A Physics-Informed Auto-Learning Framework for Developing Stochastic Conceptual Models for ENSO Diversity

Abstract Understanding El Niño–Southern Oscillation (ENSO) dynamics has tremendously improved over the past few decades. The ENSO diversity in spatial pattern, peak intensity, and temporal evolution is, however, still poorly represented in conceptual ENSO models. In this paper, a physics-informed auto-learning framework is applied to derive ENSO stochastic conceptual models with varying degrees of freedom. The framework is computationally efficient and easy to apply. Once the state vector of the target model is set, causal inference is exploited to build the right-hand side of the equations based on a mathematical function library. Fundamentally different from standard nonlinear regression, the auto-learning framework provides a parsimonious model by retaining only terms that improve the dynamical consistency with observations. It can also identify crucial latent variables and provide physical explanations. This methodology successfully reconstructs the equations of a realistic six-dimensional reference ENSO model based on the recharge oscillator theory from its data. A hierarchy of lower-dimensional models is derived, and their representation of ENSO (including its diversity) is systematically assessed. The minimum model that represents ENSO diversity is four-dimensional, with three interannual variables describing the western Pacific thermocline depth, the eastern and central Pacific sea surface temperatures (SSTs), and one intraseasonal variable for westerly wind events. Without the intraseasonal variable, the resulting three-dimensional model underestimates extreme events and is too regular. A limited number of weak nonlinearities in the model are essential in reproducing the observed extreme El Niño events and the observed nonlinear relationship between eastern and western Pacific SSTs. Significance Statement This study develops a physics-informed auto-learning approach to improve the modeling and understanding of El Niño–Southern Oscillation (ENSO), a major climate phenomenon influencing global weather and climate. The auto-learning framework explores the causality between key processes to systematically produce stochastic conceptual models with different climate factors that simulate the diversity of observed ENSO events. The key finding is that the minimal model for characterizing the ENSO diversity (with the least number of climate factors) is a four-variable model capturing thermocline depth, sea surface temperatures, and wind bursts that can reproduce intensity and spatial pattern variation. This advancement provides an interpretable tool to identify the minimum sufficient processes governing ENSO behavior for improved predictability.