Characterizing ENSO Through Topological Analysis of Jin-Timmermann Model's Chaotic Regimes

The El Niño-Southern Oscillation (ENSO) represents one of the most significant drivers of global climate variability. This study investigates the chaotic parameter regimes of the Jin-Timmermann model, particularly focusing on the dynamics identified by Guckenheimer et al. where chaotic attractors emerge. We analyze the reduced three-dimensional system with specific attention to the critical parameters δ = 0.225423, ρ = 0.3224, which govern the time-scale interactions between oceanic and atmospheric processes. Using topological data analysis (TDA), we characterize the structural transitions between periodic and chaotic behaviors in the model's parameter space. Our methodology combines persistent homology with dynamical systems theory to identify distinct topological signatures associated with strong El Niño events. We validate these theoretical findings against observational data from the ERA5 reanalysis and NOAA/ERSSTv5 Niño 3.4 index, focusing particularly on the relationship between topological features and prolonged dry conditions in Southeast Asia. This approach provides new insights into the non-systematic relationship between strong El Niño events and regional climate impacts, while establishing a novel framework for comparing theoretical models with observational data. Our results demonstrate the utility of topological methods in understanding complex climate phenomena and suggest new possibilities for improving ENSO prediction capabilities.