Data-Driven, Operator-Theoretic Approaches for ENSO Prediction

Abstract:

We present a new data-driven approach for ENSO prediction, combining kernel methods for machine learning and operator-theoretic approaches from dynamical systems theory. This method, called kernel analog forecasting (KAF), is a generalization of Lorenz's analog forecasting approach that rigorously approximates the conditional expectation of observables under partially observed, nonlinear dynamics, while also providing useful uncertainty quantification through estimates of conditional variance and conditional probability. We perform deterministic and probabilistic forecasting of the Nino 3.4 index in models and observations, and show that KAF outperforms classical linear approaches, requiring a modest amount of training data. We also find that the method significantly improves upon the spring predictability barrier.