Building a minimum statistically accurate model for ENSO complexity via causality-based learning

El Nino-Southern Oscillation (ENSO) exhibits diverse characteristics and complexity in spatial pattern, peak intensity, and temporal evolution caused by intraseasonal, interannual, and decadal processes. Modeling the ENSO by capturing the complexity features is a crucial prerequisite for understanding different types of El Nino, its relationship with MJO and decadal variability, its impact on climate change, as well as advancing skillful predictions. There is some very recent progress on the development of such models from physical justifications. In this presentation, we develop a stochastic model of the ENSO complexity from a data-driven point of view. In particular, a causality-based learning approach using information theory is utilized that systematically detects the underlying dynamics of the model. Distinct from purely data-driven regression or other classical nonparametric methods, the causality-based learning approach here automatically discovers the underlying physics from data. Meanwhile, it contains a sparse identification procedure that leads to a parsimonious model that well represents nature. The new framework also allows learning suitable stochastic parameterization that supplements the large-scale features and compensates for the uncertainty in the observations. The approach is applied to both synthetic data from a statistically accurate conceptual model and real observations. The causality-based learning algorithm shows robust results and reaches a minimum model for characterizing the ENSO complexity that justifies the recent development of the physical-based models. The approach here also distinguishes the role of nonlinearity and multiplicative noise in modeling different components of the ENSO complexity.