A Three-Factor Stochastic Radiative-Equilibrium Climate Model with Mean Reversion, Jump Diffusion, and Tail Risk

We propose a parsimonious stochastic climate model in which a large class of unresolved terrestrial, oceanic, atmospheric, cryospheric, and astronomical changes is represented by three state variables: incoming solar irradiance, planetary albedo, and effective longwave emissivity. The deterministic backbone is the global radiative-equilibrium relation obtained from the Stefan– Boltzmann law and planetary energy balance, a constraint that remains unavoidable in any physically meaningful account of Earth climate. The stochastic extension models all three factors as mean-reverting jump-diffusions. This yields a low-dimensional model capable of producing long quasi-stable climatic intervals interrupted by abrupt transitions. In rare-jump Monte Carlo experiments, both the distribution of 10-year average equilibrium temperature and the distribution of annual logarithmic temperature changes are sharply peaked relative to a fitted Gaussian benchmark and retain jump-driven outer tails. Thus the model can keep ordinary decadal temperature variability comparatively stable while still assigning non-negligible probability to abrupt shifts. The model is not intended to resolve every physical mechanism separately; instead, it treats their aggregate radiative impact as stochastic movement in a small number of physically interpretable closure variables. We discuss the foundational physics, the statistical estimation problem, the interpretation of leptokurtic temperature distributions, and the implications for climate risk management under deep uncertainty.