Topological Analysis of the "El Niño" Phenomenon

This paper applies Topological Data Analysis (TDA) to characterize the dynamics of the El Niño–Southern Oscillation (ENSO) using anomaly data from the Niño 3.4 region. We reconstruct the underlying dynamics via Takens time-delay embeddings and quantify recurring structure through persistent homology, revealing robust cyclical patterns across multiple time windows. We further use the Mapper algorithm to obtain an interpretable topological summary that separates El Niño, La Niña, and neutral regimes, highlighting an atypical cluster associated with the unusually intense 1997–1998 El Niño event. Finally, we model regime transitions with a Markov chain over ONI anomaly intervals, showing that transitions between El Niño and La Niña occur primarily through neutral states and estimating long-run stationary behavior.