We are pleased to announce the inaugural seminar of the Mathematics of Planet Earth research group in the Department of Mathematics at Imperial. This will be online (via Zoom) at 1600-1700 on Tuesday 8th June, given by Professor Valerio Lucarini (University of Reading). Zoom link will be provided to the research group mailing list prior to the event.
Prof Valerio Lucarini: Dynamical Landscape and Multistability of a Climate Model
Abstract
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 the past our planet flipped between these two states, and possibly additional ones. 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 attraction. In the weak noise limit, large deviation laws define the invariant measure, the statistics of escape times, and typical escape paths called instantons. Indeed, the system lives in an energy-like landscape with valleys and mountain ridges defined by the Graham’s quasipotential. For low (high) values of the solar irradiance, the zero-noise limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first-order phase transition in the system. We then compare the results obtained using the theory of quasipotentials with what can be obtained using a bottom-up approach. Harnessing techniques from data science, specifically manifold learning, we characterize the data landscape to find climate states and basin boundaries within a fully agnostic and unsupervised framework. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, a third intermediate, new stable state in one of the two climate models we consider. The combination of our approaches allows to identify how macroscopic, physical properties of the climate system – the role of the ocean heat transport and of the hydrological cycle – drastically change the topography of the dynamical landscape of Earth’s climate. The framework we propose seems of general relevance for the study of complex multistable systems with multiple scales of motions.
Refs:
G. Margazoglou, T. Grafke, A. Laio, V. Lucarini, Dynamical Landscape and Multistability of the Earth’s Climate, Proc. R. Soc. A, in press (2021)
M. Ghil, V. Lucarini, The Physics of Climate Variability and Climate, Rev. Modern Physics, 92, 035002 (2020)
V. Lucarini, T. Bodai, Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions, Nonlinearity 33 R59 (2020)
V. Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)
V. Lucarini, T. Bodai, Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions, Nonlinearity 30, R32 (2017)