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.