The midlatitude climate system is constantly influenced by the tropics through atmospheric bridges, with El Niño serving as the main such signal. Neighboring works in our archive explore how pressure separates superconductivity and charge order, how the echo of an invisible stone appears in data, how heat and uncertainty generate strength, how the quantum Mpemba paradox accelerates cooling, how El Niño is predicted a year and a half ahead, how a neural network learns from an algebraic skeleton, how an ultracold condensate enhances molecular asymmetry, and how heat under pressure measures the invisible. In this series, our work stands apart: it addresses the nonautonomous dynamics of climate, where time enters the equations explicitly and the attractors themselves depend on time. Until now, the multiplicity of such attractors had been demonstrated only in highly truncated ocean models, and it remained unclear whether it would persist in a more realistic coupled ocean–atmosphere system.
The authors constructed a reduced model from two modules: a tropical one, describing El Niño with three equations for the temperatures of the eastern and western Pacific and the thermocline depth, and an extratropical one, VDDG, with 36 variables for the midlatitude atmosphere and ocean. The tropical module affects the extratropical one unidirectionally through a linear term in the equation for the first barotropic mode of the atmosphere, mimicking the strengthening of the zonal flow during El Niño. Two types of forcing were considered: periodic with a period of about 13 years, and chaotic with irregular bursts every 30–50 years. For each value of the coupling parameter g, hundreds of integrations lasting up to 15,000 years were performed from various initial states in the distant past. The attractors were analyzed using the pullback method: the system starts in the remote past and is attracted to a time-dependent set, which is the PBA. The stability of the attractors was tested by perturbing initial states with amplitudes from 10⁻⁷ to 10⁻⁴ and subsequently tracking the largest Lyapunov exponent.
Under periodic forcing and with ocean–atmosphere coupling coefficient C = 0.015, two coexisting PBAs were found. The first, PBA1, has a largest Lyapunov exponent of about 0.25 day⁻¹, and its low-frequency variability is weak and tied to the forcing period. The second, PBA2, with an exponent of about 0.1 day⁻¹, exhibits pronounced multidecadal variability with a period of about 58 years, inherited from the unperturbed model. The difference in predictability is twofold. Under chaotic forcing, the picture becomes more complex: PBA2 becomes metastable, and even small perturbations with amplitude 10⁻⁷ cause transitions to PBA1. Reverse transitions require large perturbations. In the oceanic variables of PBA2, phase synchronization of trajectories is observed in three bundles, shifted in phase by 35 years, corresponding to the forcing period. Spectral analysis revealed a nonlinear resonance: the internal ocean period of 58 years and its subharmonic of 115 years relate to the forcing period of 36 years as 2:3.
This work is the first to show the coexistence of two climate attractors in a coupled midlatitude ocean–atmosphere model under El Niño forcing. Unlike neighboring studies, where attractor multiplicity was examined in purely oceanic or highly simplified models, here it arises in a more realistic configuration. This implies that the multiplicity of climate regimes is not an artifact of low order but a fundamental property of nonautonomous dynamics. The difference in predictability between PBA1 and PBA2 is fundamental: ensemble averaging, the standard method for climate prediction, becomes meaningless when trajectories can jump between regimes with different statistics.
A natural next step is a systematic exploration of the model's parameter space, especially the coupling coefficient C and the forcing amplitude g. The authors propose using the MAOOAM model with an arbitrary number of modes to test whether PBA multiplicity persists with increased resolution. Another direction is studying the 'holes' in the boundaries of basins of attraction, which may lead to intermittency between regimes. Finally, it is important to understand how these results carry over to full climate models and real data.
The results directly affect the practice of ensemble weather and climate forecasting, highlighting the need for very long integrations and large ensemble sizes to correctly estimate uncertainty. They also provide a new perspective on the signal-to-noise paradox in climate models, where low-frequency variability is systematically underestimated.
Conduct a systematic scan of parameters g and C to delineate the regions of PBA coexistence. Investigate the structure of basins of attraction and the mechanisms of transitions between regimes. Repeat the analysis on more detailed models with a larger number of modes.
An unresolved question in climatology is why models systematically underestimate low-frequency variability compared to observations. This work shows that part of this underestimation may stem from an unfortunate choice of initial states that do not fall into the basin of attraction of the correct PBA. This directly links attractor multiplicity to the signal-to-noise paradox and the limits of predictability on interannual and multidecadal timescales.
In the chaotic regime, the oceanic trajectories of PBA2 align into three distinct bundles, shifted in phase by 35 years. This resembles a troop of soldiers marching in lockstep, even though each one follows its own chaotic trajectory.
The idea of multiple climate regimes, between which the system can jump, echoes Kim Stanley Robinson's novel 'Forty Signs of Rain', where climatologists confront unexpected and abrupt shifts in the climate system that do not fit linear forecasts.