The maximum likelihood climate change for global warming under the influence of greenhouse effect and Levy noise

An abrupt climatic transition  could be triggered by a single extreme event, and an alpha-stable non-Gaussian Levy 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 Levy 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  Levy 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 1.5 degree 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 Levy process.