What Is Climate? Chaos Theory Offers a Radical New Definition

Ask a climate scientist to define climate and you may be surprised by the hesitation. The textbook answer, that climate is a statistical description of weather over some averaging period, has served humanity for decades, yet it hides a deep conceptual problem. When the Earth system is being pushed by a steadily rising concentration of carbon dioxide, as it is right now, there is no natural averaging window, and statistics computed over time need not correspond to any probability distribution that describes the state of the planet at a particular instant. A new perspective article by Gábor Drótos of the MTA-ELTE Theoretical Physics Research Group and Tamás Bódai of Pusan National University and the Institute for Basic Science, published in Earth System Dynamics, argues that the field has quietly built its most important enterprise, the comparison of past and future climates, on a definition that has never been carefully justified. Their proposed remedy draws on one of the most striking ideas in modern physics: the theory of chaos and strange attractors.

The starting point is a practice that has become standard in climate modeling over the past two decades. Large ensembles of simulations, typically tens to hundreds of members, are run with identical forcing scenarios but slightly different initial conditions. Because the climate system is chaotic, tiny differences in where a simulation starts grow exponentially, so that after some time the ensemble members scatter across the range of states the system permits. The ensemble mean is then treated as the climatological mean, the ensemble spread as internal variability, and the time evolution of these statistics as the forced response to whatever forcing scenario was imposed. Projects such as the CESM Large Ensemble and the Max Planck Institute Grand Ensemble have made this approach a pillar of modern climate science, and its popularity is only expected to grow.

But there is an assumption buried inside this procedure, and Drótos and Bódai set out to expose it. Implicitly, researchers assume that the distribution of ensemble members eventually forgets how the members were initialized and converges to something objective, a probability distribution that belongs to the system and its forcing rather than to the personal choices of whoever set up the experiment. If that assumption fails, every modeling group running the same model under the same scenario could end up defining its own private climate, a subjective object that would make comparisons between studies ambiguous. The authors call this the uniqueness criterion: a satisfactory definition of climate must rest on a probability measure that is unique, depending only on the system, the forcing, and other objective factors.

The mathematical machinery that delivers uniqueness comes from dynamical systems theory. The Earth system, and the global models that describe it, can be viewed as nonautonomous dissipative deterministic dynamical systems, in which energy is dissipated and the equations depend explicitly on time through the forcing. Under a time-dependent forcing, the appropriate geometric object is the snapshot or pullback attractor, the set of states the system can occupy at each instant, equipped with a natural probability measure. Earlier work by Drótos, Bódai, and collaborators, notably a landmark 2015 paper, showed that an ensemble of trajectories converges to this natural measure in an approximately exponential fashion, so that after a finite convergence time the ensemble represents the same distribution regardless of how it was initialized. In an intermediate-complexity climate model, that convergence time turned out to be a few decades. The naive proposal, then, is to define climate at any instant as the natural probability measure of the snapshot attractor at that instant, with climate change being the evolution of this measure under the forcing.

Elegant as it is, this naive definition runs into a serious caveat, and dealing with it is the central novelty of the new paper. The convergence process itself has multiple characteristic time scales, because the loss of memory about initial conditions decomposes into a sum of exponentially decaying contributions. In the spectral theory of transfer operators, these decay rates are given by the real parts of the eigenvalues of the Ruelle–Perron–Frobenius operator, while the imaginary parts describe predictable, oscillatory evolution. Some modes of the system forget their initial conditions within years, others within decades, and some, such as those tied to the deep ocean, may take centuries or even up to a thousand years. If a study targets the coming century, waiting for the slowest modes to converge is pointless: their unpredictable variability would swamp the analysis in what the authors, citing David Stainforth, connect to the so-called Edinburgh paradox, the explosion of uncertainty when all possible long-term behaviors are included.

The resolution proposed by Drótos and Bódai is a conditional definition of climate. If there is a sufficiently large gap in the spectrum of convergence time scales, one can demand complete convergence in the faster-converging modes while conditioning on the actual state of the slower-converging ones. Climate is then a unique probability measure, but one that is conditional on a realization of the slow variables, which the authors call the predictable context. Crucially, the slow variables need not even be identified explicitly: initializing an ensemble by small perturbations of a model state automatically yields the desired conditional measure once the fast modes have decayed. The context itself is objective, because by definition the slow modes remain predictable over the time span of interest, so their state can in principle be learned from observations. This is what rescues uniqueness without pretending that the deep ocean’s memory can be ignored or averaged away.

The definition has consequences that reach beyond philosophy. One is that climate change and forced response, usually treated as synonyms, can come apart. If the slow modes evolve predictably and influence the converged statistics of the fast ones, the conditional climate changes even without any explicit forcing in the equations of motion. Such a change is genuine climate change under the conditional definition, but it is not, or not entirely, a forced response, since it does not originate from external time dependence. Disentangling the two requires comparing against an unforced evolution, in a spirit analogous to the removal of spurious model drift when estimating forced trends. Another consequence concerns initialization: for climate projections, the authors argue, the state of the slower-converging modes should be taken from observations, whereas much current practice samples arbitrary time instants of a long control run, which may be problematic regardless of how climate is defined.

Does the real Earth system cooperate? The authors’ preliminary assessment is cautiously optimistic. Ocean response studies suggest a possible separation by roughly a factor of ten between the time scales of the mixed layer and the deeper layers, and recent work indicates that convergence associated with the Atlantic Meridional Overturning Circulation takes up to about forty years. Taken together, these findings hint that for investigations spanning around a century, climate might be meaningfully defined through a probability measure obtained after a convergence time of a few decades, perhaps up to four. But open questions remain. Observed scaling behavior in climate time series, the possible role of multidecadal oscillations, regime transitions, and intertwined basins of attraction could all complicate the picture. The authors illustrate the regime problem with a stochastic slow-fast toy model: an ensemble initialized during a transition between regimes fails to converge on the fast time scale, destroying uniqueness, whereas initialization away from transitions preserves it.

To make the framework testable, the paper proposes a concrete initialization scheme for Earth system models. Pairs of ensembles are generated, the second initialized from a member of the first after a controlled delay, and the delays are increased across successive pairs sampled from different epochs of a control run. By checking whether the perturbed ensemble converges to its parent within the delay, researchers can determine the longest time span over which a practically unique, and therefore objectively definable, climate exists for a given variable, without ever needing to compute the full spectrum of convergence time scales. The authors are careful about limits: their conclusions are qualitative, the exponential-like convergence they confirmed numerically leaves room for model-specific detail, and if the required separation of time scales proves too small, the notion of climate may have to remain subjective, treated more like probabilistic ensemble weather forecasting. Even then, the framework offers a recipe: evaluate any statistical quantifier with respect to the converged ensemble, rather than inventing ensemble-based statistics one by one, a point connected to the violation of Birkhoff’s ergodic theorem in systems with explicit time dependence. What emerges is not merely a technical fix but a conceptual foundation, one that could change how the next generation of large ensemble experiments is designed, initialized, and interpreted.

Subject of Research: A dynamical-systems framework for defining climate via ensemble convergence and time scales of convergence

Article Title: Can we define climate by means of an ensemble? A tale of time scales of convergence

Article References: Drótos, G., & Bódai, T. (2026). Can we define climate by means of an ensemble? A tale of time scales of convergence. Earth System Dynamics, 17(5), 1529-1549. https://doi.org/10.5194/esd-17-1529-2026

Image Credits: AI Generated

DOI: 10.5194/esd-17-1529-2026

Keywords: climate definition, ensemble simulations, chaos theory, snapshot attractor, pullback attractor, internal variability, convergence time scales, Ruelle–Perron–Frobenius operator, Earth system models, forced response, climate change, dynamical systems