ve given you the answer multiple times. You just keep forgetting it, purposefully I guess.”
I don;t forget it, I just know you are demonstrably wrong. For one thing you would get different results depending on which temperature scale you used.
“The heat pushed into the earth from the sun happens during daylight hours. The temperature from that driver approximates the positive half of a sine wave.”
But unless you are on the equator or it’s the equinox, the sun isn’t up for half the day.
“The average value of that curve is .63 * Tmax.”
Only if you assume the temperature is zero at sun up. You also seem to be assuming maximum temperatures will be at noon, because you are ignoring any lag.
“It should be obvious to even you that the average temperature is *NOT* (Tmax+Tmin)/2!”
I said it’s a reasonable approximation, not that it was. And I’ll remind you that if you are correct all this is meaningless becasue the concept of an average temperature during the day is not a physically meaningful thing.
Regarding your (0.63Tmax + 0.37T0)/2. Effectively if temperatures are close to max at sundown, then you are simply calculating the mean as being a bit under half the max. This can well be colder than the minimum. For example if max is 14 and min is 12, and it was 13 at sundown, you would have a mean temperature of 6.8.
“Yes. So what? You keep getting so wrapped up in your games that the meaning should be obvious.”
You are a troll. go away!
“Of course latitude has an impact on temperature. Int he Norther Hemisphere in general the higher the latitude the colder it is. But I wouldn’t assume it makes the time of maximum and minimum temperatures later. Any function is more likely to be ⱷsin(t) or sin(t) + ⱷ.”
Once again, you are confused. Why does ⱷ have to be time?
go away troll. Go take a basic calculus course.
“I don;t forget it, I just know you are demonstrably wrong. For one thing you would get different results depending on which temperature scale you used.”
You can assign any temperature scale you want. Do you see a scale detailed somewhere in sin(t)?
Go away troll. Take a basic calculus course.
“But unless you are on the equator or it’s the equinox, the sun isn’t up for half the day.”
And now you are back to the argumentative fallacy of nitpicking. Who says π has to be 12 hours?
go away troll and take a basic calculus course! Take a basic trig course. π is in radians, not time.
“Only if you assume the temperature is zero at sun up. You also seem to be assuming maximum temperatures will be at noon, because you are ignoring any lag.”
Once again, go take a basic calculus course. Learn about radians.
“I said it’s a reasonable approximation, not that it was. “
It’s not, it isn’t even close!
“And I’ll remind you that if you are correct all this is meaningless becasue the concept of an average temperature during the day is not a physically meaningful thing.”
go away troll. Take a basic calculus course. You *still* don’t understand what an integral is. I doubt if you ever will. There *is* a reason why you can add degree-days but you can’t add degrees! And an integral is *NOT* the sum of all the y-axis values. Σ f(x) ≠ ∫ f(x)dx
“Regarding your (0.63Tmax + 0.37T0)/2. Effectively if temperatures are close to max at sundown, then you are simply calculating the mean as being a bit under half the max. “
Go away troll. How did you get Tmax = T0? And who says Tmax occurs at sundown. It’s usually around 3pm standard time – far from sundown!
Take a basid calculus course and learn how to characterize a sine wave!
“This can well be colder than the minimum. For example if max is 14 and min is 12, and it was 13 at sundown, you would have a mean temperature of 6.8.”
Go away troll. Take a basic calculus course. Where do you live? At the north or south pole? T0 *is* the temperature at sundown – when the sun is no longer providing heat into the atmosphere! That’s when the exponential decay begins! (the decay actually begins earlier than that when the earth begins radiating away more than it receives). And the mean of the exponential decay is .37T0 (assuming there is definite change point at sundown).
I truly, truly, truly tire of trying to explain basic calculus and physics to you. I’m done. No more replies to you in this thread. You’ll have to remain lost in that Bizarro world you live in.
Which is it? Do you want me to go away or do you want me to answer your increasingly long list of questions?
Seriously, I don’t care how much you insult me, but do you really think these endless repetitive insults are contributing anything to this discussion, or to your credibility?
On with the show:
“Once again, you are confused. Why does ⱷ have to be time?”
You were claiming that there was some function ⱷ on latitude that that would make the temperature function approximate sin(t + ⱷ). That implies that latitude will cause a phase shift in temperature, making the time of maximum earlier or later than somewhere at a different location. I don’t see how.
Now if it were longitude then than would be a different story.
“You can assign any temperature scale you want. Do you see a scale detailed somewhere in sin(t)?”
And you will get different results each time, as your implicit assumption is that all places have a mean vales at zero degrees.
“Who says π has to be 12 hours?”
I assumed that’s what you meant when you said the daily temperature cycle could be represented by a sine wave. It’s also implicit in your mean temperature formula that is giving equal weight to the sin part, regardless of the length of daylight.
“π is in radians, not time.”
Are you saying your x axis isn’t time?
“Learn about radians.”
Radians have nothing to do with what the temperature is at sunrise. Your basic argument was that the positive portion of the sin function represented daylight temperature, and hence the mean daylight temperature is 0.64Tmax. That only makes sense if you assume sunrise temperature is zero, sunset temperature is zero and max temperature is mid way between sunrise and sunset.
“It’s not, it isn’t even close!”
Could you put some real world figures on that, and then compare it with your own formula?
“There *is* a reason why you can add degree-days but you can’t add degrees! ”
Which what I’ve been trying to tell you and the rest all this time. The claim is it’s impossible to add temperatures and so get an average temperature. But converting temperature to an extensive property (e.g. degree-days) does allow you to add them, and then get an average in degrees, hence you can get a meaningful average of an intensive property.
You can either accept that premise in which case the main argument of this essay is wrong, or you can reject it, in which case talking about mean daily temperatures is meaningless. I don’t see how you can argue both and be logically consistent. Maybe Kip will explain when the third part comes out.
“And an integral is *NOT* the sum of all the y-axis values. Σ f(x) ≠ ∫ f(x)dx”
They are not the same. But they are related. There’s some discussion of it here
https://math.stackexchange.com/questions/184979/relation-between-integral-and-summation
“How did you get Tmax = T0? And who says Tmax occurs at sundown.”
I didn’t. I said if T0 was close to Tmax. Which is often is. Another way of looking at it is Tmax / 2 is an upper limit on Tmean in your formula.
“Where do you live? At the north or south pole? T0 *is* the temperature at sundown – when the sun is no longer providing heat into the atmosphere! That’s when the exponential decay begins! (the decay actually begins earlier than that when the earth begins radiating away more than it receives). And the mean of the exponential decay is .37T0 (assuming there is definite change point at sundown).”
A beautiful theory destroyed by reality. Just think about any day, wherever you live, where say, TMax is 30°C and TMin is 20°C. As I say the mean by your formula cannot be greater than 15°C, but that’s warmer then the minimum temperature. So you are claiming it’s possible for TMean to be at least 5°C cooler than the coldest part of the day. This is just not possible.
Maybe if you got out of the rut of personal insults, you might consider the possibility that you have made a mistake somewhere. You might even be able to fix it and get a better estimate of the mean.
“Which what I’ve been trying to tell you and the rest all this time. The claim is it’s impossible to add temperatures and so get an average temperature. But converting temperature to an extensive property (e.g. degree-days) does allow you to add them, and then get an average in degrees, hence you can get a meaningful average of an intensive property.”
One quick reply. The rest of your post is garbage.
I WAS THE ONE THAT TAUGHT YOU ABOUT DEGREE-DAYS!
It’s taken you over a year to finally agree with what I originally was trying to teach you!
So don’t lecture me about degree-days and extensive properties.
TG said: “So don’t lecture me about degree-days and extensive properties.”
To be fair and as far as I can tell you still think W/m2 and j/kg are extensive so I don’t think it’s out of line to continue discussions with you regarding extensive properties. And you’ve mentioned in the past that CDD, HDD, and GDD are useful metrics so I don’t think it’s out of line to point the contradiction of your position in which you believe an average temperature is not useful yet defend its use in other metrics that depend upon it.
BTW…I’m not trying to put you down here. I make mistakes and inconsistent statements all of the time. Everybody does it. I’m just pointing out what I believe are mistakes and inconsistencies in your position in hopes that something can be learned from it.
“And you’ve mentioned in the past that CDD, HDD, and GDD are useful metrics so I don’t think it’s out of line to point the contradiction of your position in which you believe an average temperature is not useful yet defend its use in other metrics that depend upon it.”
Once again, you have no understanding of the subject you are propounding on.
What does the dimension of degree-day mean to you? What does the area under the temperature curve mean to you?
Note: The area under the curve is *NOT* an average temperature! Why do you and bellman not understand basic calculus?
The area under the curve is a continuous summation of the degree-days in a particular time period. Dividing this by the length of the time period gives you the average in degrees.
This exposes the error in the claim that it’s impossible to get a meaningful average if an intensive property because the sum is not meaningful. There may be other reasons why you cannot get a meaningful average temperature, but it has nothing to do with summing intensive properties.
No it doesn’t
It really doesn’t. My guess is that he will be unable to show how dividing degree-days by days is related in any way to 4ΣT/(pi) for a sine wave. The average value of the positive half of a sine wave is .63 * Tmax. I really want to see how 4ΣT/pi equals that!
If I knew what you meant by 4ΣT/(pi), I might be able to help.
Pure, unadulterated malarky.
Please show us how ΣT works. The link you provided earlier showed doing an integral with the operator #dx instead of just dx. #dx is a *summing* operator. Once again you’ve been caught trying to cherry pick something to throw at the wall without actually understanding the concepts.
Please elucidate how that summing operator #dx can find the sum of all the values of the positive half of a sine wave!
What you are calculating by dividing degree-days by days IS THE INTENSIVE TEMPERATURE VALUE THAT GOES WITH THE DEGREE-DAY VALUE. Please show us how that is somehow the average temperature value!
I keep telling you to go take a remedial calculus course. You are just posting meaningless malarky without understanding anything.
It is tiring as all git out having to correct your garbage all the time!
He appears to be confusing definite integration with numerical integration, which is only an approximation.
Of course I’m talking about definite integration. How else do you divide by the limits?
And I’m talking about analytical integration, though the argument works as well with numeric.
“#dx is a *summing* operator”
I think #dx was the counting measure, but this has nothing to do with what we are discussing, it was just pointing out that there is a connection between summing and integration. If you want information take a remedial class on measure theory.
“What you are calculating by dividing degree-days by days IS THE INTENSIVE TEMPERATURE VALUE THAT GOES WITH THE DEGREE-DAY VALUE. Please show us how that is somehow the average temperature value!”
I’m not sure how you can fail to understand that dividing the number of degree-days by the number of days gives you the average temperature. The clues in the units.
Let’s say I wanted to keep track of the total temperature times time over a month. I measure the temperature in degree days, where the degrees are in units of Celsius and days are in units of days. 1°C for an entire day is 1 degree-day. How I measure this will involve some amount of approximation. I could measure the temperature every hour, or every minute, or I could just look at the min and max temperature and estimate the mean by assuming it followed a sine wave.
Let’s assume I take the measurement every hour, so if at 0000 hours the temperature was 10°C, I assume that was the temperature for the entire hour. As we are adding degree days I multiply this by 1/24 to get 10/24 degree days in the first hour. Then at 0100 hours the temperature is 9°C, so I add 9/24 to the total, and so on. After 24 hours I have 24 recordings. The sum is the sum of degree-days in that one day, which is also the sum of all 24 measurements divided by 24. Hence one days worth of degree days is also the average temperature over that day.
If I keep track over a 30 day period, the sum of all the degree-days will be the total number of degree-days for that 30 day period, and dividing by 30 will give me the average daily number of degree days, which also happens to be the average daily average value, or the average temperature in °C over that 30 day period.
“I think #dx was the counting measure, but this has nothing to do with what we are discussing,”
It has EVERYTHING TO DO WITH THE DISCUSSION!
A summing operator is different from the integrating operator. Did you bother to read the WHOLE link you provided or did you, once again, just cherry pick a piece that looked like it supported you?
“ that there is a connection between summing and integration.”
Again, Σx ≠ ∫x dx
One sums values and the other sums areas! The dimensions are *NOT* the same. ΣT has a dimension of degrees. ∫T dt has a dimension of degree-days! The difference should be obvious to anyone not spouting religious dogma!
“I’m not sure how you can fail to understand that dividing the number of degree-days by the number of days gives you the average temperature. The clues in the units.”
But the average you arrive at is *NOT* ΣT/π. That gives you a dimension of degree/time, not degrees! You have never, not once, learned how to do dimensional analysis, have you?
“Hence one days worth of degree days is also the average temperature over that day.”
Back to dimensional analysis. You are saying that degree-days are the same as degrees? You *still* haven’t figured out what an integral is! Take a remedial calculus course!
” which also happens to be the average daily average value, or the average temperature in °C over that 30 day period.”
So, again, degrees are the same as degree-days? Wow. Just WOW!
Your vanity is no argument. You did not “teach” me about degree-days, but even if you had, so what? You still don’t understand how to get an average from them, or that the average is in degrees.
You had never even heard the term “degree-days” until I brought it up as a better way to handle what is happening with climate change. Stop playing dumb!
degrees/time is *NOT* degrees. degree-day is not degrees.
Check your math!
If it makes you happy, lets say you were the one who brought them to my attention. Thank you oh wise benefactor. I’ve since spent the last three years trying to explain why you don’t understand them.
Your hubris knows no bounds.
“but the point is still that the mean of tmax and tmin is a reasonable estimate of tmean, given that they are often the only data you have.
Certainly better than just multiplying tmax by 0.64.”
You just can’t give up your religious dogma even in the face of proper application of mathematics.
Mid-range values are *NOT* a good proxy for the mean. It is *way* off from being the mean or the median!
“the only data you have”? How about just using Tmax and Tmin as the data? Set the climate models up to generate Tmax and Tmin predictions! How about using the average of [ (.63*Tmax) + (.37T0) ]/2?
You’ll never admit to the right answer. They don’t give Tmax and Tmin values separately because they wouldn’t support the catastrophic climate change meme!
You *still* haven’t grasped this concept! I can only assume that it is purposeful! If you take a balloon with a volume of B that is sitting on the ground and raise it up three feet does the volume change (assuming atmospheric pressure change is insignificant)?
Why would the area beneath a temperature curve and a baseline change if you just transpose it on the x-y axes? That area between the two boundaries is just like the volume of a balloon!
““the only data you have”? How about just using Tmax and Tmin as the data? Set the climate models up to generate Tmax and Tmin predictions! How about using the average of [ (.63*Tmax) + (.37T0) ]/2?”
You believe there’s no such thing as an average temperature, why do you care about the exactness of the method for obtaining the mean?
What does T0 mean in your equation? Is it the minimum or the mean temperature? Either way it can lead to a mean temperature that is lower than the minimum. Would you consider that a problem?
“You *still* haven’t grasped this concept!”
Because you won’t explain what you are talking about. Again, what is the baseline?
“If you take a balloon with a volume of B that is sitting on the ground and raise it up three feet does the volume change (assuming atmospheric pressure change is insignificant)?”
Take your big book of argumentative fallacies, and look up argument by analogy.
“Why would the area beneath a temperature curve and a baseline change if you just transpose it on the x-y axes?”
It wouldn’t but it’s got nothing to do with daily temperatures. You are basically saying that it doesn’t matter if the maximum temperature is 10°C or 50°C the area under the curve will be the same as long as you move the baseline, whatever that is, up by 40°C.
“Degree-days are an integral of the temperature curve.”
The whole point of this essay is you cannot average temperatures because you cannot add them. But converting to measuring degree days, rather than just degree days makes them extensive, and hence you can add them. Integrating is just continuous adding. Once you have a sum of degree days, you can average them by dividing by the number of days. Hence you can average degree days even if you cannot average degrees. And dividing degree days by days, leaves you with just degrees. Hence I claim that degree days show it is possible to average temperature.
“They are not averages or means or anything.”
If the integral goes from 0 to 1, e.g. if you are integrating for one day, that integral is the average degrees in the day. You’ve already admitted that when you want to use the are under a sine curve to determine the average temperature during hours of daylight.
Bellman ==> I am going to assume now that you are just intentionally trolling this thread with comments that do nothing but argue with others because you have misunderstandings about the basic principles being discussed.
Please — the purpose of the comment section is not to have a good fight. It is to share your viewpoint with others and to share theirs. When you exhibit the basic “refusal to learn” attitude (can’t be bothered to read the pertinent links and papers that explain the things you misunderstand) — then you are just wasting digital ink and everyone else’s time.
Try to see if you can explain to Tim why Essex, McKitrick and Andresen say that one cannot average temperature. In other words, understand their viewpoint well enough to explain it to Tim, even if you don’t agree. I you can’t do so, then you didn’t understand their paper.
Essex, McKitrick and Andresen are not just some sophomoric students are some community college somewhere. They are each well-respected professors and researchers in the many science specialties involved in this question: Non-linear Thermodynamics, statisics, Statistical optimization, modeling, finite-time thermodynamics, climate science, Radiation Thermodynamics, Anomalous Diffusion, Chaos, Dynamical Systems and Predictability.
Their paper was published in a peer-reviewed specialty journal on Non-linear Thermodynamics, and
they probably have something to say, and they probably understand the subject better than you do.
It may be tough going, but it is a learning opportunity.
I do apologize for going over the top with Tim Gorman. I had intended to just stick to the topic of this post, but it’s difficult to turn your back on so many points that keep getting argued over with no progress.
If you want, I will give a more detailed explanation of why I think the paper is wrong, but your attitude seems to be an argument from authority – these people are experts so cannot possibly be mistaken.
Bellman ==> No, I want you to be able to explain why they say what they do about why temperatures cannot be averaged.
You do not understand it….or you would be able to argue in its favor in a debate.
The point isn’t that they cannot be wrong — but they do what they are talking about and YOU do not understand what they are saying.
“You do not understand it….or you would be able to argue in its favor in a debate.”
An interesting argument. Does this mean that nobody can disagree with Dr Spencer’s global average unless they can also defend his claim in a debate?
“I want you to be able to explain why they say what they do about why temperatures cannot be averaged.”
The “why” is a bit subjective. I think it’s clear from the introduction “why” they want to argue what they do. They want to cast shade on the entire concept of a global temperature in order to argue that it’s not possible to “know” if the earth is warming or not, and so we don’t have to worry about it. As long as we can’t see a problem the problem doesn’t exist. But as I say that’s just my interpretation.
As to the question of what they say about averaging temperatures, the problem is they do not say you cannot average them. In fact they average them throughout the paper. In fact they explicitly say so in the abstract.
What they do say is that the average has no physical meaning.
The main argument’s given are:
1) The average of any intensive variable will be meaningless, because the sum is meaningless and dividing that sum will not reverse the meaninglessness.
2) The average temperature cannot represent the temperature (their emphasis) as that leads to a paradox in which the temperature can change but some parts of the system don’t.
3) There are an infinite number of ways of deriving an average, all equally valid, and the choice of an average can lead to contradictory results – e.g. some showing warming some cooling. This is taken as a proof by contradiction that all averages a physically meaningless.
But please don’t make me defend this in a debate.
Bellman ==> Ah, you have gotten something from their paper, thank you for making the effort.
I doubt that Essex et al would agree with your wording, but it shows me that you have finally done your homework. I certainly don’t. But you have made a good effort.
You are not required to agree with them.
And I will not ask you to defend their viewpoint in a public debate.
Thank you.
You said:
“They want to cast shade on the entire concept of a global temperature in order to argue that it’s not possible to “know” if the earth is warming or not, and so we don’t have to worry about it.”
That is putting words in their mouths.
You copied this to your comment:
“…it is always possible to construct statistics for any given set of local temperature data…”
But you failed to show the context.
Let’s see what they really said.
As you can see, the real point is that if physical principles provide no restrictions, then it is permissible to use an infinite range of statistical analysis methods.
However, being able to interpret a temperature field as both warming and cooling depending on the statistical methods, means the design of a Global Average Temperature is “ill-posed”, i.e. not correct. Basically, there is no hypothesis backed up with functional mathematics where a deterministic value can be predicted by a GAT.
“That is putting words in their mouths.”
Which is what i was asked to do. Explain in my own words why they thought what they thought.
“As you can see, the real point is that if physical principles provide no restrictions, then it is permissible to use an infinite range of statistical analysis methods.”
Which is my point. The claim is the paper says you cannot average temperatures, the paper actually says you can average them in an infinite number of ways.
I did suggest at the start that Kip should distinguish between cannot and should not.
Oh my gosh. What do you think this means.
“… making the concept of warming in the context of the issue of global warming physically ill-posed.”
Like it or not, it means that using temperature in the context of global warming is ill-posed. What does ill-posed mean? Read this page. Well Posed and Ill Posed problems & Tikhonov Regularization – (calculushowto.com)
As I said earlier, “being able to interpret a temperature field as both warming and cooling depending on the statistical methods, means the design of a Global Average Temperature is “ill-posed”.”
Are you having questions about why using temperature as a basis for a statistical answer to the heat content of the earth is ill-posed?
You *really* don’t expect anyone to accept these conditions for a well posed question do you?
A functional linear relationship means you don’t get multiple y-values for the same x value. Yet that is what the climate scientists expect us to believe.
What do you think it means?
All they do in that section is calculate an average of 2 stations raising each to a power of 20 or even 150, and show it gives a meaningless results. By this logic all averages are “ill-posed”, though they don’t provide any evidence it is in the technical sense.
Much of this paper seems to be people showing that if they do really stupid things they can get really stupid results, and then blaming everyone else for not explaining why they shouldn’t do those stupid things.
Man you just hit the nail square on the head when it comes to averaging temperature didn’t you?
This isn’t a class room. I am not going to teach you the math for ill-posed problems. It should be self-evident.
“Integrating is just continuous adding.”
Adding of AREAS. Go take a remedial calculus course. What do you think x dx represents?
“ Once you have a sum of degree days, you can average them by dividing by the number of days.”
I’ll ask again since you refuse to answer. Why would you do that?
“And dividing degree days by days, leaves you with just degrees”
You have calculated an intensive property from an extensive property average. How is that averaging an intensive property? You and bdgwx keep trying to prove you can average intensive properties by averaging extensive properties and then calculating an intensive property from that! That is *NOT* averaging an intensive property!
“If the integral goes from 0 to 1, e.g. if you are integrating for one day, that integral is the average degrees in the day”
AGAIN – AN INTEGRAL IS NOT AN AVERAGE! IT IS THE AREA UNDER THE CURVE!
Go take a remedial calculus course – assuming you had a basic one to begin with!
“You’ve already admitted that when you want to use the are under a sine curve to determine the average temperature during hours of daylight.”
Integrating the temperature curve does *NOT* give you an average value! Do you have any concept of how you get an average value from that?
“Go take a remedial calculus course.”
These insults are getting too repetitive and boring. I suggest you take a remedial ad hominem course.
“Why would you do that?”
It doesn’t matter why you would do it. The point is you can.
“AGAIN – AN INTEGRAL IS NOT AN AVERAGE! IT IS THE AREA UNDER THE CURVE!”
Stop shouting.
The area under the curve is the continuous sum of values, dividing by the width (b – a) of the definite integral gives you the average value, if the width is 1, it follows you area will be the average.
“Go take a remedial calculus course – assuming you had a basic one to begin with!”
Did any of the calculus courses you took actually get you to understand what an integral is?
“Integrating the temperature curve does *NOT* give you an average value! ”
It does when you divide the value by the limits.
“These insults are getting too repetitive and boring. I suggest you take a remedial ad hominem course.”
It isn’t an insult. It’s a statement of fact. You simply do not understand how differentials and integrals work and what they tell you! Go take a remedial course in calculus.
“It doesn’t matter why you would do it. The point is you can.”
Yep, reality doesn’t matter to you.
“The area under the curve is the continuous sum of values”
NO IT IS NOT! The dimension of the area under the curve is *NOT* the y dimension so it can’t be a simple sum of the y values! Again, go take a remedial course in calculus.
If T = f(t) = sin(t) then the integral under the curve is ∫sin(t) dt.
How does that come out with a dimension of temperature? The dimension is degree-time and not degree!
“Did any of the calculus courses you took actually get you to understand what an integral is?”
The integral gives the AREA under the curve! An area has a dimension of y * x, not y.
∫ f(x) dx has dimensions of f(x) * x. If f(x) has a dimension of meters and x has a dimension of meters then the integral gives you a dimension of m^2. That is *NOT* a sum of meters. If the dimension of f(x) is degrees and of x is seconds then the integral gives you degree-seconds. If the dimension of f(x) is mass (kg) and of x is seconds then the integral gives you kg-sec.
“It does when you divide the value by the limits.”
If you divide m^2 by meters you get average meters. If you divide degree-sec by seconds you get average degrees. If you divide kg-sec by sec you get average seconds.
BUT THE INTEGRAL IS NOT A SUM OF VALUES. It is a calculation of area under the curve. If it gave you a sum, like in meters or degrees, and you divide by time then you would get meters/sec or degrees/sec, not meters or degrees!
You *do* need a remedial course in calculus. You can take that as an insult if you want but that is on you, not me. It is a constructive criticism!
“It isn’t an insult. It’s a statement of fact. You simply do not understand how differentials and integrals work and what they tell you! Go take a remedial course in calculus. ”
Pathetic.
“NO IT IS NOT! The dimension of the area under the curve is *NOT* the y dimension so it can’t be a simple sum of the y values!”
The values are in units of xy. When you divide by the width the average will be in units of y.
I don’t know if I can make it any simpler for you.
“If you divide degree-sec by seconds you get average degrees.”
See, even you understand it.
“BUT THE INTEGRAL IS NOT A SUM OF VALUES.”
Stop shouting.
An integral can be thought of a continuous summation. That’s what the integral sign represents.
“If it gave you a sum, like in meters or degrees, and you divide by time then you would get meters/sec or degrees/sec, not meters or degrees!”
You do have a knack for pointing out the obvious as if it was some major revaluation.
Perhaps that you should be somewhere in between. 🙂
As far as intrinsic values are concerned, my, admittedly poor, understanding would be that you cannot add intrinsic values, but you can average them. In fact I would have thought that all intrinsic values are averages
Suppose I have two bars of different metal. Their masses are extensive properties and I can add them together to find the mass of the two bars combined. But their densities are intensive. The sum of the two densities are meaningless, but their weighted average is not. It is the density of the two bars combined.
At some level aren’t all intensive properties averages? Temperature is the average of the kinetic energy of all the particles within a region, density is the average of the mass of all the atoms in a volume of material.
Bellman ==> Temperature is a spot measurement of relative hotness or coldness on arbitrary scales.
Your definitions are not scientifically correct — only “sorta”.
Well your preferred definition, the Encyclopedia Britannica, is behind a paywall, so I can’t see if it goes on to mention the average of kinetic energy. But most definitions I found online say both that it’s a measure of relative hot or coldness, and that it’s the average of kinetic energy.
Even if you only define temperature in terms of heat flow, it is still going to be the average heat flow. Even when two bodies are on equalibrium there is still flow in both directions, it’s just the average net flow is zero.
Bellman ==> Temperature just isn’t a measure of heat content or enthalpy or heat energy. The later three are Extensive Properties and temperature is an Intensive property.
Temperature will predict heat flow but alone will not inform us about the quantity of heat content or heat energy in a system.
“Temperature just isn’t a measure of heat content or enthalpy or heat energy.”
I didn’t say it was. The key point is it’s the average of kinetic energy in the body.
“Temperature will predict heat flow but alone will not inform us about the quantity of heat content or heat energy in a system.”
That’s why I said it can be defined using heat flow.
I’m not having any problem accessing the links.
Nor am I now on my laptop. But my phone only shows the first 100 words with a message to subscribe to access the full article.
I see I wasn’t missing much. Mostly just a list of different temperature scales. I’m not sure I’d regard it as a definitive scientific definition.
” But their densities are intensive. The sum of the two densities are meaningless, but their weighted average is not. It is the density of the two bars combined.”
What do their weighted densities tell you? How do you combine the density of the two bars? Melt them together? Their actual density after melting may not be the average you calculate depending on how they act when melted.
If you put both bars in a a bucket will their average density tell you how hard it will be to pick up the bucket? Nope. It’s their masses and the force of gravity, both extensive properties, that tell you that.
It’s the old problem of which falls faster in a vacuum? A pound of lead or a pound of feathers. The density of each tells you nothing. Only the mass is useful. One is an intensive property and the other is an extensive property.
It’s the same with temperature. Temperature is pretty much a relative thing. You have to combine it with other factors in order to come up with a physical meaning that is an extensive property and is useful and which can actually be averaged. Things like enthalpy, radiation intensity, etc.
Tim ==> Intensive and Extensive properties have relationships….and, quite right, ONLY extensive properties can be added, averaged, etc.
“ONLY extensive properties can be added, averaged, etc.”
Do you have a source that says it’s impossible to average any intensive property? Are you saying it’s not possible to have an average density? How do I know if my ship will float if I’m not allowed to calculate its average density?
Bellman ==> Have you looked at the references on Intensive and Extensive properties? Have you read the Essex et al paper? Just arguing from what you can see on your phone and not looking up references for fuller explanation just wastes you time. Take the time to do your homework.
“Have you read the Essex et al paper?”
Not yet, better things to do. But I thought you were trying to summarize the paper. That’s what I’ve been addressing.
I did read a different paper by McKitrick on the subject and thought it was complete nonsense.
Bellman ==> Do your homework before wasting class time arguing with the teacher.
Sorry, I didn’t realise there would be a test. I thought we were just discussing what you said, not having to read a 30 page technical and somewhat obfuscated paper before hand.
Actually it might be the same paper. Section 3.1 is the same nonsense as I remembered from before. Claiming the choice of average can result in either a warming or cooling trend.
Specifically looking at the average of a glass of water at 2°C next to coffee at 33°C. This changes to an average of 20°C over time.
But the initial average is either colder or hotter than 20°C.
How?
Because for example you might use the root mean square rather than the arithmetic mean. In one case the initial average is (2 + 33) / 2 = 17.5°C. So the system warms.
In the other it starts at ((2^2 + 33^2)/2)^(1/2) ~= 23.4°C, so it cools.
Spot the problem? They are using Celsius, and squaring obviously depends on where the zero point is. If they’d used Fahrenheit they would have different results.
The only correct way of doing it using squaring is to use an absolute scale. Then we have cold water at 275.15K and hot coffee at 306.15K.
(1) (275.15 + 306.15) / 2 = 290.65K
(2) ((275.15^2 + 306.15^2)/2)^(1/2) ~= 291.06K
And there’s less than half a K in it. Both warm to 293.15K.
It looks like the final section is also based on the same nonsense. Though there they might be using Kelvin, but they don’t say. Instead they do calculations based on just 12 stations, in which they show that if they calculate the average using powers of around 20 they can turn a positive trend into a negative one.
I think it is weird to define “global average” as is done in equation 23 anyway. First, it’s not even an average in the traditional sense. Second, it’s not spatially weighted so it’s not global in the traditional sense. As best I can tell they invent an abusive means of calculating what they call “global average temperature” and then use their abuse to claim that a global average temperature cannot exist.
Spatial weighting is not nearly enough.
Climate is based on temperature, pressure, elevation, terrain, geography, wind, precipitation, etc. It’s why 100F in Phoenix is called a “dry heat” and in Galvaston it’s called a “wet heat”. The very same temperature creates vastly different climates! Combining mid-range values (which are neither an average or a median) for the two locations tells you absolutely nothing about an “average” climate.
Bellman ==> Did you actually read the whole paper?
Bellman ==> I have taught many students much like yourself. They want to object to the teacher having a fuller understanding by relying on their own partial and sketchy misunderstandings — I have so many times asked such students to STUDY the materials before raising objections that always rest on the student’s own misunderstandings, all of which are a direct result of their refusal to actually study the material.
Only then, if they don’t understand the material after careful intentional study, they have won the right to ask questions so they can and do understand.
If you want to understand why I (and Essex and his co-authors) say “One cannot average temperature” you will have to study the 30-page paper. It seems “obfuscated” to you because of your unfamiliarity with the basic principles like the properties of matter (intensive and extensive) and the underlying principles of thermodynamics. Neither topic is easy but it is possible for anyone with a good grasp of high school science and maths (which most high school students never achieve) to muddle their way through .
If you want to understand, then do the work instead of just pestering the well-meaning people here with your misunderstandings.
You complain when I say I haven’t got round to reading the paper, then complain when I do and point out problems in it. Yet I don’t see you arguing against what I said, just insisting that if I disagree with it I must be the one who’s wrong.
I am working as a math and science teacher. We had a professional development class yesterday and one of the exercises was to list your most memorable teacher and why. You sound very much what one person said about a professor in math. He would not answer a question that argued with his presentation unless you could properly STUDY and then talk from the textbook to show where it was wrong. If you simply did not understand the textbook he was more than willing to spend the time trying to educate you.
You totally ignored the heat content of each!
Temperature is *NOT* climate! Heat content is. It’s why the heat in Phoenix is called a “dry heat” while the very same temperature in Galvaston is called a “wet heat”.
All you’ve shown is that you can mathematically average temperatures, but you have *not* shown how that has anything to actually do with climate!
“You totally ignored the heat content of each!”
It was the Essex paper’s example. (I presume you’ve read it). They make no mention of heat content in that example, only temperature.
“All you’ve shown is that you can mathematically average temperatures, but you have *not* shown how that has anything to actually do with climate!”
We are talking about a cup of coffee and a glass of water. Not climate.
All you are doing here is offering up distractions rather than admit that the paper we all have to read contains a major mistake in using Celsius rather than Kelvin, in order to make one of their main points.
As this essay says, it’s nonsense to think that 33°C is 16 times warmer than 2°C, yet that’s exactly the mistake the authors of this paper make.
“It was the Essex paper’s example. (I presume you’ve read it). They make no mention of heat content in that example, only temperature.”
Example of what exactly? It would seem that you do what you usually do – cherry pick something you think proves your point without understanding it at all!
Apparently Eq 1 didn’t make any kind of sense to you at all.
T = ẟU/ẟS
Please tell us what U is. You can find it in the second paragraph before Eq. 1.
From Essex: “There are only two options: admit the possibility that non-equilibrium systems can simultaneously warm and cool or take the position that these terms have no meaning in such cases.”
“Arbitrary averages can and do give contradictory behaviors in more complex cases, too, as we shall see below. Averaging does not represent any means of avoiding the fact that a system is not in global thermodynamic equilibrium. Thus, in the case of non-equilibrium thermodynamics, temperature averages fail in the most basic role of an average, which is for one value to represent many.” (bolding mine, tg)
“We are talking about a cup of coffee and a glass of water. Not climate.”
Again, you obviously did *NOT* read Essex for meaning!
Essex: “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition introduces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables Xa/i
and does not change in response to a change only in Xb/i.
But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, Xa/i and Xbi. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature.”
Xa/i is your glass of water and Xb/i is your cup of coffee. It doesn’t matter if you are using a glass of water and a coffee cup or two different locations on the globe.
“All you are doing here is offering up distractions rather than admit that the paper we all have to read contains a major mistake in using Celsius rather than Kelvin, in order to make one of their main points.”
No, I am trying to point out that you do what you usually do – cherry pick something you don’t understand.
Nothing in the above mentions celsius or kelvin. It is a refutation of the existence of an average temperature using standard, simple mathematics.
Equation 1 has nothing to do the problems in section 3, which was what I’m talking about here.
Yes, a statement built on the nonsensical averaging techniques they use.
“Again, you obviously did *NOT* read Essex for meaning!”
This is one of those religious texts you like, where only the true believer can read for true meaning.
The example is of a glass of water and a coffee cup. It would be just as wrong if they were averaging two places on earth. You can’t raise temperatures in °C to a particular power and expect to get a meaningful result from it.
“Essex: “Let us propose that an average over temperatures from both systems is required to be a temperature.”
And now you are jumping to a different argument, and also one that is wrong, but for different reasons.
“Xa/i is your glass of water and Xb/i is your cup of coffee.”
No it isn’t. In the first example, from section 2 the argument is the average can’t be an actual temperature, because that would require all components to have the same temperature.
In the second from section 3 the argument is that the average has no meaning as an average.
“No, I am trying to point out that you do what you usually do – cherry pick something you don’t understand.”
Then explain why I’m wrong rather than just assert I don’t understand it. It’s a pretty big cherry, it seems to be a central part of the argument that any average must be wrong, yet you won’t even accept that it’s wrong to use Celsius rather than Kelvin.
Moreover, if the argument was valid, it would have to apply to just about any average, including the ones they say are allowed, such as personal wealth.
“Nothing in the above mentions celsius or kelvin.”
Yes, because you are not quoting the parts from the example I’m talking about.
“It is a refutation of the existence of an average temperature using standard, simple mathematics. ”
And bad logic.
Here is another paper for you to read and criticize. It has the same conclusion as KIP has tried to tell you. Averaging temperatures is wrong.
[PDF] Thermodynamical definition of mean temperature | Semantic Scholar
I’ll look at it if I have the time, but the abstract literally says it is possible to determine a meaningful mean temperature, so I’m not sure how it comes to the same conclusions as Kip, who’s claiming it’s impossible.
I add (or subtract) temperatures all of the time for various skew-t calculations. One atmospheric parameter I and others use frequently is convective available potential energy. Calculating this quantity requires taking the difference between the temperature of the parcel and the temperature of environment. I also use the average temperature of the parcel and the environment when I want mixed layer quantities. Actually, MLCAPE (using temperature averages) is more useful than SBCAPE (using surface temperature). I’m just saying a bunch of people are already summing and average temperatures on a daily basis that are not only useful and meaningful, but provide actionable information to the general public.
bd ==> Please check back in AFTER reading the referenced paper: Does a Global Temperature Exist? By Christopher Essex, Ross McKitrick and Bjarne Andresen ( .pdf ) which was published in the Journal of Non-Equilibrium Thermodynamics.
Then we can assume we are talking about the same subject.
My comment was posted after I read the paper.
I would add that while extensive properties can be averaged, it wouldn’t necessarily provide a meaningful result. The old ‘average length of a piece of rope’ idea.
“What do their weighted densities tell you?”
They tell you the average density when combined.
“How do you combine the density of the two bars?”
You could just sellotape them together for all I care.
“Their actual density after melting may not be the average you calculate depending on how they act when melted.”
True, if combining them like that changed their volume.
“If you put both bars in a a bucket will their average density tell you how hard it will be to pick up the bucket?”
No. For that you’d need their mass.
“The density of each tells you nothing. Only the mass is useful.”
News at ten, if you want to know an effect caused by mass it’s no good knowing the density. Now what if you want to know their density?
“Temperature is pretty much a relative thing.”
All measurements are relative.
“You have to combine it with other factors in order to come up with a physical meaning that is an extensive property and is useful and which can actually be averaged.”
Seriously, is that your argument? That all intensive properties are meaningless?
Also, what do you mean by averaging extensive properties. Your the one who keeps telling me there’s no point averaging lengths of wood. What good would it be to know the average mass of a bar is 1kg? If I have a collection of bars in your bucket will that tell me if I can lift it, or would it be better to know the total mass?
And if you had a bucket with an unspecified quantity of water in it. Would it be more useful to know it’s temperature or it’s energy content before putting your hand in?
There is *no* point in averaging the lengths of random boards. It will tell you nothing useful. It’s not an issue of extensive or intensive properties but an issue of the distribution not being able to identify a “true value”.
If you tell me the energy content of the water I can tell you it’s temperature. Why do you offer up such inane examples?
“But their densities are intensive. The sum of the two densities are meaningless, but their weighted average is not. It is the density of the two bars combined.”
The average IS meaningless. Combining the two bars would be creating a new body with its own density. I would be surprised that the combo process would give you the correct volume to get the “average” density.
Averaging the densities of separate bars gives you a meaningless number for density. Neither bar is the average and the average is of no value.
Jim ==> See my FINAL comment to Bellman —>
https://wattsupwiththat.com/2022/08/09/numbers-tricky-tricky-numbers-part-2/#comment-3575313
I have always said that you can’t average temperatures of water and air … it’s meaningless… it’s childlike science
Of course – but these ‘climate scientists’ don’t know any better; their methods and practices are the kinds of science that used to be taught in UK primary schools – and that is the level that they’ve been taught at.
An even simpler argument is available, based upon statistical science that so many climate scientists are either ignorant of, or willingly ignore.
Any statistical variable, including measured temperatures, must represent a sample population where all members of the population being measured are alike or share the same key attributes of concern. If the measurements are not derived from a real population of shared attributes, then any statistical calculation of that population is meaningless.
For instance, the “average” of a bald eagle and a wren is not a redtail hawk. The “average” of a dead creature and a living creature is not a half alive creature.
So using Kip’s example in Topeka in the summertime, the population that is being sampled is the typical daily range of temperatures historically measured at a single point location during a particular date or range of dates that reflect the seasonality of temperature variation in Topeka Kansas.
It would not be meaningful, however, if the temperatures that constitute the “sample” were taken all year long, since it is known that the annual seasons have a large effect on measured temperatures. Likewise, if the temperatures that constitute the “sample” were limited not just to Topeka, KS but were collected from all over North America, such would render the average daily range of measured temperatures as a meaningless sample from a population that is clearly not sharing the same attributes.
As simple as this concept is – a statistic only has meaning to the degree that the sampled population is alike – is often lost on climate scientists and media writers. The average human with any life experience and common sense knows that the average of daily highs in Nome Alaska and Honolulu Hawaii is a meaningless measure. It doesn’t take a climate scientist to get that.
Duane ==> Nicely put — I wrote a whole series here on “The Laws of Averages”. Starts here:
https://wattsupwiththat.com/2017/06/14/the-laws-of-averages-part-1-fruit-salad/
I’ve pounded your point and pounded it over the past two years and seemingly have gotten nowhere with it.
Two different measurement scenarios:
Multiple measurements of the same thing multiple times using the same device
IS DIFFERENT FROM
Multiple measurements of different things using different devices.
In the first instance, if you can minimize systematic bias to an insignificant level, then you are highly likely to get a distribution whose uncertainties cancel giving a value that is very close to a true value.
In the second instance, THERE IS NO TRUE VALUE. I don’t care how you do your average, it’s like you said – the average of an eagle and a wren is not a hawk! There is no true value. Neither do the uncertainties cancel in such a case, you likely wouldn’t know if you had a hawk, a falcon, or a turtledove! Temperatures are no different!
Tim ==> You are right and it is a very difficult task to get people to unlearn the false version of the Law of Large Numbers.
But first of all you must know the true value. We are only guessing, calculating, wishing what the true temperature is supposed to be.
SPC works because we know what the length, or diameter, or weight of something should be cause we designed it to those dimensions. We didn’t design the atmosphere.
“the average of an eagle and a wren is not a hawk!”
Irrelevant red herring logical fallacy
In other words you actually have no refutation. The average of T1 and T2 is not anything. The average of an eagle and a wren is not a hawk.
“a statistic only has meaning to the degree that the sampled population is alike”
You are dismissing nearly all climate scientists as ignorant.
That is a big conclusion.
One weather station in a properly sited rural environment, not affected by population growth and economic growth, can provide a long term trend of local temperatures
1,000 such weather stations would be better for a statistical mean.
10,000 such weather stations better yet.
If all the stations are sited properly, you can get a meaningful average.
The right question is how accurate is the average, and how useful is the average. That would depend on measurement accuracy, and low margins of error relative to the net average temperature change over time.
Wrong. The average is still meaningless. However, the mean of the anomalies, e.g. from year to year, might provide some interesting data.
… if properly weighted. I’m just not sure how you would us it or interpret it.
Joe ==> You make a good point, but if you are interested in the CliSci use of anomalies, of which I am not a fan, you have to dig into the dirty nitty-gritty details to see if The Number they pass around to the press is actually a measure of what they say it is.
Adding more stations with uncertain measurements only grows the uncertainty. Sooner or later the uncertainty will overwhelm whatever you are tying to identify.
If you have two 2’x4′ boards, one at 8′ +/- 0.5″ and the other at 8′ +/- 0.25″, the uncertainty in the total length (i.e. their sum) is 16′ +/- 0.8″ at worst and 16′ +/- 0.6″ at best. it’s no different with temps. Add two temps and their uncertainty either adds directly or by root-sum-square. One method just grows the uncertainty faster than the other – but they both grow.
Wow. Someone who knows about statistical sampling. These folks want to call “stations” samples. The Standard Deviation of each “station” (sample) should form a sample distribution and by the CLT that distribution most likely will be normal. Then one find the standard deviation of the sample deviation distribution. That is the Standard Error or SEM. Then they want to divide the SEM by the Sqrt of the NUMBER of samples and not the size of the samples to determine “Uncertainty”. Ho Ho ho!
“One cannot average temperature.”
Of course one can average temperatures.
It is done every month for nations, and globally.
So the first sentence is ridiculous,
One can also not figure out the purpose of this article.
The Climate Howlers are stronger than ever, predicting a climate emergency for over 50 years, scaring people with climate computer games, claiming every bad weather event is proof of climate change, and now spending a huge amount of money to make electric grids less reliable (Nut Zero).
And this is the best a smart guy like Hansen can do to refute the climate propaganda?
The most basic facts about the average temperature are missing:
Accuracy of data / adjustments / infilling:
— Lack of sufficient Southern Hemisphere data for pre-WWII, especially before 1920
— Magical “disappearance” of global cooling from 1940 to 1975
The fact that no one lives in the average temperature
How warming mainly affects colder nations, mainly during the six coldest months of the year and mainly at night, hidden by a single average.
That there is no normal average temperature.
That based on climate reconstructions, today’s climate is probably the best climate for humans, animals, and especially plants, since the Holocene Climate Optimum ended about 5,000 years ago.
That a +1.5 degree C. or +2.0 degree C. increase of the global average temperature since “pre-industrial” is a meaningless, arbitrary “target, not some important tipping point:
— Pre-industrial (1850) is a very rough estimate based on Vostok Antarctica ice cores, with no real time measurements, and
— And +1.5 degrees C. was almost reached in April 1998 and February 2016, during the warmest month of two very large ENSO heat releases. and no one even noticed.
I believe these facts, related to the global average temperature, are important, so I wrote them for the comments.
While I can’t refute anything specific Hansen wrote, I also can’t see much here to refute those pesky Climate Howlers.
Last open issue: What was Hansen drinking immediately before writing this article? Was he past his tipping point? And should the Adolf Biden FBI raid his home to find out?
Richard ==> Did you fail to read the “Important Note: The purpose of this essay…” ? It is the second paragraph.
I was probably nauseous by then!
When I see a Kip Hansen byline, I expect a great article that will help refute climate scaremongering. When I see an article like this one, I wonder how this will help. You are one of the best writers at WUWT, and while this article is not factually wrong, it’s not useful to refute the Climate Howlers. I am disappointed. You are entitled to write about anything you want, and I’m entitled to say the subject is not very importnt and seems like a wasted opportunity at this forum. Perhaps Part 3 will change my mind — this is just a review of the “second act”.
Richard ==> Thank goodness this web site is not just about refuting Climate Howlers.
You have a misunderstanding of why and what authors write here.
But we all have differing expectations . . . .
“Of course one can average temperatures.
It is done every month for nations, and globally.”
Of course you can average them. That doesn’t make the average meaningful.
“The most basic facts about the average temperature are missing:
Accuracy of data / adjustments / infilling:
— Lack of sufficient Southern Hemisphere data for pre-WWII, especially before 1920
— Magical “disappearance” of global cooling from 1940 to 1975″
The MOST basic facts about the average temps that are missing are that averages lose data, you know longer know what minimums and maximums are – and that you have no idea what the uncertainties of the measurements are because they are ignored by the climate scientists!
UAH DATA DO REFLECT WARMING THAT MANY PEOPLE HAVE NORTICED, WE SURE NOTICED HERE IN SE Michigan — winters not as cold as in the late 1970s. We did not need a global average temperature to know what our local temperatures have done over time.
The global average temperature is a statistic that could be useful and a statistic that hides important temperature details about local climate change and patterns of climate change. An average hides warmer winter nights in Siberia, for one example.
There is a difference in the Average temperatures of Earth, Jupiter, and Pluto, and this information is useful. Clearly averaging temperatures is something that can be meaningfully done.
More importantly, the average surface temperature of the earth is a quantity that can be calculated, and observed changes in this quantity meaningfully tells us something about the energy content of the system.
Alan ==> No one has “averaged” any numerically measured temperatures of Jupiter and Pluto. They have used assigned numbers just like the assigned “Earth-like temperature” of 15°C used to judge exo-planets.
You confuse a concept (average planetary temperature) with a practice of averaging disparate temperature measurements.
It is accurate to say that Pluto has a colder average surface temperature than the Earth. If you were to place a network surface stations around Pluto and compute an average temperature anomaly you would find that it is lower than Earth’s. This statistic would meaningfully quantify some difference in the energy content of these planetary bodies.
AlanJ ==> Yes, we would expect so from what we know of the planet Jupiter.
What we would not know is the heat content of Jupiter’s atmosphere in any quantitative sense.
Q = mc△T
And we can say quite definitively that Jupiter’s atmosphere has a very different heat content than the earth does.
AlanJ ==> The formula is correct. But do we know the values of the variables? Where are those values measured and recorded?
What is the specific heat of the atmosphere just above the surface of Jupiter?
What mass are you going to plug in?
What change of temperature ? Change from what to what ? Where are the measurements ? What location are we considering?
And if we have those three variables nailed down for some exact spot and some exact time (or should we assume that the whole planet is in thermodynamic equilibrium?), what would be the meaning of the resulting calculated Q ?
The anomaly wouldn’t tell you anything about the energy content. The anomaly on Mercury is also likely quite low – it’s hot *all* the time from being so close to the sun. The anomaly on Pluto is small because it is so far from the sun.
The average max temp or min temp might tell you something about the heat content of each body but not the anomaly.
An arithmetic mean may approximate the modal temperature, which is probably the more meaningful statistic. However, it isn’t “clear” that it is the best choice. Extreme temperatures are existentially more important for living organisms. Therefore, the range is suggested as being the most important consideration for survival. The mode is probably the second most important because it informs one about the comfort or challenge presented most of the time. Calculating an arithmetic mean implies more precision and certainty than is probably warranted or needed.
Sorry Kip, I could not even read this. The phrase “not even wrong” came to mind.
Tom.1 ==> Your loss. Even if you violently disagree with another’s viewpoint or understanding, it is important to read widely. You might even read the paper referenced near the end of the essay:
Does a Global Temperature Exist? (degruyter.com)
Not even wrong?
There’s nothing wrong except the subject matter is not very important and should not have needed a three-part article. The link Hansen mentioned (below) is excellent. I read it about 15 years ago.
A adjunct of not adding temperatures is you cannot add powers (W/m2).
After slamming Nick-the-Stroker repeatedly in the Weather Station Siting article, for blindly defending all things “government”, I find myself disappointed today. And I will risk a new thumbs down personal vote record by saying Nick’s comments here make more sense than the article, probably for the first time at this website. The purpose of the article remains puzzling.
Hansen, the author of many very good articles here, and Stroker, the defender of all things “government”, should have been a predictable battle. But Hansen decided to write about a nothingburger, and Strokes provided reasonable comments. This is like some bizarro world this morning — I’m going back to sleep !
There are plenty of issues with a global average temperature
— Accuracy — is it +/- 0.5 degrees C. or +/- 0.1 degree C.
or do we even know the likely margin of error?
— No one lives in a global average temperature
— One average hides temperature changes by latitude, land versus oceans changes by month of the year, and changes by day versus night? That’s a lot of hiding details.
— No one knows what a normal average is. And it’s debatable if a +1 or +2 degree C. increase from today would be good news, or bad news. Or would that imagined increase of +1 or +2 degrees C. be better, or worse, than a -1 or -2 degree decline from today.
The global warming that affected SE Michigan where I have lived since 1977 has been wonderful and we hope for a lot more warming. Our winters are not as cold as they were in the 1970s. Much less snow in 2022 than in the prior 44 winters. Please give us more of that. I didn’t need a global average to tell me that. Nor a scientist or a computer game. Living in the same home since 1987, and four miles south for ten years before that, helped a lot in our detection of climate change — this was not a big change.
Richard ==> If only I had been writing about Global Average Temperature…..but as I made clear from the very start, I was writing about the impossibility of averaging the numerical values of Intensive Properties like temperature.
Scientific mass-turbation.
Global average temperature is a statistic, not a measurement.
We already knew that.
We have a decent UAH temperature statistic since 1979
Has that been useful in any way?
I say yes
Apparently, you say no.
That makes you wrong
Richard ==> Opinions vary….
Are you running for political office?
Richard, tracking the GAT has no predictive value about future climate or weather. The proof is that all of the predictions for the last 30 years or more have been wrong.
It is like coming up with a program that tracks winning lottery numbers.
In what way has this effort been useful? Be specific please.
In many cases trends only tell you where we have been but have no value in predicting where we are going.
UAH has another graph that shows this very well. When you look at it, you can tell that temps go up and temps go down. Flip a coin to tell where we are going in the future.
Without averaging, climate science would have nothing.
Not true
Always wrong wild guess predictions of a coming climate crisis do not require any averages of past temperatures. The predicted future warming rates are not even based on past warming rates — they are 2x to 3x higher than the cherrypicked 1975 to 2022 period. Global average temperatures and climate computer games sound “scientific” but scary climate predictions could be made without them.
The models are merely fancy linear projections of atmospheric CO2 content, entirely the assumptions of the operators.
That are required to keep their jobs !
Averaging is most useful in small, local areas. The larger you go, the less useful it is. If you were to take the averaged temperature of every planet and moon in the solar system, then average them to gather for a planetary system average temperature, you can see how meaningless it becomes. Climate by definition is local.
Yep.
If you assume the temperature profile at least approximates a sine wave then the temperature at two different stations is sin(a) and sin(a + phi). The correlation between the two is cos(phi).
phi itself is a function: phi(distance, elevation, pressure, humidity, wind, precipitation, terrain, geography, etc)
As distance increases the correlation goes down. As elevation differences grow the correlation goes down. As humidity differences grow the correlation goes down. And on and on and on.
Trying to combine temperatures whose correlation is very low into an average is a losing proposition from the word go. Not even trying to weight each temp to a normalized value is going to help much because of the time dependence of each of the factors – humidity changes minute to minute, pressure changes at least hour to hour, wind changes minute to minute, etc.
The cosmic microwave background is about as big of a thing I can think of. Except for a few contrarians on WUWT most people have found profound meaning and utility in its average temperature of 2.7 K.
Once again, you are mentioning an intensive property derived from an extensive property – electromagnetic radiation and known physical constants.
And that radiation is supposed to be emanating from the smallest local area you can think of at the beginning of the Big Bang!
Temperature is an intensive property. 2.7 K is the average temperature of the CMB. Because that 2.7 K is an average of an intensive property then per the thesis of this article it is meaningless. Do you think the CMB temperature is meaningless?
Kip, thank you for this post. This is important and thought-provoking. Here is one of those thoughts.
How does one infer temperature from space? Detection of IR emission and computation from empirically established mathematical relationships. One such known relationship is that radiated energy is proportional to absolute temperature to the 4th power.
From space, outgoing visible and IR radiation is detected by sensors aboard the geostationary satellites. Every pixel in the resulting visualizations – in relatively high resolution – is a symbolic representation of the radiance value detected from that direction.
For the GOES East satellite, here is a link to the Band 16 – the “CO2” band centered at a wavelength of 13.3 microns – animation of 12 images over a two-hour period. The “brightness temperature” color scale used for these visualizations is such that the radiance at 50C (red) is 13 times the radiance at -90C (white.)
https://www.star.nesdis.noaa.gov/GOES/fulldisk_band.php?sat=G16&band=16&length=12
So here is my point: Just as you state, “One cannot average temperatures”, it can similarly be stated that one cannot infer an overall average heat-trapping effect from GHGs when it is obviously not a “trap” but a huge array of highly variable emitter/reflector elements.
For the lower tropopause (LT) satellite measurements, the microwave sounding units (MSU) record a convolution of the temperature-dependent O2 microwave radiation with the exponentially decreasing air temperature up to an altitude of about 10km. This number is then transformed into a single “temperature”, but it isn’t anything close to an average of the LT temperature.
David ==> It would be possible to detect a change in the heat content of the Earth’s climate system. It just is not and cannot be done using any of the GAST models.
Since there are many things between the sensor and the IR radiating media that can affect the amount of IR reaching the sensor there will always be some uncertainty associated with the value. Why is that uncertainty never factored into the results?
I should clarify that the point of my comment was not about the uncertainty of the reported radiance values, nor of the calculated brightness temperatures used for the visualizations. It was to point out from space-based observed data that the operation of the atmosphere as an infrared “trap” due to GHGs is an incomplete and misleading description. The high resolution visualizations show that the motion changes everything about where to expect the energy to end up. Therefore, in my view, it is just as meaningless physically to talk about an average “heat-trapping” effect of GHGs (i.e. a “forcing”) as it is to average an intensive property like temperature attempting to characterize the energy state of the planet.
David ==> If you’d like to write an essay of opinion piece for publication here, let me know. My email is my first name at i4.net
Nice to see someone else understands that you can’t average intensive entities.
Now, to tackle the difference between counts and measurements. Counts are definite numbers, and can be averaged properly. Measurements are not precise, and averaging them must take into consideration the LEAST precise measurement in the group.
Thus, if you average these measured temperatures (32, 55.1, 78.25 and 100.001) the average can ONLY be 66. Not 66.33775. This would be true of any measurements – volts, amps, wind strength, water flow, etc. You will CONSTANTLY see climate reports where they identify two-decimal place averages. Not possible, unless every temperature in the series is also two decimal places. (It never is.)
John ==> “Counting” of course is the huge umbrella term under which measurement falls.
CliSci not only gives numerical values to far greater precision than they were measured (usually as a result of the division involved in averaging) but they average properties (such as temperature) that may not be averaged to a meaningful result.
John Shotsky said: “Measurements are not precise, and averaging them must take into consideration the LEAST precise measurement in the group.
Thus, if you average these measured temperatures (32, 55.1, 78.25 and 100.001) the average can ONLY be 66. Not 66.33775.”
That’s not technically correct. Refer to the Guide to the Expression of Uncertainty in Measurement, An Introduction to Error Analysis by Taylor, and Data Reduction and Error Analysis by Bevington.
The correct answer using GUM equation 10 is.
sqrt[(1/4)^2 * ((0.5/√3)^2 + (0.05/√3)^2 + (0.005/√3)^2 + (0.0005/√3)^2)]
thus…
avg(32, 55.1, 78.25 and 100.001) = 66.34 ± 0.07
…using the significant figures rules described in Taylor above.
You can confirm this with the NIST Uncertainty Machine using (x0+x1+x2+x4)/4 where x0…x4 are rectangular distributions with left and right endpoints defined by the specific precision. For example, 32 would be 31.5 to 32.5.
How many times have you been told that precision is not accuracy. Accuracy is defined by uncertainty not by resolution. A very precise measurement can be very inaccurate and therefore have a large uncertainty.
If you would actually study Taylor’s tome instead of trying to cherry pick things you would find on Page 15, Section 2.2, Rule 2.5:
“Experimental uncertainties should almost always be be rounded to one significant figure.”
Rule 2.9: “The last significant figure in any stated answer should usually be of the same order of magnitude (in the same decimal position) as the uncertainty”
Since no uncertainties are included with the measurements it is necessary to fall back to the significant digit rules:
In our case the number of significant digits to the right of the decimal point in 32 is ZERO! The answer should, therefore have no digits to the right of the decimal point. Thus John is correct – the answer is 66! No uncertainty can be appended since no uncertainty is included with the measurement!
PLEASE WRITE THIS AS MANY TIMES AS NEEDED TO GET INTO YOUR LONG TERM MEMORY: “Precision is not accuracy!”
It’s why the standard deviation of sample means is *NOT* an uncertainty for the mean. The uncertainty of the individual elements must be propagated onto the mean in order to determine its uncertainty. You cannot calculate uncertainty from the stated values, you can only propagate given uncertainty.
He will never grok this.
Not this nonsense, again.
Technically correct, but in application wrong. Since the composition of air is relatively constant then temperature is proportional to heat. Sure humidity changes, but it is relatively constant, e.g. it is dry in winter. Over a timespan of decades, if you get a rising temperature trend, say the 1.1C/century rise in UAH it is meaningful.
James ==> This essay is about the error of averaging temperatures which are Intensive Properties.
The density of air is not constant under changing air pressure. The heat capacity of air changes with humidity — which ranges from 50 to 95%, even across relative small distances.
A substantial increase in the heat content of the climate system would be meaningful, but it cannot be proved by averaging temperatures from disparate locationms and times and conditions. Just can’t.
Why do you say the composition of air is relatively constant and then say the humidity changes? When humidity changes the composition of the air has changed which changes its buoyancy and thus its convection, conduction properties – all of which affect the temperature that mass of air you are measuring will exhibit.
Unless the humidity is also changing.
Kip==>
I agree with you Kip, that averaging temperatures may not provide meaningful results, but not exactly for your stated reason.* I made the point some 30 years ago in the first public talk I ever delivered about what at that time was called “global warming”. My reasoning is that the measurement of temperature produces a conditional quantity — it depends on a huge number of other factors almost none of which are ever stated, measured or quantified. In fact, in engineering classes I try to stress the point that a measured number is not useful unless one provides at the same time an estimate of its uncertainty. Almost never does a person stating a temperature do this. In fact, in a metrology class I taught at WSU I found that the engineering students would often not even determine if an instrument was calibrated properly before using it.
With regard to Briggs’s statement about time series I also point out in that same talk that time series are very difficult to deal with because measurements of temperature are not a sufficient sample to quantify even the mean (smoothed value) of a time series. They only become so when conditioned with the additional assumption that the time series is stationary. It is possible I think that Earth temperature is not stationary and does not conform to the concept of a central limit.
Well, that is my view.
*-In thermodynamics we can use intensive quantities such as enthalpy per unit mass, and adding them (or even multiplying them) can produce a perfectly valid result. I.e. in order to analyze output of a steam turbine we can use a state diagram based on per mass entities and then multiply by some factor to find a mass flow rate needed to produce a design power capability.
Kevin ==> It is, in fact, possible to discover the value of an Extensive Property from formulas which involve Intensive Properties.
“The ratio between two extensive properties is an intensive property. For example, mass and volume are extensive properties, but their ratio (density) is an intensive property of matter.”
Obviously, the formula works in several ways. Energy or heat content (enthalpy) is an extensive property, mass is an extensive property. “enthalpy per unit mass” is a ratio.
Kip, excellent post. TY.
BTW, I learned this stuff in high school. Pity most apparently didn’t.
A quibble. An average of temperature anomalies from some anomaly baseline has a legitimate meaning. It is what Roy Spencer of UAH posts. It just isn’t anything to do with global atmospheric heat content or the underlying ‘global warming’.
Rud ==> “It just isn’t anything to do with global atmospheric heat content or the underlying ‘global warming’.”
Yes, Spencer’s UAH records isn’t “nothing” But it is “fruit of the poisoned tree”.
“An average of temperature anomalies from some anomaly baseline has a legitimate meaning.”
How so? If you have a 1C anomaly in Fairbanks, AK and a 1C anomaly in Miami, FL on the same day does that tell you anything about the climate at each location? Does it tell one anything about the climate somewhere in-between the two locations? Does it actually tell you anything?
BTW, the uncertainty of an anomaly is inherited from the uncertainties of the components. Using anomalies doesn’t lessen uncertainty. If your component daily absolute temps have a +/- 0.5C uncertainty the average will have +/- 0.7C uncertainty. Start averaging all those and your uncertainty will grow. The anomaly generated from that very uncertain average will inherit the same uncertainty. Pretty soon the uncertainty overwhelms the differences you are trying to identify.
Tim ==> The anomaly is formed from averaged temperatures, which cannot legitimately physically be averaged, which do not, cannot, inform as to heat content or heat energy, not even momentarily.
After all that “breaks the rules of physics”, we get to uncertainty, original measurement error/uncertainty, etc etc.
But by that point Rud, doesn’t it become little more than an interesting abstract statistic? I agree that you could, theoretically, do anything you like with numbers; but trying to then relate the result to anything in the real world becomes completely meaningless.
Richard ==> Refer to the title of this series….
Using this logic one might make the argument that the radiant heat transfer equation Q = εσA(Th^4 – Tc^4) yields a meaningless result too since it subtracts the temperature, raised to the 4th power no less, of one body from another. Note that the subtraction here has similar semantics to a sum. The 4th power of the temperature and what it means is a whole other issue that I’ll pass on for now.
Similarly the hypsometric equation Tv_avg = (g/R)[(z2-z1) – ln(p1/p2)] must be meaningless as well since it explicitly computes the average virtual temperature of a layer between height z1 and z2. BTW…the hypsometric equation can be derived from the ideal gas law PV=nRT and the hydrostatic equation ∂p/∂z = -∂p and involves an integration function of T which as you know has similar semantics to a sum function.
Unfortunately we’re going to have to indict the QG height tendency equation [σ∇^2 + f0^2(∂^2/∂p^2)∂Φ/∂t = -[f0σVg•∇(ς-f)] + fo^2∂/∂p[Vg•∇(R*Tv/p)] as well. Those familiar with QG theory may notice that the second term on the RHS of that equation is the differential temperature advection term which is based on the divergence of the gradient of the virtual temperature field. And remember from your vector calculus that divergence is the sum of the partial derivatives of the spatial components of the vector field. In other words, temperature (or least the partial derivatives) are being summed here. But, of course, all of that is meaningless per the argument put forth in this article as well.
Do you see the problem?
bdgwx ==> You make a spurious point.
“The ratio between two extensive properties is an intensive property. For example, mass and volume are extensive properties, but their ratio (density) is an intensive property of matter.” This goes the other way as well. In your thermodynamic equations, T is in K, of course.
When formulas are used to find Extensive Values…..etc.
Read the paper referenced.
https://www.fys.ku.dk/~andresen/BAhome/ownpapers/globalTexist.pdf
I’m addressing the statements..
One cannot average temperatures.
and
3. A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.
and
4. Dividing meaningless totals by the number of components – in other words, averaging or finding the mean — cannot reverse this outcome, the average or mean is still meaningless.
I’m providing real world cases where temperatures are summed and an average temperature is computed. Doing so is useful, actionable, and meaningful.
And it goes way beyond trivial sum or average concepts. Scientists create temperature fields, They turn them into vector fields like with the gradient operation. They turn them back into scalar fields with divergence operators. Scientists do all kinds of things to temperatures and temperature fields; the least of which is summing and averaging them.
It might also be interesting to note that UAH sums temperatures as well. In fact, the formula for the TLT temperature at any specific spot (not an average) is as follows:
Tlt = 1.538 * Tmt – 0.548 * Ttp + 0.010*Tls
The global average TLT is then…
Tlt_global = Σ[Tlt_x, 1, N] / N
…where Tlt_x is the lower troposphere temperature at location x and N is the number of locations in the sample.
I forgot to mention that there are lot of skew-t calculations that involve summing temperatures as well. For example, Convective Available Potential Energy metric. The formula is CAPE = g∫[(Tparcel – Tenv)/Tenv, Zlfc, Zeq, dZ]. You can replace Tparcel with Tparcel_avg. This is often referred to as MLCAPE (mixed layer CAPE). CAPE is a useful, actionable, and meaningful quantity. Again, I’m just pointing out that temperatures are summed all of the time.
“Do you see the problem?”
The problem is that you are confusing intensive and extensive properties!
weight = g X mass. Mass = density X volume. Weight is an extensive property. Mass is an extensive property. G (i.e. force) is an extensive property. Volume is an extensive property. Density is an intensive property.
You can add/subtract weight. You can add/subtract mass. You can add/subtract volume. You can’t add/subtract density.
You can calculate extensive properties from intensive properties. You can calculate intensive properties from extensive properties. You can average extensive properties because you can add/subtract them. You can’t average intensive properties because you can’t add/subtract them.
TG said: “The problem is that you are confusing intensive and extensive properties!”
That’s not the problem. And your post has little if anything to do with my post. If you want to address something I actually said then I’d be more happy to engage with your point as long as it is relevant. But I’m not going to engage with yet another one of your strawmen.
“ Q = εσA(Th^4 – Tc^4)”
Nice job of dodging! Tell us in this formula what the extensive properties and intensive properties are!
Note: “εσA” converts the intensive property of T into an extensive property of Q.
What does Th^4 – Tc^4) represent by itself? It doesn’t equal Q! It doesn’t actually equate to *anything*!
I’m not surprised you refuse to answer. You don’t understand the subject at all!
Is Th^4 – Tc^4 a sum of an intensive property or not?
“Is Th^4 – Tc^4 a sum of an intensive property or not?”
NO!
A simple, straightforward thought experiment for you.
I push you out of the air lock of the starship Enterprise into the vacuum of space between Mercury and the Sun.
I then simultaneously transport a cube (T1) of some futuristic substance from the surface of Mercury and a cube (T2) of the same stuff from the corona of the sun to right in front of you, both with temperature measuring devices attached.
Questions:
You think T^4 is extensive?
Answer my questions to you first!
You’re deflecting and diverting. I’ll ask again. Do you think T^4 is an extensive property?
You first! I asked *YOU* first.
I think T^4 is intensive. I also think you can subtract one T^4 value from another T^4 value. I also think T^4 has meaning. Specifically we can say that for bodies A and B with Ta^4 > Tb^4 that body A is warmer than body B and will have a higher radiant exitance and heat will flow from A to B in proportion to Th^4 – Tc^4. The bigger the difference in Th^4 and Tc^4 or more simply Th and Tc the more heat that will flow. Almost everyone will agree that is meaningful, useful, and actionable.
Actually T is intensive. Even if you use an exponent, it remains intensive. The fact that it used to calculate a flux doesn’t change its property. Even if you split a mass the temperature of both will still be “T”.
You are trying to decide if the radiant flux between two bodies is intensive or extensive. It is neither. It is not a property of either body. If you look at the basic S-B equation, it is described for a single black body at a given temperature.
The wiki I’ve referenced before will give you an idea about conjugate properties and transfers of those properties.
Yes. I know T is intensive. Radiant exitance is intensive as well. The net flux between two bodies is neither. Yet σTh^4 – σTc^4 is still a meaningful and useful metric.
BTW…don’t think the irony of how you promote CDD, HDD, and/or GDD is lost on me.
You forgot FDD, JDD, and SDD.
bdgwx really doesn’t understand physical science at all. He can’t distinguish between an integral of a curve, i.e. the area under the curve, and the mid-range value between max and min. He’s a statistician with no physical science training, no engineering training, and apparently no calculus training. Anyone that thinks all uncertainty cancels in a non-normal distribution and that the standard deviation of sample means is the uncertainty of the population mean is hopelessly lost in statistics textbooks that never address uncertainty.
Somehow, without any real metrology experience, he is now the world’s foremost expert on the subject.
It is obvious that he didn’t read the Essex paper, including that an ISO committee tried and failed to come up with a standard averaging document.
And in lieu of opening his mind went on another formula hunt for anything he thinks disproves Kip’s subject.
(And I had forgotten that DD is degree-days!)
If he read it he didn’t understand it. It is pretty intense and takes some pondering to actually understand.
Indeed yes.
“BTW…don’t think the irony of how you promote CDD, HDD, and/or GDD is lost on me.”
Those are *NOT* averages. Those are integrals. The area under the temperature curve! There is no dividing to come up with an average. The area under the curve *is* an extensive property!
As we’ve discussed in the past, the equation (Tmax-Tmin)/2 doesn’t give you an average! It gives you a mid-range value. The climate scientists even mis-name this value. The more closely the daily temperature curve approaches a sine wave the closer the *average* daytime value approaches 0.67 * Tmax and the “average” nighttime value approaches 0.67 * Tmin!
You really don’t understand physical science at all. You just cherry pick equations you think might stick to the wall when you throw it against the wall.
Is Tmax + Tmin a sum of an intensive property or not?
Go read the paper.
“Is Tmax + Tmin a sum of an intensive property or not?”
Tmax is an intensive property. Tmin is an intensive property.
(Tmax + Tmin) is meaningless. It’s nothing. It’s neither intensive or extensive.
You *can* calculate an extensive property from an intensive one using a functional relationship. You can then add or subtract those extensive properties.
*YOU* are letting algebra confuse you. The functional relationship is Q = εσATh^4 – εσATc^4.
Algebraically you can factor out the εσA piece. That doesn’t mean you are adding intensive properties. You are still adding extensive properties. You don’t have to do the factoring!
Tmax + Tmin is not even useful for calculating the average of a sine wave (daytime) or exponential decay curve (nighttime).
By that logic CDD, HDD, and GDD are also meaningless then.
“By that logic CDD, HDD, and GDD are also meaningless then.”
Why are they meaningless? They are areas under a curve. An area is an extensive property. Why are extensive properties meaningless?
TG said: “*YOU* are letting algebra confuse you. The functional relationship is Q = εσATh^4 – εσATc^4. Algebraically you can factor out the εσA piece. That doesn’t mean you are adding intensive properties. You are still adding extensive properties. You don’t have to do the factoring!”
I forgot to address this earlier. I’ll do so now.
You think εσAT^4 is extensive?
“You think εσAT^4 is extensive?”
εσAT^4 is the power radiated from a body. Power is measured in joules/sec or in kg-m^2/t^3
Is a kilogram an extensive property?
Is a meter an extensive property?
Is a sec an extensive property?
Does multiplying or dividing extensive properties make them intensive?
I know what εσAT^4 is. I’m asking if you think it is an extensive property?
If I have a cube radiating power toward another cube and I cut the radiating cube in half what happens?
The power radiated is cut in half but its temperature stays the same.
So, is power an extensive property? You bet. It depends on the mass of the object. The temperature does not.
You should have been able to figure that out from the dimensional analysis I provided you.
For the record I think an argument can made that power is extensive because, at least in this case, if you change the amount of matter you change the power. P is dependent on the size of A. Multiplying intensive and extensive properties with other constants can make an extensive property. Is power always extensive though?.
What if we drop the A and think about the canonical SB form εσT^4? That is W/m2 which everyone would agree is intensive since radiant exitance is independent of the size of the body. We can then do εσ(Th^4 – Tc^4) or εσTh^4 – εσTc^4 to get the net flux across the boundaries of the hot and cold body. Here we have added (technically subtracted) two intensive properties to produce something useful and meaningful.
The point is this. You can add (or subtract) temperatures of different bodies to create useful and meaningful intensive quantities. You can multiply or divide temperature with something else to create useful and meaningful extensive properties. You can even raise temperature to the 4th power. You can do all kinds of things with temperature. Claiming you can’t do this or that with temperatures can be easily challenged with real world counter examples.
“What if we drop the A”
In other words let’s just create a phantom world and play like we actually live there.
Yeah! That’s the ticket We can prove anything in Bizarro world!
I assure you and the rest of the WUWT audience that the Stefan-Boltzmann Law describes the world around us. It may be bizarre, but it is very real. I know…you challenge the SB law. I have neither the time nor the motivation right now to defend it. I’m just telling you how it is.
Whoa! bgwxyz hath spake, so mote it be!
The SB law predates me by a considerable amount of time. It was the pioneers of thermodynamics Stefan, Boltzmann, Wein, Planck, etc. that hath spake. It’s also not a law just because they said so. It’s a law because it has yet to be falsified.
I am of course referring to your bizarre version.
Again…εσT^4 isn’t mine to claim; version or otherwise. And bizarre as it may be it still describes the real world around us.
That is *NOT* the only term at play in the real world. There is also a conduction term and convection term at play.
It’s a law when the restriction of equilibrium is at play. Read Planck again, this time for meaning.
Correct. If they are not at equilibrium, then a gradient term must be introduced, (ΔT/t), and ΔT doesn’t have to be linear either. S-B as normally seen is for an infinitely small point in time, i.e., equilibrium.
It,s a law because it is confirmed by experiment and the experiments confirm/validate the mathematical predictions.
I’m glad to hear that is your position. Maybe you can convince Tim and Carlo Monte of that. I haven’t had much luck so far and I’ve lost the motivation to continue trying.
You need to study some thermodynamics. There are three physical processes at work in the transport of heat. They are radiation (S-B equation), and conduction, and convection. They are all in effect in the atmosphere.
It is one reason the “radiation diagrams” you see fail in so many ways. They uses averages too and don’t take everything into account. Gradients of heat flow for one, both in the surface and in the atmosphere.
Absolutely right! They are simplified beyond the point of utility.
from wikipedia: “In physics, Planck’s law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment. (bolding mine, tg)
I know you are just going to say this is wrong with no actual refutation to actually prove it is wrong. It’s a religious dogma issue with you.
Planck himself wrote in his Theory of Heat Radiation says: ” In a region where the temperature of the medium is the same at all there is no trace of heat points conduction.”
In other words, equilibrium!
And the sun is constantly moving so no equilibrium except at vanishingly small points in time.
They only confirm it for objects in equilibrium, no convection and no conduction.
As has been pointed out to you any number of times, S-B assumes an object in equilibrium, no convection, no conduction.
S-B has no conduction and convection term – meaning the only heat transfer process that is at play is radiation.
The world around us is *NOT* in thermal equilibrium. That may seem to be bizarre to you but it is *very* real.
You are trying to gaslight everyone. You failed.
Everyone read up on the kinetic theory of gases. It will help.
http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/imgkin/kintem3.gif
What a surprise, Stokes is the first commenter! His comment is not blatantly wrong, just misleading as usual. What he said about more energy lost to Space is true. What he did not say is how CO2 controls how much energy is lost to Space, as no one knows, and the rate cannot be calculated from First Principles.
Actually, the comment is just a quote from Roy Spencer, in WUWT as linked.
Nick ==> Yes, even recognized it. But why did you quote Spencer, with whom you more generally disagree?
Spencer is quite good at debunking the most foolish ideas that circulate. His list of ten top arguments that don’t hold water is worth re-reading. At the time (2014) scientific standards at WUWT were not so low, and most of them did not prevail. Some, as from Sky Dragons, were even banned. But they keep coming back now, at higher volume.
Actually a range of probability could be developed. The problem is that conduction and convection is involved making it very complicated.
It is more complicated than that. How does ppm CO2 vary with altitude? At what altitude does the atmosphere become translucent to 15 micron IR? What exactly is water vapor doing up there? Wow…
If you have a set of figures you can average them – in several different ways. ANY set of figures.
So you can certainly average a set of temperature readings. The question is, what does that figure actually represent? I suspect that the figure does not actually represent what most climate scientists think it does….
dodgy ==> Right you are — that’s is why this is a series about NUMBERS…you can mathematically average any set of numbers.
You CAN calculate a mean value of a distribution. But even using just numbers, you have a meaningless number without also knowing the other descriptors of the distribution the mean represents.
50 is a mean. What values contributed to it?
That’s the reason I always say global temperature anomaly index. As an index it’s somewhat meaningful, but no strict physical meaning.
Edim ==> Indexes are an interesting concept, but often their physical, real-world meanings range from obscure to entirely unknown.
What would you say “global temperature anomaly index” means? (Just curious…)
Hard to explain. Index indicates (same etymology). I simply think that an uncorrupted GTA index is a somewhat useful measure of the Earth’s surface/atmosphere thermal energy.
Edim ==> I’m quite sure it is an indicator of something. Maybe a useful indicator of ranges needed in thermometer design?
The problem I am writing about is that there is no rational choice for GTA (GAST) and no physically correct way to determine such a numerical result.
“I simply think that an uncorrupted GTA index is a somewhat useful measure of the Earth’s surface/atmosphere thermal energy.”
So you must also think that humidity, pressure, wind, etc are all the same everywhere on the earth?
If they aren’t all the same then what is the “index” telling you?
Atmospheric temperatures are smooth, no discontinuities, so any path you take between locations that have different temps will necessarily pass through a location that has the average temperature of the starting and ending points when measured at each location in the same manner.
“when measured at each location in the same manner.”
Does a passing cloud create a discontinuity?
Have you ever driven into a stationary weather front?
Jim ==> I have sailed into one…..
The transition zone may be limited but no discontinuity.
You’ve obviously never experienced a gust front where temps can change drastically.
That might be true if you could measure the temperature *continuously*. What measuring station does that?
I have thought this for a long time, we live by, actually on, the sea, the temperature readings for our city are derived from a station at the airport. There is generally a 2 to 5 degree difference. if averaging was an actual or accurate indicator then the temperature halfway between the two should be 1 to 2.5 degrees above the sea level temp which it isn’t. Nick’s examples below are asinine. A tub of bath water is a single thing and room temperature varies depending on where you are sitting, you cannot find an average in that sort of environment.
Kip, I enjoyed this post. But truth be told I have enjoyed them all.
mkelly ==> Well, thank you! (I hope, of course, that you are referring to my posts….)
I’M NOT IGNORING YOU!
But I am out for the remainder of the day and will not be back online for about 20 hours.
Please feel free to continue the discussion among yourselves — though this post is buried pretty deep already.
Note: The Danielle Dixson story has far-reaching implications for science — CliSci, medicine, biology, etc. Pielke Jr. wrote about it today as well.
Also, about this statement-
“A one cubic meter block of stainless steel at 70°F contains even more heat energy. “
Specific gravity of stainless is 7.9 so about 7,900 kg per cubic meter vs water at 1,000 kg.
Stainless has specific heat capacity of 468 j/(kg K) while water has a specific heat capacity of 4,181 j/(kg K) at 70 F (294 K) the heat stored in the stainless is about 3.7 MJ and in the water 4.2 MJ.
The cubic meter of water actually stores more heat.
The extraordinarily high heat capacity of water effectively moderates temperature changes in the natural environment.
Kip, I wonder if you have considered that the gas laws support what you say here; in that they say that Volume is inversely proportional to temperature?
This becomes all too apparent when one looks at the thermodynamics of the water Evaporation Process, particularly at the surface of the Oceans; for here Solar Radiation gets absorbed and the enthalpy involved is converted to Volume rather than Temperature. This being expressed as “Latent Heat”intrinsic to the Vapor which had been generated. Meanwhile the Oceans never get much above 30C in spite of millions of years of this relentless solar radiation. Why not one may well ask?; but that is another story.
IMO the whole Mindset around statistical analysis relating to Climate needs a good shake up. ; but unlikely to happen as too many so called scientists appear to have sold their souls to the intense political pressures we witness today.
Good luck with your efforts.
Regards
Alasdair
Be careful what you are looking at. Pressure is also a factor. Are you describing a constant pressure experiment?
Alasdair ==> This “IMO the whole Mindset around statistical analysis relating to Climate needs a good shake up.” is certainly true.
I think the real question is: not enough money in the government’s climate budget to move the Glenns Ferry structure to a proper place? From 2009, I see-maybe it’s been done.
Just an editorial comment: The chart is impossibly small to actually read. It’s too small in the body of the article, and there is no allowance to click on it to enlarge it. Sorry to say, but for me, that makes it a useless visual. I’d like to actually study the detail of it.
Right click on the graphic and open it in a new tab. Then use the zoom feature of your browser to expand it so it becomes readable in that new tab.
Robert ==> My apologies, here is the link to the original page:
https://weatherspark.com/m/9454/8/Average-Weather-in-August-in-Topeka-Kansas-United-States
Scientists all over the world use the global average temperature statistic.
Skeptical scientists use the statistic to show that climate models are overpredicting the rate of global warming.
Some scientists argue that the statistic is not accurate enough to be useful until recent decades.
I have never read any scientist claim the statistic was worthless.
But that’s what Mr. Hansen is implying.
And if he is not implying that, he needs better communication skills.
But what do all those scientists know?
They are just scientists.
Mr. Kip Hansen thinks he knows better.
The scientists must be fools to waste any time with a global average temperature statistic ?
Hansen says “One cannot average temperatures”.
Meanwhile, there are many averages of temperature measurements.
The global average temperature statistic is worthless, implies Mr. Hansen. And to convince readers he is smarter than nearly all the scientists in the world, Mr, Hansen states “Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about.”
In plain English, Mr. Hansen trashed the global average temperature statistic, and he refuses to debate it. And if you disagree with him, he implies that you are a fool. This resembles a leftist “debate” style.
Richard ==> You are demonstrating that you have not read the referenced paper, Essex et al. which was published in the Journal of Non-Equilibrium Thermodynamics.
Once you have read that paper, and studied up on the differences between an Extensive and Intensive properties, please check back in with your newly informed opinion.
“I have never read any scientist claim the statistic was worthless.”
So what? Science is not consensus. Apparently you haven’t read any of Pat Franks papers.
“In plain English, Mr. Hansen trashed the global average temperature statistic, and he refuses to debate it.”
What is there to debate? If you add 32F in Pikes Peak with 50F in Denver what do you have? It’s not length that you can add and subtract. It’s not a mass that you can add and subtract. If you add the two together and divide by two you certainly don’t have anything like an “average climate” or “average temperature” for the region.
In fact, if you think about it what do you have if you have a 6′ board and an 8′ board averaged together? What does the average tell you? Can you build a stud wall as high as the average value? How would you do it? Cut one board off and try to scab the remainder onto the shorter board? How would you join them? If you overlap the 6′ board and the 1′ piece you still won’t reach the average height of 7′.
If you have 1000 men whose average height is 5′ 9″ tall can you order 1000 T-shirts to fit the average height and expect them to fit everyone?
You have to be *very* careful using averages. In the real world they don’t always tell you what you think they do – that only happens in math world.
So let me get this straight:
“3. A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.”
So assuming the converse that “a sum over extensive variables always carries a physical meaning” except, that is, when a sum over an “extensive” variable carries no physical meaning as in the example of a sample of fish lengths in the comments;
Steven ==> Length is an Extensive Property and can be added, averaged, etc.
steven candy
Reply to Kip Hansen
August 10, 2022 9:32 pm
Lengths of a sample of fish can be added for what purpose? To represent one mega-fish OR the fish all lined up head to tail. As ridiculous as it sounds.
“4. Dividing meaningless totals by the number of components – in other words, averaging or finding the mean — cannot reverse this outcome, the average or mean is still meaningless.”
With this simple dichotomy in properties of variables (intensive vs extensive) you conflate your spurious dichotomy of which of these two types of variables can be validly averaged. To which I give a counter-example to your general theory;
Counter-example: For a normal distribution the expectation of the sample median equals the expectation of the sample mean and since the sample median is not based on the sum of sample values but their rank order it is interpretable as a measure of central tendency and therefore so does the sample mean irrespective of the interpretability of the sum of sample values.
So already a couple of inconsistencies in your theory.
I did a google scholar search on the keyword sentence “extensive versus intensive variables” with only two references by the same author coming up with one open access;
https://escholarship.org/uc/item/5mp6r34r.
No mention of “mean”, “average” or “sample” in that reference, and interestingly in Section 2 the author states
“One of the more primitive mistakes rests on the belief that the classification extensive-intensive is basic for the development of thermo dynamics. It is not. The square root of the volume clearly is neither extensive nor intensive; yet it is a well-defined property and all thermo dynamic knowledge could be expressed if we replace the volume by the new variable. It would be awkward, cumbersome and inefficient. But science could live with it. It is obviously wrong to say that only extensive and intensive variables exist.”
When does air temperature data ever have a normal distribution?
Averaging time-series data from multiple locations is not sampling a normal distribution!
They will never understand. Statistic textbooks simply do not give any knowledge of real world usage of statistics. All data values are 100% accurate and they all form a perfect distribution that can be analyzed using standard deviation and mean.
Exactly. There are a lot of metrics in widespread use that are both meaningful and actionable yet lack an obvious physical description. You and I could spend all day going back and forth on who can come up with the most mind-bending metrics out there. But more to the point not only can temperatures be summed (I provided several real world examples above), but science does all kinds of weird and mind bending things with temperatures that turn out to be quite useful. This is true for many metrics regardless of whether they are extensive, intensive, or something else. Just because we struggle to provide physical descriptions to these metrics does not make them any less useful. Their meaning is still objectively defined by how they are calculated.
Did you read the Essex paper yet?
Didn’t think so.
Metrics are only useful if they describe the real world. The average temperature reached from using the temperatures at Pikes Peak and Denver in July doesn’t really give a metric that is useful in the real world. Do you wear a coat and gloves based on the average?
But useful for whom?
Someone expounding on the impact of a 0.002 C increase in some derived averaged reported temperature over 10 years all over the planet is never going to have a scintilla of effect in any creatures’ lives.
“Bullshit Man” would only spend 2 seconds on a fly-in / fly-out visit for this.
Mr. said: “But useful for whom?”
The radiation heat transfer equation is useful to those analyzing the heat transferred via radiation between two bodies.
The QG height tendency equation is useful to those analyzing how geopotential heights change.
The hypsometric equation is useful to those analyzing the thickness of atmosphere layers.
The convective available potential energy equation is useful to those analyzing thermodynamic buoyancy above the LFC.
Different metrics are useful to different people. Just because someone doesn’t understand them or can find no use for them does not mean that they aren’t understood and useful to someone else.
How about telling us the equation that relates CO2 to GAT, and not just for the last 30 years, but for the last 150 years.
For the last 40 – 50 years at least, climate science has been doing nothing more than curve fitting to a time series. Where are equations going to come from that allows accurate enthalpy predictions that can be verified? I can’t find a paper, not one, that tries to find a relation between enthalpy and CO2 or between enthalpy and humidity on a global basis. Why not? Are these not of interest in determining what the globe is doing?
“The radiation heat transfer equation is useful to those analyzing the heat transferred via radiation between two bodies.”
That’s not an intensive property, it’s an extensive one calculated using an intensive property.
Why do you *always* insist on trying to prove you can add and subtract intensive properties by using extensive properties as proof?
note: CAPE is an *extensive* property calculated using an intensive property. It’s unit is joules/kg, both extensive properties.
Tim Gorman said: “That’s not an intensive property, it’s an extensive one calculated using an intensive property.”
Kip Hansen says “A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.”
BTW…You think W/m2 is extensive?
Tim Gorman said: “Why do you *always* insist on trying to prove you can add and subtract intensive properties by using extensive properties as proof?”
I’m just pointing out real world counter-examples to Kip’s argument.
Tim Gorman said: “note: CAPE is an *extensive* property calculated using an intensive property. It’s unit is joules/kg, both extensive properties.”
You think j/kg is an extensive property?
“You think W/m2 is extensive?”
If I have one joule flowing to the left and two joules flowing to the right, what is my net joule flow?
If I have two times, t1 = 2 sec and t2 = 4 sec, what is the interval between them?
If I have a dining room table with an area of 12 sqft and I add a leaf in the middle of size 3 sqft, what does the area of the dining room table become?
“I’m just pointing out real world counter-examples to Kip’s argument.”
No, you aren’t. You are averaging extensive properties and then calculating an intensive property from the average extensive property. That is *not* the same thing as averaging intensive properties.
“You think j/kg is an extensive property?”
Again, if I have one joule flowing left and two joules flowing right, what is my net joule flow?
If I have a 1kg chunk of iron in a bucket and I add a 5kg chunk of gold to the bucket, how many kg do I have in the bucket?
You’re not answering the questions.
Do you think W/m2 is an extensive property?
Do you think j/kg is an extensive property?
I’m not asking whether you think joules, seconds, square meters, or kilograms are extensive. I’m asking if you think watts per square meter and joules per kilogram are extensive.
I’m asking you this because I want you to really think about it.
“You’re not answering the questions.”
Of course I am. You don’t know enough physics to understand.
“Do you think W/m2 is an extensive property?”
I answered you. Go look up what a watt is!
“I’m not asking whether you think joules, seconds, square meters, or kilograms are extensive.”
You don’t know what the definition of watt is, do you?
If I give you a metal bar at T1 and then help you cut it in half does the total temperature become 2*T1 for the bars? Does the temperature of each bar become T1/2?
Does the mass of each separate bar equal M1/2? Does the total mass equal M1? Does the total mass for both together remain M1?
Extensive properties add/subtract, be they joules, kg, seconds, or meters.
Intensive properties don’t. The temperature of each piece of bar remains T1, not 2*T1 or T1/2. If I cut the bar in 50 different pieces, the temperature of each will still be T1. If I put them all back together the temperature of the re-constituted bar will remain T1.
If you are in space and I give you two bars that are in infinitely insulated containers, one at T1 and one at T2, one in your left hand and one in your right hand, is there someplace between your two hands that will be at temperature (T1+T2)/2? Will the total mass you are holding be M1 + M2, i.e. will you need more force to accelerate yourself to a certain value than if you were holding only one bar? Or no bar?
Everything you have listed is an extensive property, joules, meters, kg, and seconds. When you cut a bar in half the mass (kg) goes down by a factor of two. The temperature remains the same. One is an extensive property and the other isn’t.
Adding the temperature of the first half-bar to the temperature of the second half-bar makes no physical sense. Adding the mass of the first half-bar to the mass of the second half-bar *does* make sense. Calculating the average of the temperature of the first half-bar and the second half-bar makes no physical sense, it is nothing more than mental masturbation because you are just going to wind up back at T1, the temperature of each half-bar.
It’s the same with density. How do you add densities to create an average? What physical sense does the average make? If I have a gold piece of density D1 and a silver piece of density D2, what does the sum of the two mean in a physical sense? What does their average density mean in a physical sense?
You can do all kinds of mathematical manipulations of numbers on a number line. That doesn’t mean those manipulations make sense in the physical, real world we live in. If it makes no physical sense to add the temperatures of two different objects then what kind of physical sense does their average make?
So you think W/m2 and j/kg are extensive? Is that correct?
Absolutely!
If I have a cube radiating W/m^2 and I cut the cube in half the radiated power gets cut in half. If I have two conductors carrying an rf signal and I cut the driving voltage in half, the amount of signal goes down. If I cut the mass of an object in half it takes half as many joules to raise it the same distance as the original mass.
Extensive properties can be divided into parts and the extensive properties will change. Intensive properties will not change when the subject in question is partitioned.
It’s not obvious from your posts that you can tell the difference.
If you take a parcel of air and divide into two halves, do the amount of joules remain the same in each half? Does the mass of each half remain the same?
Intensive means the measurement stays the same when you combine or halve a given object. The two quantities that make up the specific value are extensive.
Ratios (indexes) in many cases are intensive. If you double J/kg, the ratio remains the same. If you halve J/kg, the ratio stays the same.
But, be careful, can you really average ratios and get a value that is meaningful? Ratios or indexes are most times used to calculate other values and are meaningless by themselves.
Both W/m2 and j/kg are intensive.
Steven ==> I may have mentioned this before, but it looks like you have not done your homework…please read the Essex et al paper referenced in the essay. Then check back here. Thank you.
Pip. I have given a proof that your general theory is wrong using the counter-example I give. Your theory was not restricted to temperature it was very general. All the above comments about temperature not being normally distributed miss the point entirely. One counter example (e.g. a normal distribution) is enough to disprove a general theory. Just to repeat your general theory is stated in your point 4. Let someone disprove my counter example, then I will read your referenced paper. Your homework is go and get some formal qualifications in mathematical statistics, then publish your theories in peer reviewed journals, then write your essay. Science journalists and bloggers should not try and make up the science they are supposed to be reporting on just like news reporters should simply report and not fabricate the news themselves.
Sorry that should be Kip. Typo
Steven ==> Read Essex et al and then explain to us their viewpoint. If you cannot do that, then you do not understand their paper. You are not required to agree — but you are NOT allowed to criticize if you do not undertand.
I am responding to your essay in which you propose a general theory of statistics. You have not addressed my counter-example to your theory. While my counter-example stands unchallenged because it is correct your general theory is kaput! End of story!
Steven ==> I do no such thing. I report about an interesting and valid science question. I am waiting for you to respond to the paper being referenced in an adult way.
We’re trying to discuss your thesis here; not the thesis put forth in Essex et al. 2007.
bdgwx ==> You apparently misunderstand. I am a science journalist, I write about science — I don’t do original research, nor do I propose “theses”. I am writing about the ideas in the Essex rt al. paper.
Got it. You’re just summarizing their thesis.
If you have correctly summarised points from the Essex et al paper with your thesis in Point 4 my counter-example still stands correct and Point 4 and where-ever you dug it out of that paper is still wrong. A counter-example has to be disproved to resurrect a theory.
I accept and concede this point and withdraw the comment that its your theory. Evenso, my counter-example for the contention that averages of Intensive variables have no real-world application or comonsense interpretation still stands. It is not really a theory since no proof is given by Essex et al. of the second sentence as far as it infers a sample average in their contention on page 5; “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome“. The discussion about temperature as an Intensive variable does not address the above general contention. I could find no proof of the above contention in their paper. If there was my counter-example would not be correct BUT it is in fact correct so that would explain their lack of a proof. Some contentions are harder to prove than to disprove using the counter example method. The issue they raise of different statistics for estimation of central tendency [their Eqn(9)] of simple average, harmonic mean etc, (I could add the geometric mean) does not invalidate these as alternative estimates of the population mean (central tendency) and all have a real-world interpretation whether for Intensive or Extensive variables. Which estimate is minimum mean square error depends on the underlying distribution.
“Read Essex et al and then explain to us their viewpoint”
I was criticised above for appealing to Authority, first by quoting Spencer, and then by invoking the WUWT (!) practice of posting average temperature plots on the front page, without error bars. But this seems to be a very strange appeal to Authority. Nobody actually quotes Essex et al, or seems to have a clue what they are saying.
I read Essex et al when it first came out in 2007. Despite a math veneer, it is really just an opinion piece like this one. Have you read the various rebuttals, eg here? I have.
This reminds me of a common contention on WUWT:
All those scientists over the years are wrong. Can’t quite explain why, but our man says so, and he is a professor!
Nick ==> Now, I suppose you understand their viewpoint, and thus have the right to disagree if your wish.
The others here didn’t bother to read, and having read, demonstrated that they still didn’t understand. One of them finally read to understanding, then he earned the right to disagree.
I happen to agree — though it is not clear to me why you don’t agree with Essex et al — you haven’t said.
“though it is not clear to me why you don’t agree with”
Well, here is one thing from their conclusion:
“The purpose of this paper was to explain the fundamental meaninglessness of so-called global temperature data”
I don’t think that is a slip. In rejecting the average, they say the data is meaningless, which is a logical conclusion from the arguments about the average. It’s true that if you aren’t allowed to do arithmetic with the data, it is meaningless. But then, how can we ever know anything? We have a huge temperature record, which we are enjoined to ignore.
There is another misapprehension that they have, in common with you and other commenters. That is, that the role of temperature is just as an indicator of internal energy, and so needs to be enhanced with information about enthalpy and maybe other things. But as I said above, the important role of temperature is as a potential for heat flux, where it stands on its own. Fourier’s Law Flux=-k ∇T.
Suppose you have a warm bath and a saucepan of boiling water. Which has the greater internal energy? – the bath. But it is the saucepan that can harm you. The reason is that contact with the water creates a temperature gradient, which allows heat inside you to reach temperatures which can denature proteins etc. That is a parable for the effect of an overheated atmosphere.
“But then, how can we ever know anything?”
By doing it right. Use enthalpy, not temperature. Track minimum and maximum temps separately. Provide propagated uncertainties from the individual measurements through the calculations of means and anomalies. Provide variances for the base and derived distributions. Account for different variances between winter and summer temperatures. Account for the multi-modality created from combining northern hemisphere and southern hemisphere temps. Stop using mid-range values which can be caused by widely different climates thus masking actual climate.
“But as I said above, the important role of temperature is as a potential for heat flux, where it stands on its own. Fourier’s Law Flux=-k ∇T.”
The climate models don’t output flux, they output temperature.
““The law of heat conduction, also known as Fourier’s law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area, at right angles to that gradient, through which the heat flows.””
∇is merely a vector differential, so you aren’t really snowing anyone with this. It translates to δ/δx, δ/δy, δ/δz.
So flux is associated with a temperature differential – and how does the temperature in San Diego and the temperature in Denver create a temperature differential gradient thus creating a heat flux?
“Suppose you have a warm bath and a saucepan of boiling water. Which has the greater internal energy? – the bath. But it is the saucepan that can harm you. “
So what does that have to do with averaging the temperatures of the bath and the saucepan to come up with an average temperature?
Essex covers this pretty well on Page 6. I have yet to see anyone refute his generalized analysis.
Nick ==> Do you see that your objection is not based on their findings or how they arrive at their conclusion — but you find the conclusion “objectionable”.
I’m not sure where the “misprehension” bit is from — is that something you are saying, something you think I said (I did not), or something from some other reader?
I would disagree that Essex et al enjoin us to ignore the temperature record altogether — they object to a misuse or misanalysis of the data — averaging to get a GAST.
Your last paragraph is trivial (scientifically) and an inept parable. If one accepts the versions of GAST being circulated by various groups, the Earth hasn’t even reach what NASA and others consider to be an “Earth-like planet’s” average temperature of 15°C — which means that “overheated” is not an accurate description. 20°C might be overheated….but today’s temperature (if one accepts GAST) is still running a little cool.
“an ordinary arithmetic mean will enhance the common signal in all the measurements and suppress the internal variations which are spatially incoherent”
Really? Using the mean does nothing but smooth out variation. It decreases the variance in the data. How does that enhance the common signal?
“Temperature itself can be inferred directly from several physical laws, such as the ideal gas law, first law of thermodynamics and the Stefan-Boltzmann law,
In other words temperature has to be inferred from extensive properties. How does that prove that temperature is not an intensive property that can’t be directly averaged? If you have to average some extensive properties in order to calculate an intensive property which have you averaged, the extensive properties or the intensive properties?
If the rest of the rebuttals are like this then they really aren’t rebuttals!
“One counter example (e.g. a normal distribution) is enough to disprove a general theory.”
How do you get a normal distribution of temperature? Your counter-example is just plain wrong.
The *only* way to get a normal distribution is to have multiple measurements of the same thing. You can take all the measurements of the same thing you want and generate a normal distribution for either extensive or intensive values. E.g. you can take multiple measurements of density of a metal bar but if the bar is homogeneous all you’ll get is the same value multiple times with perhaps a small deviation because of measurement uncertainty. But you can’t create a normal distribution from measuring the density of an iron bar, a silver bar, a gold bar, and a lead bar! You’ll have multiple measurements but they will *not* be a normal distribution. In fact, if your measurement device has sufficient resolution you could measure the density of 100 lead bars and *still* not create a normal distribution!
But you *can’t* take multiple measurements of the intensive property of different things and create a normal distribution. Take a simple thermometer. Every time you take a reading you are taking a measurement of a different thing. How do you create a normal distribution from measuring different things?
As Duane has pointed out: “Any statistical variable, including measured temperatures, must represent a sample population where all members of the population being measured are alike or share the same key attributes of concern. If the measurements are not derived from a real population of shared attributes, then any statistical calculation of that population is meaningless.” (bolding mine, tg)
If you can’t add intensive properties of multiple things then exactly how do you create an average since they must be summed in order to create an average!
I cannot seem to get through to some of you the fact that Kip’s theory is general since it only specifies Intensive versus Extensive variables and the statistical operation of calculating a sample average. Therefore this theory assumes it applies for every and all statistical distributions of Intensive and of Extensive variables. To disprove this general theory in an incontrovertible and mathematically precise way I only need to specify one distribution for which it is false for some notional Intensive variable to disprove Kip’s general theory that sample means of Intensive variables have no practical (real-world) value i.e. interpretation. I chose one distribution, the normal or Gaussian distribution where it is straightforward to disprove this general theory in a simple and mathematically precise way. That’s how mathematical proofs work. I DO NOT need to show that one particular Intensive variable (i.e. temperature) has a normal distribution. So I falsified the theory for the case of a Gaussian distribution so its up to Kip to mathematically prove it is valid for all non-Gaussian distributions or some defined subset of these distributions. You cannot just propose a general statistical theory without mathematically proving it including any necessary restrictions on its generality. Good luck with that Kip because you are neither a mathematician or mathematical statistician or any sort of bona fide statistician/scientist.
I gave you a simple, neat counter-example to your general theory on statistics of Intensive and Extensive variables and every mathematician and mathematical statistician knows a valid counter-example is sufficient to disprove such a general theory. However, you gave no defence of your theory in the face of my counter-example but tried to obfuscate. Your silence on this is very telling. What would happen in peer review is that you would be forced to address a review that pointed out such a fatal flaw and have to withdraw the manuscript, go back to the “drawing board” a tad bit humbled. Oh that’s right humility is not one of your strong points
“Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about.”
All your “valid counter-example” did was demonstrate that you understand very little about real temperature measurements.
Shish you are thick or being deliberately disingenuous. The issue is about more than just temperature its about so-called Intensive versus Extensive variables and modelling them with statistical methods. Have you got any critique of my counter-example? Do you even understand the issue and how mathematical proofs work?
Intensive attributes simply do not add. If I give you 100 metal bars can you add their densities to come up with a total density? If I give you 100 hot spheres can you add their temperatures to come up with a temperature that describes the total power being radiated from the 100 spheres? If I give you 100 balloons of different sizes can you add the pressures in each to come up with a total pressure?
Your counter-example assumes a normal distribution. How do you get a normal distribution of intensive attributes? You can take multiple measurements of the same object which will tend to a true value for that object. But how do you do that for multiple objects?
If you can’t add the pressures in 100 different sized balloons to get a total pressure then how do you come up with an average pressure? Especially an average that is a “true value” for the pressure inside a balloon.
At its base, an average is an expectation of what the next value might be. The standard deviation describes a range in which that next value might lie. How does averaging intensive properties of different things give me any expectation of what the density of the next object might be?
I am an engineer. Been one for going on 50 years. Math to me is a means to describe the real world. I’m sure that there are lots of things you can do with numbers that have no application to the real world. They are useless to me.
If you actually read and understood my counter-example you might have noted that it did not specifically reference temperature at all. So it could not demonstrate anything about my understanding or otherwise about “real temperature measurements”. BTW I have used ambient air temperatures quite a bit in my research Masters, PhD, and other professional work. Starting off with thermo-hygrographs in the 80’s and Starlog dataloggers in the 90’s.
Yet you treat these measurements just as if you are taking random samples from a normally distributed population!
Did *ANY* of your research involve propagating measurement uncertainty into your results? Or did you just assume all measurements were 100% accurate?
In case you didn’t find any other information on intensive vs extensive.
“Way to Tell Intensive and Extensive Properties ApartOne easy way to tell whether a physical property is intensive or extensive is to take two identical samples of a substance and put them together. If this doubles the property (e.g., twice the mass, twice as long), it’s an extensive property. If the property is unchanged by altering the sample size, it’s an intensive property.”
http://www.thoughtco.com/intensive-vs-extensive-properties-604133
Intensive and extensive properties – Wikipedia
I made a couple critical comments about your post but agree with you in some ways at a deeper level about numbers. We live in a reality that has continuous properties. We never know exact masses nor pressures nor velocities nor the circumference of a circle nor the gravitational constant etc etc. We assign numbers that approximate the real exact values. For many cases the number estimates are good enough for the purpose at hand while in other cases not nearly good enough. If you run numerical models of real physical systems there are always errors in the models of systems that evolve through time that include numerical estimates of physical properties that vary continuously. It is just the nature of the physical world that you cannot obtain exact results from assigning approximate estimates to real properties. The current problem is that too often people mistake model results for reality. Sometimes that is good enough, though not exact, and other times not nearly good enough.
Here is how it was explained to me. Measurements are not just numbers to manipulate. Measurements carry information. The amount of information is determined by the resolution of the measuring device. It is conveyed by following Significant Digit rules. If you extend the amount of information by mathematical manipulation, i.e., adding, subtracting, averaging to many decimal digits, statistical analysis, etc. you are creating information that was not there when the measurement was made. That is using mathematics in an incorrect way.
You dont know what you are talking about. Give us some examples of empirical research you have done! Mathematical modelling and statistical modelling underpins all modern empirical science. The data is used to calibrate and validate (ideally with independent data) the models. I had and still have a 47-year career getting paid to do just that and as a statistical consultant clients come to me to do just that so its not just the government jobs I had for 40 years.
Projection.
You don’t know what you don’t know.
Not projection based on comments which show no understanding of modern statistical modelling methods. I think I have more than a few runs on the board in that area having published four senior or sole author papers in statistics journals and many more in the area of applied statistics in application-specific journals.
Your words:
First, has nothing to do with the subject of extensive versus intensive properties, as a statistician, you see them all as just numbers.
Second, time-series temperature measurements do not and cannot*** have a normal distribution, so your counter example is a huge red herring.
***Do you know why this is true?
“First, has nothing to do with the subject of extensive versus intensive properties, as a statistician, you see them all as just numbers.”
My counter-example explicitly includes the statistic (sum of sample values) that discriminates between Intensive versus Extensive variables (i.e. “irrespective of the interpretability of the sum of sample values”) Just to spell it out it more for you Intensive=NOT interpretable, Extensive= interpretable.
“Second, time-series temperature measurements do not and cannot*** have a normal distribution, so your counter example is a huge red herring.”
You dont understand mathematical proofs so there is no point discussing my counter example that disproves Kip’s general theory with you until you do, whenever that might be!
“You dont understand mathematical proofs so there is no point discussing my counter example that disproves Kip’s general theory with you until you do, whenever that might be!”
The argumentative fallacy of Argument by Dismissal.
It’s apparent you didn’t read Essex at all. Here’s one of his refutations of the ability to add temperatures and develop an average:
Essex: “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition introduces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables Xa/i
and does not change in response to a change only in Xb/i.
But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, Xa/i and Xb/i. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature.”
This is true for whatever intensive property you wish to use. It is pretty general in its approach.
Once again, where is the normal distribution that you refer to in your first sentence?
The key question you keep dodging.
+100!
“. The data is used to calibrate and validate (ideally with independent data) the models. I had and still have a 47-year career getting paid to do just that and as a statistical consultant clients come to me to do just that so its not just the government jobs I had for 40 years.”
In my first electronics lab at college there were eight students. We were all assigned to design and build a single transistor amplifier and take measurements to describe the amplifier.
We all thought we would save time and each of us took one measurement at each of the various points in the circuit, averaged them, and we all put down the same answers in the lab book for bias voltage, gain, etc.
We all failed!
Multiple measurements of different things using different devices does not usually generate a distribution that is normal and therefore the average and standard deviation simply doesn’t apply.
We each used different components with 10% tolerance and the transistors had a wide range of high frequency gain. Add in the uncertainty associated with the measuring devices at each station and all we did was generate a distribution with systematic biases which did not cluster around a true value because of the tolerances in the components used! The true value was different for each amplifier.
The “model” of that transistor amplifier was pretty simple and easy to calculate. But it didn’t match reality for any of the amps. Primarily because we hadn’t yet been taught how to handle uncertainty and to propagate it into the results.
First, I suspect your models do not propagate uncertainty, the climate models certainly do not. Second, I suspect your models only focus on a similar object, not random, independent objects with different attributes conjoined into some kind of a distribution.
Science in the normal (vs quantum) world seldom uses statistical modeling unless it can provide determinant answers that can be verified. A real scientific hypothesis uses a mathematical foundation that predicts determinant answers that can be replicated and verified.
I am sure you have lots of experience in statistics and modeling certain things. However, using your bona fides will do nothing for most here. You need to provide in this case, physical facts that either support or counter the assertions here. Many of us are trained engineers with various education from working in differing fields.
Climate science has spent 50+ years trying to obtain a trend that will accurately predict a Global Average Temperature. They have utterly failed after spending billions (and probably trillions) of dollars. Besides that, they are dealing with a physical quantity that shouldn’t even be averaged. How sad.
Maybe with your help they might do better although I doubt it. Climate science is unwilling or unable to provide the statistical descriptors of the distributions they using. Simple things like standard deviation, variance, kurtosis, skewness that any statistical software package will spit out at the push of a button. Ask yourself why. It might be that an anomaly of 0.002 ±0.7 would upset the apple cart of global warming.
So according to you we should just collect data and not do anything at all with it because we might add spurious information to it! WRONG! Mathematical models and statistical models assist in extracting useful information from the data in the form of mathematical equations, statistical hypotheses, parameter estimates and their uncertainty and subsequent use of the models to answer important and interesting questions taking into account model and parameter uncertainty. The models are always up for review, revision, replacement as the scientific process of collecting more (and better fit-for-purpose) data proceeds, and all published models are subject to informed criticism (letters to editors, commentary articles etc). Some scientific fields have more fundamental laws, well-validated and understood processes to work with (e.g. physics, chemistry, physiology..) some less so (e.g. wildlife biology, psychology)…
“So according to you we should just collect data and not do anything at all with it because we might add spurious information to it! WRONG!”
You HAVE to understand what you are collecting. You can’t take data from multiple, independent things with different attributes and assume it creates a normal distribution that can be described by mean and standard deviation.
“ Mathematical models and statistical models assist in extracting useful information from the data in the form of mathematical equations, statistical hypotheses, parameter estimates and their uncertainty and subsequent use of the models to answer important and interesting questions taking into account model and parameter uncertainty.”
When you are creating a distribution from different things with different attributes, each with their own uncertainty, those uncertainties ADD. Sooner or later the uncertainties will overwhelm what you are trying to find. No amount of equations, hypotheses, or parameter estimates (which have intrinsic uncertainty) can prevent this from happening.
This is something that almost no statisticians I have met or corresponded with understands. Most have *never* been trained in measurement uncertainties and how to propagate them. To a statistician the standard deviation of sample means is the uncertainty of the mean – never considering that those sample means have propagated uncertainty from the individual elements in the sample that must also be propagated forward!
“The models are always up for review, revision, replacement as the scientific process of collecting more (and better fit-for-purpose) data proceeds,”
Any model that depends on iterative steps where inputs to the model have uncertainty will see that uncertainty grow with each iteration. That’s the problem with climate models. The parameterizations used all have uncertainty that grows with each iteration – and quickly makes the models useless as the uncertainty overwhelms the ability to determine to the next value. No amount of temperature data collection can correct this – first because the climate scientists assume all temperature data is 100% accurate and therefore no uncertainty is propagated forward so you can’t really validate the model against past data and second because the input factors to the model are inherently uncertain.
When did I say those statistical models I mentioned had to assume a normal distribution for the response? Most of my published work in the statistical literature is on generalized linear models and generalized linear mixed models which use maximum likelihood and Fisher Scoring for estimation where the distribution of the response can be Normal, Poisson, Gamma, binomial, and inverse Gaussian combined with canonical and non-canonical link functions. Sorry but you are not the first person to note the issue of measurement error and error propagation etc. You just dont know the literature whereas I spent my 47 year career pouring over the literature, applying it where relevant and adding my small contribution to it.
“When did I say those statistical models I mentioned had to assume a normal distribution for the response?”
If they are not normal then the mean, i.e. the average of all the values is not an acceptable statistical descriptor.
You totally left out multi-nodal distributions which is what you get from combining northern hemisphere temperatures with southern hemisphere temperatures. You left out the treatment of the different variances between winter and summer temperatures.
Besides, maximum likelihood and Fisher Scoring typically use the assumption of identically distributed data and equal variance for all random variables. Neither of these are met for a distribution formed from global temperature measurements. In fact, neither restriction would be met for most intensive values derived from non-similar objects.
“If they are not normal then the mean, i.e. the average of all the values is not an acceptable statistical descriptor.” By “all values” do you mean all values in the sample or the population. Any univariate random variable will have an expected value which may conditionally depend on a set predictor variables (i.e. covariates). You can generalise this to a multivariate set of random variables. An estimate of the expected value based on a sample or set of samples is possible if that expected value exists.
“maximum likelihood and Fisher Scoring typically use the assumption of identically distributed data and equal variance for all random variables.” Again you are out of your depth here. Generalized linear models (GLMs) along with a link function also involve a variance function which will depend on expected value (so not constant) in a way that depends on the response distribution and may also involve an unknown dispersion parameter. So maximum likelihood and Fisher Scoring do not require equal variances for a given set of expected values that depend on values of the linear predictor. Note that maximum likelihood and Fisher Scoring are more general than just their application in GLMs and can include other non-normal distributions and a systematic component that is nonlinear in the parameters. You also made some erroneous comments about MCMC estimation but I havent got the time or energy to correct all your misconceptions. I am not an engineer so I know well enough not to espouse engineering principles and embarrass myself in the process.
Another important point. When statisticians talk about a distribution for a random variable what is implied is that it is a family of distributions that depend on the values of distribution parameters where the probability density function has the same general form e.g. normal, F-distribution, gamma, Poisson, negative binomial, binomial, hypergeometric etc etc. Typically the expected value is a function of those distribution parameters and it can be modelled conditionally as a linear (where this makes sense) or nonlinear function of covariates. Also the variance can be similarly be jointly modelled e.g DGLMs (double GLMs). Non-statisticians are often confused by not being aware of or understanding the above.
Any expected value must assume these distributions don’t change.
And you still run away from my point about temperature measurement distributions.
Technically all parameters defining the distribution must be constant to keep the exact same distribution. The point I make is that these parameters and thus the expected value and variance can change conditionally on the covariates but the resultant set of distributions all belong to the same family. Seriously this is Linear Modelling 1.01, first year undergrad stats course.
Most of my experience is in engineering and management. My training is electrical engineering in which analysis of cyclical phenomena is certainly emphasized. However, when I went to school, training in fossil fuel power plant including the thermodynamics required to design and operate plants efficiently at their best output was required. Steam tables became a “take with you necessity” in the classes.
Temperature is a thermodynamic quality. In the atmosphere the variance in temperature is a multivariate problem. KH’s paper is trying to show that many, many dollars have been spent in trying to “trend” a metric or index of temperature called Global Average Temperature and it hasn’t even been questioned about how you average an intensive quantity. It makes you wonder about the thermodynamic training supplied to climate scientists.
I don’t want to denigrate your knowledge of the math required for statistics and performing Fisher Scoring. However, this is still “trending” a single variable in time at heart and does nothing to help develop a functional relationship of cyclical behavior involving multiple phenomena.
This isn’t exactly a statistics discussion anyway. KH wanted to elucidate what temperatures are and can they be averaged, averaged again, then averaged again, and finally one more time (daily, monthly, annual, global) to arrive at number that has any meaning.
My thermodynamic training was that you can’t average temperatures and arrive at anything resembling something you can count on. Temperature is a result of several things, mass density, specific heat, and the heat energy supplied. In other words, you need to deal with enthalpy to compare two different things.
To use temperature as a proxy means you must assume that water vapor is constant and well mixed globally which it is not.
Tou must assume that insolation is the same everywhere globally. yet that ignores several things like clouds and topology. It ignores that insolation varies with a cos(θ) variance in latitude and assumes that the earth is flat and everywhere receives an average insolation. You only need to at T^4 in radiation equations to know an average is going to give you wrong answers.
Things like altitudes, proximity to airports, proximity to large bodies of water, all kinds of geography can affect the enthalpy at different locations.
The current GAT calculations mix Decembers with the previous January and February months in order to maintain a calendar year. Climate science ignores seasons totally. You’d think they never heard of equinoxes or solstices. Why wouldn’t you make a temperature year be from December of one year to February of the next year?
Plus they also stir in the southern hemisphere with its opposite seasons!
In the first line of your alleged counter example.
Do you want to play dueling resumes?
That statement was made in my general point on statistical modelling and was unrelated to my counter example to Kip’s general theory. Nice try!
BTW just got this from Academia
Dear Steven,
Congratulations on your 1015th Mention!
3,600 downloads of my PhD thesis.
3 sole author, 1 senior author statistics journal papers
23 senior author papers in other journals
++ second or lower order author journal papers but only statistician
1,278 citations according to ResearchGate
Please list all of the fundamental relationships/physical laws that have been deduced using statistical modeling of global air temperature measurements:
1
2
3
…
For instance the sufficient statistics contain all the relevant information in the sample data about the population parameters of interest. They do not add information to the sample data but summarise it without loss of information on those population parameters.
What are the sufficient statistics for a multi-nodal distribution? For a non-normal skewed distribution?
Do you believe that mean and standard deviation are always sufficient statistics in all cases?
What is the mean, median, and standard deviation of a sine wave?
Go look at a GAT graph. Can you tell me the standard deviation, variance, kurtosis, or skewness of the distribution used to calculate the mean?
If you are saying that all the stations make up the “samples” of the population then according to the CLT the distribution should of the samples should be normal if the samples are taken properly and of the correct size.
Show us where anyone calculating a GAT has shown what the distribution of their sample means is. What is the SEM of sample means distribution? Can you find it somewhere?
Why are they dividing the SEM by the √N where N is not the sample size but the number of samples?
And lastly, information is added in many databases through “infilling”.
What ==> ” For many cases the number estimates are good enough for the purpose at hand” Yes, that is often so — but does not do for science that affects national energy policies etc.
A guess that the Earth climate is warming is OK with me — it is warming (thank goodness! The Little Ice Age was not pleasant in the US Northeast or Europe).
But GAST/GATis not a scientific measure of that…..
I would add that is likely that the LIA was world wide.
But according to the Essex paper there is no way of knowing if the LIA or the MWP was warmer or colder than today.
From proxies or thermometers, no. As for the LIA, there are historical records that can tell us that the period was colder than today. Probably much colder. Now can we get 0.002 degrees of uncertainty, gosh no. Somewhat the same thing goes for the MWP. There are historical records of what grew where. How civilization flourished. Again, history would lead one to believe that it was warmer. There are glaciers retreating and uncovering flora and fauna that tells us it was at least as warm as now and probably warmer.
If you cannot average temperature to get a global average, how on earth do historical records allow you to know what the global average was?
According to Essex it’s impossible to tell if current times are warmer or colder than any period in the past because the concept of a global temperature doesn’t even exist.
Nor can you tell by the global average temperature because there are infinity ways of averaging the global temperature which if you try hard enough can cause the change to reverse direction.
“There are glaciers retreating”
That doesn’t prove the cause is global temperature changes according to Essex. That would be tantamount to temperature at a distance.
“Somewhat the same thing goes for the MWP. There are historical records of what grew where. How civilization flourished. Again, history would lead one to believe that it was warmer.”
Essex et al, argue that it’s meaningless to argue the MWP was warmer than present because there the physical quantity of global warmth does not exist.
You don’t have a clue on what is needed to measure “‘HEAT” do you. Temperature alone will not do it. A temperature of 100 @ 15% humidity is not the same as 100 @ 90% humdity. Their enthalpies are different, e.g., the heat that the atmosphere contains is different. An average of 100 and 100 equals 100. But you will never know that the heat content of the atmosphere was drastically different. That is why a global average temperature is “ill-posed”.
Have you ever wondered why you see papers and news articles that everywhere on the globe is warming faster than everywhere else? Have you ever wondered why changes in species everywhere on the globe is because of global warming? Have you ever wondered why there are more violent storms everywhere on the globe because of global warming?
Why would enthalpy be the same globally and dependent only on a global temperature? Is the enthalpy in Australia the same in July as it is in the Southern U.S.?
Warmists somehow and for some reason believe that everywhere on the globe is experiencing unprecedented warming. You need to ask yourself if the sun’s insolation only affects temperature and doesn’t have any effects whatsoever on clouds or humidity which actually determine enthalpy.
What has this got to do with the LIA or MWP?
It doesn’t allow you to determine a temperature directly. It allows you to set boundaries.
During the LIA people skated and had ice fairs on the Themes River. Do you see that today? What judgement can you make from that?
Trees and human paraphernalia are being uncovered by melting glaciers. Does that probably mean that temperatures were at least as warm for some period of time in the past?
“It doesn’t allow you to determine a temperature directly. It allows you to set boundaries.”
According to the paper, the only way you can know if one planet is colder than another, is if there is no overlap in the range of temperatures. Do you think that was true of Earth during the LIA.
“During the LIA people skated and had ice fairs on the Themes River. Do you see that today? What judgement can you make from that?”
Very little. The Thames was very different then. Even when temperatures have been colder in the 20th century, the Thames hasn’t frozen over.
And even if it did prove colder temperatures, that would only show one small part of London was colder, and you can’t say London was colder because there’s no such thing as an average London temperature, let alone a global one.
“Does that probably mean that temperatures were at least as warm for some period of time in the past?”
So now you’ll accept a probabilistic argument?
You won’t accept that temperatures have risen over the last 150 years, because they may have cooled if you use a geometric average with temperatures raised to the 25th power, but a few trees are enough to assure you that it was probably colder all over the earth during the entire LIA.
And that’s ignoring the arguments that a global temperature simply doesn’t exist, you know from that proof on page 6. So how can the statement it was colder globally have any physical meaning?
How should I trust someone who states that one m³ of stainless steel (which one by the way) at 70°F contains more heat energy than one m³ of sea water?
What numbers did Kip Hansen take to calculate this? Or was it just a gut feeling?
Epilogue:
Well, this has been an interesting project — still requiring a Part 3 which I promise to deliver.
The majority of comments have come from 4 or five readers — who represent to opposing views. One set is what I call “Numbers People” — those who insist that “Numbers are Numbers” and can all be treated the same. The other set are science and engineering people, who realize that “Number Ain’t Just Numbers” and that they represent physical things and properties and must be treated only in manners that can deal with specific physical properties.
Thank you all for reading.
# # # # #
You just gave me chills about when I tried to point out 12 years ago that Global Average Temperature had to be based on dozens of subjective choices.
I guess you count me on the “numbers are numbers” side. Yet I’m pointing out that one of the problems with the Essex paper is it tries to treat the Celsius scale as if it was just numbers, and doesn’t seem to understand why that gives them meaningless results.
As far as I’m concerned, I and “Numbers People” have given plenty of reasons why the argument that you cannot average any intensive values, is wrong, and none of them have involved arguing that numbers are just numbers.
Let me assure you that there are many, many physicists and chemists that will go along with temperatures being intensive and that you can not average them to get a meaningful temperature. You must deal with enthalpy if you wish to thermodynamically average a condition.
Temperatures are intensive. I’ve never argued there weren’t.
All I’m saying is that the logic that intensive values can never be averaged to get a meaningful result is wrong. The logic that the sum is meaningless and so the average must also be meaningless is not correct, and that there are plenty of counterexamples, e.g. density and velocity that prove that it is possible to average some intensive values and get a meaningful result.
There may be reasons why it’s different for temperature, but don’t claim that it’s because temperature is an intensive property.
“All I’m saying is that the logic that intensive values can never be averaged to get a meaningful result is wrong.”
Can you refute the general proof offered in the Essex paper on Page 6? If you can’t then you are doing nothing but offering a non sequitur.
“The logic that the sum is meaningless and so the average must also be meaningless is not correct, and that there are plenty of counterexamples, e.g. density and velocity that prove that it is possible to average some intensive values and get a meaningful result.”
Where have you shown that you can average densities? All you’ve ever done is average mass and volume and then show you can calculate the average density from the average of those extensive properties.
In order to calculate average velocity you must have total distance travelled and total time spent – so you are deriving an intensive property from extensive properties, distance and time. You are *NOT* averaging an intensive property.
Think of it this way. You monitor the velocity of your vehicle continuously. You find that going from point a to point b the velocity forms a sine curve, start off slow, reach a velocity peak, and then coast to a stop. Integrate that velocity curve and what do you get? ∫sin(t) dt
sin(t) is in meters/sec and it is multiplied by dx in seconds so you wind up with the area under the curve in meters – i.e. distance travelled, an extensive property. If you then want to know the average velocity, an intensive property, you divide the total distance by the total time in seconds and get an average velocity. You haven’t averaged the intensive property of velocity, you’ve averaged the extensive properties of distance and time and then used that average to calculate an intensive property. How does that prove that you can average an intensive property?
“As far as I’m concerned, I and “Numbers People” have given plenty of reasons why the argument that you cannot average any intensive values, is wrong, and none of them have involved arguing that numbers are just numbers.”
You haven’t provide ANY reasons at all. You have offered that you can calculate an intensive property from an average of extensive properties. And you have offered that you can too calculate an average of temperature numbers – See?
You haven’t showed *any* reasons as to why an average of intensive properties means anything in the real world. You’ve not refuted the general proof in the Essex paper on Page 6 in any way, shape, or form. All you’ve offered is that “numbers is numbers” is both your premise and conclusion. Circular logic at its finest.
“You haven’t provide ANY reasons at all. You have offered that you can calculate an intensive property from an average of extensive properties”
Your second sentence answers your first.
Clearly I have given a reason, you just dismiss it.
“You haven’t showed *any* reasons as to why an average of intensive properties means anything in the real world.”
I have, but you keep ignoring it. E.g. does an average density mean anything in the real world? Think about ships and the Archimedes’ principle before answering.
“You’ve not refuted the general proof in the Essex paper on Page 6 in any way, shape, or form.”
Do have to refute every piece of nonsense in the paper before you exercise some critical thinking? I find it difficult to refute that part because the whole premise appears flawed and at best badly defined.
It basically says that if an average can represent the temperature of a system it leads to a contradiction, but never defines what they mean by “the temperature”.
The argument is if you have two isolated boxes A and B and an average derived from the two, then if the temperature in box A changes, so does “the temperature” even though B hasn’t changed. That apparently is their contradiction. But I’ve no idea why they assume that changing an average has to change each part. I can only assume that they think “the temperature” must mean a homogeneous temperature, but that’s obviously falsified by the fact they start with two different temperatures.
They go on to make the same claims about global temperature, except there they actually use an average global anomaly. But they still insist that if all parts don’t change at the same rate it’s not possible for it to be the global temperature.
“All you’ve offered is that “numbers is numbers” is both your premise and conclusion.”
I’ve not said that once. As always you seem to be arguing with your own imagination.
No that’s a false dichotomy. You are labelling all those who disagree with your “thesis” as those who do not consider the real-world applications of maths and statistics. You say “those who insist that “Numbers are Numbers” and can all be treated the same” but I (and others) never said that (show me that statement or words to that effect in any of the posts of mine). Of course what the measurements are about is crucial. If you knew anything about statistical theory you would know that it is the methods that can be the same across different applications. I often used statistical methods developed in medicine to model mortality in even-age tree plantations because a proportional hazards model is the same in each case. The issue is that statistics that are measures of central tendency of a particular response variable using a sampling procedure are still valid even if a sum of that response variable over the sample does not have a real-world application (e.g. my sum of fish lengths which you said was interpretable as an Extensive variable while in fact the sum has no real-world application contradicting your definition of Extensive, go figure!). You throw the “baby-out-with-the-bathwater” and the implication you make is that a huge swathe of empirical research has been a wasted effort based on your “thesis”. Sorry but its your “thesis” that is a waste of effort. Your hubris is quite extraordinary and your attempts to smear those that disagree with you with false labels is disingenuous.
“I often used statistical methods developed in medicine to model mortality in even-age tree plantations because a proportional hazards model is the same in each case.”
How do you classify mortality as either intensive or extensive? Death has no physical attributes to classify.
I think this is worth repeating here since Kip looks keen to have the last word and summarise the discussion to his advantage:
I cannot seem to get through to some of you the fact that Kip’s theory is general since it only specifies Intensive versus Extensive variables and the statistical operation of calculating a sample average. Therefore this theory assumes it applies for every and all statistical distributions of Intensive and of Extensive variables. To disprove this general theory in an incontrovertible and mathematically precise way I only need to specify one distribution for which it is false for some notional Intensive variable to disprove Kip’s general theory that sample means of Intensive variables have no practical (real-world) value i.e. interpretation. I chose one distribution, the normal or Gaussian distribution where it is straightforward to disprove this general theory in a simple and mathematically precise way. That’s how mathematical proofs work. I DO NOT need to show that one particular Intensive variable (i.e. temperature) has a normal distribution. So I falsified the theory for the case of a Gaussian distribution so its up to Kip to mathematically prove it is valid for all non-Gaussian distributions or some defined subset of these distributions. You cannot just propose a general statistical theory without mathematically proving it including any necessary restrictions on its generality. Good luck with that Kip because you are neither a mathematician or mathematical statistician or any sort of bona fide statistician/scientist.
Still running away from my point…
what point is that? Have you got any intelligent criticisms to offer about the above technical statement? I suppose not otherwise you would have made them in your reply.
Gigantic unstructured word salad—does this count?
NO it does not count. Its just your way of distracting from the fact that I have produced a valid counter example using a rigorous mathematical approach. “Rigorous mathematical” does not remotely apply to Kip’s essay and those who have tried to justify it. BTW still waiting to see your qualifications to judge statistical theory. Your postings demonstrate already that there is not much to expect in that department.
You’ve got a highly inflated hat size.
And you didn’t read the Essex paper, this is glaringly obvious.
Having no intelligent, well-reasoned response to a technical post by lazily labelling it a “gigantic unstructured word salad” shows you have nothing worthwhile to contribute. Its a tactic of desperation and over-used to deflect in WUWT posts. Silence would even be better at least then you wouldnt out yourself as a shill for the article you are desperate to defend.
So I was right, you didn’t read the paper, and instead just whined a lot.
Read this paper. [PDF] Thermodynamical definition of mean temperature | Semantic Scholar
You seem to have a chip on your shoulder about statistical analysis. That is not the purpose of KH’s paper. The issue is that intensive can not be added to obtain a sum for computing an average. The averaging beginning with daily Tmax/Tmin is not proper. You can not add the two together and get a proper value for HEAT in the system.
Can you add the numbers and take an average, sure, but not only is it meaningless from a thermodynamic sense, it makes no sense physically. You can’t even measure the temperature of latent heat in water vapor to include in the measurements. That is why enthalpy is needed.
There are certainly arguments to be made about the statistical analysis methods being used on the numbers but that is not the point here. If you want to argue about that, tell us why none of the statistical descriptors of distributions is available for purview for any of the GAT distributions. No one, and I mean no one has ever volunteered to provide these even after numerous requests. Tell us why the mean values are the only statistical descriptor available.
You’ve pretty much nailed it, Kip.
The Essex paper gives a mathematical, generalized, high level proof of why intensive properties can’t be averaged. Not a single numbers person has refuted that proof in any way. Their arguments boil down to the following:
In essence it’s all just saying that numbers are always just numbers and you can treat them in any manner you wish. It’s just math.
I just wish some of the “numbers” people would attempt to refute the general proof provided early in the paper.
Kip,
Let me point you to another paper about temperature and means.
[PDF] Thermodynamical definition of mean temperature | Semantic Scholar
Jim ==> Thanks for the link — it is in support of the ideas that “mean temperature”, as is being used in CliSCi today, is a physically improper metric.
In fact, it says that it’s crucial. Yes, materials have different specific heats and crystallization energies, but they don’t detract from the utility of mean temperature evaluations.
“The notion of mean temperature is crucial for a number of fields including climate science.”
It says:
“The notion of mean temperature is crucial for a number of fields including climate science. However, so far its correct thermodynamical foundation is lacking or even believed to be impossible.” (bolding mine, tg)
Why do you not provide the full context of what is being said? You are a cherry-picker just like bellman and bdgwx!
It was a general statistical theory you proposed that you applied to Intensive variables in general and not just temperature. So it was not a thermodynamic theory so I state again it was a statistical theory and you have to play by the rules of mathematical statistics and give a mathematical proof of your theory of statistics.
Again, for at least the second time, look at Page 6 in the Essex paper. The mathematical proof is right there in print!
Keeping things in perspective, Kip’s general theory of statistics of Intensive variables cannot do any harm to the practice of empirically-supported science or any field of empirical research, for that matter, because it will have vanishingly small, like effectively zero, influence on professionals since WUWT Essays are not citable in the peer-reviewed literature and it would never make it through review by theoretical or applied statisticians. So I will not lose any sleep over the issue. It does however lower the credibility of the WUWT web site. I wont be bothered to read instalment 3.
I’m certain Kip is absolutely devastated by this news.
Yes I am sure he is. One less to hold him to a account for lack of intellectual rigor in WUWT’s amateur (stats theory) hour. Going to save my intellectual capital for paid consultancy work and publishing in peer-review journals.
I am going to walk back my contention that this is Kip’s theory. I apologise for that false attribution. This discussion has got a bit heated. I didnt appreciate the statement I never made being attributed to me as one of the “numbers are numbers” lot and therefore apparently not in the company of the “science and engineering people”. My counter-example still stands and I have no apologies for that.
That’s my mea culpa. Any comment from Kip on my above gripe?
Steven ==> I do no such thing. I report about an interesting and valid science question. I am waiting for you to respond to the paper being referenced in an adult way.
I accept and concede this point and withdraw the comment that its your theory. Evenso, my counter-example for the contention that averages of Intensive variables have no real-world application or comonsense interpretation still stands. It is not really a theory since no proof is given by Essex et al. of the second sentence as far as it infers a sample average in their contention on page 5; “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome“. The discussion about temperature as an Intensive variable does not address the above general contention. I could find no proof of the above contention in their paper. If there was my counter-example would not be correct BUT it is in fact correct so that would explain their lack of a proof. Some contentions are harder to prove than to disprove using the counter example method. The issue they raise of different statistics for estimation of central tendency [their Eqn(9)] of simple average, harmonic mean etc, (I could add the geometric mean) does not invalidate these as alternative estimates of the population mean (central tendency) and all have a real-world interpretation whether for Intensive or Extensive variables. Which estimate is minimum mean square error depends on the underlying distribution.
You need to recognize that there are multiple problems here. One, the traditional arithmetic mean requires adding values in a sum.
If the values consist of intensive measurements you can not add them directly since they are not quantities per se, they are QUALITIES.
KH used a chart to show this. One of the intensive items is “color”. Does a mean of red, blue, green, turquoise, black have a value? Is it meaningful? Now if you use the frequencies/wavelengths of those colors in a mean is it meaningful? Is frequency/wavelength intensive or extensive? If you average the frequencies of the three primary colors, do you the wavelength of “white”? Better yet, if you cut a block of red material in half, do you get two blocks with the value of “red/2”? Can I add “red+red+red” and get a value of red3?
How about melting point? Can I average the melting points of aluminum, gold, titanium, and sulfur and have a value that is meaningful? Would it be the melting point of a mixture of equal portions of each? I hope not, because separating ethanol from the other products of fermentation would be very, very difficult!
If you know thermodynamics, you’ll know that temperature does not define the amount of heat in a substance. It is a measure of the kinetic energy within a substance. But it can not measure latent heat, which is very important due to the liquid water and water vapor in the climate. It can not tell you how much energy (heat) is required to raise the temperature of a substance, say a parcel of air, one degree.
For this reason, temperature can not tell you how much energy is contained in a certain mass. Ultimately, energy is what is important to monitor. Many of us on WUWT have maintained that for some time. The papers referenced on the thread only verify that. How much energy is contained in the surface and atmosphere is what we should be studying. This varies throughout the globe with a dependence on many things. Clouds, composition, winds, waves, etc. The only way account for all these is to have a proper base of energy content variations.
If you want to discuss the statistical methods currently being used, get the authors to start a thread about how the statistics are calculated starting with Tmax and Tmin. I would love to get some experts to even commit to whether an annual averages of stations is a sample or a population. I would like to know how they deal with variance that appears when you average winter and summer temperatures from two different hemispheres. But, that is a totally different discussion. First, a decision should be made as to what a well-posed problem contains.
Notice that he ignored all the physics in the paper (esp. the nonequilibrium discussion) and went straight to “no, it is possible to add up the number and divide by N”. He then ignored the whole discussion on how the “anomalies” are calculated.
Jim, ordinal scales are extremely common in many fields of research eg psychology, agricultural research. The colours you mention could be treated as an ordinal scale and in a study using a sample of visual observers that is all you could record. The researcher could assign an integer to each colour knowing the order of frequency ranges those colours represent. A basic approach is to average the ordinal scores given as integers but the statistically sophisticated approach is to fit an ordinal regression model that respects the order but does not attribute a metric score to the simple integer scores. The above statistical model assumes an underlying probability density function where the ordinal classes are defined by, sometimes unknown and therefore estimated, ordered cut-point parameters. For the colour example these cut-points are known from physics and could be input as known values to the fit of the ordinal regression model. That underlying distribution has an expected value (i.e. mean), which may vary systematically with continuous covariate or factor values, and has a useful interpretation in terms of estimates of difference (factors) or trends (covariates) in the mean. If the contention is that it does not because it is ordinal and thus Intensive (?) is promoted then you have just cancelled most of psychometrics and a lot of other worthwhile research. Also in the colours example we know that the cut-points and thus the mean have a useful physical interpretation as EM frequencies. So we have to careful that a focus on the physical sciences does not lead to contentions that push their restrictions onto all fields of research and data-types in a sort of all-conquering way. Again even for physical sciences the contention about Intensive variables in the discussion has yet to be proven and my counter-example says that in its general form it cannot be proven because it is disproved.
“That underlying distribution has an expected value (i.e. mean), which may vary systematically with continuous covariate or factor values, and has a useful interpretation in terms of estimates of difference (factors) or trends (covariates) in the mean. “
Let’s look at what you are doing. One is basically trying to determine how often a color appears, the other (the subject at hand in this thread) is how do you *add* colors to get a sum. In the first you *can* assign a number to a color and determine an average number. You cannot assign a number to each member of a set of colors, sum the numbers, and determine what color the average value will represent.
If you have three colors, red/green/blue, and you assign each the number 1, add them up to 3, average them to get a value of 1, exactly what does that represent? They each have a number of 1!
If you give them different numbers, say 1/2/3, then the total is 6 and the average is 2. Does that mean that green is somehow the average of red, green, and blue? What if you have 3 reds, 10 greens, and 5 blues. The average is 6. What does that average represent? It tells you nothing about how often each color appears nor does it tell you what color the average represents. There is no color with the number of 6.
What you are doing is trying to justify treating temperatures as just numbers rather than physical measurements. Kip was basically right. Treating intensive properties as just numbers on the number line really tells you nothing about the physical world. If you have five bars of gold and 100 balloons full of air in a box, averaging their densities tells you nothing meaningful. There is nothing in that box that will have that “average” density. In fact, averaging their masses won’t tell you anything either since nothing in the box will have that average mass. All the average mass does is represent a number you can multiply by the total number of elements to get the total mass back, i.e. cancel “n” out of the average. Mental masturbation at its finest. But you *can’t* multiply the average density by the number of elements and get the total density. There is no such thing as a “total density” unless you just assume that density is just another number on the number line.
“One of the intensive items is “color”.”
Not a good example. Colours can be additive, you can add and average them to get different colours and intensities. It’s how TVs and Monitors work.
In other cases, e.g printing, they are subtractive, but you can still combine them to get average colours.
No they can not be added mathematically.
(Red + Red + Red) / 3 = what?
You are talking about what you see, not the mathematical addition of physical qualities.
Again, if I have a red object and cut it in half what changes?
Length –> YES
Width –> YES
Height –> YES
Mass –> YES
Color –> NO
Temperature –> NO
Make up (elements) –> NO
Both color and temperature what something is made of are intensive qualities. They can not be added (multiplied) or subtracted (divided). They remain constant. Alchemists didn’t know this and spent years trying to change the makeup of substances.
Its really simple to show that this whole generalisation of a dichotomy of Intensive and Extensive variables and the interpretation of the sum over a sample (or any collection of discrete units of each general type) is completely inconsistent and thus not general. Yes it works for mass or volume but not for Length or Height. I have a sample of humans and I measure their height and since you say Height is Extensive and the sum of values makes sense then tell me what does the sum of the size-N sample of those Heights mean in the real world? One gigantic person or the N-individuals laying head to toe so that one could run a tape measure for the total length to validate it equals the sum of the individual heights (might be a slight difference due to compression of the spine and your favourite subject of measurement error). So total Height is really not sensible and useful in that context when considered in isolation. I pointed out this inconsistency about so-called “Extensive” variables to do with a sample of fish lengths and no one has addressed that inconsistency.
What is N for a time-series air temperature measurement?
Relevance to the above example where the sum of a so-called Extensive variable makes no real-world sense? You are a master of non sequiturs. Is that your main qualification?
It is of primary relevance to the subject of the meaninglessness of global air temperature averages, which have nothing to do with “sampling” any population regardless of distribution.
Slippery! You edited this after I replied.
And you still don’t grasp the importance of a time-series measurement.
It does depend on what you mean by colour. This is more about our perception of colour.
“(Red + Red + Red) / 3 = what?”
Red, obviously. A more interesting question is what is Red + Red + Red.
“Again, if I have a red object and cut it in half what changes?”
Nothing, that’s why it’s an intensive property. Now what happens, if you shine two red lights on a white wall, and then turn one of them off?
“They remain constant.”
In what sense? My laptop screen keeps changing colour, and it keeps getting hotter.
You’re insane.
You didn’t answer anything! If you can’t add colors and get a meaningful answer, why do you think you can temperatures and get a meaningful answer?
That’s just bad logic.
First, my point is that there are ways of adding colours that give meaningful results. But as I said, I don’t think “colour” is a good example, because it’s a complicated subject.
Second, I don;t think you can add temperatures and get a meaningful result. The question isn’t about adding it’s about averaging.
Third, you can’t argue from one case to another. Even if you can’t add colours doesn’t mean you can’t add any other intensive property. There are different types of intensive property and they don’t all behave the same way.
And you accuse others of circularity—please to explain the magic that occurs when dividing a meaningless sum of disparate air temperatures by a constant transmogrifies it into something with meaning.
He won’t explain it. It’s an article of religious faith.
Anything to keep the trends alive.
Yes, that’s right it’s against my religious belief. Either that or I can’t be bothered to explain something obvious to someone who never listens, shows no ability to lear, and will just throw up another witty one liner about me whining.
Honestly, if you can’t figure out why the average of your 100 thermometers is a more meaningful than their sum, I doubt anything I say will make a difference.
Color is a *perfect* example.
If you can add temps then how do you get an average?
What other intensive properties can you add and get a meaningful result. We know that color, density, and temperatures are out. Give us some other examples.
“If you can[not] add temps then how do you get an average?”
I keep trying to explain, but it offends your religious believe.
You can sample temperature, or you can multiply it by an extensive property.
“What other intensive properties can you add and get a meaningful result.”
If you mean average rather than add, you can get meaningful results from averaging density and velocity.
“We know that color, density, and temperatures are out.”
No idea why you think there cannot be an average density. I assume you’ve never worked in ship building, and claiming you cannot average temperatures is just begging the question.
And you need to study more logic. You don’t prove you cannot average any intensive property just by pointing to examples of intensive properties you cannot average.
And as I say, colour is an awful example as it can mean many different things, and in many contexts can be added and averaged.
“No idea why you think there cannot be an average density. I assume you’ve never worked in ship building, and claiming you cannot average temperatures is just begging the question.”
I’ve already answered this. If you have sponge and a lead weight in a bucket, what does the average density tell you? You *still* have to know the masses of each in order to judge anything about their impact! There is nothing in that bucket that exists that has the average density. Even if you have a weight of gold and one of lead in the bucket what does the average density tell you? It doesn’t tell you what the bucket will weigh on a scale.
Btw, the buoyancy of a ship is found by Fs = Vs + D + Fg. D is the density of the fluid the object is immersed in and Vs is the volume of the object. The density of the ship is irrelevant. It’s the volume of liquid the ship displaces that is of importance. Fg is the force exerted by gravity which is dependent on the mass, not the density, of an object.
“I’ve already answered this”
No. That’s just your back to front logic of arguing that if you can show a situation where the average is not useful, than the average can never be useful.
“Btw, the buoyancy of a ship is found by Fs = Vs + D + Fg.”
Very good. Now try to use that formula to determine if an object with a given average density will sink or float.
Climate Science is the modern-day equivalent of alchemy…
“The discussion about temperature as an Intensive variable does not address the above general contention. “
” I could find no proof of the above contention in their paper”
He gives a proof on Page 6. You have yet to refute that proof. The fact that you apparently didn’t understand it or bother to read it is not refutation.
You’ve been spamming this page 6 example for last few days. Could you explain what you think it actually proves?
I gave my thoughts on it here:
https://wattsupwiththat.com/2022/08/09/numbers-tricky-tricky-numbers-part-2/#comment-3576815
and you haven’t responded to it.
Let’s start from the beginning and try to make it simple.
From Page 5.
1) “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction.”
2) “The state, and the temperature, of system a, say, is completely determined by the variables {Xia} and does not change in response to a change only in {Xib}.”
3) “Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, {Xia} and {Xkb}.”
4) “That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b.”
The conclusion of this is that the average temperature must also be an intensive value, but, the average can change based on the temperature of either system. Therefore, the average temperature is not based on the extensive values of either system.
In other words, it is not reality based and can not be an actual temperature in the system. It does not describe the conditions that created it.
For example, if I tell you the temperature is Tavg, can you tell me the mass, the specific heat, and the heat that was added to that to get that temperature. If you can’t, and believe me you can’t, then you can not consider it a real temperature.
The problem only gets worse as you add additional temperatures that are a function of their local extensive variables. As you add more and more to the average, you do not have a real system because the conditions that caused the actual temperatures is subsumed and disappear.
Remember temperature is a quality, more precisely, it is a measure of kinetic energy in a substance. Temperature is not calculated, it is measured. Heat on the other hand is a calculated value of the amount of energy transferred. The general formula is Q = m * c * ΔT. Please note the ΔT. Just knowing temperature does not tell you how much energy had to be transferred to a substance to reach the final temperature. You also need to know the starting temperature. Consequently you know nothing about the heat involved when you attempt to derive a global average temperature.
Page 6 proof is a basic mathematical proof of using anomalies. It is basically the problem and generates a similar conundrum, how much energy was used where?
“Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b.”
Which is the problem, in that I don’t see any problem. Why does the average temperature have to be a temperature for either a or b?
“The conclusion of this is that the average temperature must also be an intensive value, but, the average can change based on the temperature of either system.”
Yes the average temperature is an intensive value, yes it depends on both systems. Where’s the problem?
“Therefore, the average temperature is not based on the extensive values of either system.”
I’d say it was based on both systems.
“In other words, it is not reality based and can not be an actual temperature in the system.”
It’s based on the reality of the two systems. And it doesn’t have to be an actual temperature in the system.
“For example, if I tell you the temperature is Tavg, can you tell me the mass, the specific heat, and the heat that was added to that to get that temperature.”
No. But if I tell you the temperature of a or b you cannot tell me all those things.
“Remember temperature is a quality….”
I still can’t find any explanation as to what this means, or why you think it’s important. Every reference I’ve found says it’s a physical quantity.
“… more precisely, it is a measure of kinetic energy in a substance.”
I assume mean average kinetic energy, otherwise it would be extensive.
And if it is defined as average kinetic energy it’s difficult for me to understand why there cannot be an average temperature in this two box system.
Go take a stat mech class…
Because temperatures are intensive. You can’t add them, they don’t change. Yet that is what an average does, it “creates” a new number that is not a temperature.
You are saying temperatures don’t change? I’m sure that’s not what you mean.
“Yet that is what an average does, it “creates” a new number that is not a temperature.”
I don’t care if you call it an actual temperature of an average temperature, it still has meaning.
I’m sure that in some abstract technical sense it’s impossible to assign an actual temperature to any system not in equilibrium, but that has very little to do with the real world question of is the system getting hotter or not. If the theory can’t tell you that, then I don’t think it’s of much use.
Page 6 does not give a proof of the contention (given on page 5) “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome” . It is simply restated with respect to temperature on page 26 as “Since temperature is an intensive variable, the total temperature is meaningless in terms of the system being measured, and hence any one simple average has no necessary meaning.” Restating a contention is not a proof. Show me a proof of this specific contention that is based on the property “Intensive” and not a specific variable. I cannot see one. Remember “this specific contention”… dont stray from “the straight and narrow”.
Do you see the circular reasoning in Essex et al? Contention1: “Dividing meaningless totals by the number of components cannot reverse this outcome” (page 5). Contention2:”Since temperature is an intensive variable…any one simple average has no necessary meaning” (page 26). Contention1 gives Contention2 gives Contention1. So Contention1 = Contention2. So no proof of their contention at all, just a “sleight of hand”. Despite all the complex arguments about temperature they still have to revert back to their circular argument “Since temperature is an intensive variable…”. Like I said if they had given a proof my counter example would be wrong which it is not and no one has proven any flaw in the logic of that counter example. Ignorant comments of “sorry no maths to see here (paraphrase)” on par with “that’s just a gigantic word salad” are just inane.
Stop whining.
I see no problem. It doesn’t appear to be circular, just two different assertions.
If a sum is made of intensive variables, then the result has no physical meaning.
If a sum with no physical meaning is divided by N, then the result has no physical meaning.
One assertion (or contention) since we could collapse it without loss of information:..
“since the sum of an intensive variables has no physical meaning then dividing by N also has no physical meaning”
Cut and paste the text from Essex et al that proves this assertion for Intensive variables in general or even part (b) of your two-part assertion if you want to maintain its two assertions not one. It is an assertion about Intensive variables in general and the proof needs to address that. Start with temperature if you like and use an inductive proof but it needs to be more than just temperature because in mathematics one example does not prove a general theory BUT one counter-example can disprove a general theory.
Xa/i is general, it’s not just temperature. If Xa/i is not determinstic for Xb/k then it can’t be deterministic for any other X.
For some reason you just can’t seem to accept this.
For temperature I don’t need a “mathematical” proof. You may be a dood mathematician but you also need to study some physical science as do most climatate scientists.
Here is an easy page to read from wiki that explains thermodynamic temperature. I am attaching a small portion that discusses particle motion and how it relates to temperature.
As you can see, temperature is a property of particle motion and how energetic it is. In other words translational kinetic energy.
The following is from the same wiki page:
https://en.m.wikipedia.org/wiki/Thermodynamic_temperature
“”Though the kinetic energy borne exclusively in the three translational degrees of freedom comprise the thermodynamic temperature of a substance, molecules, as can be seen in Fig. 3, can have other degrees of freedom, all of which fall under three categories: bond length, bond angle, and rotational. All three additional categories are not necessarily available to all molecules, and even for molecules that can experience all three, some can be “frozen out” below a certain temperature. Nonetheless, all those degrees of freedom that are available to the molecules under a particular set of conditions contribute to the specific heat capacity of a substance; which is to say, they increase the amount of heat (kinetic energy) required to raise a given amount of the substance by one kelvin or one degree Celsius.
The relationship of kinetic energy, mass, and velocity is given by the formula Ek = 1/2mv^2. [10]
Accordingly, particles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy, and precisely the same temperature, as those with four times the mass but half the velocity.””
Please note the part about specific heat capacity, it is important.
As you can see the kinetic translational movement of particles is what is measured as “temperature”. If you have a block of a distance, a block of iron or a parcel of air, the particle movement within it generate temperature.
If you cut the block in one-half, the particles in each block continue to move with same energy and voila, each smaller block retains the same temperature.
That is why temperature is a QUALITY (intensive) of a substance. It is like color. If a leaf reflects green light, you can cut in half and each half continues to reflect green light.
Translational kinetic energy is what makes an object read a temperature. Energy that is stored in vibrational or rotational movement of a molecule is NOT sensible, you can’t measure it with an external device, therefore it is not sensible, it is LATENT. Water has a high specific heat capacity and lots of the heat it absorbs is LATENT heat.
The sun provides the predominate amount of energy we are discussing. If you want to allocate heat energy properly, you must account for the heat you can not measure by temperature, e.g., LATENT heat. This makes temperature the wrong measurement to use in determining the heat at a location.
Water vapor can vary from location to location, so can cloud cover, and surface composition. This changes the heat measured by a thermometer when compared to another location. In other words, the conditions vary.
The ultimate question is can you compare temperatures that have varying allocations of heat energy to obtain an average.
BTW I like the term “contention” better than “assertion” because “contention” gives a sense of a “contentious assertion”. It is certainly contentious based on the comments here. More importantly, the implication of this contention is to cancel all empirical research that uses Intensive variables and Extensive variables, for that matter, whose sum has no real-world meaning. Cannot say I have seen a mass exodus of empirical scientists and applied statisticians for other vocations because of Essex et al 2007. No tsunami of hand-wringing that “we have had it all wrong all this time!”.
Poor steven, people failed to worship before his statistical greatness and brilliance.
At least I can show some humility when needed. This statement by Kip to start the discussion was more like a Papal Bull from the Vatican than an invitation to a scientific discussion.
“Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about. I will try to clarify if you ask specific questions.”
My counter-example is simple maths no need for worship.
When do you start?
refute this:
——————————————————–
Setting mixing aside, consider two disjoint isolated equilibrium systems, a and b, with functions of state Ua = f_a(Xa/1 ; Xa/2 ; … ; Xa/n) and Ub = f_bXb/1 ; Xb/2 ; … ; Xb/n) respectively, where Ua and Ub are the respective internal energies. Xa/j and Xb/j represent the corresponding extensive variables in systems a and b, respectively. Obviously, given fa, the extensive variables for system a completely define the thermodynamic state of system a. Similarly for system b. The partial derivatives, δUa= δXa/j and δUb= δXb/j , are the jth intensive variables for the respective systems. The temperature of each system is, of course, the particular partial derivative with respect to the system’s entropy,
T = δU/δS: Together, the intensive variables form the tangent spaces of the respective functions of state. As such, they are local properties of the state space and are thus independent of the scale of the system. Does a Global Temperature Exist? Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables {Xa/i) g and does not change in response to a change only in {X b/i}. But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, {Xa/i} and {Xb/k}. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature. While it is thus simple, obvious, and unavoidable that there is no one physically defined temperature for the combined system, the example illustrates the contradiction that arises in requiring an average over a local equilibrium temperature field to be itself a temperature of anything.
————————————————————–
He won’t—he’s had at least six opportunities to refute it and has run away each time.
I don’t expect an answer. He *is* a numbers-are-numbers guy. He thinks you can average anything and get something meaningful. There are several of those people on wuwt!
Absolutely, adding columns and dividing by N is pretty much all they have. No one does any detailed distribution analysis that he tossed out. It might reveal the fraudulent data mannipulation!
Even if it were very complicated maths, or the most elegant and sophisticated maths ever developed, worship is unjustified. Question: how come maths so elegantly and often so simply describes the real world as evidenced in the physical sciences? Just asking…
The Global Average Temperature was the main point of the Essex paper, and you ignored this completely.
This includes ignoring all the physics presented plus the discussion of the myriad of functions used to extract anomalies.
And there was exactly zero math in your alleged “counter example”.
“And there was exactly zero math in your alleged “counter example””.
The formula for calculating the expected value of the normal distribution is so well known by anyone with math stats training/experience that it needs no reminder of the mathematical formula but just to let you know it involves integration. Proving the population median equals the population mean for a normal distribution is even easier. The sample mean and median are consistent estimators so they both converge to the expected value as sample size increases. The variance for the sample median is less well known and is given by Wilks, S.S., 1948. Order statistics. Bull. Am. Math. Soc. 54, 6–50.
NONE of this applies to time-series measurements of air temperatures!
And again you run away from the real-world physics issues.
Yeah, yer an expert on everything, sure.
I don’t think you understand what an intensive property is nor do you understand what temperature is. An intensive property remains consistent with a change in the amount of material in an object. A red block cut in one-half results in two red blocks. The property red doesn’t change! A block at 100 degrees cut in half results in two blocks both at 100 degrees!
Now can you add two intensive properties? The answer is no. I tried to explain this to Bellman. Can I take the two 100 degree blocks above, molecular bond them and up with a block at 200 degrees (100 + 100)? How about the two red blocks? Do I end up with a doubly red block (red + red)?
The paper gives you the math for temperature, T = δU / δS. Can I say
T1 + T2 = T if,
U1 ≠ U2 or,
S1 ≠ S2.
This is the question that must be answered before proceeding to statistical analysis.
You may want to study up on thermodynamics before you go on.
“Even if it were very complicated maths, or the most elegant and sophisticated maths ever developed, worship is unjustified. Question: how come maths so elegantly and often so simply describes the real world as evidenced in the physical sciences? Just asking…”
No worship. Just an understanding of the math in the Essex paper. Where is your refutation of the math on Page 6 of the paper? *THAT* math elegantly and simply describes the real world and refutes your assertion that you can average intensive properties and get an answer that describes the real world.
As best I can tell the only thing Essex et al. are saying on pg. 6 is that for two bodies A and B not in equilibrium:
[Ta + Tb] / 2 != Ta_i for all i.
and
[Ta + Tb] / 2 != Tb_i for all i.
In other words, the average temperature of the two body system A&B does not equal Ta_i or Tb_i for all points i.
That is a rather obvious fact that is self evident. It does not require two full pages of text to communicate that idea.
Are you saying that the only way to convince you that [Ta + Tb] / 2 is meaningful and useful is to disprove the above statement?
You do understand that temperature is a composite of other conditions, right? The paper tells you that,
T = δU / δS.
If T1 = δU1 / δS1 and T2 = δU2 / δS2, can you say,
Tavg = { (δU1/δS1) + (δU2/δS2) } / 2 ?
Temperature is made up of heat content and entropy. When you add temperature numbers directly are you adding numbers that are similar?
You need to answer this question in your own mind. At a given temperature, does a parcel of dry air have the same amount of heat energy as a similar parcel of moist air?
Then you need to answer the question, does temperature accurately reflect the amount of heat energy a parcel of air absorbs from the sun? If it doesn’t, are you losing or gaining heat energy when averaging?
If [Ta + Tb] / 2 != Ta_i for all i and [Ta + Tb] / 2 != Tb_i for all i is true then how can an average temp exist?
Essex: “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables Xa/i and does not change in response to a change only in Xb/i. But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, Xa/i and Xb/k. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature.”
Think about it for a minute: Expand this to the average being Xc/h.
If Xa/i and Xb/k are independent and fully defined then they are functions only of the extensive variables in their own systems. Xa/i does not change when Xb/i changes. This also applies to Xa/i and Xc/h and Xb/k and Xc/h. Thus Xa/i and Xb/k don’t generate Xc/h meaning there is no average temperature determined by the two separate, independent systems.
Heat doesn’t exert a force field like gravity or EM radiation, there is no “temperature acting at a distance”. Thus there is no way to assume that Xa/i and Xb/k can cause a defined average temperature to exist somewhere in the space between them. Thus that “average” temperature is meaningless insofar as reality is concerned.
As Kip has already pointed out, if you are a “numbers is numbers” guy then you can do anything you want with the numbers. That simply doesn’t mean they are useful or meaningful in the real world we live in.
“If [Ta + Tb] / 2 != Ta_i for all i and[Ta + Tb] / 2 != Tb_i for all i is true then how can an average temp exist? ”
That’s not what’s being said. You are implying there are multiple different temperatures in both a and b, which would imply Ta and Tb are both averages, thus refuting the claim that an average temperature cannot be the temperature.
But as I said in response to bdgwx, if the claim is that an average temperature cannot exist if it doesn’t equal a single temperature in the system, why not just state that as the argument? That statement is easily proven – if Ta != Tb, then the average of Ta and Tb cannot be the same as Ta or Tb, so the average isn’t “the temperature” QED.
But if you are saying the average temperature only has to be present somewhere in the system to be real, then that isn’t a problem when looking at global temperatures as any average, even the silly ones they use in later sections, has to be present somewhere on the planet, because of the mean value theorem.
This also means the first argument involving two isolated systems is invalid as it assumes discontinuous temperature distributions.
So Pt. Barrow Alaska and Capetown South African are not discontinuous?
HAHAHAHAHAHAHAHAH
Keep digging, this is amusing.
He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!
It’s no wonder the CAGW crowd has so many followers.
Spooky action-at-a-distance!
“He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!”
Really? What makes you think that?
What are the variables that determine temperature? Look at the equation the text gives you for “T”. Are they all the same everywhere in space and time?
My question was why do you think that “He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!”
How else would the temperature at one place be a cause of the temperature at another place? If the temperature here doesn’t determine the temperature at another place then there is no “acting at a distance”. If there is no “acting at a distance” then an average temperature is meaningless.
The temperature at a single point is determined by a multiplicity of things, i.e. Xa/i. Those things include humidity, clouds, elevation, latitude, longitude, terrain, geography, etc. The geography at one point doesn’t determine the geography at another place or anyplace in between. The terrain at one place doesn’t determine the terrain at another place or anyplace in between. The elevation at one place doesn’t determine the elevation at another place or anyplace in between. The humidity at one place doesn’t determine the humidity at another place or anyplace in between. Clouds at one place doesn’t determine clouds at another place or anyplace in between.
I.e. NO ACTING AT A DISTANCE FOR TEMPERATURE. If there is no acting at a distance then averaging temps at two places doesn’t define the temperature at another place.
Enthalpy, on the other hand, forms a gradient field all of its own, just like pressures on a weather map or elevations on a topographic map, both of which are extensive properties. You could look at an enthalpy gradient map and know that you are looking at something that takes into account all the factors heat is involved with. You can’t do the same thing with temperature, temperature is not a good proxy for enthalpy. The same temperature could exist in Phoenix and Miami but the heat contents (i.e. enthalpy) would be vastly different.
Anyone that tries to tell you that temperature is a good proxy for heat content is either ignorant or a liar.
“How else would the temperature at one place be a cause of the temperature at another place?”
It doesn’t. The average is determined by the average of temperatures, which in turn are caused by the multitude of things that cause the temperature at individual points. Changing one temperature changes the average, but does not have to change all other temperatures.
Consider the average of personal wealth. Person A has 10000 currency units, person B has 30000. Each persons wealth is the result of multiple factors, inheritance, earnings, gambling etc.
Their average wealth is 20000, and that 20000 is indirectly derived from all these factors for both A and B.
Now suppose A comes into some money and their wealth increases to 20000. That’s due to the factors that determine A’s wealth. The average increases to 25000, but that does not mean that anything has happened to the factors that determine B’s wealth. Nor does it mean the wealth is acting at a distance.
No. The temperatures between the two places are continuous.
Little wonder you are so confused.
Is humidity the same everywhere? Are clouds the same everywhere? Is the sun’s insolation the same everywhere?
It also explains why there is no statistical description other than a mean. If a temperature exists somewhere, anywhere on the earth, how can it possibly be the mean. Location does enter in here. Another thing that gets lost in the shuffle and why everywhere is warming.
Of course that’s what is being said. Temperatures don’t act at a distance. If they don’t then they don’t determine the temperature at an intermediate point. And that is what some of us have been saying forever! It’s why the temperature on the north side of the Kansas River never matches the temperature on the south side! Different humidities, different pressures, different winds, different weather fronts, different cloud cover, etc! You would be hard pressed to average the two temperatures and find the average anywhere in between. Each local temperature is determined by its own set of extensive values.
“You are implying there are multiple different temperatures in both a and b,”
Here we go again! Xa/i is a set of extensive values at a specific location – it’s *NOT* a set of temperatures. You *really* didn’t bother reading for comprehension did you?
” if the claim is that an average temperature cannot exist if it doesn’t equal a single temperature in the system, why not just state that as the argument?”
Wow! What do you think everyone has been trying to tell you?
Why do you think we’ve been beating you up over the fact that the average of a 6′ board and an 8′ board doesn’t exist in the real world, or at least in that portion of the real world where those two boards exist?
“That statement is easily proven – if Ta != Tb, then the average of Ta and Tb cannot be the same as Ta or Tb, so the average isn’t “the temperature” QED.”
NO! It means that Ta and Tb can’t determine the temperature at a third point! Just as the average of a 6′ board and an 8′ board can’t magically create a 7′ board!
“But if you are saying the average temperature only has to be present somewhere in the system to be real, then that isn’t a problem when looking at global temperatures as any average, even the silly ones they use in later sections, has to be present somewhere on the planet, because of the mean value theorem.”
You JUST CAN’T FIGURE IT OUT, CAN YOU?
A temperature in the system is defined by its own set of extensive values, not by the extensive values somewhere else. No acting at a distance. Temperature is not subject to the mean value theorem!
“This also means the first argument involving two isolated systems is invalid as it assumes discontinuous temperature distributions.”
YOU STILL DON’T GET IT! Two isolated systems do *NOT* determine the temperature at a third system! They are not connected and they don’t act at a distance! Since they are not connected there is no discontinuity to consider!
If I just walk across the street and measure the temperature in my neighbors yard over bermuda grass and take mine over sand will they be the same? Are they causually connected? If they aren’t the same is there a discontinuity somewhere? Those two temps are related to the extensive values at each location. The extensive values at one are *NOT* the cause of the extensive values at the other! So how can there be an average calculated from them?
“That simply doesn’t mean they are useful or meaningful in the real world we live in.”
The argument in the paper is that they are not a real temperature, not that they are not useful. As always when you talk about usefulness of averages you show a very limited imagination.
So unreal is useful.
Yes, you are insane.
I’ll echo that.
“limited imagination’! So we are going to spend trillions of dollars, destroy how many birds, destroy how many economies based on someone’s imagination? That certainly sounds like a green liberal.
The average is *NOT* a real temperature!
Just as the average of a 2kg mass and a 4kg mass is *NOT* 3kg. There isn’t a 3kg mass anywhere in the system!
The average is useless for anything except mathematical masturbation!
So now you are saying the average of extensive properties are meaningless?
Are you going to give up the magical properties of the 1/N operator anytime soon?
One other point
None of this argument on page 6 has anything to do with temperature being intensive. The same logic would apply to an average of an extensive property.
Take two different metal bars, with masses Ma and Mb. Does the average of these masses equal to either Ma or Mb? Does that mean it isn’t a real mass? Does that mean all averages of masses are non-existent, or that they have no use? .
Put two bars of the same substance and size in your hands. Can you see a third bar that has the average mass? No. It is an unreal physical number. Does it have use? Surely. You can put any number of bars of different substances on a scale and get the sum of their masses (after dealing with gravity). You can find a standard deviation and a distribution and do all kinds of statistical analysis.
Now do temperatures add? Do they subtract? They actually move toward equilibrium. What does temperature tell you about the bars? Do you know their specific heat capacities just from temperature?
Now let’s get down to the nubbin.
Could certain bars of different substances have different amounts of heat contained within them, yet have the same temperature?
If that is true, how do you calculate total heat from all the bars as a whole just from an average temperature?
Ask yourself, are we after the heat being trapped in the atmosphere or the temperature or does that not matter. Can the temperature increase but the amount of heat be less? Think about water vapor that has latent heat that is unmeasurable.
“Could certain bars of different substances have different amounts of heat contained within them, yet have the same temperature?”
What do you mean by heat?
As I’ve said before my knowledge of thermodynamics is limited, but I’m not sure if you can talk about heat contained within a bar. I thought heat was to do with the movement of energy.
If the question is could they have different Enthalpy yet have the same temperature the answer is definitely yes.
“If that is true, how do you calculate total heat from all the bars as a whole just from an average temperature?”
You can’t.
“Ask yourself, are we after the heat being trapped in the atmosphere or the temperature or does that not matter.”
It depends. If you are interested in calculating total energy budgets, and modelling the greenhouse effect and what not, I assume the former. If I just want to know how hot it is, the later.
I suspect there isn’t really that much difference as the specific heat capacity of the atmosphere at the surface doesn’t change that much and so on a global scale temperature rise is roughly proportionate to total energy, at least at the surface.
“Can the temperature increase but the amount of heat be less?”
“Can the temperature increase but the amount of heat be less?”
I’ve no idea. Someone will have to do the calculations, but either way it means the climate is changing, and shows that knowing if there is a change in global average temperatures is useful.
“I suspect there isn’t really that much difference as the specific heat capacity of the atmosphere at the surface doesn’t change that much”
Is that why they call the same temperature in Phoenix a “dry” heat and in Miami a “wet” heat? Is that why cold air can’t hold as much moisture as warm air?
” on a global scale temperature rise is roughly proportionate to total energy, at least at the surface.”
Specific heat is:
Cp’ = 1005 + 1884*ω
where ω is the absolute humidity
And you think absolute humidity is the same everywhere on earth?
You’ve never once used the steam tables, have you?
You know why these discussions keep going on forever? Because the goalposts keep moving. This whole article is meant to be about whether the intensive nature of temperature means you cannot get an average. But now were on to whether humidity will have much of an effect on the global average temperature.
“You’ve never once used the steam tables, have you?”
Nope. As I keep saying I know little of thermodynamics, that’s why I was asking if someone could do the calculations.
“Is that why they call the same temperature in Phoenix a “dry” heat and in Miami a “wet” heat?”
I maybe wrong, but I thought the difference in feeling from wet and dry heat was due to are ability to lose heat through sweating, not because of the specific heat content of the air.
“Specific heat is:
Cp’ = 1005 + 1884*ω
where ω is the absolute humidity”
Yes, thanks, I looked into this just now.
At 40°C and 100% relative humidity the absolute humidity is around 0.05. So the difference in specific heat capacity between absolutely dry air and very hot and humid would be about 10%. So even if the entire planet went from on extreme to the other it would only require an extra 10% energy to get the same temperature rise.
So given moist the planet is going to have much smaller changes in humidity, I think you’ve confirmed my suspicions that changes to humidity will have a minimal effect on global temperatures.
A blazing strawman; first line of the ABSTRACT:
Who is moving goalposts? This would be YOU.
The words of a dyed-in-the-wool religionist.
Your cherished global average temperature is meaningless so all you can do is hope and pray this is true.
It isn’t.
NO!!!!
You can add extensive properties and average them. HAVE YOU READ NOTHING IN ESSEX AT ALL? That doesn’t make them useful either!
You have to join Ma and Mb into one system! Like put them in a bucket! If they are separate systems, e.g. one of 2kg in one bucket and 4kg in a second bucket then why do you think the average of 3kg would exist anywhere in between them? There’s no third bucket!
Put them in the same bucket and they will have a mass of 6kg. Why would you think they would have an average mass of 3kg?
You can certainty calculate an average mass, divide it by 2, and get 3kg. So what? If you want to know what the mass in the bucket is you need to multiply 3kg by 2 to get the total! Math masturbation! Nothing useful is transmitted by the average!
Not only that but the average has lost the data that one has 2kg in mass and the other 4kg in mass! Just like when you average daily temps, weekly temps, monthly temps, and annual temps. You lose all the data of what is happening where! Without that knowledge how do you make informed judgements about what is happening. You can’t tell from the average if max temps are going up or min temps are!
“HAVE YOU READ NOTHING IN ESSEX AT ALL?”
Yes and disagreed with it. Just as many did when it came out 15 years ago.
“You have to join Ma and Mb into one system!”
Why?
“Like put them in a bucket! If they are separate systems, e.g. one of 2kg in one bucket and 4kg in a second bucket then why do you think the average of 3kg would exist anywhere in between them? There’s no third bucket!”
For once and for all, I do not think taking an average magically conjurers up a new bucket. I just think the average can be useful.
“Put them in the same bucket and they will have a mass of 6kg. Why would you think they would have an average mass of 3kg?”
Because that’s what an average is. I agree that for an extensive property the average is probably going to be less useful than a sum. For intensive properties the average is all that is useful.
“You can certainty calculate an average mass, divide it by 2, and get 3kg. So what?”
I’ve no idea. It’s your example. What are these masses you’ve put in the bucket. If they are gold bars it might be useful to know what their average is. If they are buckets of water, than the average loses all meaning when you mix them.
“If you want to know what the mass in the bucket is you need to multiply 3kg by 2 to get the total!”
So you have found a use for the average.
“Not only that but the average has lost the data that one has 2kg in mass and the other 4kg in mass!”
Unless you wrote it down somewhere.
“Just like when you average daily temps, weekly temps, monthly temps, and annual temps. You lose all the data of what is happening where!”
In the same way as you lose all that data if you add them up. Remind me about why CDD’s are useful.
“You can’t tell from the average if max temps are going up or min temps are!”
But you can’t tell if any type of temperature is going up or down if the Essex paper is correct, so why worry about the difference between max and min?
Appeal to masses, bzzzt.
That’s how I read it.
The main complication is they want to claim the average temperature is the temperature. This in turn is based on the claim made in the introduction that some claim the global average temperature is the temperature of the globe. They don’t give any context for this, but just seem to assume that “the temperature” can only mean a single temperature that is the same for the entire globe.
If that is their argument it could have been made in a single sentence, hence my feeling that this is deliberately obfuscated to make it seem more meaningful than it is.
More insanity.
My apologies, they do say it’s required to be “a temperature” not “the temperature”.
Intellectual rigor?
Where is yours? Where have you disproved the mathematical proof offered in the Essex paper on Page 6?
Saying it is wrong just isn’t sufficient. Saying it is wrong is *NOT* intellectual rigor.
Heal thyself, physician!
Science journalists are supposed to be objective about the for and against arguments in science controversies ““But, but, but, but” ….. no buts!
One cannot average temperature”. That’s not objective reporting. This article is no different in that regard from MSM science journalist that are simply influencers for the climate alarmist scientists.
The statement sure got you going.
The global average temperature(s) was and remains a meaningless number.