Does a global temperature exist? This is the question asked in a recently published article in Journal of Non-Equilibrium Thermodynamics by Christopher Essex, Ross McKitrick, and Bjarne Andresen. The paper argues that the global mean temperature is not physical, and that there may be many other ways of computing a mean which will give different trends.
The common arithmetic mean is just an estimate that provides a measure of the centre value of a batch of measurements (centre of a cloud of data points, and can be written more formally as the integral of x f(x) dx. The whole paper is irrelevant in the context of a climate change because it missed a very central point. CO2 affects all surface temperatures on Earth, and in order to improve the signal-to-noise ratio, an ordinary arithmetic mean will enhance the common signal in all the measurements and suppress the internal variations which are spatially incoherent (e.g. not caused by CO2 or other external forcings). Thus the choice may not need a physical justification, but is part of a scientific test which enables us to get a clearer ‘yes’ or ‘no’. One could choose to look at the global mean sea level instead, which does have a physical meaning because it represents an estimate for the volume of the water in the oceans, but the choice is not crucial as long as the indicator used really responds to the conditions under investigation. And the global mean temperature is indeed a function of the temperature over the whole planetary surface.
There has been a bit of a flap here at the University of Washington over the state of the snowpack in United States Pacific Northwest region. The Seattle city mayor, Greg Nickels (a well known advocate for city-based CO2 reduction initiatives) wrote in an 
In a recent issue of the journal 