A hierarchical ensemble manifold methodology for new knowledge on spatial data: An application to ocean physics

Abstract Extracting meaningful patterns from large, complex, and nonlinear earth science data remains a major challenge. Many traditional methods, such as Principal Component Analysis and k-means clustering, impose strong statistical assumptions that often fail in these settings, leading to misleading results. I introduce the Native Emergent Manifold Interrogation (NEMI) method, a novel workflow that integrates manifold learning, dynamical systems, and ensemble clustering to reveal meaningful structures in noisy, high-dimensional data. NEMI constructs a manifold to enhance underlying associations and applies unsupervised clustering to identify coherent regions of interest. A key strength of NEMI is its intuitive validation framework, which enables practitioners to assess model reliability through visual inspection, ensemble agreement, and domain-specific expectations. By leveraging stochastic regularization, conceptualized as a smoothing of the space explored by the machine learning optimization, and uncertainty quantification, NEMI ensures that detected structures are robust and not artifacts of methodological choices. Furthermore, the method is flexible and scalable, allowing adaptation to different spatial scales, whether for identifying global dynamical regimes or resolving localized patterns within a specific region. Demonstrated on oceanographic data, NEMI provides a generalizable, interpretable, and computationally efficient approach for data-driven discovery in the earth sciences. By balancing mathematical rigor with practical usability, NEMI offers a powerful tool for exploring complex geophysical datasets while ensuring results are transparent, reproducible, and tailored to the problem at hand.