There Is No Global Temperature

One of the things which irks me the most about the Global Warming, Climate Change, Global Climate Disruption (or whatever they're calling it today), is the concept of a "global average temperature".

I'm no mathematician, I barely graduated high school, but the idea of a GAT never sat right with me. It just didn't make any sense. I was never able to quantify why, until someone mentioned the concepts of Intensive and Extensive properties of a system. And because the Earth is not a blackbody, not a system in equilibrium, the temperature of one part has little or no relevance to the temperature of another part.

Essex et al explains the whole situation very nicely here.

Their abstract states:

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.

And their conclusion states:

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.

If someone can rebut this, and show that a "global average temperature" or "global temperature anomaly" has any physical meaning, please let me know with some links.