Abstract
We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyse their interplay. First, drawing from the theory of quasi-potentials, 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, and 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 versions of PLASIM, the climate model used in this study. 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.
Highlights
The climate, an extremely high-dimensional complex system, is composed of five interacting subdomains: a gaseous atmosphere, a hydrosphere, a lithosphere, a cryosphere and a biosphere [1]
A straightforward attempt to mathematically formulate the dynamics of the climate system is by defining a set of partial differential equations (PDEs) that describe the budget of mass, momentum and energy
Modern state-ofthe-art climate models, similar to the ones featured in the latest Intergovernmental Panel on Climate Change (IPCC) report [26] are based on applying a series of necessary truncations and approximations in such a set of PDEs [27]
Summary
The climate, an extremely high-dimensional complex system, is composed of five interacting subdomains: a gaseous atmosphere, a hydrosphere (water in liquid form), a lithosphere (upper solid layer), a cryosphere (water in solid form) and a biosphere (ecosystems and living organisms) [1]. This approach has a key drawback: the choice of the variables used for the projection is arbitrary, and multiple attractors may appear erroneously merged for a too low-dimensional choice, see below To circumvent this problem, one can follow an approach borrowed from manifold learning, which allows estimating the quasi-potential as a function of a large number of variables and studying its topography directly in such a space. One can follow an approach borrowed from manifold learning, which allows estimating the quasi-potential as a function of a large number of variables and studying its topography directly in such a space As shown below, this allows identifying the deterministic attractors of a system of the form given in equation (2.2) without preselecting a small number of putative important variables, i.e. it is applicable even when n 1. In the case the analysed data have been produced using a numerical model (as is the case here), it is possible to have conclusive results on the correctness of a candidate attractor by running noiseless forward simulations from the best estimate of its position (and nearby points) and observe whether it persists indefinitely
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