Preprints
https://doi.org/10.5194/npg-2021-34
https://doi.org/10.5194/npg-2021-34

  05 Nov 2021

05 Nov 2021

Review status: this preprint is currently under review for the journal NPG.

Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model

Valerio Lucarini1,2, Larissa Serdukova1,2, and Georgios Margazoglou1,2 Valerio Lucarini et al.
  • 1Department of Mathematics and Statistics, University of Reading, Reading, UK
  • 2Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK

Abstract. 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 α-stable Lévy – α ∈ (0, 2) – noise laws, and examine the statistics of transition times and most probable transition paths. While the Gaussian noise case – used here as a reference – has been extensively studied in a plethora of studies on metastable systems, much less is known about the Lévy 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. Lévy 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 −α, in apparent agreement with rigorous results obtained for additive noise in a related – yet different – reaction-diffusion equation as well as in simpler models. 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 path cross at the single unstable edge state on the basin boundary. In the case of Lévy 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.

Valerio Lucarini et al.

Status: open (until 31 Dec 2021)

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Valerio Lucarini et al.

Valerio Lucarini et al.

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Short summary
In most of the investigations on metastable systems the stochastic forcing is modulated by Gaussian noise. Lévy noise laws, which describe jump processes, have recently received a lot of attention, but much less is known. We study stochastic versions of the Ghil-Sellers energy balance model and we highlight the fundamental difference between how transitions are performed between the competing warm and snowball states depending on whether Gaussian or Lévy noise acts as forcing.