Dynamical landscape and multistability of a climate model

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.

Applications of large deviation theory in geophysical fluid dynamics and climate science

“…Local maxima, minima, and saddles decorate the quasi-potential at all scales. From [182] point. We have shown that LDT is a key tool for studying noise-induced transitions between competing metastable states for the climate system as a whole.…”

“…There are good reasons to believe that, in fact, the climate system allows for the presence of additional competing metastable states on top of the warm and snowball climate [1,32,167]. This leads to a more complex pattern of possible transition paths between them and requires a careful statistical examination when noise is added into the system [182]. Finally, one can interpret the localised tipping elements described above as being associated with smaller and localised minima and saddles, which define the multiscale nature of the quasi-potential.…”

“…13) [176,177] . Margazoglou et al [182] have recently performed a thorough investigation of the noise-induced transitions between the competing SB and W states of the open-source climate model PlaSim [89,179], see Fig. 14.…”

“…Here σ 2 = ε. From [182] and by the difference between surface temperature at low and high latitudes, and the best estimates of the transition paths in the weak-noise limit, while panel (a) shows the estimate of the projected quasi-potential Φ. Additionally, panel (c) shows the exponential dependence of the average transitions times with respect to the inverse of the variance of the noise, as indicated in (51). Note that in this case, because of the complex structure of the basin boundary, the W → S B and S B → W transitions take place through separate M states, as can be seen in panel (d) where a third dimension, corresponding to the sea ice percentage, in included.…”

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

“…Additionally, several results indicate that the phase space of the climate system might well be more complex than the scenario of bistability described above. Various studies (Lewis et al, 2007;Abbot et al, 2011;Lucarini and Bódai, 2017;Margazoglou et al, 2021) performed with highly nontrivial climate models report the possible existence of additional competing states, up to a total of five (Brunetti et al, 2019;Ragon et al, 2021). In Margazoglou et al (2021) it is argued that, in fact, one can see the climate as a multistable system where multistability is realised at different hierarchical levels.…”