Forecasting rare but significant climate events, such as El Niño, heat waves, or floods, remains one of the most challenging problems in climate science. The dynamics of the atmosphere and ocean are chaotic: on time scales shorter than the Lyapunov time, deterministic prediction is possible; on time scales much longer than the mixing time, only climatological averages are possible. But practical interest lies in the intermediate range, which the authors call the predictability horizon. This work fits into modern efforts to use machine learning to extract dynamical quantities from data, but unlike many neighboring studies, it focuses not on improving point forecasts but on the probabilistic structure of predictability itself.
The authors use the Jin-Timmermann model, a low-dimensional system of three ordinary differential equations describing the interaction of the ocean and atmosphere in the tropical Pacific. The model has two intertwined attractors: a periodic one corresponding to strong El Niño events, and a chaotic one without such events. Adding noise allows the system to switch between attractors. The committor function is defined as the probability that a trajectory starting from a point x reaches the threshold (strong El Niño) before a given time T elapses. To estimate the committor, ensembles of trajectories are generated from each initial point. In parallel, a machine learning method is proposed: the committor is parameterized by a neural network trained to minimize the Bernoulli log-likelihood on pairs of initial state and outcome (whether the event occurred or not). The approach is first tested on a simple two-dimensional gradient dynamics with two attractors.
For the Jin-Timmermann model, the committor is computed at different noise levels. At an intermediate noise level (σ = 0.00005), four regions emerge in state space: two regions with probability 0 or 1 (complete predictability), a region with smoothly varying probability between 0 and 1 (probabilistically predictable region), and a region with extremely sensitive dependence on initial conditions (practically unpredictable). The existence of the probabilistically predictable region is a new result that the authors argue should be generic for many problems in climate dynamics. A neural network with a multilayer perceptron architecture (3 layers, 32, 64, and 1 neuron, ReLU activation) successfully recovered the committor for the simple two-dimensional system, showing small error compared to the reference obtained by direct simulation.
This work brings into climate science a rigorous mathematical framework from the theory of transitions between states. Unlike neighboring studies that often limit themselves to improving deterministic forecasts or classifying events, here a probabilistic measure of predictability is introduced and computed. This allows one to classify system states according to their intrinsic predictability, which is essential for honest assessment of forecast uncertainty. The machine learning method opens the way to estimating the committor in high-dimensional models and from real data, where direct computation is impossible due to the exponential growth in the required number of trajectories.
A natural next step is to apply the neural network approach to the Jin-Timmermann model itself, and then to more complex climate models and observational data. It is important to assess how much data is needed for reliable training of the committor in realistic dimensions. The approach could also be extended to other rare events: heat waves, droughts, extreme precipitation. Also of interest is a theoretical analysis of which dynamical properties give rise to probabilistically predictable regions.
The results could improve probabilistic forecasts of El Niño and other climate events on seasonal and interannual scales, and also influence the development of machine learning methods in Earth sciences.
Train a neural network to estimate the committor in the Jin-Timmermann model and determine the minimum amount of data required for accurate recovery of the function in this system.
This work is directly related to the unsolved problem of predictability of rare climate events on intermediate time scales, where deterministic prediction is no longer possible and climatological averages are not yet informative. Introducing the committor provides a rigorous mathematical basis for describing this 'gray zone' and allows one to quantitatively assess which states of the system truly carry predictive information.
In the Jin-Timmermann model, the two attractors, periodic and chaotic, are intertwined in state space like threads in a tangle, so that arbitrarily close initial points can lead to completely different fates.