Fokker-Planck dynamics of the El Niño-Southern Oscillation

Statistics of Stochastic Entropy for Recorded Transitions between ENSO States

We analyze the transitions between established phases of the El Niño Southern Oscillation (ENSO) by surveying the daily data of the southern oscillation index from an entropic viewpoint using the framework of stochastic statistical physics. We evaluate the variation of entropy produced due to each recorded path of that index during each transition as well as taking only into consideration the beginning and the end of the change between phases and verified both integral fluctuation relations. The statistical results show that these entropy variations have not been extreme entropic events; only the transition between the strong 1999-2000 La Niña to the moderate 2002-2003 El Niño is at the edge of being so. With that, the present work opens a long and winding avenue of research over the application of stochastic statistical physics to climate dynamics.

Gauge-Optimal Approximate Learning for Small Data Classification

Small data learning problems are characterized by a significant discrepancy between the limited number of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information and cannot derive an appropriate learning rule that allows discriminating among different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the gauge-optimal approximate learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation, and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space and that it can be approximated through a monotonically convergent algorithm that presents-under the assumption of a discrete segmentation of the feature space-a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Niño Southern Oscillation and inference of epigenetically induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems in both learning performance and computational cost.

Probabilistic projections of El Niño Southern Oscillation properties accounting for model dependence and skill

The El Niño - Southern Oscillation (ENSO) is a dominant mode of global climate variability. Nevertheless, future multi-model probabilistic projections of ENSO properties have not yet been made. Main roadblocks that have been hindering making these projections are climate model dependence and difficulty in quantifying historical model performance. Dependence is broadly defined as similarity between climate model output, assumptions, or physical parameterizations. Here, we propose a unifying metric of relative model performance, based on the probability density function (PDF) of ENSO paths. This metric is applied to assess the overall skill of Climate Model Intercomparison Project phase 6 (CMIP6) climate models at capturing ENSO. We then perform future multi-model probabilistic projections of changes in ENSO properties (from years 1850-1949 to 2040-2099) under the shared socioeconomic pathway scenario SSP585, accounting for model skill and dependence. We find that future ENSO will likely be more seasonally locked (89% chance), and have a longer period (67% chance). Yet, the jury is still out on future ENSO amplification. Our method reduces uncertainty by up to 37% compared to a simple approach ignoring model dependence and skill.

A novel approach for discovering stochastic models behind data applied to El Niño-Southern Oscillation

Stochastic differential equations (SDEs) are ubiquitous across disciplines, and uncovering SDEs driving observed time series data is a key scientific challenge. Most previous work on this topic has relied on restrictive assumptions, undermining the generality of these approaches. We present a novel technique to uncover driving probabilistic models that is based on kernel density estimation. The approach relies on few assumptions, does not restrict underlying functional forms, and can be used even on non-Markov systems. When applied to El Niño–Southern Oscillation (ENSO), the fitted empirical model simulations can almost perfectly capture key time series properties of ENSO. This confirms that ENSO could be represented as a two-variable stochastic dynamical system. Our experiments provide insights into ENSO dynamics and suggest that state-dependent noise does not play a major role in ENSO skewness. Our method is general and can be used across disciplines for inverse and forward modeling, to shed light on structure of system dynamics and noise, to evaluate system predictability, and to generate synthetic datasets with realistic properties.