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

Abstract

Understanding ENSO dynamics has tremendously improved over the past decades. However, one aspect still poorly understood or represented in conceptual models is the ENSO diversity in spatial pattern, peak intensity, and temporal evolution. In this paper, a physics-informed auto-learning framework is developed 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. Exploiting a realistic six-dimensional reference recharge oscillator-based ENSO model, a hierarchy of three- to six-dimensional models is derived using the auto-learning framework and is systematically validated by a unified set of validation criteria assessing the dynamical and statistical features of the ENSO diversity. It is shown that the minimum model characterizing 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. The limited number of weak nonlinearities in the model are essential in reproducing the observed extreme El Niños and nonlinear relationship between the eastern and western Pacific SSTs.

Figures (13)

• Figure 2.1: A schematic illustration of the auto-learning framework.
• Figure 2.2: Overview of the auto-learning framework with latent variables.
• Figure 4.1: A summary of validation metrics for assessing the model performance.
• Figure 5.1: Comparison between different models using Criterion (1a) -- assessing the fundamental dynamical properties via Bayesian inference. The correlations between the recovered mean time series and observations are used to quantify the performance of these models in the right box chart. Panel (a): correlations of the results for recovery of $u$, $h_W$ and $\tau$ by observing $T_C$, $T_E$ and $I$. Panel (b): correlations of the results for recovery of $T_C$ and $T_E$ by observing other variables. On the left side, there is an example showing the recovered time series of the reference model in two experiments. The red lines represent the observation, the solid blue lines represent the ensemble mean simulation, and the blue shading areas are the confidence intervals of the ensemble simulations. The correlation $r$ between the truth (red line) and the recovered ensemble mean time series (solid blue line) for each state variable is also listed.
• Figure 5.2: Comparison between different models using Criteria 2a--2c including the seasonal variation of the variance, PDFs, and ACFs of $T_C$ and $T_E$.