# Does a Global Temperature Exist?

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.

Is this paper a joke then? It is old and traditional knowledge that the temperature measurements made in meteorological and climatological studies are supposed to be representative of a certain volume of air, i.e. the arithmetic mean. Essex et al. argue that it is not really physical, but surely the temperature measurements do have clear practical implications? Temperature itself can be inferred directly from several physical laws, such as the ideal gas law, first law of thermodynamics and the Stefan-Boltzmann law, so it’s not the temperature itself which is ‘unphysical’. Even though the final temperature of two bodies in contact may not be the arithmetic mean, it will still be a weighted arithmetic mean of the temperatures of the two initial temperatures if no heat is lost to the surroundings. Besides, grid-box sizes for numerical weather models often have a minimum spatial scale of 10-20km, and the temperature may be regarded as a mean for this scale. Numerical weather models usually provide useful forecasts.

And what distinguishes the mean temperature representing a small volume to a larger one? Or do Essex et al. think the limit is at greater scales. For instance at the synoptic spatial scale (~1000 km)? The funny thing then is that the concept of regional mean temperature would also not be meaningful according to Essex et al. And one may also wonder if the problem of computing a mean temperature is meaningful in time, such as the summer-mean temperature or winter-mean temperature?

Essex et al. suggest that there are many different ways of computing the mean, and it is difficult to know which make more sense. But when they compute the geometric mean, they should not forget that the temperature should be in degrees Kelvin (the absolute temperature) as opposed to Celsius. One argument used by Essex et al. is that the temperatures are not in equilibrium. Strictly speaking, this applies to most cases. But in general, these laws still give a reasonable results because the temperatures are close to being in equilibrium in meteorology and climatology. The paper doesn’t bring any new revelations – I thought that these aspects were already well-known.

Update: Rabett Run has a very detailed set of posts pulling apart this paper more thoroughly.