Modeling the El Niño Southern Oscillation with Neural Differential Equations*

El Niño Southern Oscillation (ENSO) is the largest inter-annual variability phenomenon in the tropical Pacific and its influence goes beyond tropics to higher latitudes via atmospheric and oceanic teleconnections; therefore, it has a significant impact on global climate predictions.

We used Taken’s delay embedding theorem to reconstruct, from a univariate time series, the chaotic attractor towards which the ENSO system tends to evolve.  

We considered the Nino3.4 sea surface temperature (SST) index data starting from the pre-industrial era and spanning the entire period 1870-2016 as univariate time series and we used a Neural Ordinary Differential Equation (NODE) to model the embedding function. 

After learning the optimal embedding dimension and the associated time delay, our NODE model successfully captures the essential features of ENSO, the two most important features of which are ”phase locking” to the seasonal cycle, which is the concentration of abnormal ENSO events during November and December, and the predictability barrier, which is related to the increase of model uncertainties during spring. Finally, our model exhibits robust short-term prediction skills, outperforming more complex and computationally expensive models on the same tasks, demonstrating in this way the promising potential of using the NODE framework for climate modelling.