In the debate over global warming (anthropogenic global warming – AGW – being the type people think is caused by burning fossil fuels) there is often discussion about the global temperature, or the mean global temperature, or the average global temperature. We all know what that means, right? If you don’t know what an average is, go here, where I cribbed this nifty graphic.
Anyway, the argument is that the average temperature of the globe is rising, and that the cause is our use of carbon-based energy, which releases CO2, a green house gas, into the atmosphere. For a long time now, I’ve been mulling over this idea of average global temperature. I put a query to Watts Up With That, thinking I might get some critical info on it [my comment at (06:24:57) ] but the response only partly satisfied me.
Simply put, if you have a large flat area with sensors evenly spaced, it is obvious how to derive an average value. But what if the area is very large, sensors are not at all evenly spaced, vast areas (oceans) have no surface sensors, sensors are at different elevations, placed in totally different surroundings, and may not even be completely consistent as to instrumentation and method, how do you derive a single number that represents the global average temperature? And, is this a meaningful number? (A good example of a meaningless average is the one you get by finding the mean of all the telephone numbers in your town. It’s correct, but what is it..?)
Well, I am not alone in asking this fundamental, I think, question. Better mathematical minds than mine have examined it, and I came across this fascinating paper, Does a Global Temperature Exist? The extended introduction is quite accessible to non-mathematicians, and does an excellent job of explaining the crux of the issue. I quote the rather brief conclusion to the paper in full below, with my emphasis:
There is no global temperature. The reasons lie in the properties of the equation of state governing local thermodynamic equilibrium, and the implications cannot be avoided by substituting statistics for physics.
Since temperature is an intensive variable, the total temperature is meaningless in terms of the system being measured, and hence any one simple average has no necessary meaning. Neither does temperature have a constant proportional relationship with energy or other extensive thermodynamic properties.
Averages of the Earth’s temperature field are thus devoid of a physical context which would indicate how they are to be interpreted, or what meaning can be attached to changes in their levels, up or down. Statistics cannot stand in as a replacement for the missing physics because data alone are context-free. Assuming a context only leads to paradoxes such as simultaneous warming and cooling in the same system based on arbitrary choice in some free parameter. Considering even a restrictive class of admissible coordinate transformations yields families of averaging rules that likewise generate opposite trends in the same data, and by implication indicating contradictory rankings of years in terms of warmth.
The physics provides no guidance as to which interpretation of the data is warranted. Since arbitrary indexes are being used to measure a physically non-existent quantity, it is not surprising that different formulae yield different results with no apparent way to select among them.
The purpose of this paper was to explain the fundamental meaninglessness of so-called global temperature data. The problem can be (and has been) happily ignored in the name of the empirical study of climate. But nature is not obliged to respect our statistical conventions and conceptual shortcuts. Debates over the levels and trends in so-called global temperatures will continue interminably, as will disputes over the significance of these things for the human experience of climate, until some physical basis is established for the meaningful measurement of climate variables, if indeed that is even possible.
It may happen that one particular average will one day prove to stand out with some special physical significance. However, that is not so today. The burden rests with those who calculate these statistics to prove their logic and value in terms of the governing dynamical equations, let alone the wider, less technical, contexts in which they are commonly encountered.
Journey to Perplexity 
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Thanks for the pingback, but I really don’t get how these things work…
So can we use a majority of known measurements? There is lots of data out there which must have some meaning in the right context, trends, within variable, some parameters, etc…
If I link to a site all this crazy pingback stuff happens. Beats me…
Troutsky:
There is lots of data out there, true. It has some meaning, true. But use which data, how, for what?
One obvious metric we could use would be to look at specific locations and track trends there. Upwards, downwards, expanded or contracted ranges, etc. But where? And how would you calibrate the models? Chances are they do NOT produce data for specific points that matches well. Does this mean they are wrong..? Well, depends on what you want to know. And anyway, it only tells you what’s going on THERE.
I have always thought that the problem was, as the authors of the paper say, “ill posed.” Science only answers certain questions at a given time, and we can only talk about those answers. Other things may be important, but they are not subject to scientific questioning…yet.
For AGW people, if you take the approach I suggest, the situation becomes, “Well, SOME places are getting warmer, but others are not.” Which are more important? And to whom? And why? Very complicated, isn’t it?
By claiming validity for a single variable, average global temperature, and then supposedly modeling it, you simplify the problem vastly. This is the sort of thing engineers like to do, and the sort of thing for which they are often scorned by scientists. Take a complex problem and beat on it until it’s simple enough to solve, then go out and build something! It has its uses, but is it science? Is it meaningful as a way of understanding the system?
I have my doubts. Change in complex systems is VERY difficult to understand. (The economy, stupid!) Just posing the problem properly is sometimes the hardest part.
From a quick reading, the authors of the paper you link (denying the existence of a global temperature) misunderstand physics. Their assertion that there is no “absolute temperature” is incorrect. Temperature can be measured absolutely by, for instance, measuring the average velocity of particles in a system, or measuring the amount of radiation (light) produced by an object. Morever, average temperature is quite well-defined, both from a mathematical and physical standpoint. Indeed, the temperature of a gas, for instance, is only defined when averaging over large numbers of particles.
There are other important thermodynamic quantities, it is true, but this does not limit the usefulness of temperature as a quantity to measure the state of a system.
The lesson is that not everyone who can do math understand physics.
I think your real question is how does one construct a global average out of measurements at points. The answer is, you have to interpolate between the points somehow, to make a good guess at what the temperature is in places that you didn’t measure it. The measurement is more reliable if you have more points. That is why the U.S, Japan, and Europe are launching observatories on satellites missions to measure the temperature of the Earth.
It is true, temperature measurements are hard, but if the measurements are done self-consistently, uncertainties are recorded, and a trend is seen, that trend is reliable.
There is no “average global temperature” either. It’s not a temperature. It’s a statistic. It has no thermal qualities whatsoever. It’s also pretty meaningless. You can’t tell whether it’s getting hotter or colder by using an average. If I give you a day that had an average of 74 and another that had an average of 70, you could not tell me which day got hotter. There are also many ways to do averages, and there is no standard by which to measure them. Does that info help? If you want to compare temps in one specific area to the temps that area had in the past it just might mean something – but a “global average temp” means nothing. https://www.pressreader.com/@4TimesAYear/csb_SOu5-Uw28_nT0QqzMdOLZzSEEU85NtNhiIrLtfKzM2GsRAgckcJF2-5CBRXqO2NP
I understand your point about the physics. I think the point of this article, perhaps badly presented, is that nothing related to the physics process you describe is being done with temperature measurements.
We are left with dispersed, irregularly distributed measurements at the surface (however dubious their accuracy) that can be gridded (interpolated) in a variety of ways, each requiring the application of judgement which may vary from group to group, person to person. This is something with which I have much personal experience.
Yes, such a weak data record is good for discerning long-term trends. The last twenty years does not comprise such a one. The record for the years before that becomes of increasingly suspect value.
It’s not a question of understanding the physics concept of temperature – it’s a question of whether the data at hand are in sync with that definition in any way.
I think this is the point of the paper, and I agree with it.
Perhaps the problem can be considered differently – Earth temperatures vary by time and place by well over 100 Deg C. Though there are thousands of measuring points used to produce the single quoted “average” temperature, only differences of one or two Deg. are quoted. I find it very difficult to accept that one Deg is meaningful as an average from a scatter of 100 Deg. Such a result could easily be due to variation in the temperature distribution around the globe, using the same fixed point location instruments. There may be analyses of this aspect but I havn’t come across any, (nor analyses of claimed accuracies).Hence I suggest that reliance on this single temperature average is dangerous, and better presentation should be sought. I have no quarrel with using temperature measurements; it is the interpretation I am concerned about.
Well, your view seems pretty close to mine.
I think that ocean heat content is a better measure to address. 75% of the earth is ocean. Ocean heat content changes more slowly – doesn’t flucuate the way surface measures do. Requires extensive network of monitors that get stratified measures, and this is only now being expanded.
I’ve been looking into this, wondering “what is the cuurent mean global temperature?”
I want to compare it with data that shows historical mean temperatures, like this:
I can’t get an answer. The reason I can’t get an answer is that all of the research seems to be done in terms of “temperature anomaly”. From the description of this method, it seems to address the problems brought up in the above essay.
http://www.ncdc.noaa.gov/oa/climate/research/anomalies/index.html
Whether you are plotting anomalies or the straight mean, it all comes back to scattered and scarce surface measurements over time that are somehow aggregated (averaged) into a single statistic. Anomaly is used, I believe, because nobody really cares what the actual temperature in Philadelphia or Rio was, only how much hotter or colder than usual it was.
Although they can compute a “global average”, there is no “global temperature”. The “global average” is totally meaningless. It doesn’t melt ice anywhere.
I think many a scientist would be out of work if it weren’t for the creation of the term “global temperature” When did they start using it anyway?
Reblogged this on 4TimesAYear's Blog.