| Abstract: |
| We investigate the effects of stochastic forcing on the Ghil-Sellers energy balance climate model by introducing fluctuations in solar irradiance. Using numerical simulations, we analyse noise-induced transitions between coexisting warm and snowball climate states. We consider multiplicative stochastic forcing driven by Gaussian noise and $\alpha$-stable L\'{e}vynoise with $\alpha \in (0,2)$, focusing on the statistics of transition times and the structure of the most probable transition paths.
While Gaussian noise-induced transitions in metastable systems are well understood and serve here as a reference case, much less is known about the corresponding behaviour under L\'{e}vynoise, particularly in high- or infinite-dimensional systems. In the weak-noise regime, we find fundamentally different scaling laws for residence times in metastable states. For Gaussian noise, the classical Kramers-type exponential scaling is recovered, whereas L\'{e}vy noise leads to power-law scaling with exponent $-\alpha$, consistent with rigorous results for related systems with additive L\'{e}vy forcing. This behaviourcan be interpreted by modelling the L\'{e}vy noise as a compound Poisson process.
We also examine transition paths in a reduced state-space projection. Gaussian-driven transitions pass through the same unstable edge state, while L\'{e}vy-driven transitions follow distinct paths through the closest basin boundary to the originating attractor. |
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