An abrupt climatic transition could be triggered by a single extreme event, and an -stable non-Gaussian Lévy 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 -stable Lévy 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 Lévy 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 with low frequency. Additionally, the climate change for warming C under an enhanced greenhouse effect generates a steplike growth process. These results provide important insights into the underlying mechanisms of abrupt climate transitions triggered by a Lévy process.
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