Levy noise versus Gaussian-noise-induced transitions in the Ghil-Sellers energy balance model

We study the impact of applying stochastic forcing to the Ghil-Sellers energy balance climate model in the form of a fluctuating solar irradiance. Through numerical simulations, we explore the noise-induced transitions between the competing warm and snowball climate states. We consider multiplicative stochastic forcing driven by Gaussian and alpha-stable Levy - alpha is an element of (0, 2) - noise laws, examine the statistics of transition times, and estimate the most probable transition paths. While the Gaussian noise case - used here as a reference - has been carefully studied in a plethora of investigations on metastable systems, much less is known about the Levy case, both in terms of mathematical theory and heuristics, especially in the case of high- and infinite-dimensional systems. In the weak noise limit, the expected residence time in each metastable state scales in a fundamentally different way in the Gaussian vs. Levy noise case with respect to the intensity of the noise. In the former case, the classical Kramers-like exponential law is recovered. In the latter case, power laws are found, with the exponent equal to -alpha, in apparent agreement with rigorous results obtained for additive noise in a related - yet different - reaction-diffusion equation and in simpler models. This can be better understood by treating the Levy noise as a compound Poisson process. The transition paths are studied in a projection of the state space, and remarkable differences are observed between the two different types of noise. The snowball-to-warm and the warm-to-snowball most probable transition paths cross at the single unstable edge state on the basin boundary. In the case of Levy noise, the most probable transition paths in the two directions are wholly separated, as transitions apparently take place via the closest basin boundary region to the outgoing attractor. This property can be better elucidated by considering singular perturbations to the solar irradiance.

Automated summary

This study investigates the impact of applying stochastic forcing in the form of fluctuating solar irradiance to the Ghil-Sellers energy balance climate model. By conducting numerical simulations, the researchers explore the noise-induced transitions between warm and snowball climate states and compare the statistics of transition times under Gaussian and alpha-stable Levy noise laws. The study highlights significant differences in transition paths between Gaussian and Levy noise cases, especially in terms of the residence time in metastable states and the most probable transition paths.