You might as well say that there is a global average telephone number.
The thesis is argued convincingly at this link by two very persistent and insightful Canadian authors and their Scandinavian colleague.
(Those who glaze over easily when confronted by mathematics can skip to numbers 5, 6 and 7)
- Sums or averages over the individual temperatures in the field are not temperatures. Neither are they proxies for internal energy.
- Temperatures from a field (individually or averaged) neither drive dynamics nor thermodynamics. Instead dynamics are driven by gradients and differences, in temperatures and other variables.
- A global spatial average cannot be an index for local conditions, otherwise nonlocal dependence (i.e ”thermodynamics at a distance”) for local conditions would be required.
- The utility of any global spatial average of the temperature field as an index for global conditions has been presumed but not demonstrated.
- It is easily demonstrated that different spatial averaging rules over temperatures can have contrary trends in time (i.e. some increase while others decrease in time) when the two fields being compared have range-overlap, as they do in this context. This is demonstrated here in a basic example and subsequently with actual atmospheric temperature-field observations.
- No ground has been provided for choosing any one such statistic over the rest as the one proper index for global climate.
- If there are no physical or pragmatic grounds for choosing one over another, and one increases while the other decreases, there is no basis for concluding that the atmosphere as a whole is either warming or cooling.