The problem of deducing the climate from the governing equations

Abstract

The climate of a system is identified with the set of long-term statistical properties. Methods of deducing the climate from the equations which govern the system are enumerated. These methods are illustrated by choosing a first-order quadratic difference equation in one variable as a governing equation. The equation contains a single parameter. Particular attention is given to the climatic mean of the single variable.

Analytic methods yield the climate in some cases where the system varies periodically, but generally fail when the system varies nonperiodically. Numerical integration yields a value of the climatic mean for any individual value of the parameter. Additional analytic reasoning is needed to determine the nature of the climatic mean as a function of the parameter.

The progression from steady-state to periodic to nonperiodic behavior, as the parameter increases, is compared to the progression from steady-state to periodic to irregular flow in the rotating-basin experiments, as the rate of rotation increases.