"The global temperature statistic is also described as the average, as if there is only one kind of average. Of course there is an infinity of mathematically legitimate options. Indeed over one hundred different averages over temperatures have been used in meteorology and climate studies [7] with more appearing regularly. For the case of temperature, or any other thermodynamic intensity, there is no physical basis for choosing any one of these from the infinite domain of distinct mathematical options. The international standards organization ISO tried to choose one but failed [8]. The problem is not a mere absence of a convention for selecting one from among many mathematically different but physically-equivalent measures for a single underlying property. The problem is that there is no single underlying property, because there is no global temperature. But this does not stop averages from being made.
There is no experimental or theoretical way to falsify any particular choice of averaging rule, if averages are (falsely) proclaimed to be temperatures. Proclaiming them to be temperatures leads to a paradox, as any two ad hoc choices applied to a particular outof- equilibrium field can have mutually contradictory behaviors: the system can seem to be both warming and cooling simultaneously. Paradoxically, whether the system is “warming” or “cooling” becomes a property of the choice of average — a choice which is independent of the system.
The resolution of this paradox is not through adoption of a convention. It is resolved by recognizing that it is an abuse of terminology to use the terms “warming” and “cooling” to denote upward or downward trends in averages of temperature data in such circumstances. Statistics might go up or down, but the system itself cannot be said to be warming or cooling based on what they do, outside of special circumstances."
"[7] Peterson T. C., Vose R. S., An Overview of the Global Historical Climatology Network Temperature Database, Bulletin of the American Meteorological Society, 78 (12) December 1997, 2837–2849.
[8] Boehmer K., ISO and climate change: Delivering on the promise, ISO Bulletin, August 2002, http://www.iso.org/iso/en/commcentre/isobulletin/comment/2002/August2002.html "
The example more amply and accurately demonstrates the problem of why ISO could not set a standard to represent global climate change that would be accurate or statistically meaningful in a dynamic system such as that of earth's climate.
