Non-ergodicity of the Earth’s Annual Temperature in a Precession Cycle of the Equinoxes

A three-parameter paleoclimate model has revealed the non-ergodicity of the Earth’s annual temperature during a precession cycle. This result comes from the inverse problem of free parameter identification when the experimental input data are the mean winter and summer solstice temperatures for the period 1950-1975. The inverse problem is underdetermined and admits infinite solutions. However, it is possible to order these solutions in symmetric pairs according to the increasing level of entropy possessed by the annual half-cycle between the two solstices, up to the maximum value at which the two solutions collapse into one. Therefore, the parameter identification process admits uniqueness if, as a third constraint, one searches for the solution of the annual temperature profile that has the maximum entropy, i.e. the highest probability. The existence of a unique solution with the highest probability among the infinite other possible solutions implies the non-ergodic character of the annual temperature.