The Ill-Posed Question of Global Mean Temperature

Franco Battaglia, Ruggero Micheletto 

The question "Does a global temperature exist?" was answered in the negative by C. Essex, R. McKitrick, and B. Andresen (EMA), who showed that different choices of mean yield different signs of the global temperature trend. We take EMA’s result as our point of departure and argue that its root cause is more fundamental than the particular data set or averaging formula employed: the very notion of a mean presupposes a specified purpose — the physical condition that the single representative value is required to reproduce. Once this is made explicit, it becomes clear that the question "what is the mean of these temperatures?" is ill-posed until the purpose is named. In particular, the conventional arithmetic mean of station temperatures fails this requirement. We first illustrate this with elementary examples, including cases in which a legitimate mean lies outside the range of the data, contrary to a claim made by EMA. We then extend EMA’s analysis to daily minimum and maximum temperatures from 1371 NOAA stations over 1939–2025, computing 33 different means for each. Depending on the mean adopted, the "global" mean temperature ranges over tens of degrees, while the inferred warming trend varies by a factor of 36 — from 0.015 to 0.539 ◦C/decade. We argue that the difficulty is not resolved by choosing a better averaging formula, since any scalar statistic discards the spatial structure that carries the physical information. We conclude that inferences drawn from global mean temperature about weather and climate are at present premature: climate science seems to be still at its infancy.