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How to Build an El Niño Model Without Adding Extra Stuff ✛

Original: "A Physics-Informed Auto-Learning Framework for Developing Stochastic Conceptual Models for ENSO Diversity"
· Yinling Zhang, Nan Chen, Jerome Vialard, Xianghui Fang
arXiv:2402.04585 · 2024-02-07 · CC BY 4.0 · 1 min
Dynamical Systems Atmospheric and Oceanic Physics
The algorithm automatically selects only the variables needed to reproduce El Niño's diversity.

El Niño is when a huge pool of warm water in the Pacific Ocean shifts eastward. But each time it shifts differently: sometimes stronger, sometimes weaker, sometimes closer to one coast, sometimes to the other. Scientists want to build a simple model that captures all these variations.

The problem is that equations accumulate many terms, and it's unclear which ones matter. The new algorithm works like a sieve: it runs through all possible terms and keeps only those that actually help predict how the ocean will behave.

The sieve selects terms based on how much new information they add. If a term doesn't help predict changes, it gets discarded.

It turns out that to reproduce all El Niño variations, only four variables are needed. Three of them describe slow changes: the depth of the layer with a sharp temperature gradient in the western ocean and the surface temperature at two other points. The fourth variable is westerly wind bursts. Without it, the model becomes too predictable and misses strong El Niños.

The algorithm not only finds the model but also keeps it interpretable: each term in the equation has a meaning that can be explained in words.

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The causal entropy used to select model terms is computed via analytical formulas thanks to the Gaussian approximation, making the entire autogeneration process computationally cheap: on a standard computer it takes minutes, not hours.

C_{f_m \to \dot{u}_i | [f \setminus f_m]} = H(\dot{u}_i | [f \setminus f_m]) - H(\dot{u}_i | f)
The difference in conditional entropies shows how much additional information about the rate of change of the variable a specific function provides, given that all other candidates have already been accounted for.
C_{Z \to X | Y} \approx \frac{1}{2} \ln(\det(R_{XY})) - \frac{1}{2} \ln(\det(R_Y)) - \frac{1}{2} \ln(\det(R_{XYZ})) + \frac{1}{2} \ln(\det(R_{YZ}))
The approximate expression in terms of determinants of covariance matrices avoids multidimensional integration and allows fast computation of causal entropy.
Concepts
ENSO Jin-Timmermann model Multivariate ENSO Index El Niño index spring predictability barrier TAO/TRITON moorings recharge oscillator model natural variability self-supervised learning El Niño-Southern Oscillation stochastic dynamical system ERSST autoencoder Stochastic modeling physics informed neural network emergent complexity modeling Warm water volume Reinforcement Learning equatorial wave propagation Southern Oscillation