Where are the coexisting parallel climates? Large ensemble climate projections from the point of view of chaos theory

Abstract

We review the recent results of large ensemble climate projections considering them to be the simulations of chaotic systems. The quick spread of an initially localized ensemble in the first weeks after initialization is an appearance of the butterfly effect, illustrating the unpredictability of the dynamics. We show that the growth rate of uncertainty (an analog of the Lyapunov exponent) can be determined right after initialization. The next phase corresponds to a convergence of the no longer localized ensemble to the time-dependent climate attractor and requires a much longer time. After convergence takes place, the ensemble faithfully represents the climate dynamics. Concerning a credible simulation, the observed signal should then wander within the spread of the converged ensemble all the time, i.e., to behave just as any of the ensemble members. As a manifestation of the chaotic-like climate dynamics, one can imagine that beyond the single, observed time-dependent climate, a plethora of parallel climate realizations exists. Converged climate ensembles also define the probability distribution by which the physical quantities of the different climate realizations occur. Large ensemble simulations were shown earlier to be credible in the sense formulated. Here, in addition, an extended credibility condition is given, which requires the ensemble to be a converged ensemble, valid also for low-dimensional models. Interestingly, to the best of our knowledge, no low-order physical or engineering systems subjected to time-dependent forcings are known for which a comparison between simulation and experiment would be available. As illustrative examples, the CESM1-LE climate model and a chaotic pendulum are taken.

An ensemble based approach for the effect of climate change on the dynamics of extremes

“…It is worth noting that a climate model can only be credible if it is converged to the snapshot attractor of the climate (Deser, 2020;Herein et al, 2023). Previous studies show that the convergence time is approximately 40 years in PlaSim (Drótos et al, 2017;Drótos and Bódai, 2022), and similar values are found for more complex climate models, too (Drótos and Bódai, 2022).…”

“…The black line corresponds to the measured, observed global mean surface temperature. The fact that the black curve is within the gray band of the ensemble and convergence is reached as discussed in (Herein et al, 2023) illustrates that PlaSim can be considered a credible model (Deser, 2020;Tokarska et al, 2020;Suárez-Gutiérrez et al, 2021). Our simulations reported below are carried out with this PlaSim setup.…”

“…In the upper levels of the troposphere, however, the north-south temperature contrast increases, which would imply less extreme events. In the particular example of the variability of the global surface temperature, most credible climate models show practically constant variance of a climate ensemble over the last century [see, e.g., (Deser et al, 2020;Ghil and Lucarini, 2020;Pierini and Ghil, 2021;Herein et al, 2023)]. We note that the field of predicting and studying local extreme events evolves in conjunction with dynamical systems theory (Ansmann et al, 2013;Lucarini et al, 2014;Bódai, 2015;Mishra et al, 2020;Li et al, 2022).…”

“…3) would require 20 sub-ensembles, technically resulting in a 400-element ensemble with daily time resolution. However, for numerical efficiency and based on our previous experiences (Herein et al, 2023), we now follow a simplified approach with three representative 20-member sub-ensembles, corresponding to a 60-member ensemble. It is known to be usually sufficient to examine ensembles with a relatively low number of members to gain a proper characterization of internal variability for global quantities, at least [see (Milinski et al, 2020) concerning variable TS].…”