Dynamical Landscape and Multistability of a Climate Model

Abstract

<p>We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyze their interplay. First, drawing from the theory of quasipotentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states, and investigate the most likely transition trajectories as well as the expected transition times between them. Second, harnessing techniques from data science, specifically manifold learning, we characterize  the data landscape of the simulation output 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 stable state in one of the two climate models we consider. The combination of our approaches allows to identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically change the topography of the dynamical landscape of Earth's climate.</p>

Analysis of a bistable climate toy model with physics-based machine learning methods

“…Energy balance climate models exhibit the well known hysteresis behaviour with respect to the solar radiation between a cold snowball earth state and a warmer state corresponding to the present-day climate, with discontinuous transitions taking place at the lower and upper boundary of the region of bistability [1,2,[9][10][11][12][13]. Recently, it has become apparent that the climate system might indeed feature more than two competing states, associated with a complex partitioning of the phase space in competing basins of attraction [14][15][16][17]. Indeed, multistability also almost always gives rise to a potential abrupt change of the system when a bifurcation point is-adiabatically-reached and one state loses it stability.…”

“…Initial conditions located on the basin boundaries-which have vanishing Lebesgue measureare, instead, attracted to the edge states, which are saddles located on such basin boundaries [12,22,23]. Such saddles determine the global instabilities of the system and, additionally, if the system is, under fairly general conditions, forced with Gaussian noise, they are the gateways for noise-induced transitions between competing metastable states [3,13,17,24].…”