I propose to broaden the discussion somewhat. I propose to analyze the graph of temperature changes in the northern hemisphere of the Earth (above) and in the southern hemisphere of the Earth (below). Information source http://platformaxxi.org/2019/08/01/gccn/. Until 1400, the global average temperature was not an informative characteristic of the Earth's climate. In one hemisphere there was a warming, in the other - a cooling, and on average the temperature on the planet did not change. There is no reason to deny that this may happen again.

Borys Kapochkin Thank you for your reply. However, I suggest that we stay focused on the posted discussion subject: "Is it misleading to measure the Earth global warming based on moving up the average global temperature anomaly of Earth?" It seems that you missed the main point: the Earth climate cannot be characterized by the average global temperature. Such a temperature does not exist and cannot be measured for a non-equilibrium system. It is a wrong climate metrics.

Kolker

One word describes you best: charlatan

READ before you ASK

Go to NOAA via google

Anomaltyglobal temperatures

This is climatology 101 but you as all those other nitwits refuse to study and only have your own gut-feelings

You deny the work of thousands of experts: are you such a GENIUS?

Don't make us laugh

Harry Ten Brink.

First reaction. This is very rude and insulting. I would not like to read such comments in ResearchGate addressed to me. You need to be removed from this resource. You have violated the basic ethical rules of ResearchGate. The points. 1. Quote: "you refuse to study and only have your own gut-feelings." Comment. The topic has the rank of discussion. Everyone is equal here. The main criterion is the evidence base. You are not qualified to be a teacher.

Quote: "You deny the work of thousands of experts." In science, I don't mean getting ranks in education, expert opinions are not accepted as an argument of truth. You probably didn't care enough about this issue. Example 1. The meteorologist Wegener became the author of the theory of plate tectonics. He had no qualifications in geology. Another example, Newton's laws were not recognized in France for many years. The reason is that Newton was not French. The list is endless. Conclusion. You called the author of the discussion "charlatan" and "nitwits" without giving the necessary and sufficient arguments. This is the basis for removing you from the resource. Let's look at the reaction of the ResearchGate management.

Alexander Kolker

Measuring the average temperature of the Earth is a legitimate scientific activity; and it is not misleading to report that the average temperature of the Earth, and in many smaller regions, the temperature has been rising. This is a fact!

It is only misleading if it is being used to argue sometning that is false. What false conclusion do you think is being drawn?

Is it that if we continue to increase the amount of carbon dioxide in the atmosphere, eventually the result will be catastrophic for mankind? We know that carbon dioxide rose significantly 50 million years ago which led to a minor extinction during the Paleo-Eocene Themal Maximum. Is that fact also misleading?

It seems to me, and I assume Harry, that you are just a climate change denier.

It is people like you who are preventing action being taken to reduce the burning of fossil fuels. The CO2 emitted has already cost lives with wild fires in California and Australia, an increase in hurricanes, typhoons and tornadoes, and flooding in the USA, Australia and Pakistan. No wonder Harry is angry.

Alastair Bain McDonald You asked, "What false conclusion do you think is being drawn?" Without going to personal attacks and emotions, I am going to demonstrate to you mathematically using only fundamental thermodynamic concepts what false conclusion is being drawn.

Here it is:

I start with a rigorous thermodynamic definition of temperature, which is

T=(∂E/∂S)V,N

This definition applies only to a local physical system in equilibrium. E is internal energy of the local physical system, S its entropy.

From this definition it follows that T is an intensive variable, i.e. this is condition of a local physical system, and not an amount of something that this system contains.

In contrast, internal energy E and entropy S are extensive thermodynamic variables that can be added together and then averaged.

Using these properties, for a global system like Earth with numerous local geographic temperatures, 1....,n

T1=(∂E1/∂S1)V,N, ....... Tn=(∂En/∂Sn)V,N each in local quasi equilibrium,

we could define the formal global average temperature as

Tav=∂(E1+E2+⋯En)/∂(S1+S2+⋯Sn)V,N

Now, we would like to express the formal global average temperature Tav defined above through all physically measured local temperatures T1=(∂E1/∂S1)V,N, ....... Tn=(∂En/∂Sn)V,N

However, the derivative Tav=∂(E1+E2+⋯En)/∂(S1+S2+⋯Sn)V,N cannot be expressed using any combination of only local derivatives T1=(∂E1/∂S1)V,N, ....... Tn=(∂En/∂Sn)V,N, i.e. only local temperatures. In particular,

Tav=∂(E1+E2+⋯En)/∂(S1+S2+⋯Sn)V,N ≠1/n[(∂E1/∂S1)V,N, +...+.(∂En/∂Sn)V,N].

Thus, Tav ≠1/n[T1+....+Tn]

Therefore, the global average temperature cannot be presented as an arithmetic average or weighted average or any other combination of only local temperatures. This means that the global average temperature cannot be calculated in any sensible physical way using only local measured temperatures.

Adding and averaging temperatures is the same as adding and averaging, say, the phone numbers from your phone directory. The resulting average phone number is totally meaningless although it can easily be calculated.

As a last resort, one may try to present the average Tav derivative using linearity as

Tav=∂(E1+E2+⋯En)/∂(S1+S2+⋯Sn)V,N =1/n[∂E1/∂(S1+⋯+Sn)+...+.∂En/∂(S1+⋯+Sn)]

However, in this case the denominators still contain the sum of entropies, and not the separate entropies as needed for the desired average temperature expression.

The same mathematical demonstration is valid for the global temperature anomalies that are usually used to illustrate the relationship between CO2 level and global warming. Therefore, the calculated global average temperature anomalies are as meaningless physically as global average temperatures.

This is the false conclusion being drawn:

The bottom line: the whole business of demonstrating the global warming (or cooling) based on move (up or down) the single value of the calculated arithmetic average global temperatures (anomalies) is meaningless. The calculated single value arithmetic average global temperature is simply a wrong metric that does not characterize warming or cooling of such a complex non-linear and non-equilibrium system as Earth climate.

Yes, maybe it is misleading, like when a weighing machine reports the mass. But does this change the meaning of the reading, when the numbers increase from year to year and you have to buy new pants? Anyway, what is actually calculated is the heat balance and the additional heat that is stored. Obviously, additional heat increases the temperature. So nobody can really be surprised that the temperatures go up on average at most locations, ice is melting and coasts are flooded. The abundance of energy in the atmosphere increases the tendencies of heavy storms, which makes the boses of insurance companies increasingly sweat - another indication that the earth has a fever and that the heat rise is too fast to be natural. So overall the average global temperature may be the wrong quantity to be measured, but this does not change the fact that we all have a big problem.

Alexander Kolker

It is misleading to say that because averaging telephone numbers is meaningless then averaging temperature readings is also meaningless.

Moreover T=(∂E/∂S)V,P is not a definition of temperature; it is a relationship between temperature and entropy. (What is your definition of entropy?) The definition of temperature is: the average kinetic energy of all the atoms or molecules of that substance.

The average temperature of a substance can be measured using a thermometer, and reading can be averaged to give a meaningful value.

You have not atmitted that you do not believe in global warming far less that it is caused by fossil fuels, but that seems to be what you are implying. Do you accept that carbon dioxide is a major greenhouse gas and by increasing it we are causing global warming. If your answer is no then you are denying a well established scientific fact.

The catastrophe that will result from no action being taken will result in consequences far worse than those the that deniers of the Holocaust are disputing.

Alastair Bain McDonald Your reply post demonstrates to me clearly two main things:

1-your lack of understanding of the basic concepts of thermodynamics

2-your inability to stay within the posted discussion subject and promoting some political agenda and your personal political views instead.

1-you are saying "The definition of temperature is: the average kinetic energy of all the atoms or molecules of that substance." You are mixing two different concepts. Temperature is NOT energy (kinetic or otherwise). This is a common misconception rooted in 18-th century when scientists were honestly trying to understand what's the difference, if any. If these are the same, we would not need temperature at all, we would use energy or heat instead.

It is understood now by contemporary statistical physics that qualitatively temperature is an indication a condition of a physical system in terms of how energy is distributed over physical states (quantum). If you distribute a small amount of energy over only a few states, you'll get a very high value of temperature. The number of states is directly related to entropy, S~ln (number of states). This is a physical foundation of the relationship T=(∂E/∂S)v (and, no, this is not my definition of entropy-see numerous texts on statistical thermodynamics). A laser pointer is a good example. Its temperature could be in millions of degrees, and this temperature comes out of a low energy flashlight battery. You cannot even feel the warmth of that huge temperature by your hand. This alone demonstrates that temperature is NOT energy.

Next wrong statement of yours: "The average temperature of a substance can be measured using a thermometer, and reading can be averaged to give a meaningful value." Thermometers work providing a corresponding reading by going into equilibrium with the local system, not by averaging anything. Equilibrium means that the measured temperature is the same everywhere in that local system. Otherwise, the system is not in equilibrium and, as such, has the various values of temperature that cannot be averaged until a physical process of equilibration takes place.

I cannot continue here teaching you the foundations of thermodynamic principles. Do yourself a favor, pick up any text of this subject and refresh your knowledge. Otherwise, you may, of course, remain ignorant and demonstrate being wrong on the whole subject.

2-I have no desire to get involved in any political discussion. Belief or not belief in global warming without having a right metric for it does not make any sense. Beliefs could be preached in a church. Beliefs do not belong to any discussion that is supposed to be based only on justified physical arguments, not on personal attacks and naming political cliches.

Thomas Mayerhöfer I am glad that you have acknowledged (although reluctantly and with hesitation) that the global average temperature is misleading and "...it may be the wrong quantity". At least this is a step in the right direction.

But then by saying "...when the numbers increase from year to year and you have to buy new pants" you actually imply that this quantity is kind of index or proxy for that global temperature, and it bears the same units as temperature-degrees (K, C, F, etc.)

This argument is often heard that the global temperature, however it is calculated, while not being really what is physically driving the climate, is, nonetheless, an index or proxy for whatever does drive it. It is uncritically assumed that an upward move of a global average temperature anomaly index affects an underlying climate dynamic, such as changes in the numbers or severity of storms, trends in rainfall, or melting of glaciers or many other local physical dynamical processes.

What connection exists between these dynamical processes and such an average temperature index? intensive variables, like temperature, do not drive the dynamics of the atmosphere and oceans, whose dynamics is driven by gradients, or differences over the distances in thermodynamic variables, rather than the variables themselves.

If absolute variables (temperature, pressure, chemical potential) don’t drive climate dynamics, there is no reason to expect that averages over them will.

So, if you insist that the global temperature index affects the melting of glaciers at some location, then that melting becomes a function of temperatures elsewhere on the planet too, which is physically untenable. Claiming otherwise is equivalent to temperature at a distance! While forces at a distance are reasonable concept for classical gravity and electromagnetism, they are not suitable for thermodynamic processes.

Moreover, on top of that, melting becomes also depending explicitly on temperatures from the past because the index anomaly includes a past baseline (pre-industrial years) that is subtracted from the current year average temperature. So, not only are the fate of glaciers today explicitly dependent on temperatures in, say, a remote desert, but also on temperatures in that desert from the past years. This is nonsense.

You are also saying that "The abundance of energy in the atmosphere increases the tendencies of heavy storms". I have already explained above that the amount of internal energy in the atmosphere does not cause heavy storms or other natural dynamic phenomena: only the gradients of energy (and related gradients of local temperatures and local pressures) cause them.

To summarize: "...this does not change the fact that we all have a big problem."

From the physical arguments above it does not follow that we have a big problem or any imminent climate crisis. Climate system is the open chaotic non-linear non-equilibrium system. It will be slowly changed over the centuries on its own regardless of cutting the CO2 emission. And climate change is not equivalent to temperature change alone. A lot more factors and corresponding metrics comes into play.

Alexander Kolker Wow... you really wrote a lot based on what I might imply. Can you also response to what I have actually written? So what about the extra heat that is stored based on the extra amount of CO2? Certainly it is not evenly distributed over the earth, reflection varies depending on the surface, sea is storing heat differently from land, water is more abundant above sea, so the concentration of water vapour increases there stronger than over land. So there you have your gradients and reasons for them to increase. So from the physical arguments above it follows that we have a big problem or an imminent climate crisis. Certainly, climate system is the open chaotic non-linear non-equilibrium system. It will be slowly changed over the centuries on its own regardless of cutting the CO2 emission - but what has this to do with man influencing it strongly by increasing CO2 levels drastically? We are not talking about slow effects as they were always present, we are talking about changes two order of magnitudes faster than that.

Small addendum: Alexander Kolker present us a literature where it is stated that T=(∂E/∂S)V,P is the definition of temperature. This relation is simply derived from the fundamental equation of the internal energy, where the derivative of the extensive variable gives the conjugated intensive variable, but it is not used as a definition of temperature (do you also claim that pressure is defined by p=-(∂E/∂V)S,n instead of p=∂F/∂A?). It also contains an error and actually is given by T=(∂E/∂S)V,n - have yourself a look at the textbooks of Physical Chemistry! By the way, in the 18th century people did not know the structure of matter (not even in the 19th century), so your claim that "This is a common misconception rooted in 18-th century when scientists were honestly trying to understand what's the difference, if any." is simply a smoke grenade. The same is true for "Equilibrium means that the measured temperature is the same everywhere in that local system". In this case equilibrium means that the thermometer must be in equilibrium with the system of which one wants to measure the temperature". Looks to me that you have yourself not a good grasp of the concepts. By the way, I would define an averaged temperature as Tav=ΣxiTi/Σxi. If you like, you can write Tav=Σxi(∂Ei/∂Si)V,n/Σxi where xi is the molar fraction, but could, for gases, be the volume fraction as well (if we assume ideal gases which should be allowed for the atmosphere). If you mix, e.g., 20 ml of water at a temperature of 300 K and 60 ml of water at a temperature of 330 K, guess what average temperature the mixture will have... ;-)

Thomas Mayerhöfer I prefer to finish our exchange because I see that it leads to nowhere. I am dropping now only a few summary lines instead of writing a lot:

1. A meaninglessly calculated temperature metric can result only to an unsubstantiated conclusion about calculated (not directly measured) global warming, whether it exists at all as a global phenomenon and how much, if any (two orders of magnitude faster than natural??)

2. I appreciate that you have acknowledged that "Certainly, climate system is the open chaotic non-linear non-equilibrium system." Now, I suggest that you make a next step: learn the dynamic properties of such system using rich literature on this subject. When try to conclude whether it is possible to control and predict the behavior of such system using only one factor (one control knob)- human CO2 emission ignoring numerous other factors (internal and external) that form multiple positive and negative feedback loops. Good luck....

I see that concrete questions make you fire up more smoke grenades to cover up your escape:

1. Global warming does not need to be calculated, it can be measured, but actually measurement and predictions agree with regard to the, very stable, trend upwards.

2. Chaotic system does not mean that you cannot calculate any state of the system. Calculations also do not involve only one factor. E.g., water vapor concentration and that of other gases is also very important.

In any way, to understand the greenhouse effect in principle, you do not need to be able to calculate it by yourself - everyone can experience this effect by her/himself, just enter a greenhouse....

Thomas Mayerhöfer I really wanted to finish our discussion because I value my time. However, I just noticed your examples in your 'small addendum'.

What a mess....You must be missing the entire point...So, it is my final attempt.

You write "I would define an averaged temperature as Tav=ΣxiTi/Σxi."

OK, but what if I now want to define an average temperature as Tav=T1 x1 *T2x2 …*Tnxn . This is an extended geometric average. Why not? Or I may pick as an average 1/Tav=1/n*(1/T1x1 +1/T2x2 +...1/Tnxn )- an extended harmonic average, and so on. Why not? There are numerous possible constructs that make an average out of a set of values T1, ...Tn. Why is it that a simple arithmetic average (or weighted arithmetic average) is much preferred? Without an underlying physical process that directs the choice of averaging, any of possible averages are equally a good choice (or equally bad choice). There is no basis for picking the right one. And all these averaging schemes will result in a different numerical value of the average. If the physics does not prescribe one average to be used over another, as it does not for non-equilibrium temperatures, we may use any average. If one chooses one averaging formula, while another chooses a different formula, there is no way to settle a disagreement as to whether the system is getting “warmer” or “cooler” with time.

Averaging does not represent any means of avoiding the fact that a system is not in global thermodynamic equilibrium. Thus, in the case of nonequilibrium thermodynamics, temperature averages fail in the most basic role of an average, which is for one value to represent many.

If I measure, say, a local temperature +30C on the equator and -10C on the Northen pole, then the simple arithmetic average using the same weights Xi for simplicity will be +10C. Can you conclude from the average temperature +10C that the ice on the Northern pole is melting? Or that the plants in Africa will not develop because of low temperature +10C for that region? There is no physical system to which that average +10C can be assigned. It is either -10C or +30C unless there is a physical process of mixing these two areas and equating these temperatures to an equilibrium. But these are disjoint physical areas, with no contact and no way of mixing.

And this leads to your example. "If you mix, e.g., 20 ml of water at a temperature of 300 K and 60 ml of water at a temperature of 330 K, guess what average temperature the mixture will have... ;-). Exactly, one can easily calculate the equilibrium temperature of this mix when physical process of equilibrating is complete. But even this seemingly simple example demonstrates that the final equilibrium temperature will not be uniquely specified by the original states. Indeed, it will also depend on the path taken by the process. Suppose two thermal systems a and b have equal heat capacities and the same mass (for simplicity here) but initially different temperatures, Ta and Tb . After putting them in thermal contact they will equilibrate at the common temperature (T a + T b )/2-looks like an arithmetic average that you like. If on the other hand they equilibrate reversibly, i.e. while producing work, their final temperature will be √ T aT b - i.e. geometric average which is always lower than the arithmetic one.

So, when you formally average without taking into account the physical path, your averaging is not unique, and in fact your result could be anything, as well as your conclusion on the relative warming or cooling vs. the original states.

And finally, it is a good catch of yours: T=(∂E/∂S)V,n. rather than T=(∂E/∂S)V,P. Subscript P is a typo of mine, although it does not change anything here.

Sorry for a lot of writing again but this concludes the case. ....Good luck in your learning path...

Alexander Kolker I would be eager to learn, but you deny us the textbooks where one can find that T=(∂E/∂S)V,n defines the temperature... ;-)

It looks like the whole discussion is anyway pointless, because it is not the temperature itself that is averaged...https://scied.ucar.edu/image/measure-global-average-temperature-five-easy-steps

Alexander Kolker

This is the 2d time you pose this here at RG

AND you refuse to read the simple answer at the appropriate site of NOAA

What makes YOU think you know better than a bunch of meteorological experts?

Hi Alexander Kolker

I am not a professional but I like learning and I enjoy discussions.

I wanted to give two comments:

Ali Mazrati Ghohroudi Thank you for your interest to this discussion and your comments.

1. Geometric or harmonic averages are just two out of numerous possible averaging constructs taken as a first guess. I can easily demonstrate another example with real measurements that result in 'warming' or 'cooling', say, a room using different averages.

In the summer day the classroom with open windows has temperature, say, 20C everywhere. Now, we want to see if there is 'cooling' or 'warming' inside this room the next day when the windows are closed.

We've measured temperatures the following day as: 17 C; 19.9C; 20.3C and 22.6C. Now, let the arithmetic average be calculated as (17+19.9+20.3+22.6)/4 =19.95C. So, we would conclude some 'cooling' vs open window previous day because 19.95-20=-0.05C. This is exactly what's go on using the globe temperature anomaly: subtraction previous period average from the current periods average (and averaging it all over the globe again).

Now, let's use another average, say, the average sum of squares of the same measured temperatures. And why not? Sum of squares is as good or as bad as any other average. So, this time the average will be: sqrt(17^2+19.9^2+20.3^2+22.6^2)/4)=20.049C. Hence, the temperature anomaly will be 20.049-20=0.049C. It is now positive; we conclude the 'warming' of the room over the previous day. Root mean square is always greater than the mean, or geometric, or harmonic, etc.

Obviously, there is a problem: we have to conclude that the same system (room) both 'cooling' and 'warming' ?! Nonsense.

This simple example demonstrates again and again: if there is no physical reason to pick one average over another then we are making guesses on 'warming' or 'cooling' depending on our favorite averaging method, and not on the actual measurement data.

You are saying "...but no one can argue against the trend."

Yes, by picking the right statistic you can compute that average anomaly that goes up with years. However, this does not mean that the global non-equilibrium system is 'warming'; nor would a downward trend in such a statistic means it is 'cooling' or staying flat because, again, such a statistic is not a measure of temperature at all. It is just statistical properties of your choice, but not the measured values of temperatures themselves.

2. Yes, the atmosphere is well considered as an ideal gas.

You write "The temperature of the ideal gas at any given time only dependent on its internal energy when number of moles is kept conserved."

This way, temperature is viewed as equivalent to internal energy, u(n, T).

However, in u(n, T) = 3 /2 nkT (single atomic gas) , measuring changes in T cannot determine changes in u in environments where the number density is also variable. And it is.

du /u = dP/ P = dn /n + dT/ T . As dP/P is about 5% across the entire Earth’s surface while dT/T would be closer to 20%, variation of n cannot be ignored in comparison to variation in T. As T varies about four times as much as u over the Earth, temperature cannot be a proxy for internal energy in climate. In fact, these numbers suggest that places of high T tend to correspond to low n, which agrees with the well-known tendency of an aircraft to have diminished takeoff performance at high air temperatures.

Therefore, the temperature is not proportional to only sum of local internal energies, as you say, T ave ∝ Qtotal = Q1 + Q2 + Q3 + ... which each Qn ∝ Tn. It is also inversely proportional to the sum of the corresponding entropies, which is reflected in the general relationship mentioned earlier:

Tav=∂(E1+E2+⋯En)/∂(S1+S2+⋯Sn)V,n1....

And that's why the average temperature is not a linear combination of each subsystem temperature, and one cannot conclude that Tave∝ Tn, hence the arithmetic mean is not the right choice.

"....where the number density is also variable. And it is..."

1. n is not the number density, but the number. Otherwise, if E = 3/2 nkt then E would be the energy density, which it is not.

2. How large are the changes concerning the number? Are they really relevant?

This is another illustration that the choice of average MUST be dictated by the physical process, and NOT be taken arbitrarily. This is a high school level example. I could construct many similar examples.

Suppose a car moving the distance S from A to B with the speed V1=40 km/h, and back from B to A with speed V2=60 km/h. What's the average speed, Vav?

The average speed is defined as the total distance (S+S=2S) traveled over the total time. In this case Vav=2*S /(S/V1 + S/V2)= 2/(1/V1+1/V2)=2V1*V2/(V1+V2)=2*40*60/(40+60)=48 km/h. This is an example of harmonic average speed.

Now, suppose the car is moving t1=1 hour with the speed V1=40 km/h and another hour t2 =1 hour with the speed V2=60 km/h. What's the average speed? Vav=total distance traveled over total time, as above. However, now

Vav=(V1*t1+v2*t2)/(t1+t2) = (v1+V2)/2=(40+60)/2=50 km/h. Great!!! We have simple arithmetic average to our relief.

Now, if the car traveled different time with different speed, say, t1=1 hour and t2=2 hours, then Vav=(1*40+2*60)/(1+2)=53.3 km/h. This is a weighted (1/3) arithmetic average, and it could be any weight.

So, if you don't know the actual process using only the given speeds 40 km/h and 60 km/h, what's the average speed? 48 km/h or 50km/h or 53.3 km/h, or anything else? This is exactly what's going on with the temperature averaging using only the locally measured values without any other additional physical process information.....

This is an example how the choice of temperature averaging affects the conclusion of warming or cooling for the same subsequent periods compared to the previous baseline period, i.e., the average temperature anomaly.

I used the actual temperature records of Climatological observations presented by National Oceanic & Atmospheric administration (NOAA) for one particular station located in East Meza, Arizona (see attached file).

This file includes temperature records for each day of the month: Max daily, min daily and temperature at time of observation which was 17:00pm.

I used the column of temperature data: at observation time (At Obs.).

I chose as the baseline period the first 2 weeks.

The question was: are the subsequent weeks 1 and 2 warmer or colder compared to the baseline 2 weeks period?

I started with the standard simple arithmetic average:

the baseline first 2 weeks average was: 56.29; The 1-st week average was 61, hence the average anomaly was 4.71; similarly, the 2-nd week average anomaly was 6.88. Thus, we conclude an accelerating warming trend for weeks 1 and 2 (vs the baseline period).

Now, let's use the median as the average. And why not? After all, median is robust averaging which is not sensitive to some random extreme temperature values which might skew the arithmetic average.

Using, exactly the same data as above, we get: the baseline 2 weeks median was 56.0; the 1-st week anomaly was 6.0; and the 2-nd week anomaly was 6.5. Thus, we also conclude a warming trend but the 1-st week warmer by 1.29 vs. arithmetic average, and the 2-nd week cooler by 0.38 vs. arithmetic average.

Now, let's use the mode temperature as the estimate of the average temperature. Mode presents the most frequent value of temperatures, i.e., it might serve as a valid choice as well as the above averages. Nothing prevents of using it. The mode for the baseline 2 weeks period was 60; the 1-st week anomaly was 5.0; and the 2-nd week anomaly was -1!

So, we have to conclude that the 1-st week is warmer than that based on arithmetic average but cooler than that based on median. Moreover, the 2-nd week anomaly is now negative, i.e., it is colder than the baseline?!

So, using exactly the same data we have to conclude that the 2-nd week is warmer than the baseline based on arithmetic and median averages (and to the various degree) but at the same time it is colder (!!) than the baseline based on mode averaging. This is nonsense-warmer or cooler at the same time depending on the choice of average.

But any average can be equally used because physics does not guide us on the right choice of the average. All of them are equally good or bad. In fact, there are numerous ways to average a set of data. The average is the value that best represents a set of values (best on some criterion). If there is no physical guidance to pick one or another, all are equally good or bad. And conclusions on warming or cooling (and numerical values) will depend on an arbitrary choice of averaging method. Temperature is a continual 4-dimensional non-equilibrium field (3 spatial dimensions and 1 time dimension). Such a field cannot be represented by only one ('best") value-its average.

Therefore, any conclusion of warming based on an upward move of the so-called global average anomaly calculated as a weighted arithmetic average is meaningless.

Now, look at the so-called critical global warming of 1.5 C that the Paris accord has established as a target not to be exceeded. It is also based on an arbitrary use of arithmetic averaging ignoring all other numerous possible methods of averaging. DOESN'T this make this value 1.5C totally meaningless and baseless?? As it was demonstrated in the example above?

I hope that I made my point clear. This nonsense of making alarming conclusion of global warming based on an upward trend of arithmetic average global temperature anomaly should be stopped.

Kolker

You are essentially a complete dilettante and YOU present ONE table to show your wisdom

This here becomes more ridiculous by the entry

Man STUDY before you waffle down your gut-feelings

Start with global temperature anomaly at the NOA site written for the complete ignorants applying to you in particular

It is a disgrace for this Research forum

Thomas Mayerhöfer Re: "I would be eager to learn, but you deny us the textbooks where one can find that T=(∂E/∂S)V,n defines the temperature... "

I have a chance to come back to this thread after I've finished teaching my online course on data analytics for the National Health Systems, the UK.

Here is the textbook reference: Landay, L., Lifshitz, E., Course of Theoretical Physics. vol.5. Statistical Physics. chapter 2, section 12.

The quote: "In other words, temperature will be defined as the derivative of the body's energy with respect to its entropy taken at the constant volume: T=(∂E/∂S)V,n"

This course is one of the most authoritative world-known courses on theoretical physics for professional physicists.

If it makes any difference for you, anyway.

Alexander Kolker Thanks, but I found it myself in the meantime. Anyway, it is not important to decide the matter at hand.

Landau&Lifschitz

but also in all 1st year textbooks on physico-chemistry

Re: Does a climate (stable) exist? That is, does the Earth’s weather have a long-term (stable) average?

The primary purpose of this post was to argue and demonstrate that the concept of the Earth's global average temperature (and anomaly) is ill-defined and misleading. In fact, the global average temperature does not exist.

The purpose of this post is even deeper. It is to argue that the concept of the Earth's stable climate is ill-defined.

Climate is traditionally defined as a long-term average weather pattern. But the question of existence of such an average was so deep that almost no one had thought to ask it before Edward Lorenz-one of the founders of the contemporary meteorology and climatology.

Most climatologists, then and now, take the answer as self-evident: yes, of course, long-term stable average (climate) always exists. Any measurable climate variables, no matter how they vary now, must have a stable unique average in a long run. However, for deep minds, it is far from obvious. E. Lorenz published one of his most deep-thought works in 1964 titled “The problem of deducing the climate from the governing equations” in a little-known journal Tellus, 16, 1964, pp.1-11. DOI: 10.1111/j.2153-3490.1964.tb00136.x

In it he posted the fundamental questions: (i) Was there one climate that changed to another one for some physical reason? (ii) Is there a long-term climate periods within which climate system is unstable and fluctuates on its own without any external physical reason? (iii) Is it possible that a system like the weather may never converge to any stable average?

These are some quotes from the Lorenz paper: ”It is often assumed that the climate, i.e., the set of long-term statistical properties of the atmosphere, is determined by the same system of (non-linear) equations. It should be observed that climate is not universally identified with averages over infinite time intervals. The fact that such expressions as “change of climate” are in common use indicates that many investigators are concerned with averages over long but finite time intervals. In this work, however, we shall be exclusively concerned with averages (or other statistics) over infinite intervals, i.e., with the limits of averages over finite intervals, as the lengths of the intervals approach infinity.

In the special case of the atmosphere, theory alone does not tell us that a climate exists. Recourse to observations is not much more enlightening; the weather of the current century does seem to resemble the weather of the past century, but the weather of the past 12,000 years presumably does not resemble that of the previous 12,000 years, when an ice age flourished.” Page 1.

“Next, even if a climate does exist, there is no a priori reason why this climate should be unique. There are systems of equations which have the property that different solutions, originating from different initial conditions, possess different long-period averages…when a stable climate exists, there is no a priori reason why this stable climate should be unique.

In the case of the atmosphere, theory does not tell us whether a stable climate, if one exists, is unique. Observations also are of no avail; the atmosphere is essentially a one-shot experiment, and we cannot introduce new initial conditions and perform the experiment again.” Page 2.

“We shall pay particular attention to the climatic mean noting particularly how the mean varies with parameter a.” Page 4.

Lorenz concluded that the climate average fluctuated unstably. In other words, as a conclusion of fundamental importance, the Earth’s climate might never settle into one equilibrium with one unique long-term stable average.

Final food for thought:

1. In chaotic deterministic non-linear and non-equilibrium systems, as the Earth’s climate system, there could be more than one stable state. One kind of behavior could last over a very long time, yet a different state could be just as natural for the same system (with an external kick or without any obvious external kick at all).

2. If contemporary ‘climate science’ would spend its resources performing research in the right direction of analysis the chaotic non-linear climate system, we would witness a lot of progress in climate understanding for 70 years since the time of fundamental Lorenz’s publication. Not much was published after him.

Instead, ‘climate science’ has focused on producing physically meaningless ‘global average temperature anomalies’ and blaming CO2 as the main culprit for ‘global warming and climate change’. Unfortunately, most ‘climate scientists’ have traded real scientific methodology for politically ‘correct’ agenda.

Kolker

NOONE argues about a Global ABSOLUTE temperature but ANOMALY in case of the AGW effect

Why do you REFUSE to once study ANOMALY?

That should be YOUR agenda instead of your own wrong ideas

Re: one more time on a single average value of global Earth's temperature and its anomaly.

I’ve pointed out several times that global average temperature anomaly is a wrong metric for concluding on global warming or cooling. I presented both thermodynamic and mathematical arguments to justify why this average metric is wrong. Therefore, all graphs of an upward global anomaly trend presented by both NASA/GISS, NOAA and UAH are equally bad and non-conclusive. This type of data cannot answer a question whether the Earth as a whole is warming or cooling.

Now, there seems to be a natural question: if the current metric is wrong, then what's a right metric? A sensible answer is that there is no single physical variable that completely describes warming or cooling of the whole Earth. In other words, continual scalar non-equilibrium temperature field (as the Earth's atmosphere temperature field) cannot in principle be represented by a single value-its average (or average sliding deviation from a baseline-an anomaly).

A single value of global temperature (or global temperature anomaly) does not exist for such a complex non-equilibrium chaotic system as the Earth as whole. This is just a basic fact of properties of temperature as it is defined and used in thermodynamics. I realize that this answer might look unsatisfactory for the majority of those here who are seeking a single and simple number, that the majority will not like it and discard it.

However, for a real demonstration of a global increase of temperature, all the infinity of local temperatures would be saying the same thing: it is warming (or cooling) everywhere and everwhen, and no temperature averaging would be needed at all. Currently, this is not the case.

One might say that a possible way to force a simple warming (or cooling) picture into a complex non-equilibrium field of local temperatures is to demonstrate that the number of places where it is warming outnumbers the number of places where it is cooling. However, thermodynamic properties of temperature as an intensive variable do not allow to weight temperature at one point against temperature at another point. Temperature is a condition of a local system, not an amount of something in the system like, say, energy or entropy.

Otherwise, a thermodynamic concept of temperature and its meaning must be redefined, and a new variable should be developed- a 'climate temperature'. Anyone dare to accept such a challenge?

The bottom line: there are two options to stay within scientific boundaries: (i) stop using Earth's global average temperature anomaly for concluding on global warming, or (ii) develop a new concept of 'non-thermodynamic temperature', i.e., the so-called 'climate temperature' and demonstrate how to operate it outside of thermodynamic to conclude on global warming.

Re: Why is the cliche 'Climate Change' is now used instead of 'Global Warming?'

History is repeated, only with the opposite sign.

It turns out that all that hysteria of imminent global crisis began with 'global icing' in the early 1970.

I was pointed out (by Harpo Veld) to some fascinating newspapers clips:

see attached word doc images from the issues of The Boston Globe, Apr 16, 1970 (page 1); The Guardian, January 29, 1974 (page 2); The Washington Post, 1971, July 9 (page 3).

As you see, it’s exactly the same hysteria, exactly the same “arguments”, exactly the same unanimous “scientific community”, but only… about a new ice age!

When it became clear that the new ice age story couldn’t be maintained anymore, the alarmists switched to “global warming”.

Some time later, the same shift happened again with 'global warming', for the exact same reasons, and now we have “climate change”.

“Climate change” has one great advantage compared to “new ice age” or “global warming”: Any change - of any parameter, in any direction - is claimed to be a disaster. Totally opposing trends could allegedly “prove” the same thing - that a disaster is imminent, unless we all agree and support to spend trillions $ for 'decarbonization' or becoming 'carbon neutral' (say, by 2050) in the name of fighting and stopping 'climate change'.

Oh, and to pay more for 'green energy' and redistribution wealth, of course, from the developed countries to underdeveloped ones and to their governments ... that’s a proven method for keeping state of fear and the population control.

Kolker

To call you a nitwit is even too much of an honour

As complete ignorant you continuously refuse to consult the literature and keep on venting you own gut instead

The global mean surface temperature is result of an averaging procedure over the Earth surface and a time span (30 years) over the temperatures measured on the weather stations. The averaged temperature over the surface is the area weighted mean. The weight is given by the ratio of the i-th cell aera to the surface area. So far so good. What is the physical meaning of a sum of (weighted) temperatures? Ultimately none. The Richmann’s rule gives the averaged temperature for a mixture of two gases. If you consider each area as an isolated thermodynamic system (?) with constant temperature, you can use this rule to calculate a kind of mean temperature. The temperature obtained is no longer an area average (specific heat, density, pressure?). I have found no discussion about this point.

Essex has discussed the existence of global temperature. Article Does a Global Temperature Exist?

Henry Schau Thank you for your post. In a number of other RG threads I referenced this excellent paper by Essex et al who demonstrated in detail why the temperatures of isolated bodies (not in thermal contact) cannot be averaged to produce a temperature of anything in any physical sense. The same is applied to 'temperature anomaly' presented in numerous publications and IPCC reports. The book by Essex and McKitrick "Taken by Storm. The troubled science, policy and politics of Global warming" 2-nd Ed 2007 is a must read for anyone who wants to understand the meaning of what they are talking about regarding 'global warming'.

I've demonstrated using specific temperature values (even in this thread above) that conclusion of 'warming' or 'cooling' for the same set of data depends on the type of chosen averaging (arithmetic, mode, median, sq. root average, etc) and there is no physical process that allows to prefer one average over another one. Thus, all targets on limiting 'the global average temperature rise to 1.5 C or another one' based solely on one type of averaging-the arithmetic one-are meaningless.

Thanks again for showing an open independent mind. It is currently so rare to see....

That Essex pulp is not accessible! and 15 years old

In the mean time he added similar pulp also debunked

Can you give a physical derivation of an area average surface temperature or a physical interpretation?

Would you please specify and clarify your question regarding derivation of an area surface temperature?

If you mean T average= area fraction1*T1+.....+area fraction2*T2+ so on..

this averaging is as meaningless as any other. It is a generalization of the simple arithmetic averaging with equal area fractions. Temperature is fundamentally local intensive thermodynamic variable. It is a condition of a physical system in equilibrium, not an amount of anything in the system. Or you mean something else?

Meanwhile, I suggest that you take a look at some previous pages on this same thread:

page 1, Nov 17, 2022 to Alastair Bain McDonald;

page 2, Nov 18, 2022 to Thomas Mayerhofer; Nov 24, 2022 to Ali Mazrati Ghohrondi;

page 3, Feb 22, 2023.

That's what I mean by area weighted. The question went to Harry ten Brink. For BEST, a description is in Rohde et al., Berkeley Earth Temperature Averaging Process, Geoinfor Geostat: An Overview 2013, 1:2 (http://dx.doi.org/10.4172/2327-4581.1000103).

The global surface temperature anomalies are usually referred to as climate index. This is presumably done to avoid physical interpretation.

Sorry

just saw the question was to me

A good intro is by Clive Best on the averaging

also by Nick Stokes

global temperature anomaly

and anomalies are very well defined versus absolute temepratures

because the anomaly is the DIFFERENCE over the years and further more the difference is representative for a larger area even though absolute temperatures depend on the station height for instance

google for NOAA anomalies

Scientist Admits Omitting ‘Full Truth’ From Climate Study To Get It Published.

Patrick T. Brown, a climate scientist, wrote Tuesday in The Free Press that he deliberately omitted the “full truth” from a paper he recently authored in order to increase its chances of publication in a prestigious journal. Brown explained his decision-making asserting that he overlooked the truths in his work in order to make it more appealing to the editorial biases of leading journals like Nature and Science. Brown and seven other authors wrote a paper which examined the relationship between climate change and wildfire risks in California, and Nature published the paper in August 2023.

Brown stated that scientists hoping to advance their careers by getting published in leading journals are inclined to tailor their findings to align with the biases of editors and reviewers, a dynamic which “distorts a great deal of climate science research, misinforms the public and most importantly, makes practical solutions more difficult to achieve.”

I knew not to try to quantify key aspects other than climate change in my research because it would dilute the story that prestigious journals like Nature and its rival, Science, want to tell,” Brown wrote of his paper. He asserted that reviewers and “editors of these journals have made it abundantly clear, both by what they publish and what they reject, that they want climate papers that support certain preapproved narratives—even when those narratives come at the expense of broader knowledge for society.”

The authors are inclined to highlight the problem of greenhouse gas emissions, which skews scientific analysis and facilitates legislation like the Inflation Reduction Act that takes aim at problems rather than facilitating solutions, Brown asserted in the piece. “In my paper, we didn’t bother to study the influence of these other obviously relevant factors. Did I know that including them would make for a more realistic and useful analysis? I did,” Brown wrote in The Free Press. “But I also knew that it would detract from the clean narrative centered on the negative impact of climate change and thus decrease the odds that the paper would pass muster with Nature’s editors and reviewers.”

The process of customizing the research for an eminent journal caused it to be less useful than it could have been. ”

Representatives for Nature did not respond immediately to a request for comment.

Is anyone surprised by this self-disclosure?

The argument seems to be that an average temperature is meaningless. However it is common knowledge- and a scientific fact - that the average temperature in say, Canada is lower than the average temperature in Florida, despite the fact that both countries represent complex systems. Or that the average winter temperature in Britain is lower than the summer one. So if we can talk about average temperatures for one country, why not for the whole globe? Where would you draw the line on the area involved?

On another minor point, Kolker states:

" If on the other hand they equilibrate reversibly, i.e. while producing work, their final temperature will be √ T aT b - i.e. geometric average which is always lower than the arithmetic one.*

But he seems to have forgotten that "while producing work" means that this energy will, by the 2nd law eventually appear as heat. An internal combustion engine produces heat and useful work in the motion of a vehicle. However that work eventually is transformed into heating the atmosphere through frictional processes. So the concept of a simple arithmetical average appears quite reasonable.

But in the end, however you define the term "average", if the temperatures of two bodies both increase, then clearly their average temperature will also increase.