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Abstract Multi-year El Niño-Southern Oscillation (ENSO) events, where the warming (El Niño) or cooling (La Niña) extends beyond a single year, have become increasingly prominent in recent decades. Using observations and climate model simulations, we show that the South Pacific Oscillation (SPO) plays a crucial, previously unrecognized role in determining whether ENSO evolves into a multi-year event. Specifically, when an El Niño (La Niña) triggers a positive (negative) SPO in the extratropical Southern Hemisphere during its decaying phase, the SPO feedbacks onto the tropical Pacific through the wind-evaporation-sea surface temperature mechanism, helping sustain ENSO into a multi-year event. This SPO–ENSO interaction is absent in single-year ENSO events. Furthermore, whether ENSO can trigger the SPO depends systematically on the central SST anomaly location for El Niños and the anomaly intensity for La Niñas, with interference from atmospheric internal variability. These findings highlight the importance of including off-equatorial processes from the Southern Hemisphere in studies of ENSO complexity dynamics. 

Abstract End‐member mixing analysis (EMMA) is widely used to analyze geoscience data for their end‐members and mixing proportions. Many traditional EMMA methods depend on known end‐members, which are sometimes uncertain or unknown. Unsupervised EMMA methods infer end‐members from data, but many existing ones don't strictly follow necessary constraints and lack full mathematical interpretability. Here, we introduce a novel unsupervised machine learning method, simplex projected gradient descent‐archetypal analysis (SPGD‐AA), which uses the ML model archetypal analysis to infer end‐members intuitively and interpretably without prior knowledge. SPGD‐AA uses extreme corners in data as end‐members or “archetypes,” and represents data as mixtures of end‐members. This method is most suitable for linear (conservative) mixing problems when samples with similar characteristics to end‐members are present in data. Validation on synthetic and real data sets, including river chemistry, deep‐sea sediment elemental composition, and hyperspectral imaging, shows that SPGD‐AA effectively recovers end‐members consistent with domain expertise and outperforms conventional approaches. SPGD‐AA is applicable to a wide range of geoscience data sets and beyond.