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H 1 Multistability of the climate : noise-induced transitions across Melancholia states, invariant measure, and phase transition

Auteurs : Lucarini, Valerio (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one, the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the ice-albedo feedback. In a previous work, we defined the Melancholia states that sit between the two climates. Such states are embedded in the boundaries between the two basins of attraction and feature extensive glaciation down to relatively low latitudes. Here, we explore the global stability properties of the system by introducing random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noise-induced transitions. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. At this regard, we relate our results to the debate around the prominence of contigency vs. convergence in biological evolution. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edge-tracking algorithm.

    Codes MSC :
    37D45 - strange attractors - chaotic dynamics
    60Gxx - Stochastic processes
    76E20 - Instability of geophysical and astrophysical flows
    82C26 - Dynamic and nonequilibrium phase transitions (general)
    85A20 - Stellar atmospheres

      Informations sur la Vidéo

      Réalisateur : Recanzone, Luca
      Langue : Anglais
      Date de publication : 31/07/2019
      Date de captation : 04/07/2019
      Collection : Research schools ; Dynamical Systems and Ordinary Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 00:57:57
      Domaine : Dynamical Systems & ODE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-07-04_Lucarini.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair 2019 - Research School: Thermodynamic Formalism: Modern Techniques in Smooth Ergodic Theory / Chaire Jean-Morlet 2019 - Ecole : Formalisme thermodynamique : techniques modernes en théorie ergodique
    Organisateurs de la rencontre : Pollicott, Mark ; Vaienti, Sandro
    Dates : 01/07/2019 - 05/07/2019
    Année de la rencontre : 2019
    URL Congrès : https://www.chairejeanmorlet.com/2019-2-...

    Citation Data

    DOI : 10.24350/CIRM.V.19541903
    Cite this video as: Lucarini, Valerio (2019). Multistability of the climate : noise-induced transitions across Melancholia states, invariant measure, and phase transition. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19541903
    URI : http://dx.doi.org/10.24350/CIRM.V.19541903


    Voir aussi

    Bibliographie

    1. LUCARINI, Valerio et BÓDAI, Tamás. Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View. Physical review letters, 2019, vol. 122, no 15, p. 158701. - https://doi.org/10.1103/PhysRevLett.122.158701

    2. LUCARINI, Valerio et BODAI, Tamas. Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions. arXiv preprint arXiv:1903.08348, 2019. - https://arxiv.org/abs/1903.08348

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