The maximum likelihood climate change for global warming under the influence of greenhouse effect and L\'evy noise

An abrupt climatic transition could be triggered by a single extreme event, an $\alpha$-stable non-Gaussian L'evy noise is regarded as a type of noise to generate such extreme events. In contrast with the classic Gaussian noise, a comprehensive approach of the most probable transition path for systems under $\alpha$-stable L'evy noise is still lacking. We develop here a probabilistic framework, based on the nonlocal Fokker-Planck equation, to investigate the maximum likelihood climate change for an energy balance system under the influence of greenhouse effect and L'evy fluctuations. We find that a period of the cold climate state can be interrupted by a sharp shift to the warmer one due to larger noise jumps, and the climate change for warming $1.5{}^{\mathrm{o}}\mathrm{C}$ under an enhanced greenhouse effect generates a step-like growth process. These results provide important insights into the underlying mechanisms of abrupt climate transitions triggered by a L'evy process.