Topological and Information-Theoretic Analysis of Climate-Driven Indonesian Throughflow Dynamics

The Indonesian Throughflow (ITF) represents the sole tropical pathway connecting Pacific and Indian Oceans, yet quantitative understanding of climate mode influences on its variability remains incomplete. We applied information-theoretic and topological frameworks to analyze 34 years (1984-2017) of observational ITF transport data alongside ENSO and IOD indices. Bootstrap analysis revealed pronounced ITF seasonality with 13.28 Sv amplitude peaking in September, contrasting with negligible climate index annual cycles, indicating scale separation in forcing mechanisms. Multi-method extrema detection identified 36-41 extreme events per variable, with 23.1% coincidence between ENSO and IOD high extrema confirming known co-occurrence patterns. Ensemble information-theoretic metrics demonstrated ENSO exerts moderately stronger influence on ITF (mean score 0.524) compared to IOD (0.500), with component-specific optimal lag relationships ranging 4-9 months. Transfer entropy quantified directional information flow with causality ratios of 0.528-0.571. Topological analysis through persistent homology identified stable second homology features (7-11 voids) across climate states, suggesting robust dynamical constraints. Two regime shifts were detected with 100% accuracy and 2.3-month average lead time during near-neutral climate conditions. Extended predictive lead times (22-33 months) indicate gradual phase space reorganization preceding transport anomalies. These findings demonstrate nonlinear analytical frameworks reveal climate-ocean coupling mechanisms obscured by traditional approaches, with implications for improving ITF projections under changing climate.