It is rather difficult and perhaps impossible to define what precesely "average temperature of Earth" means. Even if somehow one defines, only approximately, the meaning of this strange concept, then the new problem of how to measure the "average temperature of Earth" arises and will necessarily cause a lot of problems.

It will be much more appropriate to intruduced, by using some sensible criteria, many zones and to measure the average temperature in each of these zones.

Even more useful could be to draw curves showing, in each zone, the monthly variation of the mean temperature, for every year over a long-term period, and after that to compare these curves. Much more information and much more useful information can be gathered and carefully studied in this way

People need to learn how describe random variables.

It's not an issue about stochastics (which is well understood), but an issue about a quantity, whose average over different systems (or subsystems of a big system such as Earth) is as such in principle ill-defined.

There are variations on a daily basis is almost impossible to predict or measure something as complete as the temperature of the planet.

It is rather difficult and perhaps impossible to define what precesely "average temperature of Earth" means. Even if somehow one defines, only approximately, the meaning of this strange concept, then the new problem of how to measure the "average temperature of Earth" arises and will necessarily cause a lot of problems.

It will be much more appropriate to intruduced, by using some sensible criteria, many zones and to measure the average temperature in each of these zones.

Even more useful could be to draw curves showing, in each zone, the monthly variation of the mean temperature, for every year over a long-term period, and after that to compare these curves. Much more information and much more useful information can be gathered and carefully studied in this way

Zlatev,

Indeed that approach is acceptable but will be there always a temptation to describe the whole system using just one number. As I already said, people need to learn that compression of information in real life are lossy not lossless.

I read a recent technical paper on measuring average surface temperatures on Earth. They use a whole set of weighing factors to compensate errors in the data. However, there's still the fundamental issue that *the average of T over subsystems that don't have the same amount of heat (energy)* is ill-defined.

This example illustrates the problem: take 1 g of ice (T_1=0 C) and 1 kg of water (T_2=20 C). The average T=10 C. Take 1 kg of ice (T_1=0 C) and 1 g of water (T_2=20 C). The average is again T=10 C. *Neither of these is the real average T when the two systems are mixed*, because intensive thermodynamic variables cannot be averaged.

It would be better to talk in terms of energy. Yet this would not be possible given a general descriptor as 'earth's average". My thermodynamics is not good, but what do we get if we talk about the energy of a closed system? Is the atmosphere a closed system, given thermal loss/input to and from space? And how do we speak of entropy?...It would depend on the system. If we could say..YES we will/have affected an avergae increase of x billion kilojoules within y years would it send the message home any better than describing average temperature rises? If I tell my 12 yr old son that the average temperature will rise by 2C within the next decade does it mean anymore to him than me describing how much energy is required to raise billions of tons of gas by 2C. Seems to me the difficultiy is not that a problem exists (yet many still believe themselves worthy to doubt the consensus - always healthy practice yet very dangerous within this field) but how to really push this into all corners of society. Nevertheless my son has recently been asking why we, often only a single person in a large sedan, all still drive such large petrol engine cars???? My response..."great question son", send it to the directors and shareholders of GMC.

If I remember correctly some post at this topic already addressed the problem of accuracy in data.

The real problem presented here is:

Is it misleading to report the average temperature of Earth?

Seems like everyone think we really have a problem.

So, how we can describe this system in a proper form?

I'm using statistics in daily basis and cannot think in a better form. Anyone can describe a better method?

Zlatev, I really appreciate your contribution. It will be helpful to understand the dynamic of the whole system. We have the same approach. I am already using that approach and I can assure that it can lead to satisfactory results.

Of course it makes sense, the issue for surface temperature is that weather stations are not uniformly distributed. So you need some weighting scheme. The main practical issues are the low coverage in the arctic and antarctic regions which can't be interpolated easily and dealing with the urban heat island effect. Those are the issues that have been most debated recently - see revisions to the Hadley-CRU dataset and the Berkeley Earth Surface Temperature project....

Thanks David; I read a recent paper by the Berkeley group, but the fundamental issue I'm trying to address here is that one cannot average temperatures over systems, which don't have identical heat capacities (to put this in technical terms). In other words, only extensive thermodynamical variables can be averaged. I cannot find this issue addressed in the papers.

Obviously, I'm not a physicist, but this issue doesn't seem to be a problem to all the physicists working on climate change issues or even meteorology in general. Averaging is a vague term though so maybe that is causing problems here. Are you saying that you can't compute or estimate the expected value of temperature for the Earth as a whole? I can see that there is a problem in "averaging" - computing the simple mean of temperatures of regions of different areas.

The average temperature usually quoted is the average of standard 2 m weather station temperatures. To first approximation, the average is over measurements in the air, using a standard protocol, as an index of temperature as perceived by humans. To a first approximation, heat capacity does not vary (of course it does, a bit, with humidity and pressure). When doing thermodynamic calculations, meteorologists use more appropriate units and measures. The average tropospheric temperature is sometimes also quoted, based on satellite observations in the microwave and these too are to first order independent of heat capacity since they are based on the microwave brightness of a specific molecule.

Thanks David S. for the clarification. However, isn't the heat capacity at 2 m almost completely controlled by the surrounding land/water mass, and not the air itself? If this is the case, averaging is not well-defined unless the

surroundings at measuring points are identical (which is probably not the case at al). Am I missing something trivial here :-)?

Yes. The issue in air temperature -which is the quantity being averaged- is the thermodynamics of air. The effect of changes in radiative forcing on the local temperature is influenced by the local presence of water bodies, the albedo and the local energy balance (sensible and latent heat fluxes). There are other metrics for global energy balance. Climate science does not use temperature to define that (although the local rate of temperature change is influenced by sinks for heat).

You seem to be using temperature as a proxy for global energy balance-it is not, that is a far more complex discussion, usually boiled down to Top of the Atmosphere fluxes as computed or directly measured by satellites. Temperature is averaged not to define the total heat flux but to describe the average perceived environment. The time derivative of average temperature has well-defined physical properties since dheat capacity/dt is approximately zero.

This is an interesting topic, which I spent some thought on a little while back. The results are available online at :

"Temperatures of the Earth -- a Globe in Space" .

The main conclusions were:

1. As most have said, the actual concept of 'average temperature of the Earth' is pretty meaningless.

2. In any case, measured figures are irrelevant except for locally-considered areas. For the whole Earth, the planet is in dynamic thermal equilibrium -- at every microsecond, energy in equals energy out. So any change in the equilibrium value (which could be considered an 'average temperature') must be due to a corresponding change in the input/output balance.

For those with the time to look at the web article, I'd welcome comments on any errors or things not expressed clearly.

(2012 Apr 13)

Thank you Davids :-)! I emphasize that I'm not an expert in climate physics (although I am a theoretical physicist), so your inputs here are highly appreciated.

@David S. I have read a couple of technical papers (e.g. by the Berkeley group) but I find it hard to interpret the meaning if the weight factors that they use to calculate the average T. If these factors somehow contain the physics of inbound/outbound heat fluxes, then I concur that the equations they use could be justified. My main concern nevertheless is that very small differences in the reported average T of Earth are used to support global warming. If such figures are not truly accurate, reliable and justifiable there's a danger that this whole issue is undermined in the public eye (which is what many special interest groups are obviously trying to achieve by any means).

This also concerns the important point that David N. makes above. To be precise, Earth is under time-dependent non-equilibrium conditions, both w.r.t. the daily and annual rotational cycles. As an expert in thermodynamics and statistical physics, I know how difficult it is to define any thermodynamic quantities for such system, especially if high precision and reproducibility of experimental measurements are required.

Unfortunately, the link of David N. seems not to work.

Maybe this discussion is getting too technical for this forum, but any comments are appreciated.

Sorry, there was a bit extra got tucked on the link. The proper link is:

http://www.aoi.com.au/bcw/EarthTemp/index.htm

A number of points:

1) The differences in surface temp are not so small and the global effort to develop calibration is large

2) The are multiple lines of measurement. The satellite microwave measurement shows consistent results as well and is not sampled in the same way (see Jim Hurrell's work)

3) The ocean heat content measurements are not subject to anything like the same degree of heterogeneity. Ocean heat budgets show significant warming. We don't have enough deep ocean data to close ocean heat budgets but the trends are unequivocal

4) Stratospheric temperatures are cooling, as predicted from the theoretical analysis of energy balance

5) Terrestrial glaciers are, with very few exceptions, shrinking and this reflects energy balance in a way not subject to the sampling issues surrounding air temperature since they integrate th water and energy budgets

6) Biological indicators that again integrate and have different uncorrelated sampling issues show change_ literally thousands of species show poleward trends consistent with temperature measurements

7) The admittedly noise surface air temps are consistent with all of the above measurements. Many of these have little or different sampling biases. All of them are consistent with a warming planet.

8) Finally, as a theoretical physicist, the fundamantals of this are straightforward derivations from theory. Radiation is absorbed and re-reradiated in the atmosphere consistent with blackbody radiation theory and molecular spectroscopy. Water vapor increases consistent with the Clasius-Claperon equation and amplifies the CO2 effect. This again produces warming consistent with physical first principles.

A large number of independent data sets are consistent with an analysis based on simple principles of physics. If you have an alternate hypothesis consistent with these data, the world waits.. otherwise I'd argue there is not a strong case to reject the current hypothesis.

Thanks again David S. for a comprehensive answer. I hope that I haven't given the false impression that I would somehow criticize various indicators of global warming - quite to the opposite! The only purpose of this thread is to ask, whether or not the reported increase in the average T of Earth is a reliable indicator of global warming. I am pretty well read on the actual physical mechanisms of global warming, but as I have mentioned a few times already, when I read the Berkeley group papers I can't convince myself to trust their formulas. In any case, your points about the satellite microwave measurements and ocean heat content is well-taken, and if all the T values derived from different measurements agree, it's enough of a consistency check .

Exactly right- no one data set alone is the key. Each approach has advantages and limitations.

I have no doubts about that: it is completely wrong to report and to use the average temperature of Earth for any useful purpose.

Global mean surface temperature anomaly data sets are often calculated.

They serve the purpose of tracking the warning of the planet.

There's no way I can think of that they're misleading. Temperature is intensive, but the heat capacity of the Earth's surface doesn't change much.

Zlatev has very rightly pointed out "It is rather difficult and perhaps impossible to define what precisely "average temperature of Earth" means. Even if somehow one defines, only approximately, the meaning of this strange concept, then the new problem of how to measure the "average temperature of Earth" arises and will necessarily cause a lot of problems." if anyhow energy balance of a number of similar zone is worked out and averaged for the Earth as whole in terms of degrees C or F even then it will not work. T is in C or F is measured in interval scale. 40 degree temperature at a place does not amount that it is twice hot compared to another place where at the same moment temperature is only 20 degrees. Conversion of energy balance into K and working out reversely into C or F may help a lot, but cannot solve the problem entirely. Other units of measurement of energy balance may help but again to express them in C or F would involve lot of information loss. It should also b kept in mind as the original post has pointed out that "temperature is an intensive thermodynamic variable [over time also].

It is not the average temperature of Earth that is reported but the average air temperature near the surface (2 m) of the Earth. This is a useful quantity because we live there. In terms of energy budget a much more useful quantity is the average temperature (or heat content) of the ocean. The ocean absorbs the vast majority of heat.

YES The a single number for our global temperature is a misleading fiction. It does not exist in physics.

ABSTRACT

Physical, mathematical and observational grounds are employed to show that there is no physically meaningful global temperature for the Earth in the context of the issue of global warming. While it is always possible to construct statistics for any given set of local temperature data, an infinite range of such statistics is mathematically permissible if physical principles provide no explicit basis for choosing among them. Distinct and equally valid statistical rules can and do show opposite trends when applied to the results of computations from physical models and real data in the atmosphere. A given temperature field can be interpreted as both “warming” and “cooling” simultaneously, making the concept of warming in the context of the issue of global warming physically ill-posed. Short title: Global Temperature?

https://pdfs.semanticscholar.org/860c/5a03ace0f1df81a6423b4494dcda4c024ee0.pdf

Authors Christopher Essex and Ross McKitrick are experts in statistics and mathematics.

I think the global mean surface temperature does not have a physical meaning. Rather, it is defined entirely by how it is calculated from the sets of individual measurements. The individual measurements are taken at different localities, at different times, and themselves have inconsistencies (daily min-max, vs at set times in the day, vs averages from regular time measurements in the day...). In any case the said global average is the result of the calculation, including the spacial averaging using cells, and interpolations for cells with little or no data... In my view, the real problem is error calculation (including sensitivity analysis) on the said global average. This would need to include consideration of "local" natural perturbations at a given station... (such as cloud cover, atmospheric conditions that affect radiation balance, heat transfer conditions with respect to the diurnal variations, ETC.) I don't believe any of this has really been done, sufficiently seriously. There needs to be detailed station-specific studies to gauge the temporal variations and their causes and statistics (which could be vastly different from station to station), before realistic error analysis (estimation) is done. Decades from now, either we will drop all this stuff or laugh at how bad it was.

I agree with Filippo. No one is claiming that they know the temperature of the Earth. They are saying they have calculated an average temperature. NOAA, NASA and the Hadley Centre all produce their own estimates which largely agree. These are produced using "detailed station-specific studies to gauge the temporal variations and their causes and statistics." D. G. Rancourt Where do you think the idea of the Heat Island Effect came from? That was a scientific correction long before the climate change deniers latched on to it.

But to imply that, because no exact measurement of global temperature exists, then global warming is not happening is absurd.

I agree with most of the answers, the "temperature of the Earth" isn't a specifically determinable quantity, the results of any study depend on the factors taken into account. I've made a detailed study of this point (see below), and was surprised to find so many factors operating. As examples, measured temperatures on a Japanese rooftop were greatly reduced by growing a plant cover. And even if measurements are very accurate, final quoted figures depend on whether they are midway between minimum and maximum, or are summed from the area under the curve for a given day, among other methods.

And there are global factors too. General landscape-wide loss of tree cover generally leads to higher maxima on the ground, not so much lower minima. The "averages" in such cases will be higher in more "developed" areas.

In the following, note the "s" on temperatures!

"Temperatures of the Earth -- a Globe in Space: (a re-analysis with some surprising results)" .