# Is global average temperature a useful or thermodynamically valid concept?

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Climate scientists are concerned with deviations in the average global temperature, but what does an average temperature mean from a thermodynamic perspective? Temperature is inherently a local measurement of molecular kinetic energy, and therefore an average temperature across a large region seems to have little meaning in a thermodynamic context. At best we could try to demonstrate that global average temperature is a predictive metric for some other variable of interest, but the burden of proof would be on us.

I could calculate a weighted average by volume temperature of my car by measuring the dimensions of various devices and parts in the vehicle along with their temperature and then taking their sum weighted by their proportion of the car's total volume. For example perhaps the air in the cabin is measured to be 25 °C, the air underneath the hood measured to be 50 °C, the temperature of the oil is 200 °C, etc. After taking all of the appropriate temperature and volume measurements I might calculate that the average temperature of the car is 100 °C. But what does that tell us? Is that a useful metric?

Now assume that I told you that the average temperature of the car increased to 101 °C. Should you be concerned? Well your first question might be where did the temperature increase, and when/why did it increase. If I told you the air in the cabin increased in temperature to 40 °C you would be correct to be alarmed, since that temperature would be uncomfortable or perhaps outright dangerous to the occupants. However if I told you that the temperature of the oil increased to 250 °C you may then ask when did the temperature of the oil increase? If I told you it increased when you put your foot down of the throttle for a period of time then you would not be alarmed at all since it makes complete sense for the temperature of the oil to increase when the engine is throttled. We can see here that the average temperature of the car contains little useful information.

From this metaphor we can see that an increase in average temperature weighted by area/volume is not necessarily useful, and that we need more information to understand what is really going on. Has there been any research in this area?

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12 hours ago, VenusPrincess said:

From this metaphor we can see that an increase in average temperature weighted by area/volume is not necessarily useful, and that we need more information to understand what is really going on. Has there been any research in this area?

Not necessarily useful, true. It’s like the joke about the statistician whose head was in the oven and feet were in an ice bath, who declared “On average, I’m comfortable”

But it doesn’t mean that applies to other situations. If you want to rebut the usefulness as applied to climate, you’ll have to analyze the actual problem. Your analogy is poor, and not a substitute for science. If the average temperature is going up, it means more energy is coming in than going out. Where exactly this is temperature increase is happening is unimportant if that’s what you are trying to determine.

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13 hours ago, VenusPrincess said:

But what does that tell us? Is that a useful metric?

13 hours ago, VenusPrincess said:

From this metaphor we can see that an increase in average temperature weighted by area/volume is not necessarily useful, and that we need more information to understand what is really going on. Has there been any research in this area?

Surely the average is useful for some purposes but not for others in both cases.

So clearly knowledge of the value of that average alone is worthless without knowledge of the intended use.

I see that you joined 13 hours prior to this post and have already made 5 posts here.
Welcome, but I expect you don't realise that new members are allowed only 5 posts in their first 24 hours.
After that they can post normally.
This is a (sadly) much needed anti spam measure

So I look forward to your clarification of your topic in around 11 hours time.

22 minutes ago, swansont said:

If the average temperature is going up, it means more energy is coming in than going out

I don't agree that this conclusion follows from that premise for either the car or the Earth's average 'temperature'.

Both contain internal heat sources.

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6 minutes ago, studiot said:

I don't agree that this conclusion follows from that premise for either the car or the Earth's average 'temperature'.

Both contain internal heat sources.

The context being what it is, the comparison regarding the earth is to an earlier state, in which average temperature was roughly constant.

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8 minutes ago, swansont said:

The context being what it is, the comparison regarding the earth is to an earlier state, in which average temperature was roughly constant.

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On 10/16/2020 at 12:37 PM, studiot said:

Surely the average is useful for some purposes but not for others in both cases.

So clearly knowledge of the value of that average alone is worthless without knowledge of the intended use.

I see that you joined 13 hours prior to this post and have already made 5 posts here.
Welcome, but I expect you don't realise that new members are allowed only 5 posts in their first 24 hours.
After that they can post normally.
This is a (sadly) much needed anti spam measure

So I look forward to your clarification of your topic in around 11 hours time.

I don't agree that this conclusion follows from that premise for either the car or the Earth's average 'temperature'.

Both contain internal heat sources.

The global average temperature deviation (or anomaly) is used by climate scientists to justify their concern over man-made climate change, but if that calculation of the global average temperature has no thermodynamic validity then its use is questionable, just as the calculation of the average temperature of my car has no thermodynamic validity; it is not representative of anything material without more information.

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Not everything that's useful or meaningful as an average must have a valid thermodynamic definition. The average receding speed of the galaxies is increasing, yet the universe is not a thermodynamic system.

The concept of temperature that's used in these atmospheric models is more akin to the concept of temperature in the heat equation. It is not the thermodynamic concept of temperature but for small cells of material that have a definite specific heat. Do you suggest the Earth's atmosphere does not have a useful concept of specific heat?

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3 hours ago, joigus said:

Do you suggest the Earth's atmosphere does not have a useful concept of specific heat?

Yes. To illustrate how ridiculous it is to summarize in a single number the heat in an entire planet's atmosphere consider if we were engineers designing a rover to land on Mars. There are a million questions we could ask regarding temperature, including:

1.  How hot could the rover capsule's heat shield get as it cuts through the atmosphere?
2. What are the 90% (typical) and 99.99% (extreme) confidence intervals for the temperature at the locations where we intend to operate the rover?
1. How do the temperature confidence intervals depend on season?
2. How do they depend on time of day?
3. What weather events can create local disturbances in pressure and temperature?
1. How often do they occur at the locations where we intend to operate the rover?
2. Does their frequency change with season?
4. What is the cloud cover like at the locations where we intend to operate the rover? How does it influence temperature and availability of solar power?
1. Dependence on season and time of day...

And I could go on and on and on.

If you told me the average temperature on the Martian surface was -60 °C that would be utterly useless for our efforts to engineer a rover to survive on Mars. A useful understanding of the thermodynamics of planet's atmosphere simply cannot be summarized in a single number. It contains very little useful information.

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8 hours ago, VenusPrincess said:

The global average temperature deviation (or anomaly) is used by climate scientists to justify their concern over man-made climate change, but if that calculation of the global average temperature has no thermodynamic validity then its use is questionable, just as the calculation of the average temperature of my car has no thermodynamic validity; it is not representative of anything material without more information.

How fortunate the climate scientists provide an abundance of other information concerning temeprature variations in the oceans, the land and the atmosphere, locally and regionally, over the short term ( hours and days) to the long term (years, decades, millenia and beyond), relating it to such diverse issues as ocean currents, weather, atmospheric composition, albedo influences, etc.

In short, you have erected a strawman upon which you are making a pointless and ill-informed attack.

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4 hours ago, VenusPrincess said:

If you told me the average temperature on the Martian surface was -60 °C that would be utterly useless for our efforts to engineer a rover to survive on Mars.

A statistical distribution is made up of an infinite series of statistical moments. What you're saying is that the first statistical moment is not significant.

Never mind that reports of global temperature are meant to monitor general trends, not to build a rover to operate here or there.

@Area54 has seen your strawman miles away. I was distracted.

<T_Mars> = -63 ºC

<T_Venus> = 453 ºC

So this is utterly useless even to build a rover? I don't know why you want to build a rover in order to monitor Earth's global climate, by the way.

If you wanted to build a rover, it would be silly to rely only on average global temperature as "the" parameter.

I wouldn't describe the behaviour of an ant's colony only in terms only of its average position either.

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52 minutes ago, joigus said:

<T_Mars> = -63 ºC

<T_Venus> = 453 ºC

Before I decided to go for the jugular this contrast/comparison was the one I was going to make. It's almost as telling and probably more practical. Thanks for adding it.

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16 hours ago, VenusPrincess said:

The global average temperature deviation (or anomaly) is used by climate scientists to justify their concern over man-made climate change, but if that calculation of the global average temperature has no thermodynamic validity then its use is questionable, just as the calculation of the average temperature of my car has no thermodynamic validity; it is not representative of anything material without more information.

It was pointed put that your car analogy is poor, so you go ahead and use it again.

As Area54 observed, all you are doing is attacking a strawman. Average temperature is simply a proxy for total energy content that is perhaps easier to grasp than if one used energy units. That energy is either from a source that has changed or it’s being trapped from existing sources. Science tells us it’s the latter.

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16 hours ago, VenusPrincess said:

If you told me the average temperature on the Martian surface was -60 °C that would be utterly useless for our efforts to engineer a rover to survive on Mars. A useful understanding of the thermodynamics of planet's atmosphere simply cannot be summarized in a single number. It contains very little useful information.

Surely, you are going too far.  If we know that the average temperature of the Martian surface is -60C, how can that be "utterly useless" in our efforts to engineer a rover capable of surviving on Mars?  On the contrary, it has enabled us to engineer numerous recent examples of rovers capable of operating in this low-temperature Martian environment.

Edited by Charles 3781
tidying
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I find it really hard to get a coherent picture of the opening post. I see three different aspects that trigger different tones of response, some of which are pretty redundant with the replies given already. So maybe I'll just briefly touch all three aspects to show why at least I have problems with getting a clear picture of this thread.

First, there is the relatively long explanation about sums or averages not giving the full information about the individual components that contribute to them. That is correct, mathematically trivial and well known to everyone working in any field of complex systems. It is also pretty banal, and applies to pretty much every science or society related number you ever hear in the TV news: the gross-domestic product, the number of Covid-19 infections, salaries in the IT sector, the time that kids spend on social media,  ... . Now, admittedly, there are a lot of people who, for different reasons, appear to limit the discussion of a topic essentially to these numbers. So for this aspect of the opening post I am torn between a sarcastic "great work, Sherlock" and an honest "it is great that you are aware that this one number is not the full picture". I think the relative volume of the sub-optimal example pushed a few people towards the former reaction.

Second, there is the aspect of the specific role of an average temperature in climate science, or more specifically its role in the climate change debate. For me, this would be a great topic of debate and learning. I worked as a scientist in a somewhat related field for several years, and still my understanding of it is very basic and with a lot of "that's how I imagine it is". I'll not formulate a coherent story for this post, but just throw in a few imho relevant pieces: In the context of the greenhouse gas effect the average temperature is a very sensible, experimentally-measurable observable with some weaknesses (energy stored in the oceans). Climate scientists don't model average temperatures but create sets of future scenarios for the evolution of complex systems. The evaluation of these scenarios cannot be reduced to a  single number that tells you how good or bad the scenario is. What you can do is group your scenarios according to some meaningful parameter, see what typical scenario effects are for that parameter, and then have some delegates barter about how bad you want it. Remember: The problem with climate change is not the increase in the mean temperature, but increase in extreme weather conditions, change in habitability on the planet, the self-enforcing mechanism (loss of reflective ice, melting of permafrost, methane emissions from the oceans), and possibly a bit of land loss from rising sea waters.

And finally, there is the third aspect of the opening post which really turns me off: The first half of the first sentence and the last sentence. Thanks to them, the post with potential for an interesting discussion comes in a wrapping that says "troll, ignorant or political agenda inside" to anyone with a bit of experience in social media. So despite giving the OP a huge benefit of doubt with the time I put into this post I don't want to leave them without comment: 1) "Climate scientists are concerned with deviations in the average global temperature": No, they are mostly not. Type "climate science" into Google and check out what they do. 2) "Has there been any research in this area [of what is really going on]?": Yes. There is a complete scientific discipline called Climate Science that is concerned with these questions.

Edited by timo
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21 hours ago, VenusPrincess said:

The global average temperature deviation (or anomaly) is used by climate scientists to justify their concern over man-made climate change, but if that calculation of the global average temperature has no thermodynamic validity then its use is questionable, just as the calculation of the average temperature of my car has no thermodynamic validity; it is not representative of anything material without more information

Did you say you were some sort of engineer ?

Surely you understand that engineers use parameters that are single numbers to describe an environment or regime for instance Reynold's Number  in fluid mechanics distinguishes between quite different mechanical environments in fluids.

In the same way the average surface temperature can form part of another dimensionless environment number ( Xi) that indicates whether a planet has an atmousphere at all and, if so, what the gases are likely to be.

$\Xi = \frac{{3{k_B}T}}{{4\pi G{r^2}\rho u}}$

where kB is Boltzman's constant, and u is the atomic mass unit = 1.66054 x10-27 kg

Ref

Douce  : Thermodynamics of the Earth and Planets     :   Cambridge University Press.

Douce gives a derivation and interpretation of Xi for all the planets and some moons on pages 616 -620

The other informatom contained in this parameter, I would suggest would be very useful for someone designing a rover as it contains the gravitational potential energy at the surface,

(That is it compares the gravitational potential to the escape kinetic energy via Boltzman)

Which I would think very useful in stability/ traction and other mechanical considerations for a rover, apart from the obvious materials considerations of the operating temperatures such as brittle transition temperature/ phase change temperatures etc etc.

What were you saying about climate change and what does that have to do with a mars rover ?

Edited by studiot
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12 hours ago, Area54 said:

you have erected a strawman

Policy makers rely heavily upon the global average temperature anomaly to make conclusions and decisions. If they did not then your strawman claim might be valid.

11 hours ago, joigus said:

Never mind that reports of global temperature are meant to monitor general trends

Monitor the trend in what? The averaged temperatures of a turbulent gas measured over wide spans of time and space which have highly heterogeneous pressure and surface conditions is supposed to be an estimate of what exactly? Within the next 100 years people will look at back at this as junk science.

12 hours ago, joigus said:

<T_Mars> = -63 ºC

<T_Venus> = 453 ºC

So this is utterly useless even to build a rover?

Yes. It tells us nothing about dependence on latitude, time of day, season, local weather events. It's useless. The average surface temperature on Earth is ~15 ºC, but it can range from -80 ºC to 50 ºC depending on time and location.

5 hours ago, swansont said:

Average temperature is simply a proxy for total energy content

This demonstrates a poor understanding of thermodynamics. We cannot hope to measure tiny deviations in the energy content of an atmosphere by averaging surface temperature measurements over wide spans of time and space which have highly heterogeneous pressure and surface conditions.

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12 minutes ago, VenusPrincess said:

This demonstrates a poor understanding of thermodynamics. We cannot hope to measure tiny deviations in the energy content of an atmosphere by averaging surface temperature measurements over wide spans of time and space which have highly heterogeneous pressure and surface conditions.

Let’s see an analysis, then. Quantify the “tiny deviations in the energy content of an atmosphere” and also the effect of pressure on the measurements.

Is this a measurement of the atmosphere or the surface (i.e. land and water)? climate.gov suggests it’s the latter https://www.climate.gov/news-features/understanding-climate/climate-change-global-temperature

(they also disagree the with “tiny” characterization of the energy deviations)

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12 minutes ago, VenusPrincess said:

Monitor the trend in what?

Monitor the trend of the averaged temperatures of a turbulent gas measured over wide spans of time and space which have highly heterogeneous pressure and surface conditions. Exactly.

14 minutes ago, VenusPrincess said:

is supposed to be an estimate of what exactly?

Of the average temperatures of a turbulent gas measured over wide spans of time and space which have highly heterogeneous pressure and surface conditions.

You seem to have a very basic problem of understanding.

And @VenusPrincess, don't go further in that direction, because I can see very clearly now how much you ignore about ergodicity and the role it plays in physics.

Doh!

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23 hours ago, VenusPrincess said:

The global average temperature deviation (or anomaly) is used by climate scientists to justify their concern over man-made climate change

It has been useful to have a simple, single measure that shows global change but that global average is the tip of a very large iceberg. The last IPCC report - AR5 - ran to 2,000 pages, citing nearly 10,000 scientific studies. Claiming all concern over man made climate change is justified by one global average surface air temperature is not true.

Admittedly most Presidents or Prime Ministers will not have read any full IPCC reports, but Synthesis reports and Summaries for Policymakers are reasonably accessible and understandable. Also they can call upon science agencies and experts to help them understand - as well as confirm that the science that produced those reports is valid. They can also run checks for evidence of fraud or conspiracy - but the "worst" anyone has managed is a few phrases in emails taken out of context and the fact that there are people in the UN who are dedicated to reducing global inequality and poverty and they want to incorporate those ends into climate policy.

The use of global average surface temperatures may be more accident of history; a whole lot of local temperature records - minimums and maximums mostly - being in existence when climate change became a subject for study offered a way to find out if the world is warming (or cooling). At it's most basic it is a way to confirm or not that global warming is actually taking place. Whether viewed as a history of warming that needs explanation or viewed as real world confirmation of theoretical understanding of The Greenhouse Effect and how it should be expected to change global heat balance when CO2 levels change, it does give confirmation.

Dive into the data and variability across the world is there too ; it gets used in many different ways, including with respect to local and regional change.

2018-19 regional average temperature anomalies for example -

But I think of all measures of real world change that most closely shows the heat gain from man made climate change, this one is best -

Edited by Ken Fabian
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1 hour ago, swansont said:

Is this a measurement of the atmosphere or the surface (i.e. land and water)? climate.gov suggests it’s the latter https://www.climate.gov/news-features/understanding-climate/climate-change-global-temperature

I assumed the global average temperature deviation focused on the latter as well. Your own link shows how useless a global average temperature is from a practical perspective. A graphic on that page shows that the majority of months in North America had for the most part cooler temperatures today than during the pre-industrial average:

1 hour ago, joigus said:

Monitor the trend of the averaged temperatures of a turbulent gas measured over wide spans of time and space which have highly heterogeneous pressure and surface conditions. Exactly.

The question is about the usefulness and predictive power of that statistic. If you can't even define what you are trying to measure then you can't even begin to answer that question.

1 hour ago, joigus said:

I can see very clearly now how much you ignore about ergodicity and the role it plays in physics.

You cannot use temperature measurements to deduce the statistical properties of a thermodynamic process if you cannot establish a valid thermodynamic connection between the measurement and the process. You haven't even gotten as far as clearly defining the process you are trying to measure, much less established a connection between the measurements and the process.

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2 hours ago, VenusPrincess said:

Policy makers rely heavily upon the global average temperature anomaly to make conclusions and decisions.

No. Policy makers rely heavily upon the global average temperature as a means of simplifying the concept of climate change for the generally uneducated and under informed public who lack the inclination to study the data and the resultant science to the degreee* necessary to move beyond such simplifications. You have fixed, even fixated, upon average temeprature as if it was the apex and all subsuming acme of climate science. That is why I say, beyond doubt, you have erected a strawman. I ponder now on your motives. Perhaps you would explain them.

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38 minutes ago, VenusPrincess said:

I assumed the global average temperature deviation focused on the latter as well. Your own link shows how useless a global average temperature is from a practical perspective. A graphic on that page shows that the majority of months in North America had for the most part cooler temperatures today than during the pre-industrial average:

How do you figure that?

“This animation shows monthly temperatures for January–December 2019 compared to each month's 1981-2010 average.”

1981-2010 is not considered pre-industrial by most historians

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19 minutes ago, swansont said:

How do you figure that?

“This animation shows monthly temperatures for January–December 2019 compared to each month's 1981-2010 average.”

1981-2010 is not considered pre-industrial by most historians

Sorry, I read the text on the graphic that referenced the pre-industrial average and assumed that it pertained to the graphic. The point still stands.

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9 hours ago, VenusPrincess said:

You cannot use temperature measurements to deduce the statistical properties of a thermodynamic process if you cannot establish a valid thermodynamic connection between the measurement and the process. You haven't even gotten as far as clearly defining the process you are trying to measure, much less established a connection between the measurements and the process.

Thermodynamics is the study of equilibrium. The Earth is not a system in equilibrium. Climate science most emphatically is not sheer thermodynamics.

Thermodynamics, e.g., does not allow you to calculate anything statistical, like, e.g., fluctuations. Statistical mechanics does.

In (most) statistical mechanical systems, you can see that the temperature is the average kinetic energy per degree of freedom. These degrees of freedom are coded in what I called specific heat.

Because systems are ultimately Hamiltonian, they satisfy an interesting mathematical property: The phase-space points can mix all they want (and in chaotic systems they do, which makes averages more robust, not less), but they do not contract in volume, meaning that microscopic systems spread their dynamical information very efficiently.

IOW, there is no chance that a small region of phase space can store big quantities of energy making local averages non-robust, as you are suggesting.

As to local cooling:

If the first statistical moment of the distribution is shifting, an increase in the second moment is exactly what I would expect before the system reaches the next closer-to-stationary stage. If the variance goes up, some places would overheat and others would "overcool." Nothing unexpected there, because the system is "trying to equilibrate."

So temperature measurements are significant.

But they're not the whole story, as has been pointed out to you over and over. The sea is nearly a perfect absorber of radiation and the ice caps are nearly a perfect reflector (albedos.) There is the question of sea currents too. The ice caps should be building up by now because we are well within a Milankovitch cycle. They're not: It's just the opposite. This will interrupt the circulating flow in the seas.

None of these important details seem to have caught your attention, which would have amounted to an interesting conversation. All you're interested in is to not let go of your strawman (the average temperature parameter) and punch its face repeatedly. The average temperature, being significant, is the catchphrase you've chosen to attack. It's your voodoo doll against climate science.

8 hours ago, VenusPrincess said:

The point still stands.

Your point does not stand, it's a blurry blob. Your strawman does.

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On 10/20/2020 at 4:03 AM, VenusPrincess said:

if we were engineers designing a rover to land on Mars. There are a million questions we could ask regarding temperature, including:

You introduced a Mars Rover.

I asked you two straightforward uncontroversial questions and provided quite a bit of useful information about both planetary thermodynamics in general and its application to both Mars Rovers and this thread.

You have failed to respond.

Is there a problem ?

Edited by studiot

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