Time-dependent solutions of the Fokker–Planck equation of maximally reduced air–sea coupling climate model

The time-dependent solutions of a reduced air–sea coupling stochastic-dynamic model are obtained using the Fokker–Planck equation and the quantum mechanical method. The analysis of the time-dependent solutions suggests that when the climate system is in the ground state, the system behaves in a Brownian motion, thus theoretically revealing the foothold of Hasselmann’s stochastic climate model; when the system is in the first excitation state, it evolves in a form of time-decaying, or a 2.3-year periodic oscillation under certain condition. At last, the results are used to discuss the impact of the doubling of carbon dioxide concentration on climate system.